Mathematics College

## Answers

**Answer 1**

A** function** f with domain R is strictly increasing provided that -** f(x) < f(y).**

A function f with domain R is not strictly increasing provided that -** f(x) >= f(y).**

A function f with domain R is not strictly increasing provided that - **x < y, but f(x) >= f(y)**

(a) A **function** f with **domain R** is** strictly increasing** provided that for all real numbers x and y, if x < y, then f(x) < f(y).

(b) A function f with domain R is not strictly increasing provided that there exist real numbers x and y such that x < y, but f(x) >= f(y).

(c) A function f with domain R is not strictly increasing provided that there exist two** real numbers** x and y such that x < y, but f(x) >= f(y), i.e., the function does not strictly increase between x and y.

For more questions on **function:**

https://brainly.com/question/17043948

#SPJ4

## Related Questions

Oht

Find the length

of the diagonal

4 in

11 in

### Answers

The length of the **diagonal **of the **rectangle **is 11.70 in.

What is a diagonal?

A **diagonal **of a polygon is a line segment that **joins **two vertices of the polygon which are not already **joined **by an edge of the polygon.

Since, there is no information about which polygon's **diagonal **length we are asked to find, so let us consider that the given side lengths are of a **rectangle**,

Now, please refer to the figure attached in the solution,

We know that, the **diagonal **of a **rectangle **divides it into two **right triangles**,

Here our **rectangle **is ABCD and the **diagonal **AC divides it into rt. Δ ABC and rt. Δ ADC,

Considering the rt. Δ ABC,

The **diagonal **AC is acting as the **hypotenuse **of rt. Δ ABC,

So, using **Pythagoras theorem**,

AC² = AB² + BC²

AC = √4²+11²

AC = √121+16

AC = 11.70

Since, the **diagonals **of a rectangle are congruent so, AC = BD = 11.70

Hence, the length of the **diagonals **of the **rectangle **is 11.70 in.

Learn more about **diagonals**, click;

https://brainly.com/question/12274248

#SPJ9

The polynomial of degree 3, P(x), has a root of multiplicity 2 at x = 1 and a root of multiplicity 1 at x = -5. The y-intercept is y = -0.5. Find a formula for P(x). P(x) =

### Answers

The **expression **of the **polynomial **is 0.1(x - 1)^2(x - 5)

How to determine the polynomial

From the question, we have the following parameters that can be used in our computation:

A root of **multiplicity** 2 at x = 1 and A **root **of multiplicity 1 at x = -5**y-intercept **= -0.5

A **polynomial **is represented as

P(x) = a * (x - zero)^multiplicity

Using the above as a guide, we have the following:

P(x) = a * (x - 1)^2(x - 5)

The **y-intercept **is -0.5

So, we have

a * (0 - 1)^2(0 - 5) = -0.5

This gives

a =0.1

So, we have

P(x) = 0.1(x - 1)^2(x - 5)

Henc,e the expression is P(x) = 0.1(x - 1)^2(x - 5)

Read more about **polynomial** at

brainly.com/question/7693326

#SPJ1

If the daughter's quilt has a length of 2 yards and a width of 1 yard, and the doll's quilt has a length of what is the width of the doll's quilt?

### Answers

The **similar **doll's quilt has a width of (1/4) yards.

What is similarity of shapes?

Two or more than two shapes are said to be similar if they have equal corresponding measures of angles and the **ratio **of corresponding sides should be the same.

Given, The daughter's quilt has a length of 2 yards and a width of 1 yard

and the other **similar **quilt ahs a length of (1/2) yards.

Now, (1/2)/(2) = 1/4.

Therefore, The width of a similar quilt is (1/4)×1 = 1/4 yards.

**Q.** A woman sews similar quilts for her daughter's doll. If the daughter's quilt has a length of 2 yards and a width of 1 yard, and the doll's quilt has a length of 1/2 yard, what is the width of the doll's quilt?

learn more about the **similarity **here :

https://brainly.com/question/26451866

#SPJ1

Yall please help fast Veronica went on three hikes. On each hike, she saw the following numbers of animals:

Hike Length of hike

(

km

)

(km)left parenthesis, start text, k, m, end text, right parenthesis Number of animals seen

Rivers Edge

3

33

8

88

Wooded Marsh

8

88

24

2424

Canyon Creek

15

1515

35

3535

Veronica tried to order the hikes from least to greatest by the number of animals seen per kilometer, but she made a mistake. Here's her work:

Choose 1 answer:

WILL GIVE ALL MY PONITS

### Answers

**Answer:**

**Veronica's attempt at ordering the hikes from least to greatest by the number of animals seen per kilometer is not correct.**

**To order the hikes by the number of animals seen per kilometer, we need to calculate the number of animals seen per kilometer for each hike. We can do this by dividing the number of animals seen by the length of the hike in kilometers.**

**Using this method, we can calculate the number of animals seen per kilometer for each hike as follows:**

**Rivers Edge: 8/3 = 2.67 animals/km**

**Wooded Marsh: 24/8 = 3 animals/km**

**Canyon Creek: 35/15 = 2.33 animals/km**

**Based on these calculations, the correct order of the hikes from least to greatest by the number of animals seen per kilometer is Rivers Edge, Canyon Creek, Wooded Marsh.**

**Veronica's mistake appears to be that she simply ordered the number of animals seen in each hike from least to greatest, rather than calculating the number of animals seen per kilometer.**

find the inverse of each function f(x) = x-3/2

### Answers

The answer:

F^-1 (x) = x+3/2

Find what is multiplied by to get ÷. Then, multiply to solve the problem. Do not reduce your answer. Enter your answers.

### Answers

The **Fraction **9/18 should be **multiplied **by 1/4 to get the **value **Equivalent to 9/18 ÷ 2.

What is Fraction?

The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.

The **number** of **parts** into which the **whole** has been **divided **is shown by the **denominator**. It is positioned in the fraction's lower portion, below the fractional bar.How many **sections** of the **fraction** are **displayed **or **chosen **is shown in the numerator. It is positioned above the fractional bar in the upper portion of the fraction.

We have to solve,

9/18 ÷ 2

As, **Fraction **does **not support** the **division **as usually number does.

So, we have to perform the **multiplication **by **reciprocating **the number,

9/18 x 1/2

= 9/ 36

= 1/4

Learn more about **fraction **here:

https://brainly.com/question/19634536

#SPJ9

label the protein structure level on lines 1,2,3, and 4 and label the two structures on the lines under (2). describe the characteristics of each structural level in the corresponding boxes below the drawings.

### Answers

The **characteristics **of each structural level in the corresponding boxes are **hydrogen bond**s, **amino acids, **and **disulfide bonds**

**Protein **structure is a key concept in biology, and it refers to the organization of amino acid sequences into **three-dimensional structures. **The different levels of protein structure are primary, secondary, tertiary, and quaternary.

On line 1, we have the primary structure, which refers to the **linear** sequence of amino acids in a protein. It is determined by the DNA sequence of the gene that encodes the protein. Each amino acid is joined to the next one by a peptide bond, forming a **polypeptide chain.**

On line 2, we have the secondary structure, which refers to the local folding of the polypeptide chain. The two structures depicted on the **lines **under line 2 are the **alpha-helix** and the beta-sheet. The alpha-helix is a coiled structure in which the polypeptide chain is twisted into a spiral shape, held together by hydrogen bonds. The beta-sheet is a flat structure in which the polypeptide chain is folded into a zigzag pattern, also held together by **hydrogen **bonds.

On line 3, we have the tertiary structure, which refers to the overall three-dimensional shape of a single polypeptide chain. It is determined by the interactions between amino **acid side chains**, such as hydrophobic interactions, hydrogen bonds, disulfide bonds, and van der Waals forces. The tertiary structure can be globular or fibrous, depending on the protein's function.

On line 4, we have the **quaternary structure,** which refers to the arrangement of multiple polypeptide chains in a protein complex. Some proteins consist of a single polypeptide chain, while others consist of two or more chains that interact with each other to form a functional unit. The quaternary structure is also determined by the same types of interactions as the tertiary structure.

To know more about **lines **here.

https://brainly.com/question/25727583

#SPJ4

for the phrase “x times the quantity 5 plus y,” what part goes in parentheses?

1. x(5)

2. y

3. x

4 5+y

5. 5

### Answers

The **part **of the **expression **x(5 + y) that goes to the **parentheses **is 5 + y.

The correct option is 4.

What is an expression?

One mathematical **expression **makes up a term. It might be a single variable (a letter), a single number (positive or negative), or a number of variables multiplied but never added or subtracted. **Variables **in certain words have a number in front of them. A coefficient is a number used before a phrase.

Given:

A **phrase**: “x **times **the **quantity **5 plus y.”

5 plus y 5 + y

x **times **the **quantity **5 plus y = x(5 + y)

The complete **expression **is,

x(5 + y).

Therefore, 5 + y is the required **expression**.

To learn more about the **expression**;

brainly.com/question/24242989

#SPJ1

Find an equation for the plane that passes through the point $(2,-1,3)$ and is perpendicular to the line $\mathbf{v}

### Answers

The **equation of the plane** that passes through the point [tex]$(2,-1,3)$[/tex] and is perpendicular to the line [tex]$\mathbf{v}$[/tex] can be expressed in terms of a normal vector [tex]$\mathbf{n}$[/tex] and a point [tex]$\mathbf{p}$[/tex] on the **plane** as [tex]$\mathbf{n}\cdot(\mathbf{x}-\mathbf{p})=0$[/tex].

To find the **normal vector** [tex]$\mathbf{n}$[/tex], we must first find a vector parallel to the line [tex]$\mathbf{v}$[/tex]. We can do this by taking the cross product of two **non-parallel** vectors [tex]$\mathbf{u_1}$ and $\mathbf{u_2}$[/tex] that lie on the line. Let [tex]$\mathbf{u_1} = (1,2,1)$ and $\mathbf{u_2} = (3,4,3)$[/tex]. Then, [tex]$\mathbf{n}=\mathbf{u_1}\times\mathbf{u_2}=(-4,8,-4)$[/tex].The equation of the plane that passes through the point [tex]$(2,-1,3)$[/tex] and is perpendicular to the line [tex]$\mathbf{v}$[/tex] can be expressed in terms of a normal vector [tex]$\mathbf{n}$[/tex] and a point [tex]$\mathbf{p}$[/tex] on the **plane** as [tex]$\mathbf{n}\cdot(\mathbf{x}-\mathbf{p})=0$[/tex].

We can now calculate the **equation of the plane** as [tex]$\mathbf{n}\cdot(\mathbf{x}-\mathbf{p})=0$[/tex], where [tex]$\mathbf{x}=(x,y,z)$ and $\mathbf{p}=(2,-1,3)$[/tex]. Thus, the equation of the plane is [tex]$-4x+8y-4z+17=0$.[/tex]

Learn more about ** equation for the plane **here:

https://brainly.com/question/17085465

#SPJ4

i need with this question

### Answers

The **height** of the wall is 14 feet

What are similar triangles?

**Similar** **triangles** are **triangles** that have the same shape, but their sizes may vary. All equilateral **triangles**, squares of any side lengths are examples of **similar** objects. In other words, if two **triangles** are **similar**, then their corresponding angles are congruent and corresponding sides are in equal proportion.

Therefore ;

TH/ JS = TV/VS

4/JS = 6/21

21× 4 = 6 JS

JS = 21× 4/6

JS = 84/6

JS = 14 feet

therefore the **height** of the wall is 14 feet

learn more about **similar** **triangles** from

https://brainly.com/question/14285697

#SPJ1

You have 1,000,000 number cubes, each measuring one inch on a side. If you arranged the cubes on the floor to make a square, would the square fit in your classroom?

### Answers

In a case whereby you have 1,000,000 number **cubes**, each measuring one inch on a side. If you arranged the cubes on the floor to make a square, then the** square** *would fit* in your classroom.

How can the square fitbe determined?

You possess one inch on each side, one million number cubes. How tall would the cubes be if they were placed one on top of the other to form a massive tower?

The fact that the high of one cube= 1 inch

The high of 1,000,000 cubes can be calculated as :

=1*1,000,000 = 1,000,000= 1 * 10^6 inch.

The area of a square A= b^2

b= length side of the square

1,000,000 = b^2

b = 1000 inch

Therefore, the **dimensions of** the square can be expressed as ( 1,000 in x 1,000 in)

But 1 in = 2.54 cm

1,000 inch = (1,000*2.54)

=2,540 cm-

=25.40 meters

Considering this in metres, the dimensions of the square can be expressed as: ( 25.40 m x 25.40 m)

We can conclude that it possible that the square will fit in the classroom.

Learn more about **cubes** at:

https://brainly.com/question/10947050

#SPJ1

A binomial experiment consists of 12 trials. The probability of success on trial 5 is 0.85. What is the probability of failure on trial 9?

0.17

0.72

0.64

0.9

0.15

0.44

### Answers

The **probability** of failure on the trial 9 for the given **binomial experiment** is 0.15.

What is binomial experiment?

An experiment with a set number of **independent trials** and just two results is referred to as a binomial experiment. The results of these experiments can be classified as either successes or failures. Due to the nature of the experiment's subject, results may only be categorised as successes or failures.

Due to the set number of outcomes that might occur in each experiment's trial, binomial experiments are unique from other types of studies. Binomial experiments, in particular, can only ever produce one of **two outcomes**.

The probability of success and failure of a trial is same for every number of trials.

Given that,

n = 12 trials

Success = 0.85

The failure is given as:

failure = 1 - success of trial

failure = 1 - 0.85

failure = 0.15

Hence, the probability of failure on the trial 9 for the given binomial experiment is 0.15.

Learn more about **binomial experiment** here:

https://brainly.com/question/15351475

#SPJ1

T/F If you want to compare the value 3 to the value 5 to see if 3 is greater than 5, you would enter the following formula: =3>5.

### Answers

**Answer:**

**Step-by-step explanation:**

The answer is TRUE, If you want to compare the value 3 to the value 5 to see if 3 is greater than 5, you would enter the following formula: =3>5.

if given two numbers of the following forms, which ones do not result in the correct mathematical result in the same form? assume there is no overflow (i.e., the result can fit in the available wires).

### Answers

The two **numbers **of the form a+bi and c+di where a,b,c, and d are real numbers, and i is the imaginary unit, always resulting in the correct **mathematical **result in the **same form**.

This is because complex numbers are a mathematical construct and the operations defined on them, such as addition, subtraction, multiplication, and division, follow the rules of **arithmetic**. These operations preserve the form of the numbers, so that the result of any two complex numbers, when operated upon, will always be in the form of a **complex** number.

For example, when adding two complex numbers (a + bi) and (c + di), the real parts add up to form a new **real **part, and the imaginary parts add up to form a new **imaginary **part, resulting in a new complex number in the form (a + c) + (b + d)i.

Learn more about **Mathematical Problems**:

https://brainly.com/question/2228446

#SPJ4

Emily parents put $1,500 in her bank account for college tuition. At an interest rate of 8.25% compounded annually. What will be the total balance after 2 years?

(A) $1,314.08

(B) $2,385.72

(C) $3,273.50

(D) $1,757.71

### Answers

**Answer:(A) 1.314.08**

**Step-by-step explanation:**

Inflation

A stemplot titled speed limit. The values are 10, 45, 45, 45, 45, 50, 50, 55, 55, 55, 55, 55, 60, 60, 60, 65, 65, 65, 65, 65, 65, 70, 70. The stemplot shows the speed limit on different signs. Which statement is true about the data shown in the stemplot?

### Answers

The statement that is true about the data shown in the stemplot is that the most common** speed limit is 55**.

**What is stemplot ?**

A stemplot, also known as a stem-and-leaf plot, is a type of **chart **used to **display **data. It shows the **distribution **of a set of values by **separating **each value into a **stem and a leaf**.

**Given by the question:**Based on the values given, the stemplot titled "speed limit" could be constructed as follows:

1 | 0

4 | 5 5 5 5

5 | 0 5 5 5 5 5

6 | 0 0 0 5 5 5 5

7 | 0 0

The stem represents the tens digit of each value, and the leaves represent the ones digit. For example, the first value of 10 has a **stem **of 1 and a **leaf **of 0.

Based on the stemplot, we can make the following observations:

The speed limits range from 10 to 70.There are no speed limits between 11 and 44.The most common speed limit is 55, which appears 5 times.There are four speed limits of 45 and two speed limits of 50 and 60.There are a total of 23 speed limits.

Therefore, the statement that is true about the data shown in the stemplot is that the most common speed limit is **55**.

To know more about **stemplot **visit:

https://brainly.com/question/28273786

#SPJ1

Linda wants to buy a charm bracelet. Greenville Fine Jewelry charges $12 per charm, plus

$14 for the bracelet. Hanson Jewelers, in contrast, charges $11 per charm and $21 for the

bracelet. If Linda wants to add a certain number of charms to her bracelet, the cost will be

the same at either jewelry shop. What would the total cost of the bracelet be? How many

charms would that be?

### Answers

The **answers** to each part is given below.

What are algebraic expressions?In mathematics, an expression or **mathematical expression** is a finite combination of symbols that is well-formed according to rules that depend on the context.**Mathematical symbols** can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of **logical syntax**.

Given is that Greenville Fine Jewelry charges $12 per charm, plus $14 for the bracelet. Hanson Jewelers, in contrast, charges $11 per charm and $21 for the bracelet.

For the **Greenville Fine** Jewelry, we can write -

A{x} = 14 + 12x

For the **Hanson Jewelers**, we can write -

B(x) = 21 + 11x

To add a certain number of charms to her bracelet, the cost will **not** be same.

Therefore, the **answers** to each part is given above.

To solve more questions on **functions & expressions**, visit the link below

brainly.com/question/17613163

#SPJ9

A kite is flying at an angle of elevation of 43o. If the string is 37 m long and is stretched tight, find the height of the kite to the nearest tenth of a meter.

### Answers

The required height of the kite to the **nearest tenth** of a meter is 25.2 m.

**What is the sine ratio in a triangle?**

In a right-angled triangle, the **ratio** of the perpendicular (with respect to an angle) to the hypotenuse gives the sine value of that angle. This **relationship** is used to solve problems regarding height and distance chapter.

Draw the **figure** as per the given instructions.

The position of the** kite** is at A and the string is AC which is 37 m long. The angle of **elevation** is ∠ACB, which is 43°. The **height** of the kite is AB.

So, apply the formula of **sine ratio** (perpendicular/hypotenuse) = sinα, where α be the opposite angle of that perpendicular.

AB/AC = sin∠ACB

AB/37 = sin43°

AB = 37sin43°

≈37×0.68

= 25.16

≈ 25.2

Therefore, the obtained **answer** is 25.2 m.

To learn more about the **sine ratio** visit this link

https://brainly.com/question/11723777

#SPJ9

What values of x

and y

satisfy the system {y=−2x+3

{y=5x−4?

Enter your answer as an ordered pair, like this: (42, 53)

If there is no solution, enter "no"; if there are infinitely many solutions, enter "inf."

### Answers

The **solution **to the **system **of **equation **y = -2x + 3 and y = 5x - 4 is (1,1).

What is the solution to the system of equation?

Given the **system **of **equation **in the question;

y = -2x + 3

y = 5x - 4

To solve the **system **of **equation**, plug equation one to into equation two and solve for x.

y = 5x - 4

Plug in y = -2x + 3

-2x + 3 = 5x - 4

Solve for x

-2x - 5x = - 4 - 3

-7x = -7

x = -7 / -7

x = 1

Now, plug x = 1 into **equation one **and solve for x.

y = -2x + 3

Plug in x = 1

y = -2( 1 ) + 3

y = -2 + 3

y = 1

Therefore, the **value** of x is 1 and y is also 1.

Learn more about **simultaneous equation** here: brainly.com/question/30319215

#SPJ1

I will give brainliest and ratings if you get this correct

### Answers

[tex]D(x)=\frac{f(x)}{g(x)}[/tex]

[tex]D'(x)=\frac{f'(x)g(x)-g'(x)f(x)}{(g(x))^{2} }[/tex]

What is quotient formula of differentiation?

Quotient rule in calculus is method finding the derivative of the **differentiable functions** which are in the** division** form

There are **different methods** to prove the quotient rule formula, given as,

Using derivative and limit propertiesUsing implicit differentiationUsing chain rule

Here, we are using **implicit differentiation method** to solve this quotient rule,

Let us take a differentiable function ,

[tex]D(x)=\frac{f(x)}{g(x)}[/tex]--------(1)

So, [tex]f(x)={D(x)}*{g(x)}[/tex]

Using the **product rule **we get,

[tex]f'(x)= D'(x).g(x)+g'(x).D(x)[/tex] solving for [tex]D'(x)[/tex] we get,

[tex]\frac{f'(x)-g'(x).D(x)}{g(x)} = D'(x)[/tex]------(2)

substitute for D(x) sub (1) in (2)

[tex]D'(x) =\frac{f'(x)-g'(x).\frac{f(x)}{g(x)} }{g(x)}[/tex]

⇒[tex]D'(x) =\frac{f'(x)g(x)-g'(x){f(x)} }{(g(x))^{2} }[/tex]

Hence,[tex]D'(x)=\frac{f'(x)g(x)-g'(x)f(x)}{(g(x))^{2} }[/tex] proved.

Learn more about** quotient rule **here:

https://brainly.com/question/29255160

#SPJ1

An online wholesaler sells novelty hats in bulk. The purple and leopard print hat sells for $3.50 each

when you buy less than 25 hats. For orders of 25 or more, the price is $2.97 per hat. Express the total

cost of the order as a function of the number of hats ordered, and graph this function in an appropriate

window on your paper. If your group has a budget of $80 for hats, how many hats can you purchase?

### Answers

we can purchase a **maximum** of 23 hats if we buy them for $3.50 each, or a maximum of 27 hats if we buy them for $2.97 each.

What is Equation?

Two or more expressions with an Equal sign is called as Equation.

**Function** to represent the total cost of the order in terms of the number of hats ordered:

C(n) = {3.50n, if n < 25;

2.97n, if n >= 25}

where n is the **number of hats** ordered, and C(n) is the cost of the order.

If the budget for hats is $80, we can set C(n) equal to 80 and **solve** for n:

3.50n = 80, if n < 25;

2.97n = 80, if n >= 25

For n < 25, we get:

n = 80/3.50 ≈ 22.86 =23

if the budget is $80 and the **hats** **cost** $3.50 each, we can buy a **maximum** of 23 hats.

For n >= 25, we get:

n = 80/2.97 ≈ 26.96

So if the budget is $80 and the hats cost $2.97 each, we can buy a **maximum** of 27 hats.

Therefore, we can purchase a **maximum** of 23 hats if we buy them for $3.50 each, or a maximum of 27 hats if we buy them for $2.97 each.

To learn more on **Equation**:

https://brainly.com/question/10413253

#SPJ9

X

5

Z

10

5√3

Y

Find sin cos tan

### Answers

The **trigonometry ratios **have their values to be

sin(x) = √3/2cos(x) = 0.5tan(x) = √3

How to determine the trigonometry ratios

The complete question is added as an attachment

From the question, we have the following parameters that can be used in our computation:

**Hypotenuse **= 10

Adjacent = 5

Opposite = 5√3

Using the above as a guide, we have the following:

sin(x) = **Opposite**/Hypotenuse

cos(x) = **Adjacent**/Hypotenuse

tan(x) = Opposite/Adjacent

Using the above as a guide, we have the following:

sin(x) = 5√3/10 = √3/2

cos(x) = 5/10 = 0.5

tan(x) = 5√3/5 = √3

The above are the values of the **trigonometry ratios **based on the attached figure

Read more about **trigonometry ratios **at

https://brainly.com/question/24349828

#SPJ1

what’d the inequality of x > 23

### Answers

The graph of the given **inequality **of x > 23 is attached.

What is an Inequality?

The relationship between two **expressions **or values that are not equal to each other is called inequality.

A number line can be used to represent numbers placed on regular **intervals**. A number line can be used to represent an inequality.

Given that the **inequality **of x > 23

We are asked to plot the given inequality on a number line.

x > 23

The above inequality says that, the **value **of x is equal to or greater than 23.

Hence, the **graph **of the given inequality is attached.

For more references on **inequality**, click;

brainly.com/question/28823603

#SPJ1

Shelly spent 45 minutes jogging and 30 minutes cycling and burned 1350 calories. The next day, Shelly swapped times, doing 30 minutes of jogging and 45 minutes of cycling and burned the same number of calories. How many calories were burned for each minute of jogging and how many for each minute of cycling?

Number of calories burned per minute =

### Answers

The **number **of calories burned per minute be 23.33333.

What is meant by system of equations?

Equations simultaneously, or a system of equations Several equations in algebra must be solved concurrently (i.e., the solution must satisfy all the equations in the system). There must be an equal number of equations and unknowns for a system to have a **singular solution.**

In order to locate the point where the lines intersect when the equations are graphed, systems of equations must be solved. The (x,y) ordered pair of this intersection point is regarded as the system's solution.

Let j be the number of calories burned by Shelly while running and c be the number of calories she burns while cycling.

The **system of equations **be

45j + 30c = 1350

30j + 45c = 1350

45j + 30(10)=1350

j = 23.33333

Therefore, the value j be 23.33333.

To learn more about **system of equations** refer to:

**https://brainly.com/question/28586904**

#SPJ1

In Exercises 19 and 20, choose h and k such that the system has (a) no solution, (b) a unique solution, and (c) many solutions. Give separate answers for each part. 19. x1 +hx2 = 2 4x1 + 8x2 =k 20. X1 – 3x2 = 1 2x +hx2 = k

### Answers

The **equations **must intersect at a single point then it have the **unique solution** and the value of h and k are **h = -1 **and **k = 6**

A system has no solution if the equations are **inconsistent**, meaning there is no way to satisfy both equations simultaneously. It has a **unique **solution if the **equations **intersect at a single point, meaning there is only one set of values that satisfies both equations.

Let's take a look at the first system of equations, 19.

**Equation **1: x + hx = 2

Equation 2: 4x + 8x = k

For the system to have no **solution**, the equations must be inconsistent. This means they must be parallel and never intersect. To achieve this, we can set the slopes of the lines to be equal but the y-intercepts different. In other words, we need to choose h and k such that:

h = -2 and k = 5

**Substituting **these values into the equations, we get:

Equation 1: x - 2x = 2

Equation 2: 4x + 8x = 5

You can see that these two equations do not have a **common **solution. They are inconsistent, meaning there is no point that satisfies both equations.

For the system to have a unique solution, the equations must intersect at a single point. This means the slopes and** y-intercepts** must be different. To achieve this, we can choose h and k such that:

h = -1 and k = 6

To know more about **equation **here.

https://brainly.com/question/10413253

#SPJ4

ben bought six and three fifths bags of rocks to use in his garden. He used four and one fifth bags. How many bags does Ben have left?

### Answers

**Answer:**

**To find the answer, we need to subtract the amount of bags Ben used from the amount he bought:**

**6 and 3/5 - 4 and 1/5**

**To subtract fractions, we need to have a common denominator. The smallest common denominator for 5 and 20 is 20, so we'll convert both fractions:**

**6 and 3/5 = 6 * 5/5 + 3/5 = 30/5 + 3/5 = 33/5**

**4 and 1/5 = 4 * 20/20 + 1/5 = 80/20 + 1/5 = 81/20**

**Now we can subtract:**

**33/5 - 81/20**

**We need to convert the mixed number to an improper fraction and find a common denominator:**

**33/5 - 81/20 = 132/20 - 81/20**

**Now we can subtract:**

**132/20 - 81/20 = 51/20**

**So Ben has 51/20 bags of rocks left. This can be simplified to 2 and 11/20 bags.**

**Answer:**

2 2/5

**Step-by-step explanation:**

6 3/5 **-** 4 1/5 **=** 2 2/5

Jaxson works in a department store selling clothing. He makes a guaranteed salary of $250 per week, but is paid a commission on top of his base salary equal to 15% of his total sales for the week. How much would Jaxson make in a week in which he made $1800 in sales? How much would Jaxson make in a week if he made

�

x dollars in sales?

Answers: Base salary 520:

When selling for X:0.15

Total sales:250+0.15 or 0.15+250

### Answers

**Answer:**

**Step-by-step explanation:**

250 per week base

15%of 1800 he made is = 270

270+250 =520

He made 520$ in the week he made 1800$ in sales

Final answer:

Jaxson's salary is a combination of a fixed $250 plus 15% commission on his weekly sales. For $1800 in sales, he will earn $520. If the sales amount is x dollars, then he will earn $250 + 0.15*x dollars in a week.

Explanation:

Jaxson's income consists of a guaranteed **base salary** of $250 per week and a **commission** of 15% on his total weekly sales. If Jaxson made $1800 in sales in a week, his total income for the week would be his base salary plus his commission i.e., $250 + 0.15*$1800 = $520.

Similarly, if Jaxson made x dollars in sales in a week, his total **income** for that week would be his base salary plus his commission on the sales i.e., $250 + 0.15*x dollars.

Learn more about Salary and Commission here:

https://brainly.com/question/31627828

#SPJ2

You start driving west for 3 miles, turn right, and drive north for

another 13 miles. At the end of driving, what is your straight line

distance from your starting point? Round to the nearest tenth of a

mile.

### Answers

**Answer:**

13.3 miles

**Step-by-step explanation:**

Picture a right triangle with legs of 3 and 13. The hypotenuse is the straight line distance back to the starting point. Use the Pythagorean theorem to find the hypotenuse (c):

c² = 13² + 3² = 178

c = √178 = 13.3 miles

for

6. Tami multiplies two fractions. The first fraction is greater than -1 but less than 0. The

notei

second fraction is greater than 0 but less than 1.

Which statement describes the product of the two fractions Tami multiplied?

### Answers

The **product **of the two **fractions **Tami multiplied will be a **negative number **between 0 and -1.

How to find the product of the multiplication

Since the **first fraction **is negative greater than -1 but less than 0

and the second fraction is positive, greater than 0 but less than 1, their product will be negative.

This is because when a negative number multiplies a positive number the product is a **negative number**

Moreover, since both numbers are in fraction and less than whole their multiplication will also be a reduction tending towards **zero**

Learn more about **fractions **at:

https://brainly.com/question/78672

#SPJ1

A 1.08 km diameter asteroid has a density of 3000 kg/m3 and impact the surface at 23.0 km/sec. Assuming a spherical asteroid, what is the kinetic energy (in joule) of the asteroid? Convert the answer to megatons of TNT, where 1 megaton is about 4e15 joule. For comparison, the most energetic weapon in the human arsenal is about 100 megatons.

### Answers

The **kinetic **energy (in joule) of the **asteroid **is, 33 million

What is kinetic energy ?

The kinetic energy is the energy associated with the particle having **mass **m and moving with the **velocity **v.

To find the kinetic energy of the asteroid, we need to use the formula:

KE = (1/2)mv²

where KE is the kinetic energy, m is the mass of the asteroid, and v is its velocity.

The mass of the asteroid can be calculated using its **density **and volume:

V = (4/3)πr³

where V is the volume of the asteroid, r is its **radius**, and π is the mathematical constant pi.

Since the asteroid is spherical, its radius is half its diameter, which is 0.54 km.

So,

V = (4/3)π(0.54 km)³

= 0.65 km³

The mass of the asteroid is then:

m = density × volume

= 3000 kg/m³ × 10⁹ m³/km³ × 0.65 km³

= 1.95 × 10¹² kg

Now we can calculate the kinetic energy:

KE = (1/2)mv²

= (1/2) × 1.95 × 10¹² kg × (23.0 km/sec)²

= 1.32 × 10²³ joule

To convert this to megatons of TNT, we divide by the energy of one megaton:

= 1.32 × 10³ joule / (4 × 10¹⁵ joule/megaton)

= 3.3 × 10⁷ megatons

Hence, the **KE** of asteroid is 33 million

To know more about **kinetic energy** check:

https://brainly.com/question/114210

#SPJ1