Julissa is running a 10-kilometer race at a constant pace. After running for 18 minutes, she completes 2 kilometers. After running for 54 minutes, she completes 6 kilometers. Her trainer writes an equation letting t, the time in minutes, represent the independent variable and k, the number of kilometers, represent the dependent variable.

Which equation can be used to represent k, the number of kilometers Julissa runs in t minutes?
k – 2 = k minus 2 equals StartFraction 1 Over 9 left-parenthesis t minus 18 right-parenthesis.(t – 18)
k – 18 = k minus 18 equals StartFraction 1 Over 9 left-parenthesis t minus 2 right-parenthesis.(t – 2)
k – 2 = 9(t – 18)
k – 18 = 9(t – 2)

2 over 45

Step-by-step explanation:

i divide 8over9 by 20

Answer:

[tex]y=-2,\:\\x=1,\:\\z=-3[/tex]

Step-by-step explanation:

[tex]\begin{bmatrix}y+4z=-14\\ x+3z=-8\\ 2x-3y=8\end{bmatrix}\\\\Isolate\:y\:for\:y+4z =-14\: : \:y=-14-4z\\\\\mathrm{Subsititute\:}y=-14-4z\\\\\begin{bmatrix}x+3z=-8\\ 2x-3\left(-14-4z\right)=8\end{bmatrix}\\\\Isolate\:x\:for\:x+3z =-8\: :\:x =-8-3z\\\mathrm{Subsititute\:}x=-8-3z\\\\\begin{bmatrix}2\left(-8-3z\right)-3\left(-14-4z\right)=8\end{bmatrix}\\\\Simplify\\\\\begin{bmatrix}6z+26=8\end{bmatrix}\\\\Isolate\:z\:for 6z+26=8 \: ;\:z =-3\\\\\mathrm{For\:}x=-8-3z\\\\[/tex]

[tex]\mathrm{Subsititute\:}z=-3\\\\x=-8-3\left(-3\right)\\\\-8-3\left(-3\right)=1\\\\x=1\\\\\mathrm{For\:}y=-14-4z\\\\\mathrm{Subsititute\:}x=1,\:z=-3\\\\y=-14-4\left(-3\right)\\\\-14-4\left(-3\right)=-2\\\\y=-2\\\\\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}\\\\y=-2,\:x=1,\:z=-3[/tex]

Answer:

A) 98.94 sq. meters

B) 42 sq. meters

Step-by-step explanation:

A) So first we calculate the area for the square which is 15*20 = 300. Then we calculate the area of the circle which is pi*r^2 and in this case the radius is 4 which is 1/2 of 8. The area is approx. 201.06. Then we subtract that from 300. 300-201.06 = 98.94. The answer for A) is approx. 98.94

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B)First we calculate the area of the whole square which is 8*6 = 48. Then the area of the garden which is 2*3 = 6. 48-6 = 42. The answer is B) is 42 then.  

Given:

The function for size of a square frame is

[tex]f(x)=x+2[/tex]

where, x is the side length of the picture.

The function for the price in dollars for the frame is

[tex]p(x)=3x[/tex]

To find:

The single function for the price of a picture with an edge length of x.

Solution:

We know that, for a picture with an edge length of x.

Size of a square frame = f(x)

Price in dollars for the frame = p(x)

Single function for the price of a picture with an edge length of x is

[tex](p\circ f)(x)=p(f(x))[/tex]

[tex](p\circ f)(x)=p(x+2)[/tex]       [tex][\because f(x)=x+2][/tex]

[tex](p\circ f)(x)=3(x+2)[/tex]           [tex][\because p(x)=3x][/tex]

Let the name of this function is c(x). So,

[tex]c(x)=3(x+2)[/tex]

Therefore, the required function is [tex]c(x)=3(x+2)[/tex].

Answer:

480 in 5hrs

Rate is 96 per hour

Step-by-step explanation:

In 5 hours there are 300 minutes (5x60) and 300min/25min = 12. So 25 mins pass 12 times in 5 hours. Since each 25 mins its 40 ppl then 12x40 = 480.

480 in 5 hours so 480/5= 96 per hour

Answer:

It is 13 21/32 hope this helps

Answer:

Let the number be x

According to the question,

6x -7 = 35

=> 6x = 35 + 7

=> x = 42/6

=> x = 7

The solution to the equation is x = 7.

We have,

Let's assume the unknown number is represented by the variable 'x'.

- Translate the given information into an equation:

6x - 7 = 35.

- To isolate the variable 'x', start by adding 7 to both sides of the equation:

6x - 7 + 7 = 35 + 7.

- Simplify:

6x = 42.

- Next, divide both sides of the equation by 6 to solve for 'x':

(6x)/6 = 42/6.

x = 7

Therefore,

The solution to the equation is x = 7.

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Answer:

Step-by-step explanation:

Hello,

let s regroup the terms

2ax - 15 = 3(x + 5) + 5(x - 1) *** add 15 to both sides ***

<=> 2ax = 15 + 3x + 15 + 5x - 5 *** develop to remove the parentheses***

<=> 2ax = 8x + 25 *** simplify ***

<=> (2a-8)x = 25 *** subtract 8x from both sides ***

<=> (a-4)x=25/2 *** divide by 2 both sides ***

There is no solution is a-4 = 0 ,

because it would mean 0 = 25/2 and this is not possible

So it gives a = 4

Thanks

In the case when no value of x satisfies the equation so there the value of a should be 4.

Since

the equation is  

2ax - 15 = 3(x + 5) + 5(x - 1)

2ax = 15 + 3x + 15 + 5x - 5

2ax = 8x + 25

(2a-8)x = 25

So a = 4

hence, In the case when no value of x satisfies the equation so there the value of a should be 4.

Learn more about an equation here https://brainly.com/question/22358515

Answer:

354 feet below sea level

Step-by-step explanation:

Subtract 23 from  215, then add 119

Answer:

32 purple marbles.

Step-by-step explanation:

Turn 3:8 into 3x+8x.

Equation:

3x+8x=44

x=4

Now, refer back to 3x:8x. We know that x=4, so 4*8=32.

32 purple marbles.

Answer:

There are 32 purple marbles and 12 red marbles

Step-by-step explanation:

The ratio is 3:8 and the total is 44. For 3 red marbles, they have 8 purple marbles but we don't know how many each marble we need if the total sum is 44. So we do...

3x+8x=44

11x=44

x=4

We need to know the number of purple marbles so we do,

8*4=32

Answer:

The answer to this is: 3160 and can i have brainliest?? please

Step-by-step explanation:

Answer:

YOU NEED TO DOWNLOAD CYMATH RIGHT NOW

Step-by-step explanation:

I got this answer one time and that is a great app seriously it WILL save your life

Answer:

125 inches^3

Step-by-step explanation:

To solve for cubes it is L^3 or Length Cubed. Whcih is simply L×L×L where L is Length.

Answer:

D

Step-by-step explanation:

The rest of the question is the attached figure and the statement options.

A. Over the interval [–4, –2], the local minimum is 0.

B. Over the interval [–2, –1], the local minimum is 25.

C. Over the interval [–1, 4], the local minimum is 0.

D. Over the interval [4, 7], the local minimum is -7.

============================================================

According to the graph, we will check the options:

A. Over the interval [–4, –2], the local minimum is 0.  (Wrong)

Because the minimum is -12

B. Over the interval [–2, –1], the local minimum is 25.   (Wrong)

Because the minimum is 18

C. Over the interval [–1, 4], the local minimum is 0.  (Wrong)

Because the minimum is at x = 4 less than zero

D. Over the interval [4, 7], the local minimum is -7.    (True)

Answer:

The answer would be D

Step-by-step explanation:

Answer:40

Step-by-step explanation:

Answer:

512

Step-by-step explanation:

Let the number of 7th graders in the school is x.

As three-quarters of them play at least one sport, so, the number of 7th graders who play sport = [tex]\frac 3 4 x[/tex].

Among the 7th graders who play sports, half of them play more than one sport. So, the number of 7th graders who play more than one sport [tex]= \frac 1 2\times \frac 3 4 x=\frac 3 8 x[/tex].

Among the 7th graders who play more than one sport, one-third of them play more than two sports. So, the number of 7th graders who play more than two sport [tex]= \frac 1 3\times \frac 3 8 x=\frac 1 8 x[/tex].

Among the 7th graders who play more than two sports, one-quarter of them play more than three sports.

So, the number of 7th graders who play more than three sport [tex]= \frac 1 4\times \frac 1 8 x=\frac{1}{32} x[/tex].

7th graders play more than three sports at the school= 16

[tex]\Rightarrow \frac{1}{32} x=16[/tex]

[tex]\Rightarrow x =16 \times 32[/tex]

[tex]\Rightarrow x = 512[/tex]

Hence, the total numbers of 7th graders in the school are 512.

Answer:

x=1

Step-by-step explanation:

Answer:

it is C

Step-by-step explanation:

it is reflected so the angles and the sides stay the same.

The statement best describes the relationship between the two figures is: figure JKL is similar to figure J'K'L'.

Similar triangles are defined as two triangles with the same shape, equal pair of corresponding angles, and the same ratio of the corresponding sides.

As per the given figure,

In triangles ΔJKLand ΔJ'K'L',

side JK = side J'K'

side KL= side K'L'

side JL = side J'L'

According to Side-Side-Side criterion, two triangles are similar if three sides of a triangle are equal to the corresponding sides of the other triangle.

Thus, ΔJKLand ΔJ'K'L' are similar triangles due to equal pairs of corresponding sides.

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The correct answer is 7.3e +22

Answer:

Yes

Step-by-step explanation:

Answer: Yes it is equivalent

Step-by-step explanation:

If you crossed out the 12 and put it under 15, it would be 15/12=1.25.

Same for the second one cross out the 4 and put it under the 5 and it would be 5/4 is 1.25.

Answer:

17/12

Step-by-step explanation:

find a common denominator for each number so 8/12 and 9/12

Answer:

Step-by-step explanation:

We know that the volume of a sphere/globe is given as

V=4 /3πr^3

but the circumference is expressed as

C=2πr

solving for r given  that C=24

24=2*3.142r

24=6.284r

r=24/6.284

r=3.8in

put r=3.6 in the expression for volume we have

V=4 /3π(3.8)^3

V=4 /3π(55

V=(220.59*3.142)/3

V=693.12/3

V=231in^3

The volume of the globe is 231in^3

The volume of the globe is 233  cubic inches.

Important information:

We need to find the volume of the globe.

Let [tex]r[/tex] be the radius of the globe.

Circumference of the globe along the equator is:

[tex]C=2\pi r[/tex]

[tex]24=2\pi r[/tex]

[tex]\dfrac{24}{2\pi }=r[/tex]

[tex]\dfrac{12}{\pi}=r[/tex]

Volume of the globe is:

[tex]V=\dfrac{4}{3}\pi r^3[/tex]

[tex]V=\dfrac{4}{3}\pi \left(\dfrac{12}{\pi}\right)^3[/tex]

[tex]V=\dfrac{4}{3}\pi \left(\dfrac{1728}{\pi^3}\right)[/tex]

[tex]V=233.444...[/tex]

[tex]V\approx 233[/tex]

Therefore, the volume of the globe is 233  cubic inches.

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Answer:

-5,-2,1,and 5

Step-by-step explanation:

Answer:

But you just gave us the steps-

Answer:

Step-by-step explanation:

Well for this you wouldn't necessarily solve you you simplify, to simplify you would do 56- 12 which would get you 3x - 44.

answer:1.935825×10 to the sixth power

step by step: your going to move the decimal point 6 places to the left. which became 1.935825x10 to the sixth power.