USING STRUCTURE An athletic facility is building an indoor track. The track is composed of a rectangle and two semicircles, as shown. A drawing shows an indoor track. It is shaped like a rectangle with a semi-circle on each of the shorter sides. The length of the rectangle is labeled x. The radius of each semi-circle is labeled r. A. Write a formula for the perimeter of the indoor track. $P=$ b. Solve the formula for $x$ . $x=$ Question 2 c. The perimeter of the track is 660 feet, and $r$ is 50 feet. Find $x$ . Round your answer to the nearest foot. $x=$ feet

Answer:

2. the answer is 5 because the square of 5 is 25 and 4 x 25 = 100 which is 20 x 5

Step-by-step explanation:

We are required to find the unknown number from the expression

2.

let

the number = x

four times the square of a number equals 20 times that number

4x² = 20x

Divide both sides by 4x

x = 5

The number is 5

3.

let

x = the unknown number

Twice the square of the sum of a number and 3 is 98

sum of a number and 3 = x + 3

square of the sum = (x+3)²

Twice the square = 2(x + 3)²

2(x + 3)² = 98

2(x² + 6x + 9) = 98

2x² + 12x + 18 = 98

2x² + 12x +18 - 98 = 0

2x² + 12x - 80 = 0

x² + 6x - 40 = 0

using factorization method to solve the quadratic equation

x² + 10x - 4x - 40 = 0

x(x + 10) - 4(x + 10) = 0

(x + 10) ( x - 4) = 0

x + 10 = 0 or x - 4 = 0

x = -10 or x = 4

Therefore, the unknown number is -10 or 4

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Answer:

34 divided by 2

Step-by-step explanation:

come onnnnnnnnnn

Answer:

C, he did not divide properly .

Step-by-step explanation:

Answer:

B. -1

Step-by-step explanation:

Use the slope formula to find the slope  m .

Answer:

B

Step-by-step explanation:

Calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (1, - 3) and (x₂, y₂ ) = (3, - 5)

m = [tex]\frac{-5+3}{3-1}[/tex] = [tex]\frac{-2}{2}[/tex] = - 1 → B

a.) y= 0.2x + 9 and y= 0.5x

b.) 30 emails

c.) the first plan

Step-by-step explanation:

a.) cost per email is a variable

b.) graph and find intersection of the lines

c.) plug in 500 for x in both equations

The number of email messages where both plans will cost the same will be 300 messages.

The system of equations to model the cost of the two internet plans based on the information given will be:

Internet provider 1 = 9 + 0.02m

Internet provider 2 = 0.05m

where m = number of mails

The number of email messages where both plans will cost the same will be:

9 + 0.02m = 0.05m

Collect like terms

0.05m - 0.02m = 9

0.03m = 9

m = 9/0.03

m = 300

When there's 500 messages for the month, the cost for each plan will be:

Internet provider 1 = 9 + 0.02m

= 9 + 0.02(500)

= 9 + 10

= 19

Internet provider 2 = 0.05m

= 0.05(500)

= 25

Therefore, based on the calculation, the first plan is cheaper.

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Answer:

the first choose

Step-by-step explanation:

29/200. 145 / 5 = 29, and 1000 / 5 = 200. 29 is a prime, so that's the lowest you can go: 29/200.

Answer:

it's not important.........

Answer:

3000 meters

Step-by-step explanation:

1 kilometer = 1000 meters

3 kilometers = 3(1000 meters)

3 kilometers = 3000 meters

Hope this helps!!!

Answer:

Put a Greater than symbol >

Step-by-step explanation: That question is showing absolute value which is basically the amount it takes to get there from zero.

-5 with absolute value becomes a regular 5

Answer:

its >

Step-by-step explanation:

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▹ Answer

x = -2

▹ Step-by-Step Explanation

4(x + 1) = -3x - 10

Distribute 4:

4x + 4 = -3x - 10

4x + 3x

Move the terms:

4x + 3x + 4 = -10

Collect like terms:

7x = -10 - 4

7x = -14

FINAL ANSWER:

x = -2

Hope this helps!

CloutAnswers ❁

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Answer:

see below

Step-by-step explanation:

65 - 32 = 13

13 divide by 65 = 0.20

0.20 x 100% = 20%

so the percentage drop is 20%

therefore, Marcus is correct.

Answer:

2)  Expand the distribution of terms.

6x+3+2x+6

3)  Collect the like terms.

(6x+2x)+(3+6)

4) simplify.

8x+9

Step-by-step explanation:

First, put the equation of the line given into slope-intercept form by solving for y. You get y = -2x +5, so the slope is –2. Perpendicular lines have opposite-reciprocal slopes, so the slope of the line we want to find is 1/2. Plugging in the point given into the equation y = 1/2x + b and solving for b, we get b = 6. Thus, the equation of the line is y = ½x + 6. Rearranged, it is –x/2 + y = 6.

Answer: A

Step-by-step explanation:

Answer: the night temperature was 3 degrees below the afternoon temperature

Step-by-step explanation:

Answer:

[-2,8]

Step-by-step explanation:

Answer:

Fifth option

Step-by-step explanation:

Answer:A combination of variables, numbers, and at least one operation.

Example: x+4

Step-by-step explanation:

Answer: 308

Step-by-step explanation: Divide 70 by 5 which is 14 and then 14 times 22 is 308

Answer:

3.5 hours

Step-by-step explanation:

2*77/44=154/44=3.5 hours

Answer:

4. Given that the distance from one place to another are placed in ranges of a thousand, then the distances from Sao Paulo to Chicago Illinois which is 5,252 miles and from Chicago Illinois to Istanbul Turkey which is 5,784 miles will be in the same 5,000 kilometer distance range and both distances will taken as the same distance

The same situation can also be arrived at by rounding down both distances

Step-by-step explanation:

The given information are;

The flight distances given;

From Sao Paulo to Chicago Illinois = 5,252 miles

From Chicago Illinois to Istanbul Turkey = 5,784 miles

From Beijing China to Chicago Illinois = 6,579 miles

Lees conjectured the flight distance from Chicago to Istanbul is the same as the flight distance from Chicago Sao Paulo when the distances are rounded to the nearest thousand

Placing the distances in ranges of 1000, we have the 5,252 miles and the 5,784 miles will be in the same 5,000 to 5,999 miles range.

Answer:

x= -10

Step-by-step explanation:

-8x+10x+20=0

2x+20=0

2x=0-20

2x=-20

x=-20/2

x= -10

Answer:

x = -10

Step-by-step explanation:

8x (-10x)= 10x +20 (-10x)

subtract 10x from both sides of the equation

-2x/-2 = 20/-2

divide both sides by -2

x = -10

Answer:

x = 12

Step-by-step explanation:

insert 2 into the equation where x is.

2(2)2 + 4

so this is 2 * 2 * 2 + 4 = 12

Answer:

0.2

Step-by-step explanation:

20/100= 2/10

2/10= 0.2

Answer:

35

Step-by-step explanation:

Answer:

y=-7

m=0

Step-by-step explanation:

y=mx+b

line is perpendicular to y axis and passes through point(5,-7)

which means that our line equation is y=-7

so y=0*x-7

so m=0 and b=-7

Answer:

Side length of each booth is 8.35 ft approximately.

Step-by-step explanation:

There are 11 companies set up equal sized square booths in a row along one wall of a convention center.

Now, refer the diagram to answer the problem.

It is given area is 1200.

So, length x width =1200

(11x+24)(x+2)=1200

Multiply using FOIL method.

[tex]11x^{2}[/tex]+22x+24x+48=1200

[tex]11x^{2}[/tex]+46x+48-1200=0

[tex]11x^{2}[/tex]+46x-1152=0

Solve using quadratic formula

x=[tex]\frac{-46+/- \sqrt{46^{2}-4(11)(-1152 } }{2(11)}[/tex]

x=[tex]\frac{-46+/-\sqrt{2116+50688} }{22}[/tex]

x=[tex]\frac{-46+/-\sqrt{52804} }{22}[/tex]

Simplify it

[tex]x=\frac{-49+/- 229.79}{22}[/tex]

Simplify to get two values for x.

x=8.35; x=-12.67

Here negative does not work.

Side length of each booth is 8.35 ft.

Answer:

g) x = 30

h) x = 30

i) m = 55

j) x = 24

k) k = 45

Step-by-step explanation:

G)

all angles of a triangle add up to 180.

the square in the bottom right of the triangle is 90 btw

2x + x + 90 = 180

3x + 90 = 180

3x + 90 - 90 = 180 - 90

3x = 180 - 90

3x = 90

3x/3 = 90/3

x = 30

H)

this is an Isosceles triangle.

that means the bottom two angles are equal.

75 + 75 + x = 180

x + 150 = 180

x + 150 - 150 = 180 - 150

x = 180 - 150

x = 30

I)

2m is supplementary to the bottom right angle of the triangle.

that means they add together to make 180.

80 + 30 + (180 - 2m) = 180

110 - 2m = 180 - 180

110 - 2m = 0

110 = 2m

110/2 = m

55 = m

J)

to save time I'm not going to write out the steps, its the same as the i.

2x + 3x + (180 - 120 ) = 180

5x + 60 = 180

5x = 180 - 60

5x = 120

x = 120/5

x = 24

K)

imagine this as a triangle and a square.

sorry I'm not sure how to explain this -.-

but the equation would be

k + k + 90 = 180

2k + 90 = 180

2k = 180 - 90

2k = 90

k = 45

L)

Im not sure how to solve this, I'm sorry :( hope you figure it out!

Answer:

area square inches is less than 1.2

Step-by-step explanation: