You began membership in a new health and fitness club which has access to a dietician and personal trainer. They help you develop a special eight-week diet and exercise program. The data in the following table represents your weight, w, as a function of time, t, over an eight-week period.

Time (weeks)
0
1
2
3
4
5
6
7
8
Weight (lb)
150
144
143
141
140
137
137
132
129

If you lost 13 pounds in the first five weeks, what is the average rate of change of weight with respect to time over the first five weeks of the program?
a.
+0.38 pounds per week
b.
-0.38 pounds per week
c.
+2.6 pounds per week
d.
-2.6 pounds per week

Answer:i

Step-by-step explanation:

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

Explanation:

The similar red marks on the angles tell us those angles are congruent. So they are the same measure.

The sides opposite those congruent angles are the same length. This means AC = BC. This triangle is isosceles.

--------------

Solve for x

AC = BC

5x-8 = 2x+7 .... substitution

5x-8-2x = 7 ... subtract 2x from both sides

5x-2x = 7+8 ..... add 8 to both sides

3x = 15

x = 15/3 ... divide both sides by 3

x = 5

---------------

Use that x value to compute each side length

AB = 3x+11 = 3*5+11 = 15+11 = 26

BC = 2x+7 = 2*5+7 = 10+7 = 17

CA = 5x-8 = 5*5-8 = 25-8 = 17

Note how BC and CA are the same length (17 units). This helps confirm we have the right x value.

----------------

The last step is to add up all the side lengths to get the perimeter

perimeter of triangle = sum of all the sides

perimeter of triangle = side1 + side2 + side3

perimeter of triangle ABC = AB + BC + CA

perimeter of triangle ABC = 26 + 17 + 17

perimeter of triangle ABC = 60 units

Answer:

Step-by-step explanation:

Remark

The sides opposite the 2 base angles are equal. That gives you x. Then all you have to do is substitute in the 3 binomials.

Equation

5x - 8 = 2x + 7                 Add 8 to both sides

Solution

5x - 8 + 8 = 2x + 7 + 8   Combine

5x = 2x + 15                   Subtract 2x from both sides

5x-2x = 2x-2x + 15        Combine

3x = 15                           Divide by 3

x = 5

Side length

5x - 8 = 5*5 - 8 = 25 - 8

5x - 8 = 17

3x + 11 = 3*5 + 11 = 15 + 11 = 26

Perimeter

17

17

26    Add

Perimeter = 60

Answer:

sinθ = [tex]\frac{3}{4}[/tex]

Step-by-step explanation:

Using the trigonometric identity

sin x = [tex]\frac{1}{cscx}[/tex] , then

sin

θ = [tex]\frac{1}{\frac{4}{3} }[/tex] = [tex]\frac{3}{4}[/tex]

9514 1404 393

Answer:

  140, 35, 260/35, 7.43, 8

Step-by-step explanation:

The last section is just a summary of the preceding sections, a short description of the problem and how you worked it.

She sells the jackets for 140% of $25, or $35. 260/35 = 7.43 She can only sell a whole number of jackets, so she needs to sell 8.

Answer:

Length of one of the shorter congruent side is: 6 cm

Step-by-step explanation:

In order to find the length of congruent sides we have to solve the system of equations

Given systems of equation is:

y = x + 2

2x + 3y = 36

Putting y = x+2 in second equation

[tex]2x + 3(x+2) = 36\\2x+3x+6 = 36\\5x+6 = 36\\5x = 36-6\\5x = 30\\\frac{5x}{5} = \frac{30}{5}\\x =6[/tex]

As we know that x represents the shorter side, the length of short side is: 6 cm

Hence,

Length of one of the shorter congruent side is: 6 cm

Step-by-step explanation:

[tex]v \: cylinder = \pi \times r {}^{2} \times h \\ 3.14 \times 3.5 {}^{2} \times 20 \\ 3.14 \times 12.25 \times 20 \\ = 769.3[/tex]

you should round to nearest tenth place...I dont know...hope it helps

Answer:

4/6

Step-by-step explanation:

look for the LCM of the denominators then divide with each denominator and multiply the answer you have got with the numerator after add it you want change it to it's simplest form

Answer:

$36 per day plus $0.22 per mile

Step-by-step explanation:

For Ben,

Total miles driven = 550 miles

Number of days = 6 days

Total cost = $337

For Lisa

Total miles driven = 350 miles

Number of days = 3 days

Total cost = $185

Solving Simultaneously;

6d + 550m = 337

3d + 350 m = 185

Multiply equation 2 by 2  we have

6d + 550m = 337   ----1

6d + 700m = 370------2

So;

Subtracting equation  1 from equation 2

150m = 33

m = 33/150

m = $0.22

Substitute m=0.22 into equation 1

6d + 550(0.22) = 337

6d + 121 = 337

6d = 337 - 121

6d = 216

d = 216/6

d = $36

Hence the charge is $36 per day plus $0.22 per mile

Answer:

≈ 22 ft

Step-by-step explanation:

The area (A) of a square is calculated as

A = s² ( where s is the side length )

Given A = 479, then

s² = 479 ( take the square root of both sides )

s = [tex]\sqrt{479}[/tex] ≈ 22 ft ( to the nearest foot )

Answer:

A = 479 sq ft

479 = x²

square root of 479 = square root of x²

21.89 = x

rounded= 22 ft

The answer is C: (-3,-1)

To test if points satisfy an equation, all you need to do is test the numbers in both of the equations it provides you

Here is proof the answer is C :

y > x - 2

(lets plug in point C)

-1 > -3 - 2

solve

-1 > -5 ?

Yes this statement is true- onto the next inequalitity!

y > 2x + 2

-1 > 2(-3) + 2

solve

-1 > -6 + 2

-1 > -4 ?

Yes, this inequality is true too!

Know we know answer c (-3,-1) is the right answer!

Answer:

3.2t - 2.4

Step-by-step explanation:

Given

- 3.6 - 1.9t + 1.2 + 5.1t ← collect like terms

= (- 1.9t + 5.1t) + (- 3.6 + 1.2)

= 3.2t + (- 2.4)

= 3.2t - 2.4

Answer:

repeating -0.428571.....

Where are the answers?

Step-by-step explanation:

Answer:

im not sure but maybe d

Step-by-step explanation:

Step-by-step explanation:

x - is the amount of DVDs

so 2x + 5x + 7x = 56

14x = 56

x = 4

so comedy is 2x4 = 8; action 7x4 = 28 and horror is 5x4 = 20 DVDs

Answer:

0.35

Step-by-step explanation:

[tex]\frac{7}{20}[/tex]

  20 ) 7   ( 0.35

          0

           70

          60

            100

            100

                0

Answer:

7\20 as a decimal is

0.35

Answer:

120

Step-by-step explanation:

First, you want to find the third angle

to do that you 180-33+87=60

x=60

since x and y are on a straight line, to find y would be 180-x

180-60=120

y=120

-8*-10/-8*-10

= 80/80

=1

So, 1 is the correct answer. (:

Answer:

-4r+2s-15

Step-by-step explanation:

collect like terms

r-5r= -4r

-6s+8s= 2s

therefore -4r+2s-15

Answer:

It's table D

Step-by-step explanation:

I just took the test.

Answer:

The answer is table D!

Step-by-step explanation:

Answer:

B: 4

Step-by-step explanation:

The graph shows that there is 4 units between the numbers 30-36.

Hope this helps!

Unit rate is the quantity of an amount of something at a rate of one of another quantity.

The multiplication equation to determine the cost C in dollars of each ticket is C = 99 x 1/6.

The cost of each ticket is $16.5.

It is the quantity of an amount of something at a rate of one of another quantity.

Example:

6 miles in 2 hours

0ne hour will be 3 miles.

We have,

6 tickets = $99

Divide both sides by 6.

1 ticket = 99/6

1 ticket = $16.5

The multiplication equation to determine the cost C in dollars of each ticket:

$C = 99 x 1/6

Thus,

The multiplication equation to determine the cost C in dollars of each ticket is C = 99 x 1/6.

The cost of each ticket is $16.5.

Learn more about unit rates here:

https://brainly.com/question/28394073

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Answer:

x = 2

y = 5

Step-by-step explanation:

3x + y = 11 equation (1)

-x + y = 3 multiply this equation by -1

x - y = -3 equation (2)

by adding 2 equations

4x = 8

x = 2

by sub. in Equation (2)

2 - y = -3

y = 2+3

y = 5

Answer:

35 degrees

Step-by-step explanation:

I think that's a right angle? If so, right angles always are 90 degrees, and 90 - 55 = 35.

Answer:

There are 11 Girls for every 12 Boys in the sixth-grade class

Step-by-step explanation:

For this problem, you want to take the original rate which is 88 girls / 96 boys.

Once you have that number, you want to divide both sides by 8.

88/96 = 11/12

The correct option is D. 11 girls for every 12 boys.

We need to determine the ratio of the number of girls to the number of boys.

Given:

Number of girls = 88

Number of boys = 96

The ratio of girls to boys can be represented as "girls : boys."

To simplify the ratio, we can divide both the number of girls and the number of boys by their greatest common divisor (GCD). In this case, the GCD of 88 and 96 is 8.

Dividing both numbers by 8, we get:

Number of girls (after dividing) = 88 ÷ 8 = 11

Number of boys (after dividing) = 96 ÷ 8 = 12

So, the simplified ratio of girls to boys is 11 : 12.

Now, let's check which option matches the simplified ratio:

A. 88 girls for every 96 boys (Does not match)

B. 1 girl for every 1.09 boys (Does not match)

C. 44 girls for every 48 boys (Does not match)

D. 11 girls for every 12 boys (Matches)

The correct option is D. 11 girls for every 12 boys.

Learn more about Ratios here:

https://brainly.com/question/32531170?

#SPJ2

Answer:

A) Scale factor from A to B is 2

B) Length of left side is 3 and length of right side is 5.

Step-by-step explanation:

A) Length of the top side is 2.5 in A and is 5 in polygon B. 5/2.5 = 2, therefore scale factor is 2.

B) Because the scale factor is 2, each of the sides double while the angles stay the same. Therefore, the length of the side on the left is 3 and length of the side on the right is 5.

1.5 x 2 = 3

2.5 x 2 = 5

Part (a)

Divide the upper horizontal lengths of the two figures:

5/2.5 = 2

The scale factor is 2. This means figure B has side lengths twice as long compared to figure A.

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

Part (b)

The missing side length seems to be the diagonal side of figure B. I'm not sure what's going on with the vertical side 89.4 as that should be 3 instead (since 1.5*2 = 3).

The diagonal side is 5 units long since we double 2.5 to get 5.

Answers:

vertical side = 3

diagonal side = 5