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Fudgin [204]
2 years ago
14

type the correct answer in the Box. Use Roman numerals instead of words. The graphs of functions f and g are shown. Function g i

s defined as g(x) = k f(x). what is the the value of k? NO LINKS! ​

Mathematics
1 answer:
marysya [2.9K]2 years ago
4 0

Answer:

  • k = 2

Step-by-step explanation:

<u>Take some reference points on the graph of f and g:</u>

  • f(2) = 1, g(2) = 2
  • f(4) = 2, g(4) = 4
  • f(8) = 4, g(8) = 8

<u>According to the numbers above we can state:</u>

  • g(x) = 2f(x)

So the value of k is 2

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FASTTTTTTTTT PPPPPPPPPPPPPPLLLLLLLLLLLLLLLLZZZZZZZZZZZZZZZ
Deffense [45]

Answer:

(a) B

(b) $2

Step-by-step explanation:

(a) Let's say the cost of a ticket is t and the cost of popcorn is p. Then we can write the two equations from the table:

12t + 8p = 184

9t + 6p = 138

We need to solve this, so let's use elimination. Multiply the first equation by 3 and the second equation by 4:

3 * (12t + 8p = 184)

4 * (9t + 6p = 138)

We get:

36t + 24p = 552

36t + 24p = 552

Subtract the second from the first:

    36t + 24p = 552

-    36t + 24p = 552

________________

       0 = 0

Since we get down to 0 = 0, which is always true, we know that we cannot determine the cost of each ticket because there is more than one solution (infinitely many, actually). The answer is B.

(b) Our equation from this, if we still use t and p, is:

5t + 4p = 82

Now, just choose any of the two equations from above. Let's just pick 9t + 6p = 138. Now, we have the system:

5t + 4p = 82

9t + 6p = 138

To solve, let's use elimination again. Multiply the first equation by 6 and the second one by 4:

6 * (5t + 4p = 82)

4 * (9t + 6p = 138)

We get:

30t + 24p = 492

36t + 24p = 552

Subtract the second from the first:

    36t + 24p = 552

-    30t + 24p = 492

________________

      6t + 0p = 60

So, t = 60/6 = $10. Plug this back into any of the equations to solve for p:

5t + 4p = 82

5 * 10 + 4p = 82

50 + 4p = 82

4p = 32

p = 32/4 = $8

So the ticket costs 10 - 8 = $2 more dollars than the popcorn.

5 0
2 years ago
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harina [27]

Answer:

14 more flower would bloom if 21 more tulip bulb is planted.

Step-by-step explanation:

Given ratio for tulip bulbs and flowers is 15:10.

Now, finding number of flower to bloom if 21 tulip bulb are planted.

Assume if 21 tulip bulbs are planted then number of flower would bloom be"x"

ratio given: \frac{Tulip\ bulbs}{ Flower} = \frac{15}{10} = \frac{21}{x}

Cross multiplying the ratio to get:

⇒x= \frac{21\times 10}{15} = \frac{210}{15}

∴x= 14\ flowers

Hence, 14 flowers would bloom if 21 tulip bulb are planted.

If total tulip bulb is 15+21= 36, then 10+14= 24\ flowers would bloom.

5 0
3 years ago
Roll a die. Spin a spinner. How many outcomes are there?
natali 33 [55]
I got 10! [_-_]-{-_-}-(_-_)
7 0
2 years ago
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Rus_ich [418]

Answer:

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Step-by-step explanation:

3 0
2 years ago
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The ratio of the dimensions of a rectangular patio are 4:7. if the shorter
Cerrena [4.2K]

If the ratio of the dimensions is 4:7 and the shorter dimension is 10ft, we know that the 10ft corresponds to the 4 in this scenario. We can set up the equation as follows:

\frac{4}{7} =\frac{10}{x}

You have to multiply by 2.5 to get from 4 to 10. And since we want to make sure we are maintaining the ratio, we have to multiply the denominator, 7, by 2.5 as well.

\frac{4}{7}*\frac{2.5}{2.5}=\frac{10}{17.5}

This means your shorter side has a length of 10ft and your longer side has a length of 17.5ft.

AREA

The formula for the area of a rectangle is: w*l

So we can plug our dimensions into the formula: 10*17.5=175

So 175 is our area. But we can't forget about units! Since this is area and we multiplied our units together, our units would be squared. That means our answer is <u>175 square feet</u>.

PERIMETER

The formula for the perimeter of a rectangle is: 2(w+l)

We can plug our dimensions into the formula: 2(10+17.5)=55

So 55 is our perimeter. Of course, we can't forget about our units. Because this is perimeter, we only added our units together, so they don't change. That means our answer is <u>55 feet</u>.

4 0
2 years ago
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