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Luden [163]
3 years ago
6

The graph shows the functions f(x), p(x), and g(x): Graph of function g of x is y is equal to 1 plus the quantity 1.5 raised to

the power of x. The straight line f of x joins ordered pairs 4, 1 and 2, negative 3 and is extended on both sides. The straight line p of x joins the ordered pairs 0, 2 and 1, negative 5 and is extended on both sides. Courtesy of Texas Instruments Part A: What is the solution to the pair of equations represented by p(x) and f(x)? (3 points) Part B: Write any two solutions for f(x). (3 points) Part C: What is the solution to the equation p(x) = g(x)? Justify your answer. (4 points)
Mathematics
1 answer:
satela [25.4K]3 years ago
3 0
Part A:

Given that the <span>straight line p(x) joins the ordered pairs (0, 2) and (1, -5), thus the equation of the line joining ordered pairs (0, 2) and (1, -5) is given by

\frac{y-2}{x} = \frac{-5-2}{1} =-7 \\  \\ \Rightarrow y-2=-7x \\  \\ \Rightarrow y=-7x+2

Thus, p(x) = -7x + 2

</span>Given that the <span>straight line f(x) joins the ordered pairs (4, 1) and (2, -3), thus the equation of the line joining ordered pairs (4, 1) and (2, -3) is given by

\frac{y-1}{x-4} = \frac{-3-1}{2-4} =\frac{-4}{-2}=2 \\  \\ \Rightarrow y-1=2(x-4)=2x-8 \\  \\ \Rightarrow y=2x-7

Thus, f(x) = 2x - 7
</span>
The solution to the pair of equations represented by p(x) and f(x) is given by

p(x) = f(x)
⇒ -7x + 2 = 2x - 7
⇒ -7x - 2x = -7 - 2
⇒ -9x = -9
⇒ x = -9 / -9 = 1

Substituting for x into p(x), we have

p(1) = -7(1) + 2 = -7 + 2 = -5

Therefore, the solution to the pair of equations represented by p(x) and f(x) is  (1, -5)



Part B:

From part A, we have that f(x) = 2x - 7

when x = -8

f(-8) = 2(-8) - 7 = -23

Thus, (-8, -23) is a solution to f(x).

When x = -10

f(-10) = 2(-10) - 7 = -27

Thus, (-10, -27) is a solution to f(x).

Therefore, two solutions of f(x) are (-8, -23) and (-10, -27).



Part C:

From part A, we have that p(x) = -7x + 2, given that g(x) = 1 + 1.5^x

From the graphs of p(x) and g(x), we can see that the two graphs intersected at the point (0, 2).

Therefore, the solution to the equation p(x) = g(x) is (0, 2).

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4 0
3 years ago
Grace has a 15 inch diameter bicycle tire. How many revolutions will it make traveling 500 feet?
Brums [2.3K]

Answer:

Revolution = 127.24 revolutions

Step-by-step explanation:

<em><u>Circumference of the tire = πD</u></em>

Where D = 15 inch

So,

C = 15π = 47.1 inch

<u><em>In feets:</em></u>

47.1 inch = 3.93 feet.

So, <u>one revolution = 3.93 feet</u>

<u><em>Travelling 500 feet will make the following revolutions:</em></u>

Revolution = 500 feet/3.93 feet

Revolution = 127.24 revolutions

5 0
2 years ago
8(x+2)=56 HELP PLZZ ANYONE<br> Use the Distributive Property to solve the equation.
xenn [34]

Answer:

x = 5

Step-by-step explanation:

1. 8 (x + 2) = 56                 Distribute the 8

2. 8x + 16 = 56              Subtract 16 from both sides

3. 8x = 40                      Divide both sides by 8

4. x = 5

6 0
3 years ago
How many times do you multiply 5 by itself if the exponent is 56?
3241004551 [841]
56 times!!

This is because the exponent indicates how many times you multiply a number. For example:
5^2= 5x5
5 0
2 years ago
I’m a little confused
Vikki [24]
Hello lol

Answer:

(-1,-4)

Explanation:

I literally just did this lol
3 0
2 years ago
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