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miskamm [114]
3 years ago
15

Here’s a clearer picture

Mathematics
1 answer:
yaroslaw [1]3 years ago
5 0

Answer:

6/12

Step-by-step explanation:

Note the shaded amount of "parts". You are supposed to put the shaded amount of parts over the <em>total</em> amount of parts.

In the first rectangle, it shows 2 of 3 parts as shaded, and so the fraction is: 2/3

In the second rectangle, it shows 3 of 4 parts shaded, and so the fraction is: 3/4

Finally, the 3rd rectangle shows 6 of 12 parts shaded, and so the fraction is:

6/12

Check by multiplying the fractions across:

(2/3) x (3/4) = (2 x 3)/(3 x 4) = 6/12

6/12 is your answer.

If you need to simplify, divide common factors from both the numerator and denominator, in this case being 6.

(6/12)/(6/6) = 1/2

1/2 is your reduced answer.

~

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6 0
3 years ago
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
satela [25.4K]
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).

3 0
3 years ago
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