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3 years ago

If f (x) = -3x +4 and g (x)= x squared, find (g*f) (-2)

1 answer:

6 0

The easiest way to do this is to work out f(-2) first, =-3(-2)+4=10, then find g(-2)=(-2)²=4.
(g*f)(-2)=4×10=40.
However, if g*f means g of f the answer is different, because having worked out that f(-2)=10 we put this result into g, so we find g(10)=10²=100.
So you need to determine whether g*f means g(x)×f(x) [answer 40] or g(f(x)) [answer 100] when x=-2.

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The volume of a CONE-shaped hole is 75pi ft cubed. If the hole is 9 feet deep, what is the radius of the hole?

Arturiano [62]

Answer:

The radius of hole is 5 feet

Step-by-step explanation:

Depth of conical hole = 9 feet

Let the radius of hole be r

Volume of conical hole = $\frac{1}{3} \pi r^2 h$

So, Volume of conical hole = $\frac{1}{3} \pi \times r^2 \times 9$

We are given that volume of a CONE-shaped hole is 75pi ft cubed.

So, $\frac{1}{3} \pi \times r^2 \times 9=75 \pi$

$\frac{1}{3} \times r^2 \times 9=75$

$r^2=\frac{75 \times 3}{9}$

$r=\sqrt{\frac{75 \times 3}{9}}$

r=5

Hence The radius of hole is 5 feet

6 0

3 years ago

Which set of side lengths can form a triangle?

emmainna [20.7K]

Answer:

C:4 cm, 8 cm, 5 cm

Step-by-step explanation:

sum of length of any two sides of a triangle will be larger than the third side.

4 0

2 years ago

The number pi goes on forever with no repeating pattern; therefore, it is rationa

cricket20 [7]

No
it is irrational for that reason - it goes on without bound

3 0

3 years ago

Ella Buys a book and a pen for $14. The cost of the book is two dollars more than twice the cost of the pen. Write a system of l

Vilka [71]

Answer: The book costs $10 and the pen costs $4✔️

Step-by-step explanation:

Let B the cost of the book and let P the cost of the pen.

Then we know:

The book and the pen cost $14:

B + P = $14 } Equation 1

We also know:

The cost of the book is two dollars more than twice the cost of the pen.

B = 2P + $2 } Equation 2

Now we can substitute the value of B from the equation 2 in the equation 1:

2P + $2 + P = $14

3P = $14 - $2 = $12

P = $12/3 = $4 , cost of the pen

Since we know the value of B from the equation 2, we can calculate B:

B = 2P + $2 = 2x$4 + $2 = $8 + $2 = $10 , cost of the book

Answer: The book costs $10 and the pen costs $4✔️

<h3>Verify </h3>

We can substitute these values in equations 1 and 2 and check the results:

B + P = $14 } Equation 1

$10 + $4 = $14 ✔️check!

B = 2P + $2 } Equation 2

$10 = 2x$4 + $2 = $8 + $2 = $10 ✔️check!

<h2><em>Spymore</em></h2>

5 0

3 years ago

Complete the square x^2-10=16<br><br>

Hatshy [7]

Answer:

(x - 5)² = 41

Step-by-step explanation:

* Lets revise the completing square form

- the form x² ± bx + c is a completing square if it can be put in the form

(x ± h)² , where b = 2h and c = h²

# The completing square is x² ± bx + c = (x ± h)²

# Remember c must be positive because it is = h²

* Lets use this form to solve the problem

∵ x² - 10x = 16

- Lets equate 2h by -10

∵ 2h = -10 ⇒ divide both sides by 2

∴ h = -5

∴ h² = (-5)² = 25

∵ c = h²

∴ c = 25

- The completing square is x² - 10x + 25

∵ The equation is x² - 10x = 16

- We will add 25 and subtract 25 to the equation to make the

completing square without change the terms of the equation

∴ x² - 10x + 25 - 25 = 16

∴ (x² - 10x + 25) - 25 = 16 ⇒ add 25 to both sides

∴ (x² - 10x + 25) = 41

* Use the rule of the completing square above

- Let (x² - 10x + 25) = (x - 5)²

∴ (x - 5)² = 41

3 0

3 years ago