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3 years ago

Suppose that the functions u and w are defined as follows.

Mathematics

1 answer:

leonid [27]3 years ago

3 0

Step-by-step explanation:

(a○b)(x) is the same as a(b(x)).

it is really that simple.

first you calculate the result of the inner function, and then that result is the input for the outer function.

that's it.

so,

(w○u)(2) = w(u(2))

u(2) = -2 -1 = -3

w(-3) = 2×(-3)² + 1 = 2×9 + 1 = 19

so, 19 is the first answer.

(u○w)(2) = u(w(2))

w(2) = 2×2² + 1 = 2×4 + 1 = 9

u(9) = -9 - 1 = -10

so, -10 is the second answer.

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Aleena expands 2xx+3-5(x-2) as 2x2+3-5x-10. Has she expanded it correctly? Please identify the mistakes and write the correct wa

Nimfa-mama [501]

The given expression is :

2xx+3-5(x-2)

We know that, $x{\cdot}x=x^2$

$=2x^2+3-5(x-2)\\\\=2x^2+3+(-5)(x)+(-5)(-2)\\\\=2x^2+3-5x+10$

Aleena expands 2xx+3-5(x-2) as 2x²+3-5x-10. She is mistaken because the sign before 10 should be +10 instead of -10. Hence, the correct expanded form is 2x²+3-5x+10. Hence, this is the required solution.

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3 years ago

In the figure, Z ABC and Z BCD are supplementary angles.

sertanlavr [38]

Answer:

x = 22

Step-by-step explanation:

line AD is 180°

so 40° + (5x + 30°) = 180°

solve for x.

5x = 180-30-40

5x= 110

x = 110/5

x= 22

4 0

3 years ago

Read 2 more answers

A 20-ft by the 40-ft rectangular swimming pool is surrounded by a walkway of uniform width. If the total area of the walkway i

Jlenok [28]

<h3>Answer: 2 feet</h3>

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

Explanation:

x = width of the walkway in feet

This is some positive real number.

The dimension of 20 feet bumps up to 20+2x when adding on x from both directions. Similarly, the 40 ft dimension becomes 40+2x

Refer to the diagram below.

The 20 ft by 40 ft pool is surrounded by a larger rectangle that is 20+2x ft by 40+2x ft

The pool itself is 20*40 = 800 sq ft. Add on the walkway area to get 800+256 = 1056 sq ft.

-----------

Area = length*width

1056 = (20+2x)*(40+2x)

1056 = 20*40 + 20*2x + 2x*40 + 2x*2x ... FOIL rule

1056 = 800 + 40x + 80x + 4x^2

0 = 4x^2 + 40x + 80x + 800 - 1056

0 = 4x^2 + 120x - 256

4x^2 + 120x - 256 = 0

4(x^2 + 30x - 64) = 0

x^2 + 30x - 64 = 0

Let's use the quadratic formula to finish solving for x.

Plug in a = 1, b = 30, c = -64

$x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-30\pm\sqrt{(30)^2-4(1)(-64)}}{2(1)}\\\\x = \frac{-30\pm\sqrt{1156}}{2}\\\\x = \frac{-30\pm34}{2}\\\\x = \frac{-30+34}{2} \ \text{ or } \ x = \frac{-30-34}{2}\\\\x = \frac{4}{2} \ \text{ or } \ x = \frac{-64}{2}\\\\x = 2 \ \text{ or } \ x = -32\\\\$

Recall we made x be positive. This is because a negative walkway width does not make sense. This means we'll ignore x = -32.

The only practical solution is x = 2

Therefore, the walkway is <u>2 feet wide</u>

4 0

2 years ago

The area of the shaded region

lbvjy [14]

Answer:

27.74cm^2

Step-by-step explanation:

area of circle: 3 times 3 times pi = 28.26cm^2

area of square: 8 times 7 = 56cm^2

subtract area of circle from square

56-28.26=27.74cm^2

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