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1 year ago

If f(x)=8-10x and g(x) =5x +4, what is the value of (fog)(-2)?

Mathematics

1 answer:

swat321 year ago

8 0

Answer:

Step-by-step explanation:

Any function is evaluated by putting the argument value where the variable is, then doing the arithmetic. When the argument is another function value, that function value is evaluated first.

The "o" in (fog) is a stand-in for the "ring operator" (∘) which is the operator used to signify a composition. A composition is evaluated right-to-left. That means (f∘g)(x) ≡ f(g(x)). The value of g(x) is found first, and is operated on by the function f.

Writing the composition in the form f(g(x)) lets you identify the layers of parentheses. As with any expression evaluation, the Order of Operations applies. It tells you to evaluate the expression in the innermost parentheses and work your way out.

To evaluate (f∘g)(-2) = f(g(-2)), we must first evaluate g(-2). That is ...

g(x) = 5x +4

g(-2) = 5(-2) +4 = -10 +4 = -6 . . . . . put -2 where x is, do the math

Now that we know g(-2) = -6, we know this expression is ...

f(-6) = 8 -10(-6) = 8 +60 = 68 . . . . . substitute for x in 8-10x

Then the value we're looking for is ...

(f∘g)(-2) = 68

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the function p(t)=3(e^0.0866t describes how to find the pollution level p(t) in relation to any time t, where t is the number of

ddd [48]

The pollution level in 1980 was 7.13 to the nearest hundredth ⇒ answer c

Step-by-step explanation:

The function $p(t)=3(e^{0.0866t})$ , where

p(t) is the population level at any time t
t is the number of years after 1970

We need to find the pollution level in 1980

∵ $p(t)=3(e^{0.0866t})$

∵ t is the number of years after 1970

∴ t = 1980 - 1970 = 10 years

- Substitute the value of t in the equation above

∴ $p(t)=3(e^{0.0866*10})$

∴ $p(t)=3(e^{0.866})$

∴ p(t) = 7.13214 ≅ 7.13 to the nearest hundredth

The pollution level in 1980 was 7.13 to the nearest hundredth

Learn more:

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6 0

2 years ago

TotCo is developing a new deluxe baby bassinet. If the length of a newborn baby is normally distributed with a mean of 50 cm and

Delicious77 [7]

Answer:

The interior length of the bassinet to ensure that 99 percent of newborn babies will fit = 1.7 cm

Step-by-step explanation:

Explanation:-

step(i):-

Given mean of population = 50 cm

standard deviation of Population = 5 cm

Given Margin of error = 10 cm

The Margin of error is determined by

$M.E = \frac{Z_{\alpha } S.D}{\sqrt{n} }$

Step(ii):-

Given level of significance ∝ = 99 % or 1 %

Z₀.₀₁ = 2.576

$10 = \frac{2.576 X 5}{\sqrt{n} }$

$\sqrt{n} = \frac{2.576 X 5}{10}$

√n = 1.3

squaring on both sides , we get

n = 1.69≅ 1.7 cm

Final answer:-

The interior length of the bassinet to ensure that 99 percent of newborn babies will fit = 1.7 cm

4 0

3 years ago

Which choices are equivalent to the expression below? Check all that apply

ipn [44]

The expression which is equivalent to √(-9) is 3i.

<h3>What is Complex number?</h3>

A complex number is the sum of a real number and an imaginary number. A complex number is of the form a + ib and is usually represented by z.

Here, given expression;

y = √(-9)

y = √9 X √(-1)

y = 3√(-1)

y = 3i

Thus, the expression which is equivalent to √(-9) is 3i.

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5 0

2 years ago

The greater of two numbers is 5 more than the smaller. If the

xenn [34]

Answer:

First number = 4

Second number = 9

Step-by-step explanation:

If the first number = x, the second number = x + 5.

The calculation can be expressed as follows:

x + 2(x + 5) = 22

First, expand the bracket 2(x + 5):

x + 2x + 10 = 22

Combine like terms:

3x + 10 = 22

Subtract 10 from both sides:

3x = 12

Divide both sides by 3:

x = 4

First number = 4

Second number = 4 + 5 = 9

5 0

1 year ago

What is not a description of slope?

Gelneren [198K]

Answer:

Option (d) is wrong.

Step-by-step explanation:

Slope is:

rise over run
The rate of change of a line
Change in y over the change in x
The ratio of vertical change to the horizontal change.

It can be given by mathematically as follows :

$m=\dfrac{y_2-y_1}{x_2-x_1}\\\\\text{and}\\\\m=\dfrac{dy}{dx}$

Hence, the option which is not a description of slope is (d) "the ratio of horizontal change compared to vertical change"

7 0

3 years ago