Find the surface area of the prism. 6 in. 3 in. 12 in.

If the function f(x) has a domain of (g,h) and a range of (j,k), then what is the domain and range of g(x) = m(f(x)] + p?

sertanlavr [38]

Answer:

$Dom\{g(x)\} = Dom\{f(x)\} = (g, h)$ .

$Ran \{g(x)\} = (m\cdot j+p,m\cdot k +p)$

Step-by-step explanation:

From Mathematics we remember that the domain of a functions corresponds to the set of values of the independent variable ( $x$ in this case) so that images exist and the range of a function is the set of images.

In this case, we know the domain and range of $f(x)$ and we must find the domain and range of $g(x)$ .

Domain

The domain of $g(x)$ is the domain of $f(x)$ . That is, $Dom\{g(x)\} = Dom\{f(x)\} = (g, h)$ .

Range

We have to define the bounds of the range of $g(x)$ , given that range $f(x)$ is modified by streching and horizontal translation operations:

Lower bound ( $f(x) = j$ )

$g(x) = m\cdot j +p$

Upper bound ( $f(x) = k$ )

$g(x) = m\cdot k +p$

In consequence, the range of $g(x)$ is $Ran \{g(x)\} = (m\cdot j+p,m\cdot k +p)$

3 0

3 years ago

Type the correct answer in each box. Use numerals instead of words.

lora16 [44]

Answer:

the answer is -4x^2-3x-5

8 0

2 years ago

5 roommates share the cost of an apartment: rent,electricity, and gas. rent costs 1800 and gas costs 150 per month. each roommat

Naddik [55]

Answer:

Electricity bill is 175

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Step-by-step explanation:

Given

$Rent = 1800$

$Gas = 150$

$Each\ Roommate = 425$ monthly

$Number\ of\ Roommate = 5$

Required

Determine the electricity bill

If each roommate pays 425, then 5 roommates pay 5 * 425

$Total = 5 * 425$

$Total = 2125$

This implies that: the monthly cost of room, gas and electricity add up to 2125.

In other words,

$Gas + Rent + Electricity = 2125$

$150 + 1800+ Electricity = 2125$

$1950+ Electricity = 2125$

$Electricity = 2125 - 1950$

$Electricity = 175$

<em>Hence, the electricity bill is 175</em>

4 0

2 years ago

2x - 5y=-15<br> can someone walk me through this?

HACTEHA [7]

The equation given in the question has two unknown variables in the form of "x" and "y". The exact value of "x" and "y" cannot be determined as two equations are needed to get to the exact values of "x" and "y". This equation can definitely be used to show the way for determining the values of "x" in terms of "y"and the value of "y" in terms of "x". Now let us check the equation given.
2x - 5y = - 15
2x = 5y - 15
2x = 5(y - 3)
x = [5(y - 3)]/2
Similarly the way the value of y can be determined in terms of "x" can also be shown.
2x - 5y = - 15
-5y = - 2x - 15
-5y = -(2x + 15)
5y = 2x + 15
y = (2x +15)/5
= (2x/5) + (15/5)
= (2x/5) + 3
So the final value of x is [5(y -3)]/2 and the value of y is (2x/5) + 3.

3 0

3 years ago

A sample of 36 observations is selected from one population with a population standard deviation of 4.2. The sample mean is 101.

Digiron [165]

Answer:

Step-by-step explanation:

Given that :

the null and the alternative hypothesis are computed as :

$H_o: \mu_1 = \mu_2$

$H_a : \mu _1 \neq \mu_2$

This is a two tailed test

This is because of the ≠ sign in the alternative hypothesis which signifies that the rejection region in the alternative hypothesis are at the both sides of the hypothesized mean difference .

Decision Rule: at the level of significance ∝ = 0 . 10

The decision rule is to reject the null hypothesis if z < - 1 . 64 and z > 1 . 64

NOTE: DURING THE MOMENT OF TYPING THIS ANSWER THERE IS A TECHNICAL ISSUE WHICH MAKES ME TO BE UNABLE TO SUBMIT THE FULL ANSWER BUT I'VE MADE SCREENSHOTS OF THEM AND THEY CAN BE FOUND IN THE ATTACHED FILE BELOW

5 0

3 years ago