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anzhelika [568]

3 years ago

15

If the function h is defined by h(x)=

lign="absmiddle" class="latex-formula">-3x+5,then h(2x+1)=

1 answer:

harkovskaia [24]3 years ago

3 0

Given:

The function is:

$h(x)=x^2-3x+5$

To find:

The value of $h(2x+1)$ .

Solution:

We have,

$h(x)=x^2-3x+5$

Putting $x=2x+1$ , we get

$h(2x+1)=(2x+1)^2-3(2x+1)+5$

$h(2x+1)=(2x)^2+2(2x)(1)+(1)^2-3(2x)-3(1)+5$

$h(2x+1)=4x^2+4x+1-6x-3+5$

On combining like terms, we get

$h(2x+1)=4x^2+(4x-6x)+(1-3+5)$

$h(2x+1)=4x^2-2x+3$

Therefore, the required function is $h(2x+1)=4x^2-2x+3$ .

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To make lemonade, Kate uses 1 cup of lemon juice and 2 cups sugar. If she makes a larger amount of lemonade with 10 cups of suga

juin [17]

For this problem, I will use diagram.
First if all, we know that Kate used 1 cup of lemon juice and 2 cups sugar, so we have this:
1 cup of lemon juice=2 cups sugar
Then, the problem asked to find how many cups of lemon juice does Kate needs with 10 cups of sugar, and now we have have the complete tree diagram

1 cup of lemon juice= 2 cups of sugar
?cups of lemon juice=10 cups of sugar
Step 1:
Use cross multiply
10×1=10
Step 2:
Use division
10÷2=5
As a result, Kate will need 5 cups of lemon juice with 10 cups sugar
But there is another way to find the answer, too. If you curious, here is the second way:
The ratio between cup of sugar/cup of lemon juice, so
2 cups of sugar/1 cup of lemon juice. In conclusion, Kate use double amount of sugar than lemon juice, so the question asked us to find how many cups of lemon juice does Kate needs with 10 cups sugar. To find the answer, take 10÷2=5 cups of lemon of juice is your final answer. Hope it help!

5 0

3 years ago

Read 2 more answers

A rectangle has a total area of 1116 square feet. If the length of the rectangle is 12 ft, what is the width of the rectangle?

Pani-rosa [81]

the width of the rectangle is 93

5 0

3 years ago

Read 2 more answers

Suppose you carry out a significance test of h0: μ = 8 versus ha: μ > 8 based on sample size n = 25 and obtain t = 2. 15. Fin

OLEGan [10]

Using a t-distribution calculator and finding the p-value, the correct option regarding the conclusion is given by:

a) the p-value is 0.02. We reject h0 at the 5% significance level because the p-value 0.02 is less than 0.05.

<h3>What is the relation between the p-value and the conclusion?</h3>

It also involves the significance level, as follows.

If the p-value is less than the significance level, we reject the null hypothesis $h_0$ .

If it is more, we do not reject.

In this problem, a t-distribution calculator for a right-tailed with <em>t = 2.15 and 25 - 1 = 24 df</em> is used to find a p-value of 0.02.

It is less than 0.05, hence option a is correct.

More can be learned about p-values at brainly.com/question/26454209

5 0

2 years ago

How ti find absolute value

andreyandreev [35.5K]

Absolute value describes how far away a number is from 0

The absolute value of a number is always positive even if you are looking at the absolute value of a negative number.

Examples
The absolute value of 6 = 6
The absolute value of -6 = 6

4 0

3 years ago

PLEASE HELP ME I HAVING TROUBLE

viktelen [127]

Answer: f(-6) = $-\frac{12}{11}$ , f(-4) = $\frac{8}{9}$ , f(4) = $-\frac{8}{9}$ , f(6) = $\frac{12}{11}$

<u>Step-by-step explanation:</u>

(-6, f(-6)) is an x,y coordinate. They are asking what the y-value is when you plug in -6 for x.

f(x) = $\frac{2x}{x^{2}-25}$

f(-6) = $\frac{2(-6)}{(-6)^{2}-25}$

= $\frac{-12}{36-25}$

= $-\frac{12}{11}$

f(-4) = $\frac{2(-4)}{(-4)^{2}-25}$

= $\frac{-8}{16-25}$

= $\frac{-8}{-9}$

= $\frac{8}{9}$

f(4) = $\frac{2(4)}{(4)^{2}-25}$

= $\frac{8}{16-25}$

= $\frac{8}{-9}$

= $-\frac{8}{9}$

f(6) = $\frac{2(6)}{(6)^{2}-25}$

= $\frac{12}{36-25}$

= $\frac{12}{11}$

5 0

3 years ago