5 to the 2nd power

A chocolate chip cookie recipe requires one and three quarters cups of flour to one cup of chocolate chips. If four and two thir

nikitadnepr [17]

1 cup of chocolate chips for every 1and 3/4 cup of flour

so divide 4 and 2/3 x 1 and 3/4

turn them both into fractions

4 2/3 = 14/3

1 3/4 = 7/4

14/3 / 7/4 = 14/3 x 4/7 = 56/21 = 2 and 2/3 cups of chocolate chips are needed

8 0

3 years ago

The function h(x) = 12x8 + 49 is an even function. Which transformation of h(x) would result in a function that is neither even

Irina-Kira [14]

Answer: translation 8 units to the right

Step-by-step explanation:

An even function is a function such that:

h(x) = h(-x)

and the function is odd if:

h(-x) = -h(x)

Now, let's talk about transformations:

A) Reflection over the x-axis:

When we have a point (x,y) and we do a reflection over the x-axis, the reflected point will be:

(x, -y).

Then for the case of a function:

y = h(x).

then the reflection will be:

g(x) = - y = -h(x).

And if h(x) is even, -h(x) is also even, so this is not the correct option.

B) Vertical stretch by a factor of 7.

This is written as:

g(x) = 7*h(x).

then:

g(x) = 7*h(x)

g(-x) = 7*h(-x) = 7*h(x) = g(x)

the transformation is even.

C) Translation of 8 units to the right.

We can write this as:

g(x) = h(x - 8).

Then:

g(-x) = h(-x -8) = h(x + 8)

Then g(-x) is not equal to g(x)

and also g(-x) ≠ -g(x)

So in this case the transformation is neither odd or even.

C) horizontal compression by a factor of One-half.

This transformation is written as:

g(x) = h( (1/2)*x)

And, similar as the case of the vertical compression, in this case the transformation is also even.

3 0

3 years ago

4TH TIME ASKING THIS!!! Please help me! Someone pleaseeee. I need the correct answers. I don’t want to fail

Alexeev081 [22]

Answer:

The functions are inverses; f(g(x)) = x ⇒ answer D

$h^{-1}(x)=\sqrt{\frac{x+1}{3}}$ ⇒ answer D

Step-by-step explanation:

* <em>Lets explain how to find the inverse of a function</em>

- Let f(x) = y

- Exchange x and y

- Solve to find the new y

- The new y = $f^{-1}(x)$

* <em>Lets use these steps to solve the problems</em>

∵ $f(x)=\sqrt{x-3}$

∵ f(x) = y

∴ $y=\sqrt{x-3}$

- Exchange x and y

∴ $x=\sqrt{y-3}$

- Square the two sides

∴ x² = y - 3

- Add 3 to both sides

∴ x² + 3 = y

- Change y by $f^{-1}(x)$

∴ $f^{-1}(x)=x^{2}+3$

∵ g(x) = x² + 3

∴ $f^{-1}(x)=g(x)$

∴ <u><em>The functions are inverses to each other</em></u>

* <em>Now lets find f(g(x))</em>

- To find f(g(x)) substitute x in f(x) by g(x)

∵ $f(x)=\sqrt{x-3}$

∵ g(x) = x² + 3

∴ $f(g(x))=\sqrt{(x^{2}+3)-3}=\sqrt{x^{2}+3-3}=\sqrt{x^{2}}=x$

∴ <u><em>f(g(x)) = x</em></u>

∴ The functions are inverses; f(g(x)) = x

* <em>Lets find the inverse of h(x)</em>

∵ h(x) = 3x² - 1 where x ≥ 0

- Let h(x) = y

∴ y = 3x² - 1

- Exchange x and y

∴ x = 3y² - 1

- Add 1 to both sides

∴ x + 1 = 3y²

- Divide both sides by 3

∴ $\frac{x + 1}{3}=y^{2}$

- Take √ for both sides

∴ ± $\sqrt{\frac{x+1}{3}}=y$

∵ x ≥ 0

∴ We will chose the positive value of the square root

∴ $\sqrt{\frac{x+1}{3}}=y$

- replace y by $h^{-1}(x)$

∴ $h^{-1}(x)=\sqrt{\frac{x+1}{3}}$

4 0

3 years ago

Divide the polynomials:<br> x^2-3x+9/x-2

Kruka [31]

The value of dividing x^2-3x+9 by x-2 is x + 3

<h3>Ways of dividing polynomials</h3>

There are several ways to divide polynomial functions; some of these ways include

By factorization
By long division
By synthetic division
By using technology such as graph

<h3>How to divide the polynomials?</h3>

The expression for the polynomial division is given as:

x^2-3x+9/x-2

To divide polynomial functions, we make use of the division by factorization method

Start by expanding the numerator of the polynomial division

x^2-3x+9/x-2 = x^2 + 3x - 6x + 9/x-2

Factorize the equation

x^2-3x+9/x-2 = x(x + 3) - 2(x + 3)/x - 2

Factor out x + 3 from the numerator

x^2-3x+9/x-2 = (x- 2)(x + 3)/x - 2

Cancel out the common factors

x^2-3x+9/x-2 = x + 3

Hence, the value of dividing x^2-3x+9 by x-2 is x + 3

Read more about polynomial division at:

brainly.com/question/25289437

#SPJ1

5 0

2 years ago

The board of examiners that administers the real estate broker's examination in a certain state found that the mean score on the

Goshia [24]

Answer:

The passing score is 645.2

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 553, \sigma = 72$