I need help with this. What is the answer? (13 x 4 +5²)

Which equation is the inverse of 5 y + 4 = (x + 3) squared + one-half?

8_murik_8 [283]

The inverse of the given function is y = √5x + 7/2 - 3

<h3>Inverse of a function</h3>

Given the function expressed below;

5y + 4 = (x+3)² +1/2

5y = (x+3)² - 7/2

y = 1/5(x+3)² - 7/10

Replace y as x

x = 1/5(y+3)² - 7/10

Make y the subject of the formula

5x = (y+3)²- 7/2

(y+3)² = 5x + 7/2

y+3 = √5x + 7/2

y = √5x + 7/2 - 3

Hence the inverse of the given function is y = √5x + 7/2 - 3

learn more on inverse of a function here: brainly.com/question/3831584

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4 0

2 years ago

Mrs. Spect lost 1.25 pounds last week. She lost 2 pounds two

kenny6666 [7]

Answer:

On average she looses 1.33 pounds per week

Step-by-step explanation:

3/4=0.75

1.25+2+0.75=4 -> total weight loss

There are 3 weeks in total.

4/3=1.33

5 0

2 years ago

Suppose cos(x)= -1/3, where π/2 ≤ x ≤ π. What is the value of tan(2x). EDGE

AVprozaik [17]

Answer:

D

Step-by-step explanation:

We are given that:

$\displaystyle \cos x = -\frac{1}{3}\text{ where } \pi /2 \leq x \leq \pi$

And we want to find the value of tan(2<em>x</em>).

Note that since <em>x</em> is between π/2 and π, it is in QII.

In QII, cosine and tangent are negative and only sine is positive.

We can rewrite our expression as:

$\displaystyle \tan(2x)=\frac{\sin(2x)}{\cos(2x)}$

Using double angle identities:

$\displaystyle \tan(2x)=\frac{2\sin x\cos x}{\cos^2 x-\sin^2 x}$

Since cosine relates the ratio of the adjacent side to the hypotenuse and we are given that cos(<em>x</em>) = -1/3, this means that our adjacent side is one and our hypotenuse is three (we can ignore the negative). Using this information, find the opposite side:

$\displaystyle o=\sqrt{3^2-1^2}=\sqrt{8}=2\sqrt{2}$

So, our adjacent side is 1, our opposite side is 2√2, and our hypotenuse is 3.

From the above information, substitute in appropriate values. And since <em>x</em> is in QII, cosine and tangent will be negative while sine will be positive. Hence:

<h2> $\displaystyle \tan(2x)=\frac{2(2\sqrt{2}/3)(-1/3)}{(-1/3)^2-(2\sqrt{2}/3)^2}$ </h2>

Simplify:

$\displaystyle \tan(2x)=\frac{-4\sqrt{2}/9}{(1/9)-(8/9)}$

Evaluate:

$\displaystyle \tan(2x)=\frac{-4\sqrt{2}/9}{-7/9} = \frac{4\sqrt{2}}{7}$

The final answer is positive, so we can eliminate A and B.

We can simplify D to:

$\displaystyle \frac{2\sqrt{8}}{7}=\frac{2(2\sqrt{2}}{7}=\frac{4\sqrt{2}}{7}$

So, our answer is D.

7 0

3 years ago

Determine the GCF of<br>the following:<br>60 and 144

Alla [95]

12, Find the prime factorization of 60

60 = 2 × 2 × 3 × 5

Find the prime factorization of 144

144 = 2 × 2 × 2 × 2 × 3 × 3

To find the gcf, multiply all the prime factors common to both numbers:

Therefore, GCF = 2 × 2 × 3

8 0

3 years ago

Place the quadratic y=2x^2+24x+79 into vertex form by using the method of completing the square and then state the coordinates o

katrin2010 [14]

Answer:

$y=2(x+6)^2+7$

$(-6,7)$

Step-by-step explanation:

$y=2x^2+24x+79$

Completing the square is a process of converting a quadratic equation in standard form into vertex form.

The first step in completing the square is grouping the quadratic and linear terms of the quadratic equation.

$y=(2x^2+24x)+79$

Factor out the coefficient of the quadratic term,

$y=2(x^2+12x)+79$

Now complete the square, add a term to make the grouped part of the equation a complete square, then balance the equation.

$y=2(x^2+12x+36-36)+79$

Simplify,

$y=2(x^2+12x+36)+79+(2)(-36)$

$y=2(x+6)^2+79-72$

$y=2(x+6)^2+7$

The x-coordinate of the vertex of the equation is equal to (-1) times the numerical part of the quadratic term, and the y-coordinate is equal to the constant.

$(-6,7)$

7 0

3 years ago

I need help with this. What is the answer? (13 x 4 +5²) - 2