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1 year ago

Find the equation of the quadratic function with vertex (– 2, – 6) that goes through the point (-4, -18)

Mathematics

1 answer:

torisob [31]1 year ago

3 0

Answer:

y = -3(x+2)^2 - 6

Step-by-step explanation:

y = a(x+2)^2 -6

-18 = a(-2)^2 - 6

-12 = 4a

a = -3

y = -3(x+2)^2 - 6

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A group of hikers buys 8 bags of mixed nuts. Each bag contains 3 and 1/2 cups of mixed nuts. the mixed nuts are shared evenly am

nika2105 [10]

Answer:

2 1/3 cups for each hiker

Step-by-step explanation:

8bags x 3.5 cups in each bag =28 cups in total
28 cups shared among 12 hikers = 28/12 = 2 1/3 cups for each hiker

4 0

2 years ago

What is the answer a, b, c, or d

podryga [215]

Answer: Choice B

(-2, 5)

==================================================

Explanation:

The original system is

$\begin{cases}-4x+3y = 23\\ x-y = -7\end{cases}$

Multiply both sides of the second equation by 3. Doing so leads to this updated system of equations

$\begin{cases}-4x+3y = 23\\ 3x-3y = -21\end{cases}$

Now add straight down

The x terms add to -4x+3x = -1x = -x

The y terms add to 3y+(-3y) = 0y = 0

The terms on the right hand sides add to 23+(-21) = 2

We end up with the equation -x = 2 which solves to x = -2

Now use this to find y. You can pick any equation with x,y in it

----------------

-4x+3y = 23

-4(-2)+3y = 23

8+3y = 23

3y = 23-8

3y = 15

y = 15/3

y = 5

x-y = -7

-2-y = -7

-y = -7+2

y = -5

y = 5

Either way, we get the same y value.

So that's why the solution is (x,y) = (-2, 5)

6 0

2 years ago

How many yards<br> carpeting is needed to cover a 60 feet length room and 40 feet width

Bad White [126]

Answer:

$266$ $\frac{2}{3}$ $yards$

Step-by-step explanation:

1. Approach

First, convert the dimensions of the room from feet to yards. Remember, the conversion rate between feet and yards is, $3feet=1yard$ . Next, find the area of the room by multiplying the length by the width.

2. Convert the unit of measurement

The measurement unit is given in feet, one must convert it into yards. The conversion rate between yards and feet is, $3feet=1yard$ .

$60feet=20yards\\\\40feet=13\frac{1}{3}yards$

3. Find the area of the room

Now multiply the length by the width to find the area of the room.

$20yards*13\frac{1}{3}yrads\\\\= 20 * \frac{40}{3}\\\\=\frac{800}{3}\\\\= 266\frac{2}{3}_{.}yards^{2}$

5 0

2 years ago

A researcher wants to investigate whether there is a relationship between annual company profit ($) and median annual salary pai

ahrayia [7]

Answer:

D. There is not convincing evidence of a relationship between annual company profit and median annual salary paid by the company.

Step-by-step explanation:

In this hypothesis test, the null hypothesis usually states that there is no relationship between the two variables in study.

In opposite, the claim that is being tested is the speculative hypothesis: that there is a significant relationship between both variables.

The researcher takes a sample and the P-value indicates the probability of getting that sample by pure chance <em>if the null hypothesis is true</em>.

Then, a very small P-value, below the significance level, indicates that the sample is very unusual if the null hypothesis is true, what gives evidence to reject the null hypothesis.

In this case, a P-value of 0.56 indicates that the sample is not unusual if the null hypothesis is true, so it gives no support to the claim that the null hypothesis is false and that there exists a relationship between the two variables in study.

6 0

3 years ago

Find all solutions to the equation:

crimeas [40]

Let z = sin(x). This means z^2 = (sin(x))^2 = sin^2(x). This allows us to go from the equation you're given to this equation: 7z^2 - 14z + 2 = -5

That turns into 7z^2 - 14z + 7 = 0 after adding 5 to both sides. Use the quadratic formula to solve for z. The only solution is z = 1 (see attached image). Since we made z = sin(x), this means sin(x) = 1. All solutions to this equation will be in the form x = (pi/2) + 2pi*n, which is the radian form of the solution set. If you need the degree form, then it would be x = 90 + 360*n

The 2pi*n (or 360*n) part ensures we get every angle coterminal to pi/2 radians (90 degrees), which captures the entire solution set.

Note: The variable n can be any integer.

7 0

2 years ago