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3 years ago

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Suppose a parabola has an axis of symmetry at x = -2, a minimum height at -6, and passes through the point (0, 10). Write the eq

uation of the parabola in vertex form.

1 answer:

lesantik [10]3 years ago

3 0

What answer choices that you have

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(4x + 3)(4x - 3)<br> Help pls

tekilochka [14]

Answer:

$16x^2-9$

Step-by-step explanation:

$\left(4x+3\right)\left(4x-3\right)$

We´ll <u>Apply Difference Two Squares Formula:</u>

$\left(a+b\right)\left(a-b\right)=a^2-b^2$

$\longmapsto$ $\left(4x+3\right)\left(4x-3\right)$

$\longmapsto$ $\left(4x\right)^2-3^2$

<u>Apply exponent rule</u>:

$\left(a\times \:b\right)^n=a^nb^n$

$\longmapsto$ $4^2x^2-3^2$

$\longmapsto$ $16x^2-9$

_________________________

6 0

2 years ago

Read 2 more answers

The vertex of the parabola is at the point (2,-5). which of the equations below could be the one for this parabola?

timofeeve [1]

Hello,
Answer is Dsince y=k(x-2)²-5 and if k=1 ==>D.

7 0

3 years ago

Read 2 more answers

PLEASE HELP I DON’T UNDERSTAND, WILL BE MARKED AS BRAINLIEST

andre [41]

13.) A=9cm^2
If the area is l•h, and there are 9 cubic squares, that means that the length of each side on the square is 3cm, each square on it equals 1cm.
14.) V=27cm^3
If the volume is l•w•h, then we find the third power square root of 27, so 3•3=9•3=27, the answer is 3cm for the length, width, and height.
15.) V=4,913cm^3
If volume is l•w•h, then what number when raised to the third power equals 4913? The answer is 17, since 17•17=289•17=4913. So the length is 17cm
16.)V=216cm^3
If volume is l•w•h, then what number when raised to the third power equals 216? The answer is 6, since 6•6=36•6=216.
17.)A=121
Is area is l•w, then what number raised to the second power equals 121? The answer is 11, since 11•11=121. Therefore it WILL NOT fit a car with a length of 13ft.
18.)A=141
If area is l•w, then what number raised to the second power equals 141? The answer is 12, since 11.87•11.87=141 (answer was rounded to nearest whole number) meaning that she will need 12ft of fence to enclose her garden.

3 0

3 years ago

Formulate the situation as a system of two linear equations in two variables. Be sure to state clearly the meaning of your x- an

slega [8]

Answer:

1) There were 33 $4,000 investors and 27 $8,000 investors.

2) The solution in x = 4, y = 9.

3) There were 24 nickels and 56 dimes.

Step-by-step explanation:

1) A lawyer has found 60 investors for a limited partnership to purchase an inner-city apartment building, with each contributing either $4,000 or $8,000. If the partnership raised $348,000, then how many investors contributed $4,000 and how many contributed $8,000?

I am going to say that:

x is the number of investors that contributed 4,000.

y is the number of investors that contributed 8,000.

Building the system:

There are 60 investors. So:

$x + y = 60$

In all, the partnership raised $348,000. So:

$4000x + 8000y = 348000$

I am going to simplify by 4000. So:

$x + 2y = 87$

Solving the system:

The elimination method is a method in which we can transform the system such that one variable can be canceled by addition. So:

$1)x + y = 60$

$2)x + 2y = 87$

I am going to multiply 1) by -1. So we have

$1)-x - y = -60$

$2)x + 2y = 87$

By addition, the x are going to cancel each other

$-x + x - y + 2y = -60 + 87$

$y = 27$

For x:

$x + y = 60$

$x = 60-y = 60-27 = 33$

There were 33 $4,000 investors and 27 $8,000 investors.

2) Solve the system by row-reducing the corresponding augmented matrix.

$2x + y = 17$

$x + y = 13$

This system has the following augmented matrix:

$\left[\begin{array}{ccc}2&1&17\\1&1&13\end{array}\right]$

To help the row reducing, i am going to swap the first with the second line:

$L1 L2$

So we have:

$\left[\begin{array}{ccc}1&1&13\\2&1&17\end{array}\right]$

Now, reducing the first column.

$L2 = L2 - 2L1$

So we have:

$\left[\begin{array}{ccc}1&1&13\\0&-1&-9\end{array}\right]$

Now we do:

$L2 = -L2$

And the matrix is:

$\left[\begin{array}{ccc}1&1&13\\0&1&9\end{array}\right]$

Now to reduce the second column, we do:

$L1 = L1 - L2$

$\left[\begin{array}{ccc}1&0&4\\0&1&9\end{array}\right]$ .

So the solution is:

x = 4, y = 9.

3) A jar contains 80 nickels and dimes worth $6.80. How many of each kind of coin are in the jar?

I am going to say that x is the number of nickels and y is the number of dimes.

Each nickel is worth 5 cents and each dime is worth 10 cents.

Building the system:

There are 80 coins in all:

$x + y = 80$

They are worth $6.80. So:

$0.05x + 0.10y = 6.80$

Solving the system:

$1)x + y = 80$

$2)0.05x + 0.10y = 6.80$

I am going to divide 1) by -10, so we can cancel y. So:

$1)-0.10x - 0.10y = -8$

$2)0.05x + 0.10y = 6.80$

Adding:

$-0.10x + 0.05x - 0.10y + 0.10y = -8 + 6.80$

$-0.05x = -1.2$ *(-100)

$5x = 120$

$x = \frac{120}{5}$

$x = 24$

Also

$x + y = 80$

$y = 80-x = 80-24 = 56$

There were 24 nickels and 56 dimes.

8 0

3 years ago

6) Evaluate for x = 3:<br> 3•4x/2

Nikolay [14]

Answer:

18

Step-by-step explanation:

3×4(x)/2

Plug in 3 to x

3×4(3)/2

3×12/2

36/2

18

5 0

3 years ago