what is the equation of the parabola in vertex form with vertex (2,-4) and directrix y=-6​

Answer:

343 in^3

Step-by-step explanation:

The volume of a cube is found by V = s^3. Here s = 7. So the volume is 7*7*7 = 343 in^3.

Final answer:

The volume of a cube with an edge length of 7 inches is 343 cubic inches.

Explanation:

The volume of a cube is calculated by multiplying the length, width, and height of the cube. Since all sides of a cube are equal, we simply need to cube the length of one side.

In this case, the edge (length, width, and height) of the cube is 7 inches.

The volume of a cube with an edge length of 7 inches can be calculated as follows:

Therefore, the volume of the cube is 343 cubic inches.

1. The variables are “money sold total ($10)” and “money kept by student council($5)”

2. The “money sold total ($10)” can be represented by T. (For Total)

The “money kept by student council($5)” can be represented by K. (for kept)

3. As T increases, K increases.

4. K= t/2

Good luck!

The variables in this problem are the amount of candy sold and the amount of money student council keeps. They are related by the equation m = 0.5c. This equation allows us to find out the amount of money student council will make for any amount of candy they sell.

The variables in this problem are the amount of candy sold and the amount of money student council keeps.

We can represent these variables with the letters 'c' for candy sold and 'm' for money kept by student council.

The relationship between the variables is that for every $10 worth of candy sold, student council keeps $5. So, the amount of money student council keeps is half of the amount of candy sold.

We can express this relationship with the equation m = 0.5c.

This equation allows us to find out the amount of money student council will make for any amount of candy they sell.

For example, if they sell 20 worth of candy, we can substitute c = 20 into the equation and solve for m: m = 0.5(20) = 10.

Therefore, student council will make $10 for selling $20 worth of candy.

Answer: The slope is -1

Step-by-step explanation:

The slope of the line in Slope-intercept form is:

[tex]y=mx+b[/tex]

Where "m" is the slope of the line and "b" is the y-intercept.

You can observe that the equation of the line [tex]y= -x + 8[/tex] is written in Slope-intercept form. Therefore, you can identify that the slope of the line described by this equation is:

[tex]m=-1[/tex]

And the y-intercept is:

[tex]b=8[/tex]

For this case we have that by definition, the volume of a cube is given by:

[tex]V = l ^ 3[/tex]

Where "l" is the length of the side.

We have to:

[tex]l ^ 3 = 300\\l = \sqrt [3] {300}\\l = 6,69432950[/tex]

If we multiply the sides by 7, we will have:

[tex]l '= 6,69432950 * 7\\l '= 46.86030650[/tex]

Then, the new volume will be:

[tex]V '= l' ^ 3\\V '= 102900 \ cm ^ 3[/tex]

Answer:

[tex]102900 \ cm ^ 3[/tex]

ANSWER

{1, 4, 9, 16, 25, 36, 49, 64}

EXPLANATION

The perfect square integers between 1 and 80 inclusive are obtained by squaring the natural numbers from 1 to 8

[tex] {1}^{2} = 1[/tex]

[tex] {2}^{2} = 4[/tex]

[tex] {3}^{2} = 9[/tex]

[tex] {4}^{2} = 16[/tex]

[tex] {5}^{2} = 25[/tex]

[tex] {6}^{2} = 36[/tex]

[tex] {7}^{2} = 49[/tex]

[tex] {8}^{2} = 64[/tex]

The square of the next number does not fall within the given range.

Therefore "The perfect square integers between 1 and 80 inclusive" are

{1, 4, 9, 16, 25, 36, 49, 64}

(1,9,16,25,36,49,64)Answer:

Step-by-step explanation:

Answer:

x=-3 10/16

Step-by-step explanation:

5x-9-21x-42=25 (opening parenthesis)

-16x-33=25

16x+58=0

x=-58/16=-3 10/16

Answer:

$1441.90

Step-by-step explanation:

Formula-

A = P (1 + r/n)^(nt)

A= 1250(1 + 8/1)^(1*.065)

Answer:

2102.53

Step-by-step explanation:

1250e (0.065)8

Answer:

The numbers are 44 and 46

Step-by-step explanation:

Let

x, x+2 ----> the two consecutive positive even integers

we know that

[tex](x+x+2)^{2} =4,048+x^{2} +(x+2)^{2} \\ \\(2x+2)^{2} =4,048+x^{2} +x^{2}+4x+4\\ \\4x^{2}+8x+4=2x^{2}+4x+4,052\\ \\2x^{2} +4x-4,048=0[/tex]

Solve the quadratic equation using a graphing calculator

The solution is x=44

see the attached figure

[tex]x+2=44+2=46[/tex]

therefore

The numbers are 44 and 46

Answer:

Length of arc AB is 14. So, option E is correct

Step-by-step explanation:

Circumference of circle == 56 cm

We need to find length of arc AB?

Formula used will be l = rФ

We know, C = 2πr

56 = 2πr

56/2π = r

=> r = 8.91

Ф = 90° = 1.57 radians

So, l= rФ

l = 8.91 * 1.57

l = 13.98 = 14

So, Option E is correct

Answer:

Length of arc AB is 14. So, option E is correct

Step-by-step explanation:

[tex]\bf (\stackrel{x_1}{-14}~,~\stackrel{y_1}{-10})\qquad (\stackrel{x_2}{12}~,~\stackrel{y_2}{18}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{18-(-10)}{12-(-14)}\implies \cfrac{18+10}{12+14}\implies \cfrac{28}{26}\implies \cfrac{14}{13}[/tex]

Answer:

28/26

Step-by-step explanation:

We can find the slope using the equation

y2-y1/x2-x1

We are give two points so lets plug them into the equation above

18-(-10)/12-(-14)

= 18+10/12+14

=28/26

Answer:

1 and 7/24

Step-by-step explanation:

2/3 + 5/8

= 16/24 + 15/24

= 31/24

= 1 and 7/24

Hope this helps!

For this case we must simplify the following expression:

[tex]\frac {2} {3} + \frac {5} {8}[/tex]

Then, we add the fractions making cross product:

[tex]\frac {2} {3} + \frac {5} {8} = \frac {8 * 2 + 3 * 5} {3 * 8} = \frac {16 + 15} {24} = \frac {31 } {24}[/tex]

Thus, the fraction can not be simplified.

How mixed number we have:

[tex]\frac {31} {24} = 1 \frac {7} {24}[/tex]

ANswer:

[tex]\frac {31} {24}[/tex]

ANSWER

[tex]A = 80.98 \degree[/tex]

EXPLANATION

The angle with the greatest measure corresponds to the longest:

Since we know the three side lengths, we use the cosine rule to obtain;

[tex] {a}^{2} = {b}^{2} + {c}^{2} - 2bc \cos(A) [/tex]

where a=21, b=18 and c=14

[tex] {21}^{2} = {18}^{2} + {14}^{2} - 2 \times 18 \times 14\cos(A) [/tex]

[tex]44 1= 324+ 196 - 504\cos(A) [/tex]

[tex]44 1= 520 - 504\cos(A) [/tex]

[tex]44 1 - 520 = - 504\cos(A) [/tex]

[tex] - 79 = - 504\cos(A) [/tex]

[tex]\cos(A) = 0.1567[/tex]

[tex]A = \cos ^{ - 1} (0.1567) = 80.98 \degree[/tex]

correct to the nearest hundredth.

-51

First, find the axis of symmetry, or the x value where the line switches directions. This is also the x value of the vertex. Find this by using the equation -b/2a. In this case, -10 is b, and 1 is a.

-(-10)/2(1)

10/2

5

So, the x value of the vertex is 5. Now, find the y value by putting the x value back into the equation.

y = -(5)^2 - 10(5) + 24

y = -25 - 50 + 24

y = -75 + 24

y = -51

So, the y value of the vertex is -51.

Hope this helps 1/2x(27)z

Answer:

The correct answer is B. 0.0000135

Step-by-step explanation:

I just did the assignment :D

have a nice day <33

The answer is 0! The input value would be 0!

the function rule is to add 6, so:

y = x + 6        (y is the output, x is the input)

Since they gave you an output value of 6, you can plug it into the equation

y = x + 6          Plug in 6 for y

6 = x + 6    Subtract 6 on both sides to find the input value

0 = x

Answer: x=21

Step-by-step explanation:

To solve for x you must first combine you like terms on each side of the equal sign. So you problem will become 8x+1=22+7x. Then get your x on one side and your numbers on the other by taking the one away from the right side and 1 away from 22. Then take away 7 from the left side to cancel it out. Then take 7x away from 8x to leave you with x. making your answer x=21

Answer:

Step-by-step explanation:

3x + 1 + 5x = 7 + 15 + 7x          combine like terms

(3x + 5x) + 1 = (7 + 15) + 7x

8x + 1 = 22 + 7x            subtract 1 from both sides

8x = 21 + 7x           subtract 7x from both sides

x = 21

Answer:

The graph in the attached figure

Step-by-step explanation:

step 1

Find the equation of the line into point slope form

The equation of the line is equal to

[tex]y-y1=m(x-x1)[/tex]

substitute the given values

[tex]y-1=(2/3)(x+2)[/tex]

step 2

To graph the line find the intercepts

Find the y-intercept

The y-intercept is the value of y when the value of x is equal to zero

so

For x=0

[tex]y-1=(2/3)(0+2)[/tex]

[tex]y=(4/3)+1[/tex]

[tex]y=(7/3)[/tex]

The y-intercept is the point (0,7/3)

Find the x-intercept

The x-intercept is the value of x when the value of y is equal to zero

so

For y=0

[tex]0-1=(2/3)(x+2)[/tex]

[tex]-1=(2/3)x+(4/3)[/tex]

[tex](2/3)x=-(4/3)-1[/tex]

[tex](2/3)x=-(7/3)[/tex]

[tex]2x=-7[/tex]

[tex]x=-7/2[/tex]

The x-intercept is the point (-7/2,0)

step 3

Plot the intercepts to graph the line

see the attached figure

Answer:

(C) is 0.14 that is your probability

Step-by-step explanation:

Final answer:

The price of the shirt after including a $5 tax is represented by the expression 'g + 5', where 'g' is the original price of the shirt.

Explanation:

When calculating the price of an item after tax, you simply add the tax amount to the original price of the item. In this case, the original shirt price is represented by the variable g dollars, and a $5 tax is added to this price. Therefore, the correct answer to the question 'The price of a shirt with a $5 tax. The original shirt price is g dollars.' is g + 5.

ANSWER

6.4 hours

EXPLANATION

if it takes 10 hours to get 50%, then it will take less number of hours to get 32%

We use proportion to solve this question.

If less more divides.

The number of hours it will take to get 32% is

[tex] = \frac{32\% \times 10}{50\%} [/tex]

[tex] = 6.4[/tex]

Hence it will take 6.4 hours to get 32%

Answer:

694.44 sheets of paper

Step-by-step explanation:

we know that

The height of terry’s trays is [tex]h=2\frac{1}{2}\ in=\frac{2*2+1}{2}=\frac{5}{2}\ in[/tex]

using proportion

2,500/9=x/(5/2)

x=2,500*(5/2)/9

x=694.44 sheets of paper

It’s going to be 8 because you add all the toys together and divide that by the container number

Answer:

There will be 8 transportation toys

Step-by-step explanation:

So first you would all the toys up. Then divide it by 3.

6+4=10 + 6= 16 +8=24

24 / 3 = 8

14+14= 28= 48-28= 20/2= 10

Answer:

raul donated more money than mike did is

Step-by-step explanation:

raul donated 1/10 of 60 so

1/10*60=6

mike donated 1/10 of 30 so

1/10*30=3

so raul donated more money than mike did is the correct statement

Answer: B.

Step-by-step explanation:

So it's B because...

So if they donated 1/10th of their money, that means they donated 10%. So, 10% of 60 is 6 and 10% of 30 is 3. which means that Raul donated more money than Mike did.

10 % of 60 = 6

10% of 30 = 3

ANSWER → B

* Hopefully this helps:) Mark me the brainliest:)!!

∞ 234483279c20∞

Answer:

40

Step-by-step explanation:

Since she has a total of 200 pages and 5 days you would divide to get 40.

[tex]\text{Hey there!}[/tex]

[tex]-1\frac{3}{5}\div\frac{2}{3}[/tex]

[tex]-1\frac{3}{5}=-\frac{8}{5}[/tex]

[tex]\text{Problem becomes:}-\frac{8}{2}\div\frac{2}{3}[/tex]

[tex]\text{Solve that, and you will get:}\frac{-4}{5}\div{\frac{3}{1}}[/tex]

[tex]-4\times1=-4[/tex]

[tex]5\times3=15[/tex]

[tex]\rightarrow =\frac{-4}{15}[/tex]

[tex]\boxed{\boxed{\boxed{\bf{Answer:\frac{-4}{15}}}}}}\checkmark[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{LoveYourselfFirst:)}[/tex]

Answer: it is c

Step-by-step explanation:

[tex]d. \: 35m + 50 + 25 \\ \\ 1. \: 35m + (50 + 25) \\ 2. \: 35m + 75[/tex]

14,  she will be 14 when she has more

Answer:

sebastian will be 14 when he gets more money than lorena

Answer:

1

Step-by-step explanation:

2%= 0.2

0.2*5= 1

When finding Percent of whole multiply.

To figure this out you must do a proportion. Typically you would do [tex]\frac{part}{whole}[/tex]

This means that you would set up your proportions like this:

[tex]\frac{x}{50} =\frac{2}{100}[/tex]

^^^you want to find 2% of 50, so 50 is the "whole" and x (what you are looking for) is the part. The reason there is the 100 is because % are always taken out of 100% , and therefore 100 is the "whole". 2 is on top of 100 because it is a "part" of 100

the next step is cross multiplication so you would get:

100x= (50*2) ---> 100x = 100

^^^you then solve this like a normal algebra equation to get x = 1

Hope this helped! Let me know if there is anything else I can do!

Answer:

(1), (3)

Step-by-step explanation:

5.  If m starts at 1, a geometric series has the form a₁ (r)ᵐ⁻¹.

If m starts at 0, a geometric series has the form a₀ (r)ᵐ.

Here, m starts at 0.  The first term, a₀, is 150.  The temperature is decreasing, so we're looking for an r < 1.  Therefore, the answer must be (1) 150 (0.85)ᵐ.

7.  A quadratic written in vertex form is:

y = a(x - h)² + k

We can find the vertex of the parabola using x = -b/(2a).

x = -12 / (2*3)

x = -2

f(-2) = 3(-2)² + 12(-2) + 11

f(-2) = -1

So the vertex (h, k) is at (-2, -1).

Therefore, the answer must be f(x) = 3(x + 2)² - 1

We can also show this by completing the square.

f(x) = 3x² + 12x + 11

f(x) = 3(x² + 4x) + 11

f(x) = 3(x² + 4x + 4) - 3(4) + 11

f(x) = 3(x + 2)² - 1