Writing Linear Equations from Key Information slope = 3, y-intercept = −1

Answer:

The given equations are;

y = a·(x - h)² + k or y = a·x² + b·x + c

We have;

(x - h)² = 4·p·(y - k),

Where;

(h, k) are the x, and y coordinates of the vertex

p = The distance from the focus to vertex distance;

Comparing, we have;

y - k = a·(x - h)²

(y - k)/a = (x - h)²

(x - h)² = 4·p·(y - k)

4·p·(y - k) = (x - h)²

∴ 4·p = 1/a

p = 1/(4·a)

Therefore, the focus to vertex distance inversely proportional to the value of a

The distance of every point on the parabola is equidistant from the directrix and the focus

Therefore, the equation of the directrix is y = k - p

For example, we have;

y = 2·x² + 3·x + 1

h = -b/2a = -3/4

k = (4ac - b²)/4a = (4×2×1 - 3²)/(4×2) = -1/8

The coordinate of the focus is (h, k + p) = (-3/4, -1/8 + 1/8) = (-3/4, 0)

The directrix, y = k - p = -1/8 - 1/8 = -1/4

For a point x = 2, we have, y = 2·2² + 3·2 + 1 = 15

The coordinate of the point is (2, 15)

The distance of the point from the directrix = 15 - (-1/4) = 15 + 1/4 = 15.25

The distance of the point from the focus is √((2 - (-3/4))² + (15 - 0)²) = 15.25

Therefore, all points on the parabola have equal distances from the focus and the directrix

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

Let's isolate x on one side.

2x - x - 2/3x = -8+5+4

1/3x=1

x=3

Answer:

X = 3

Step-by-step explanation:

-8 + 2/3x + 4 = 2x - 5 - x

2/3x - 2x - x = -5 + 8 - 4

-1/3x = -1

x = -1 * -3

x = 3

Answer:

0.86016949152

Step-by-step explanation:

This is the answer because 29 divided by 59 is 0.49152542372 and 42 divided by 24 is 1.75 and 0.49152542372 multiplied by 1.75 is 0.86016949152

Answer:

[tex]a=9[/tex]

Step-by-step explanation:

In this problem, you can use the Pythagorean Theorem ([tex]a^{2} +b^{2} =c^{2}[/tex]) to find what a is. The steps are shown below:

Steps (variables a, b, and c are in italics):

-You can rearrange the formula from the Pythagorean Theorem, which is[tex]a^{2} +b^{2} =c^{2}[/tex] to only get a because we want to know what a is.

Rearranged: [tex]a=\sqrt{c^{2}-b^{2} }[/tex] or [tex]a=-\sqrt{c^{2}-b^{2} }[/tex]  It has to ways/options for a because when finding the square root of a number, it can be either positive or negative. But in this problem, it’s going to be positive because we’re finding the length of something.

-Since we know what c and b are, you can plug them into the new formula:

[tex]a=\sqrt{15^{2}-12^{2} }[/tex]

-Simplify it:

[tex]a=\sqrt{225-144}[/tex]

-Subtract inside the radical:

[tex]a=\sqrt{81}[/tex]  Then simplify it to get [tex]a=9[/tex].

You can check your answer by putting a back into the original Pythagorean Theorem formula ([tex]a^{2} +b^{2} =c^{2}[/tex]):

Steps

-Plug a, b, and c into the formula [tex]a^{2} +b^{2} =c^{2}[/tex]:

[tex](9)^{2} +(12)^{2} =(15)^{2}[/tex]

-Simplify to get:

[tex]81+144=225[/tex]

-Add:

[tex]225=225[/tex]  This is very true. So our answer is correct.

ANSWER: [tex]a=9[/tex]

Sorry for the long explanation, but I hope you understand and that this helps with your question! :)

Answer:

Step-by-step explanation:

lets make is short and simple

Pythagorean theorem: a² + b² = c²

a² + 12² = 15²

a² = 15² - 12²

a = √81

a = 9

Answer:

Time taken per slides = 131.77 minutes.

Step-by-step explanation:

Given the following data;

Total time, t = 1713 mins

Number of slides, n = 13

To find the amount of time spent on each slides;

Time taken per slides = t/n

Substituting into the equation, we have;

Time taken per slides = 1713/13

Time taken per slides = 131.77 minutes.

Therefore, the amount of time Stephanie spent on each slide is 131.77 minutes.

It took Stephanie about 1 minute to finish each slide of the 13-slide presentation.

Equation is used to show the relationship between two or more numbers and variables.

Le x represent the amount of time spent on each slide.

Given that she spent  13 minutes to finish a 13-slide presentation. Therefore:

Divide through by 13:

It took Stephanie about 1 minute to finish each slide of the 13-slide presentation.

Find out more on equation at: https://brainly.com/question/13763238

Answer:

1,000,000 times larger

Step-by-step explanation:

2 x [tex]10^{8}[/tex] = 200,000,000

2 x [tex]10^{2}[/tex] = 200

200,000,000 divided by 200 is 1,000,000

It can also be solved by subtracting the exponents from 10. Then dividing the two number being put the scientific notation.

[tex]10^{8} - 10^{2}[/tex] = [tex]10^{6[/tex]

2 ÷ 2 = 1

Now solve:

1 x [tex]10^{6[/tex] = 1,000,000

9514 1404 393

Answer:

  y = -3/4x -1

Step-by-step explanation:

The given equation is in the slope-intercept form, which lets you see that its slope is 4/3.

The slope of the perpendicular line will be the negative reciprocal of this:

  -3/4

Then the slope-intercept form equation will be ...

  y = -3/4x +b . . . . . . for some b

We can find the value of b that makes the line go through (4, -4) by using those values in this equation.

  -4 = -3/4(4) +b

  -4 +3 = b . . . . . . . . add 3

  -1 = b

Then the equation you're looking for is ...

  y = -3/4x -1

Answer:

The answer is stan twice

Step-by-step explanation:

simple

Answer:

x=10

Step-by-step explanation:

Answer:

Quadrant III and Quadrant I

Step-by-step explanation:

Answer:

Zero; 0

Step-by-step explanation:

(-5+5)/(18+2) = 0

Answer:

i dunno man you worded it weird

Step-by-step explanation:

Answer:

FV= $712.88

Step-by-step explanation:

Giving the following information:

Initial investment (PV)= $500

Number of periods (n)= 12 years

Interest rate (i)= 3% compounded annually

To calculate the future value, we need to use the following formula:

FV= PV*(1+i)^n

FV= 500*(1.03^12)

FV= $712.88

Answer:

25%

Step-by-step explanation:

Because she divided it

Answer:

where is tge other half question?

Answer:

f(x)=x+6

-2+6

4

when x=0

0+6

6

when x=5

5+6

11

Step-by-step explanation:

Answer:

Up 5, 2 to the right (5/2)

Step-by-step explanation:

I just counted the units of the Cartesian Plane

Answer:

132 miles

Step-by-step explanation:

Answer: the answer is 93.7 miles

[tex]f(x)=-3x-4[/tex]

Substitute x = 1 in the equation.

[tex]f(1)=-3(1)-4\\f(1)=-3-4\\f(1)=-7[/tex]

Therefore, the answer is f(1) = -7

Answer:

c=a2+b2

Step-by-step explanation:

Find the value of x.

The side opposite the right angle is the side labelled x. ...

x=√100=10.

Maybe you remember that in an equation like this, x could also be –10, since –10 squared is also 100. ...

Find the value of y.

y=√80=√16×5=4√5.

x=√17.45≈4.18 miles.

Answer:

thats the formula

a^2 + b^2 = c^2

Step-by-step explanation:

a =  side of the right angle/adjacent side

b = side of the right triangle/opposite side

c= hypotenuse

Answer:

it would be 70

Step-by-step explanation:

you are not stupid

Answer:

the answer is -50

Step-by-step explanation:

It is equal to 32y+32 if you wanted to simplify it.

Answer:

32y + 32

Step-by-step explanation:

8 × 4y + 8 × 4

Answer: -18m x 4 (I think)

Step-by-step explanation:

If this isn’t correct, what you have to do is simplify, hopefully this helps

come to your house to pick it lowest to go with D

Answer:

All of them have different answers so gonna say D because its only one number  

Step-by-step explanation:

Hope this helps

sorry If its wrong

Answer:n=-3.1

Step-by-step explanation:

2n + 3 = -3.2

Subtract 3 on both sides

2n+3-3=-3.2-3

2n=-6.2

Divide 2 on both sides

2n/2=-6.2/2

n=-3.1

Answer:

n= -3.1

Step-by-step explanation:

hope this helps have a nice day :)

Answer:

x^3−2x2+4x+3=x2−5x+15+−41x+3

Step-by-step explanation:

1.Divide the leading term of the dividend by the leading term of the divisor: x3x=x2.

Write down the calculated result in the upper part of the table.

Multiply it by the divisor: x2(x+3)=x3+3x2.

Subtract the dividend from the obtained result: (x3−2x2+4)−(x3+3x2)=−5x2+4.

2.Divide the leading term of the obtained remainder by the leading term of the divisor: −5x2x=−5x.

Write down the calculated result in the upper part of the table.

Multiply it by the divisor: −5x(x+3)=−5x2−15x.

Subtract the remainder from the obtained result: (−5x2+4)−(−5x2−15x)=15x

3.Divide the leading term of the obtained remainder by the leading term of the divisor: 15xx=15.

Write down the calculated result in the upper part of the table.

Multiply it by the divisor: 15(x+3)=15x+45.

Subtract the remainder from the obtained result: (15x+4)−(15x+45)=−41.

Answer:

287

Step-by-step explanation:

70/100*410

(cross out the zeroes then multiply 7 by 41 and you'll get 287)

Answer: 14 dimes and 3 quarters

Step-by-step explanation:

14x10=140+25=165+25=190+25=215 aka $2.15 meaning that there is 14 dimes and 3 quarters

Answer:

They travel 5/18 in one hour

Step-by-step explanation:

Answer:

In an hour the car can cover 5/18 of the distance