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The equation of the parabola whose focus is (-2,2) and whose directrix is x​= -8 is [tex](y+2)^2=-20(x+5)[/tex]

The standard formula for finding an equation of a parabola is expressed as [tex]y^2=4ax[/tex]

If the curve is shifted to the left and down, the equation becomes [tex](y-k)^2=4a(x-h)[/tex] where:

(h, k) is the vertex of the parabola

If the focus is at (-2, 2) and the directrix is at x = -8, the equivalent vertex of the parabola will be at (-5, -2) and the midpoint between the vertex and directrix is at a = -5

Substitute these values into the formula of the parabola.

[tex](y-k)^2=4a(x-h)\\(y-(-2))^2=4(-5)(x-(-5))\\(y+2)^2=-20(x+5)\\[/tex]

Hence the equation of the parabola whose focus is (-2,2) and whose directrix is x ​​= -8 is [tex](y+2)^2=-20(x+5)[/tex]

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Answer:

The rate of change will be the number of bags Fred fills for 1 customer.

Write a ratio.

21 : 3

x : 1

To solve for x, cross multiply.

3x : 21

Divide both sides by 3.

x = 7

Fred’s average rate of change is 7 bags.

:)

Answer:

$255

Step-by-step explanation:

Equation would be

60x+0.5y= $ charged

x= days

y = per mile

60 * 3 + 0.5 * 150 = $

180+75=

=255

Greg would have to pay $255

Hope this helps!

(Pls mark brainiest)

Thanks!

Answer:

20.4

Step-by-step explanation:

If you are using D = r × t

                         10.2 = 0.5(t)

                          10.2/0.5 = t

                           20.4 = t

Answer:

20.4

Step-by-step explanation:

Answer:

The ratio would be 5 to 3

Step-by-step explanation:

I know this because you would divide the amount of grapes and the amount of cashews by 3 which would equal 5 to 3

The ratio of grapes to cashews that she ate is 5:3.

A ratio is the comparison of two quantities and that can be the comparisons of parts to parts, parts to wholes, and wholes to parts are all examples of ratios.

Given that, Regina ate 25 grapes and 15 cashews.

We need to simplify the ratio of grapes to cashews that she ate.

The ratio = 25/15

= 5/3

Hence the ratio of grapes to cashews that she ate is 5:3.

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Answer:

First drop down: √4 and √9

Second drop down: 2 and 3

Third drop down: 10 and 15

Step-by-step explanation:

the root of four is 2

the root of nine is 3

thus √ 7 is between 2 and 3

5√7 is between 10 and 15 because 2x5 is 10 and 3x5 is 15.

Problem 1

The price for one super skateboard is £75.00 which is found in cell C8. When it comes to excel spreadsheets, we always read across the top first before reading the left hand side. So the format is columnRow which may seem strange if you're used to reading the row first.

Right next to cell C8 is D8 and that's the number of super skateboards sold (26 of them). Multiply the unit price by the number of units sold to get the revenue for this particular type of item.

75*26 = 1950

Now the question is: what if the company sells more than 26 skateboards? Let's say there was an error and 30 boards were sold. To quickly recompute the correct answer, we can rely on references rather than hardcoded values.

Typing out [tex]=C8*D8[/tex] will compute the multiplication of items C8 and D8. The equal sign out front is very important. It tells the spreadsheet program that you want to do this type of operation (rather than just write out plain text). If you were to simply type in C8*D8 without the equal sign, then the result is exactly C8*D8 without filling in the variables.

Don't forget about the equal sign out front

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

Problem 2

Like before, we'll have an equal sign as the first thing we type in. Then we'll type in Sum(E5:E14) to sum of the values from E5 to E14. You could type in Sum(E5,E6,E7,E8,E9,E10,E11,E12,E13,E14) or you could type in E5+E6+E7+E8+E9+E10+E11+E12+E13+E14; however, that would be a tedious approach prone to error. The spreadsheet program interprets the colon as a way to fill in the gap from start to end. We start at E5 and end at E14, and add up everything in between.

Note that all the cells referenced are the various revenues for each type of item. Each of these cells is computed by multiplying the C and D column items.

Don't forget about the equal sign out front

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Problem 3

There are a few other alternatives, but your teacher might be talking about adding each item one at a time. Refer to problem 2 for more info.

Or

Don't forget about the equal sign out front

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

Problem 4

Explanation: Simply pick out the smallest item. The excel command is "min" and you provide it a list of values to pick from. In this case, that list being E5:E14 to represent E5,E6,...,E13,E14. So you'll type in =Min(E5:E14) similar to what you did for the "sum" command.

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Problem 5

Explanation: As you can probably guess, the "max" function is used here. It picks out the largest value of a list. The command is =Max(E5:E14)

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Below I've attached two images. Figure 1 shows the commands to type in, while figure 2 shows the result of each command. In other words, it's the before and after. I used LibreOffice spreadsheet, but this applies to any spreadsheet program as they all tend to follow the same idea.

Check the picture below.

Answer:

the answer is a federalist and your welcome

Step-by-step explanation:

The Federalists, led by Secretary of Treasury Alexander Hamilton, wanted a strong central government, while the Anti-Federalists, led by Secretary of State Thomas Jefferson, advocated states' rights instead of centralized power.

Answer:

slope = - 2, y- intercept = 5

Step-by-step explanation:

Calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, 5) and (x₂, y₂ ) = (3, - 1) ← 2 points on the line

m = [tex]\frac{-1-5}{3-0}[/tex] = [tex]\frac{-6}{3}[/tex] = - 2

The y- intercept is the point on the y- axis where the line crosses

The y- intercept = 5

Answer:

Triangle

Step-by-step explanation:

A parallelogram have four sides

Answer:

126/1=126

Step-by-step explanation:

630:5 as a fraction would be 630/5.

630/5 simplified would be 126/1.

Hope this helps :)

Answer:

630:5 would be 126:1

Step-by-step explanation:

To solve this we would divide 630 by five giving us 126, and divide 5 by 5 giving us one

Now we have 126:1, or 126 km/hour

9514 1404 393

Answer:

  E.  31.64

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you of the relation between the legs of a right triangle:

  Tan = Opposite/Adjacent

You are given trig values for 36°. That means ...

  tan(36°) = 23/x

  x = 23/0.727 ≈ 31.64

Answer:

SAS similarity

Step-by-step explanation:

LO and LP are proportional to LN and LM, as shown by:

[tex]\frac{LO}{LN} =\frac{LP}{LM}[/tex]

Because these are equal, both pairs of corresponding lines have the same scale factor and are proportional as a result. The angle between them is congruent due to the reflexive property as given, and with 2 pairs of proportional sides including the angle, ΔLMN is similar to ΔLPO by the SAS similarity postulate

Answer: The first graph

Step-by-step explanation:

A proportional graph always goes through the origin

Answer:

The first graph

Step-by-step explanation:

Answer:

Step-by-step explanation:

The first part is a computation, combining the chain and quotient rules. We know that the derivative of f(x)=arcsin(x) is 1/sqrt(1-x2), and we need to differentiate the denominator. We use the chain rule: let u=1-x^2, and v=sqrt(u). Then du/dx=-2x, and dv/du = 1/(2 sqrt(u)). Combining, dv/dx=-x/sqrt(1-x2). Now, we put everything together using the quotient rules: y' = (f'v-v'f)/v2. Multiplying by (1-x2)=v2, we obtain (1-x2)y'= sqrt(1-x2)/sqrt(1-x2) +xarcsin(x)/sqrt(1-x2), which we can rewrite as 1+xy, as desired. Let's call this equation ().

We prove the second part by induction on n. To do this, we need two things: a base case, that is, proving the case n=0, and an inductive step, where we prove case n+1 from case n. To do the base case, we differentiate both sides of equation (*) that we proved above: d/dx ((1-x2 )y') = d/dx (xy+1 ). On the left-hand side, we get -2xy'+(1-x2 )y'', using the product rule, and on the right-hand side, we get xy'+y, similarly. Rearranging, we've proven the case n=0 of the desired statement. The inductive step is similar: we differentiate the equation from case n using the chain rule. Each of the first two terms splits into two: respectively, -2xy(n+2)+(1-x2)y(n+3), and (2n+3)y(n+1)+(2n+3)xy(n+2). If we combine the terms with the same numbers of derivatives on y, we get (1-x2)y(n+3)-(2n+5)xy(n+2)-((n+1)2+2n+3)y(n+1)=0 -which is what we wanted to prove, since ((n+1)2+2n+3) simplifies to (n+2)2.

Answer:

X would be 1,000

Step-by-step explanation:

Answer:

"given figure"

No figure was given.

Step-by-step explanation:

Answer:

L - 10 . W - 5

Step-by-step explanation:

Length = 3*width - 5

area = length * width

50 = (3w-5)* w

50 = 3w^2-5w

0 = 3w^2 - 5w -50

0= (3w+10)(w-5)

w = 5 , w can't equal -10/3 because width can't be negative

width is 5

Length = 3 * 5 - 5

Length = 10 , width = 5

Answer:

first lets say w is the width

50(area)=w(idth)+3(w-5)

50=w+3w+15

50=4w+15

35=4w

8.75=w

w equals 8 3/4

Hope This Helps!!!

Answer:

24

Step-by-step explanation:

4x6=12or 2x6=12so then 12+12=24

Answer:

6 songs per hour, so multiply that with the number asked which is four

so four times six is24

so she can play 24 songs in four hours!

~ ...

~ !

~ !

Answer:

18 and 29

Step-by-step explanation:

8+0=8

8+1=9

9+2=11

11+3=14

14+4=18

18+5=23

23+6=29

As you can see, the number that you add to the previous number in the sequence is increased by 1 as the sequence grows in length. The number added goes from 0 to 1 to 2 to 3 and so on. :-)

Answer:

16

Step-by-step explanation:

8x8 is 64, so half of 8 is 4 so 4x4 is 16

Answer: y=7, x=2

Step-by-step explanation:

∠Q+∠P=180° (∠s between 2 // lines)

97°+(12y-1)°=180°

12y-1=83°

12y=84

y=7

5x+6=8x (Iso triangle)

x=2

Answer:

i dont know

Step-by-step explanation:

i dont know

The amount of Plutonium that remains after 36 months is 0.05

The equation for the amount of Plutonium after t months is

[tex]\mathbf{P(t) = 12e^{-0.1507t}}[/tex]

After 36 months; we have: t = 36.

Substitute 36 for t in P(t).

So, we have:

[tex]\mathbf{P(36) = 12e^{-0.1507 \times 36}}[/tex]

Simplify the exponent

[tex]\mathbf{P(36) = 12e^{-5.4252}}[/tex]

Evaluate the exponent

[tex]\mathbf{P(36) = 12 \times 0.004404}[/tex]

Multiply

[tex]\mathbf{P(36) = 0.052848}[/tex]

Approximate to 2 decimal places

[tex]\mathbf{P(36) = 0.05}[/tex]

Hence, the amount that remains is 0.05

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Answer:

8x + 16 = 2(4x + 8) = 4(2x + 4) = 8(x + 2) = 16((1/2)x + 1) = -8(-x - 2)

Step-by-step explanation: