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Consider a point (x,y) on the parabola.

Determine the distance between focus (0,-4) and point (x,y) by using the distance formula.

Determine the distance between directrix y=4 and point (x,y).

For the parabola distance between focus and point is equal to distance between directrix and point.

Answer:

B. g(x)=(x+7)^2-3

Step-by-step explanation:

Vertex form is F(x)= a(x-h)^2+k

a is the reflection

h and k are the vertex (x,y) = (h,k)

in this case there is no shrink or stretch (a)

if it is translating left or right it is "h". In this case it is translated left so its -7.  However if you look at vertex form it is "x-h" so -7-7= +7

If it translating up or down it is "K".  In this case it is translated down so its -3.  

If it was translated up or right then its positive.  If it was translated down or left its negative.

After you figure out what h and k are then you just plug it in.  h=-7, k=-3

so the answer in vertex form is, g(x)=(x+7)^2-3

Answer:

15 dollars per lawn

Step-by-step explanation:

45 divided by 3= 15

Answer:

He earned $45 dollars when he mowed 3 lawns.

So get 45 and divide it by 3.

That's 15.

So Dylan earned $15 per lawn.

Hope this helped!!

Answer:

(g ￮ f)(-2) = 32

Step-by-step explanation:

Given

\(f(x)=5x+4\)

\(g\left(x\right)=x^2-4\)

We have to evaluate (g ￮ f)(-2), so first we will evaluate f(-2) then use this value to evaluate g(x).

Finding f(-2)

\(f(x)=5x+4\)

\(f(-2) = 5(-2)+4\)

          \(= -10 + 4\)

          \(= -6\)

Then

\(g\left(-6\right)=\left(-6\right)^2-4\)

          \(=36-4\)

          \(= 32\)

Therefore,

(g ￮ f)(-2) = 32

The steps the he could use to solve the quadratic equation include:

8(x2 + 2x) = –3

8(x2 + 2x + 1) = –3 + 8

x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot

Quadratic equations can also be solved without the use of the known quadratic formula solver. One of the most-used methods consists of completing squares and solving for x.

By factoring the equation, this will be:

8(x² + 2x) = -4

Factoring the perfect square:

8(x + 1)² = 5

Solving for x will give x = -1 + ✓5/8.

Therefore, the correct options are illustrated above.

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Answer:

A, B, E

A: 8(x2 + 2x + 1) = –3 + 8

B: x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot

E: 8(x2 + 2x) = –3

Step-by-step explanation:

Got 100% on quiz

Answer: 1) for 75° is in quadrant 1, which is on top right.

2) draw a line on quadrant 2 in the half, each square is 90° so add to the nearest 160.  -draw a circle from top right to the top left in the half of that square.

3) for 430 youll do one entire circle because each square is 90°, and 90x4 is 360 degrees so youll end with a line between quadrant 1 and 2

Step-by-step explanation: you gotta calculate about where the lines are gonna be, it aint easy to explain in just words.

This is a separable differential equation, which means we can separate the variables y and x on either side of the equation. To do this, we'll move all the terms involving y to one side and all the terms involving x to the other side.

dy/dx = (1+y²)e^x

We'll divide both sides by (1+y²)e^x:

dy/(1+y²)e^x = dx

Now we'll integrate both sides with respect to their respective variables. The integral of dy/(1+y²) with respect to y is the inverse tangent (tan^-1) function, so we'll use that on the left side:

∫ dy/(1+y²) = ∫dx + C

tan^-1(y) = x + C

On the right side, we'll integrate e^x with respect to x, which gives us e^x. So we have:

tan^-1(y) = e^x + C

We can solve for y by reversing the tan^-1 function:

y = tan(e^x + C)

Where C is an arbitrary constant of integration.

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Answer:

no they share the same y value for two different x values

Based on the information, it should be noted that the difference between the scores of the girls and boys aren't significant.

From the information, the average score for boys was 48.4 with standard deviation 12.96 and the girls had an average score

of 48.9 with standard deviation 11.85.

The computed upper limit = 2.1119

The computed lower limit = -3.1119

Since the interval (-3.1119, 2.1119) contains the between the value 0 thus the difference of boys and girls scores isn't significant.

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Answer: 23100 voters

Step-by-step explanation:

42*55000=2310000

2310000/100=23100 voters

Answer:

I love you sweetheart I want to look and love you

Answer:

slope- 1/4

y intercept- 1

Answer: x=4

Step-by-step explanation:

 -8-x=x-4x

  -8-x=-3x

-x+3x=8

    2x=8

      x=4

The probability of drawing a king from a standard deck of 52 cards is 1/13.

In a standard deck of 52 playing cards, there are four kings: the king of hearts, the king of diamonds, the king of clubs, and the king of spades.

To find the probability of drawing a king, we need to determine the ratio of favorable outcomes (drawing a king) to the total number of possible outcomes (drawing any card from the deck).

The total number of possible outcomes is 52 because there are 52 cards in the deck.

The favorable outcomes, in this case, are the four kings.

Therefore, the probability of drawing a king is given by:

Probability = (Number of favorable outcomes) / (Number of possible outcomes)

= 4 / 52

= 1 / 13

Thus, the probability of drawing a king from a standard deck of 52 cards is 1/13.

This means that out of every 13 cards drawn, on average, one of them will be a king.

It is important to note that the probability of drawing a king remains the same regardless of any previous cards that have been drawn or any other factors.

Each draw is independent, and the probability of drawing a king is constant.

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Answer:

2.401 x 10\(^{4}\)

Step-by-step explanation:

24,010 (twenty-four thousand ten) is an even five-digits composite number following 24009 and preceding 24011. In scientific notation, it is written as 2.401 × 104.

Answer:

x z y

Step-by-step explanation:

i took the assignment

Answer:

X , Z , Y

Step-by-step explanation:

Answer:

66.341 Feet

Step-by-step explanation:

length 819

width 818

(Length x width)

divide both by 100.5

819/100.5

818/100.5

8.14925373134

8.13930348259

round

8.15

8.14

length times width

8.15*8.14

66.341

Answer:

6 people will take 16 days

Assumption: they all work at the same rate

8 people-------- 12 days

6 people--------> ?

8x12

6

= 16 days

Answer:

I think the assumption is that 6 men would take longer to build the same bridge

so 16 days is how long it would take 6 men

Step-by-step explanation:

I thought this because if it takes 8 men twelve days it's gonna probably take six men 16 days

12/8 = x/6

hope this helps

Answer:

Step-by-step explanation:I found the answer on this web\(^{}\)site. It seems correct! Link Below!ly/3fcEdSx

bit.\(^{}\)

Answer:

800

Step-by-step explanation:

Answer:

r≈4.775

Step-by-step explanation:

the formula for this is: r=(3V /4π)^⅓

0.9976 percent of the time, the automobile won't start immediately away.

An example of a continuous probability distribution is the normal distribution, in which the majority of data points cluster in the middle of the range, while the remaining ones taper off symmetrically toward either extreme. The distribution's mean is another name for the center of the range.

Given that,

X = number of morning car starts right away

X          0            1            2             3               4              5

p(x)  0.0024   0.0283   0.1323   0.3087    0.3601    0.1681

So now we are able to find the given probability

p(x ≥ 1) = 1 - p(0)

1 - 0.024 = 0.9976

Here we used complementary rule to find the answer

p(A') = 1 - p(A)

Therefore, the probability that the car does not start right away is 0.9976.

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The graph shows a positive association. There is a nonlinear association shown. There is no correlation shown on the scatter plot.

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Using the Central Limit Theorem, the standard error of the distribution of differences in sample means is of 1.97.

According to the Central Limit Theorem, it is given by the standard deviation of the sample divided by the square root of the sample size, hence:

It is given by the square root of the sum of the standard errors of each sample squared, hence:

s = sqrt(1.1² + 1.63²) = 1.97.

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Answer:

A

Step-by-step explanation:

Given that the cones are similar then corresponding dimensions are in proportion, that is

\(\frac{12}{2}\) = \(\frac{3}{x}\) ( cross- multiply )

12x = 6 ( divide both sides by 12 )

x = 0.5 → A

In polar coordinate, R is the set of points

{(r, θ) | 1 < r < 5 and 0 < θ < π/2}

So the integral is

\(\displaystyle\iint_R\sin(x^2+y^2)\,\mathrm dA = \int_0^{\frac\pi2}\int_1^5 r\sin(r^2)\,\mathrm dr\,\mathrm d\theta\)

\(=\displaystyle\frac\pi2\int_1^5 r\sin(r^2)\,\mathrm dr\)

\(=\displaystyle\frac\pi4\int_1^5 2r\sin(r^2)\,\mathrm dr\)

\(=\displaystyle\frac\pi4\int_1^{25} \sin(s)\,\mathrm ds\)

(where s = r ²)

\(=\displaystyle-\frac\pi4\cos(s)\bigg|_1^{25}= \boxed{\dfrac\pi4 (\cos(1) - \cos(25))}\)

Answer:

16 for both

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

the scale factor is the ratio of corresponding sides, image to original, so

scale factor = \(\frac{EF}{BC}\) = \(\frac{11}{66}\) = \(\frac{1}{6}\)

Answer:

it 21

Step-by-step explanation:

rr

old version of which the answer may be