A cheetah can run at speeds up to 70 mph. How fast is this in kilometers per hour?

The equation y^2+8y−x+18=0 represents a parabola. Drag and drop the expressions into the boxes in the equation to rewrite the eq

mario62 [17]

Answer:

The equation of parabola is standard form is $x=\left(y+4\right)^2+2$

Step-by-step explanation:

Given equation of parabola is,

$y^2+8y-x+18=0$

In order to find the equation of parabola in standard form, eliminate x from left side of equation and use completing square method to find the equation.

First step is to add x on both side of equation.

$y^2+8y-x+18+x=0+x$

$y^2+8y+18=x$

Rewriting,

$x=y^2+8y+18$

Now applying completing square method as follows.

Following are the steps for calculation of this method.

Find the last term of above equation by using below formula,

$Last\:term\:of\:square=\left(\dfrac{coefficient\:of\:y}{2}\right)^{2}$

Now coefficient of y is 8.

$\therefore Last\:term\:of\:square=\left(\dfrac{8}{2}\right)^{2}$

Simplifying,

$Last\:term\:of\:square=\left(4\right)^{2}$

$Last\:term\:of\:square=16$

Second step is to add and subtract the last term.

$x=y^2+8y+18+16-16$

Rewriting,

$x=y^2+8y+16+18-16$

Since $\left(a+b\right)^{2}=a^{2}+2ab+b^{2}$

Using above formula,

$x=\left(y+4\right)^{2}+2$

Therefore, the equation of parabola in standard form is $x=\left(y+4\right)^{2}+2$

4 0

3 years ago

In Pant Science (May 2010), a group of Japanese environmental scientists investigated the ability of a hybrid tomato plant to pr

Neporo4naja [7]

Answer:

a) P(x > 120) = 0.03288

b) P(100 < x < 110) = 0.46777

c) value of a for which P(x < a) = 0.25

a = 99.91

Step-by-step explanation:

This is a normal distribution problem with

Mean = μ = 105.3

Standard deviation = σ = 8.0

a) P(x > 120)

To work this, we first need To convert 120 go standardized/normalized/z-scores.

The standardized score for any value is the value minus the mean then divided by the standard deviation.

z = (x - μ)/σ = (120 - 105.3)/8.0 = 1.84

To determine P(x > 120) = P(z > 1.84)

We use the tables for these probabilities now.

P(x > 120) = P(z > 1.84) = 1 - P(z ≤ 1.84) = 1 - 0.96712 = 0.03288

b) P(100 < x < 110)

We normalize the two value in the inequality

For 100,

z = (x - μ)/σ = (100 - 105.3)/8.0 = -0.66

For 110,

z = (x - μ)/σ = (110 - 105.3)/8.0 = 0.59

To determine P(100 < x < 110) = P(-0.66 < z < 0.59)

We use the tables for these probabilities now.

P(100 < x < 110) = P(-0.66 < z < 0.59) = P(z < 0.59) - P(z < -0.66) = 0.72240 - 0.25463 = 0.46777

c) value of a for which P(x < a) = .25

Let the z-score of a be z'

z' = (x - μ)/σ = (a - 105.3)/8.0

P(x < a) = P(z < z') = 0.25

Using the table, z' = - 0.674

-0.674 = (a - 105.3)/8

a - 105.3 = -5.392

a = 105.3 - 5.392 = 99.91

Hope this Helps!!!

5 0

3 years ago

A 5.5 ounce breadstick weighs the same as 16

givi [52]

Answer: top right

Step-by-step explanation: in order to seperate p, we need to multiply each side by 6, as this will make the right side just p. Then, since we mutiplied by 6 on the right side, we multiply by 6 on the left side too, so we get 5.5*6

8 0

3 years ago

Help ASAP pls giving brainliest

inna [77]

After arranging the data from least to greatest:

Q1: 12.5
Q3: 16
IQR ( Q3-Q1) : 3.5

6 0

3 years ago

Y=-1/2x +7

yarga [219]

Answer:

B; (2,-4)

Step-by-step explanation:

The general equation of a straight line is;

y = mx + b

where m is the slope and b is the y-intercept

So from the question, when we look at the given equation, its slope is -1/2

mathematically, when two lines are perpendicular, the product of their slopes is -1

thus;

m1 * m2 = -1

m2 * -1/2 = -1

-m2 = -2

m2 = 2

The general equation form is;

y-y1 = m(x-x1)

where (x1,y1) = (4,0)

y-0 = 2(x-4)

y = 2x - 8

So, now we look at the point that will work for this equation

For the line that will work, if we substitute its x-value, we get the y-value

Let us take a look at option B

y = 2(2) -8 = 4-8 = -4

we can see that (2,-4) works

4 0

3 years ago