F(x) = 4x - 9 <br> i need helpp

An ellipse has vertices along the major axis at (0, 8) and (0, -2). The foci of the ellipse are located at (0, 7) and

mr Goodwill [35]

Answer:

The values are a = 5 , b = 3 , h = 0 , k = 3

The equation is x²/9 + (y - 3)²/25 = 1

Step-by-step explanation:

* Lets revise the standard equation of the ellipse

- The standard form of the equation of an ellipse with center (h , k)

and major axis parallel to y-axis is (x - h)²/b² + (y - k)²/a² = 1 , where

-The length of the major axis is 2a

- The coordinates of the vertices are (h , k ± a)

- The length of the minor axis is 2b

- The coordinates of the co-vertices are (h ± b , k)

- The coordinates of the foci are (h , k ± c), where c² = a² - b²

* Now lets solve the problem

∵ The vertices of the ellipse along the major axis are (0 , 8) , (0 , -2)

∴ The major axis is the y-axis

∴ The vertices are (h , k + a) and (h , k - a)

∴ h = 0

∴ k + a = 8 ⇒ (1)

∴ k - a = -2 ⇒ (2)

∵ The foci of it located at (0 , 7) , (0 , -1)

∵ The coordinates of the foci are (h , k + c) and (h , k - c)

∴ h = 0

∴ k + c = 7 ⇒ (3)

∴ k - c = -1 ⇒ (4)

- To find k and a add equations (1) and (2)

∴ (k + k) + (a + - a) = (8 + -2)

∴ 2k = 6 ⇒ divide both sides by 2

∴ k = 3

- Substitute the value of k in equation (1) or (2) to find a

∴ 3 + a = 8 ⇒ subtract 3 from both sides

∴ a = 5

- To find the value of c substitute the value of k in equation (3) or (4)

∴ 3 + c = 7 ⇒ subtract 3 from both sides

∴ c = 4

- To find b use the equation c² = a² - b²

∵ a = 5 and c = 4

∴ (4)² = (5)² - a²

∴ 16 = 25 - b² ⇒ subtract 25 from both sides

∴ -9 = -b² ⇒ multiply both sides by -1

∴ b² = 9 ⇒ take √ for both sides

∴ b = 3

* The values are a = 5 , b = 3 , h = 0 , k = 3

* The equation is x²/9 + (y - 3)²/25 = 1

7 0

4 years ago

Read 2 more answers

What is the solution to the following system of equations?<br> y = x2 + 10x + 11<br> y = x2 + x − 7

marishachu [46]

Hello,

y=x²+10x+11
y=x²+x-7

==>x²+10x+11=x²+x-7
==>9x=-18
==>x=-2

Sol={(-2,-5)}

8 0

4 years ago

Select the correct answer from each drop-down menu. Rafael wants to construct a square inscribed in a circle. He divides the cir

Soloha48 [4]

The circle's square is an inscribed square.

Rafael made his first error in (B) Dividing the circle in six parts.
The square can be constructed by first (c) Drawing a diameter

<h3>How to spot Rafael's mistake?</h3>

CIRCLE: A circle is the collection of all points on a plane that are at a specified distance from another point (the radius) (the centre). A radius is any distance separating a point on a circle from its center. Any two radii are equal in length under the concept of a circle.

SQUARE: In geometry, a square is a flat shape having four equal sides & four right angles (90°). A square is an unique sort of parallelogram as well as an equilateral rectangle.

Estimation for the error;

The diameter of a circle must be drawn first when drawing the square inside of a circle, following the circle itself.

This indicates that Rafael made two mistakes: first, he divided the circle into six halves, forgetting that a square is produced by first sketching a diameter.

To know more about square is inscribed in a circle, here

brainly.com/question/8797902

#SPJ4

The complete question is -

Select the correct answer from each drop-down menu.

Rafael wants to construct a square inscribed in a circle. He divides the circle into six equal arcs and then draws line segments between four of the points. What was the first error Rafael made?

1. The first error Rafael made was

A.Connecting points F and E

B. Dividing the circle in six parts

C. Connecting points B and F

2. A square is constructed by first

A. Drawing a radius

B. Drawing a chord

C Drawing a diameter

5 0

1 year ago

. The time required for a technician to machine a specific component is normally distributed with a mean of 2 hours and a standa

erma4kov [3.2K]

Answer:

a) There is a 3.84% probability that the technician can machine one component in 1.5 hours or less.

b) There is a 0.42% probability that the technician will require at least 2.75 hours to complete one component

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by

$Z = \frac{X - \mu}{\sigma}$

After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X.

In this problem, we have to be careful. The mean is in hours, while the standard deviation is in minutes. I am going to work with both in hours, as the problem states. 17 minutes is 0.283 hours, so:

$\mu = 2, \sigma = 0.283$

(a.) What is the probability that the technician can machine one component in 1.5 hours or less?

This probability is the pvalue of the Zscore when $X = 1.5$ . So:

$Z = \frac{1.5 - 2}{0.283}$

$Z = \frac{-0.5}{0.283}$

$Z = -1.77$

$Z = -1.77$ has a pvalue of 0.0384.

This means that there is a 3.84% probability that the technician can machine one component in 1.5 hours or less.

(b.) What is the probability that the technician will require at least 2.75 hours to complete one component?

The pvalue of the score of $X = 2.75$ is the probability that the technican will require less than 2.75 hours to complete one component. The probability that he will require at least 2.75 hours to complete one component is 1 subtracted by this pvalue. So: