Part 4: model a real world problem using an ellipse
An artist wants to make an elliptical sign out of a rectangular piece of wood. The wood piece has a length
of 60 inches and a width of 40 inches. The artist wants to make the largest elliptical piece possible from
the wood.
a) Write the equation of the ellipse by placing the center at the origin of the coordinate plane and making
the x-axis the major axis. (3 points)

PLEASE ANSWER ALL AND GRAPH

Variable is a data characteristic that stands for a value that changes or varies over time.

A variable is any characteristics, number, or quantity that can be measured or counted. A variable may also be called a data item. Age, sex, business income and expenses, country of birth, capital expenditure, class grades, eye colour and vehicle type are examples of variables.

Information is that portion of the content of a signal or message which conveys meaning. (so this is the wrong option)

A fact is a quantitative piece of information - such as a sale or a download. (so this is also the wrong option)

Hence, a Variable is a data characteristic that stands for a value that changes or varies over time.

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The coordinates of D is (-8 , -16 )

Coordinates are the location of a point on the x-y plane.

It is given that the coordinates of C are  (4,4)

the midpoint of CD is at M(-2,-6)

The distance between D to the midpoint is equal to distance between C and the mid point M .

The distance between C and M is

( -2 - 4 , -6 -4 )

( -6 , -10)

Adding this to the mid point will give the location of D

(-2 -6 , -6 , -10 )

(-8 , -16 )

Therefore the coordinates of D is (-8 , -16 ).

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Answer:

-8, -16

Step-by-step explanation:

got it right on the est.

First, we multiply the numbers : 10 x 5 = 50

Now, we multiply r squared to r^6. To do this, we add the index numbers together : r^2 x r^6 = r^(2+6) = r^8

So, the answer is 50r^8, or b.

Step-by-step explanation:

1. multiply by 8

2. divide by 2

Answer:

4096, 125

Step-by-step explanation:

In the first sequence, notice that each term increases by a factor of 8 (multiplied by 8 each time). Therefore, the fourth term would be 64*8 = 512, so the fifth term is 512*8 = 4096.

In the second sequence, each term decreases by a factor of 2 (divided by 2 each time). The fourth term would be 500/2 = 250, so the fifth term is 250/2 = 125.

The position of point L is halfway between points K and L

The line segment is given as:

JK

This means that the endpoints of the line are:

J and K

Also, we have:

JL = LK

So, we have:

JK = JL + LK

Substitute JL = LK

JK = JL + JL

This gives

JK = 2JL

Divide by 2

JL = 1/2 JK

Hence, the position of point L is halfway between points K and L

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The radius of the circular cross-section of the can of soup is; 3.4cm.

Since, the can has a height of 10cm and the volume of the can is 363cm³, it follows that the area of the circular cross-section can be evaluated as;

A = 363/10 = 36.3cm²

Hence, it follows that the radius can be evaluated as follows;

36.3 = 3.14 × r²

r² = 36.3/3.14

r² = 11.56

r = 3.4cm

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Answer: 11

Step-by-step explanation:

By the secant-secant theorem,

[tex]5(5+7)=(JK)(15)\\\\60=(JK)(15)\\\\JK=4\\\\\implies IJ=15-4=11[/tex]

The question posed in the task content is a goal seeking analysis type of question.

How many servers will be needed to reduce the waiting time of restaurant customers to less than 9 minutes is a goal seeking analysis question.

A goal seeking analysis question is a type of question which helps to determine the efficient and effective measure of achieving a goal either individually or in a group.

The question will help the manager of the restaurant to determine how many servers is needed in order to reduce the waiting time of customers.

Complete question:

The question "How many servers will be needed to reduce the waiting time of restaurant customers to less than 9 minutes?" is a type of

a. goal-seeking analysis.

b. what-if analysis.

c. sensitivity analysis.

d. utility modeling.

a. goal-seeking analysis.

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Answer:

A

Step-by-step explanation:

given a quadratic function in standard form

y = ax² + bx + c (a ≠ 0 ) then the x- coordinate of the vertex is

x = - [tex]\frac{b}{2a}[/tex]

y = 2x² + 8x + 1 ← is in standard form

with a = 2 , b = 8 , then

x = - [tex]\frac{8}{4}[/tex] = - 2

substitute x = - 2 into the equation for corresponding y- coordinate

y = 2(- 2)² + 8(- 2) + 1 = 2(4) - 16 + 1 = 8 - 16 + 1 = - 7

vertex = (- 2, - 7 )

The number of quasi-prime numbers that are less than 500 = 92

Quasi-prime numbers are those numbers that are also known as semi prime numbers which can not be divided by 2,7 or 11.

They are often derived from prime numbers which are 95 in number from 2 - 499. ( less than 500).

The 95 prime numbers - 3 numbers( such as 2,7 or 11) = 92

Therefore, the number of quasi-prime numbers that are less than 500 = 92

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Answer:

m=months

clark= 10000-105m

lois= 7500-50m

10000-105m=7500-50m

+50m

10,000-55m=7500

-10000

-55m=-2500

simplify

55m=2500

divide by 55

m=45.45

so i would say b

Hope This Helps!!!

Answer:

33.55

Step-by-step explanation:

Answer:

α = 33.56°  (nearest hundredth)

Step-by-step explanation:

Trigonometric ratios

[tex]\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}[/tex]

where:

Given:

As all sides of the right triangle have been given, any of the trigonometric ratios can be used to find α.

Sine Ratio

[tex]\begin{aligned}\sf \sin(\alpha) & = \sf \dfrac{\sqrt{11}}{6}\\\implies \alpha & = \sf \sin^{-1}\left(\dfrac{\sqrt{11}}{6}\right) \\& = \sf 33.55730976...^{\circ}\end{aligned}[/tex]

Cosine Ratio

[tex]\begin{aligned}\sf \cos(\alpha) & =\sf \dfrac{5}{6}\\\implies \alpha & = \sf \cos^{-1}\left(\dfrac{5}{6}\right) \\& = \sf 33.55730976...^{\circ}\end{aligned}[/tex]

Tangent Ratio

[tex]\begin{aligned}\sf \tan(\alpha) & =\sf \dfrac{\sqrt{11}}{5}\\\implies \alpha & = \sf \tan^{-1}\left(\dfrac{\sqrt{11}}{5}\right) \\& = \sf 33.55730976...^{\circ}\end{aligned}[/tex]

Therefore, α = 33.56°  (nearest hundredth)

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Answer:

96 ft^2.

Step-by-step explanation:

Area of shaded region = area of the original rectangle - area of the one removed

= 8 * 16 - 8*4

= 128 - 32

= 96

Answer:

The two numbers are:

8 and 13

Step-by-step explanation:

a = 2b - 3       Eq. 1

a + b = 21        Eq. 2

Replacing Eq. 1 in Eq. 2:

(2b-3) + b = 21

3b - 3 = 21

3b = 21 + 3

3b = 24

b = 24/3

b = 8

from Eq. 1

a = 2*8 - 3

a = 16 - 3

a = 13

Check:

From Eq. 2:

a + b = 21

13 + 8 = 21

Answer:

89

Step-by-step explanation:

[tex] \sqrt{ {80}^{2} + {39}^{2} } = 89[/tex]

The distance between the top of the pillar and the foot of the shadow is  80 meters.

Let's call the distance we want to find "x".

In particular, set up the following proportion:

pillar height / shadow length = distance / shadow length

Plugin the given values

80 / 39 = x / 39

Simplifying and solving for x

x = (80 / 39) * 39

x ≈ 80

Therefore, the distance between the top of the pillar and the foot of the shadow is  80 meters.

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Answer:

sin D = 28/53

Step-by-step explanation:

sin D = opp/hyp

For angle D, the opposite leg is FE with length 28.

The hypotenuse is DE with length 53.

sin D = 28/53

Answer: sinD=28/53.

Step-by-step explanation:

[tex]sinD=\frac{FE}{DE} =\frac{28}{53} .[/tex]

Answer:

72

Step-by-step explanation:

9×8 = 72 which means that 72 is a multiple of 9 lying between 60 and 80.

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Answer:

14

Step-by-step explanation:

when two lines intersect, the opposite angles are equal: vertical angles rule

this means that 88 and 6x + 4 are the same, therefore we get the equation 6x+4 = 88.

subtracting 4 from both sides, we find that 6x = 84

we get our final answer by dividing each side of the equation by 6:

x = 14

Answer:

Medians: Using the methods previously described, the medians of each

group were found to be: Low: ( , ) Medium: ( . ) High: ( . ) Use these points to find the equation of the median fit regression line. Slope: What is the slope of the median regression line? m = Jig—y" = (Round to the nearest H—xL hundredth.) Y-lntercept: What is the y-intercept of the median regression line? kW _ 3 b _ (33—(—U.01)(2300))+(27—(—0.01)(3350))+(19—(—U.01)(4400)) _ 3 m (Round to the nearest hundredth.) Regression Line: The equation of the median regression line isy= x+

The equation of the perpendicular line to the given line is: y = -5/4x - 30.

The slope values of two perpendicular lines are negative reciprocal of each other.

Given that the line is perpendicular to y = 4/5x+23, the slope of y = 4/5x+23 is 4/5. Negative reciprocal of 4/5 is -5/4.

Therefore, the line that is perpendicular to it would have a slope (m) of -5/4.

Plug in m = -5/4 and (x, y) = (-40, 20) into y = mx + b to find b:

20 = -5/4(-40) + b

20 = 50 + b

20 - 50 = b

b = -30

Substitute m = -5/4 and b = -30 into y = mx + b:

y = -5/4x - 30

The equation of the perpendicular line is: y = -5/4x - 30.

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Answer:

[tex]a = 18 \sqrt{3} [/tex]

[tex]c = 36[/tex]

The explicit formula for the sequence is an = 5 + (n - 1)(-4)

The formula for calculating the nth term of an arithmetic sequence is expressed as:

an = a + (n - 1)d

where

a is the first term

d is the common difference

n is the number of terms

From the given data

a = 5

a2 = a1 - 4

a2 = 5 - 4

a2. = 1

d = a2 - a

d = 1 - 5

d = -4

Substitute

an = 5 + (n - 1)(-4)

Hence the explicit formula for the sequence is an = 5 + (n - 1)(-4)

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Answer:

[tex] \pink{ \rule{1pt}{3000000pt}}[/tex][tex] \red{ \rule{1pt}{3000000pt}}[/tex][tex] \purple{ \rule{1pt}{3000000pt}}[/tex]

Answer:

24 unit²

Step-by-step explanation:

use Pythagoras to calculate the height of triangle

which gives you 6 √100-64

then half hight x base

the average cost per class is $14.

Think of this as an algebraic equation, which would be expressed as 40+10s=total cost

The (s) would be the number of spinning classes you decide to take.

Therefore to find the average cost of the class, you would plug in 10 classes for s.

This brings the total cost to $140 dollars.

To find the average you must divide this cost by the number of classes you took.

This will be the price per class, which is $14.

Statement of the equality of two expressions formulated by way of making use of a set of variables the algebraic operations, particularly, addition, subtraction, multiplication, department, elevating to energy, and extraction of a root.

In arithmetic, an algebraic equation or polynomial equation is an equation of the form P=0 where P is a polynomial with coefficients in some area, regularly the field of rational numbers.

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Answer:

$63422.42

Step-by-step explanation:

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Answer:

Step-by-step explanation:

Is there a graph or more information?

can I get your number personally

Answer: D. It is the graph of f translated 3 units up and 7 units to the right

Step-by-step explanation:

the +3 part of the equation makes the function translated vertical 3 units

then the x - 7 part makes it translate horizontal to the right 7 units (always the opposite of the sign)

because when

x-7=0,

x=7

The distance travelled by the train with constant speed of r miles will be 3r.

We know the formula of distance linking the speed and the time.

Distance = speed × time

Substituting the given values to get:

Distance = r × 3

Distance = 3r

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