What is the standard form equation of an ellipse that has vertices (−2,−18) and (−2,8) and foci (−2,−14) and (−2,4)?

[tex]number \: of \: movies = 3 \\ permutations = 2 \\ \\ c( \gamma ) = 2! \times 1 = 2 \: ways[/tex]

[tex]g(1) \: \: \: \: g(2) \: \: \: \: nc(17) \\ g(2) \: \: \: \: g(1) \: \: \: \: nc(17)[/tex]

The only ordered pair that is a solution to the given system of equations is (-2, -6)

From the question, we are to determine if each ordered pair is a solution to the given system of equations

The given system of equations is

-9x + 2y = 6

5x - 3y = 8

That is,

x = 7, y = 9

Putting the values into the first equation

Is -9(7) + 2(9) = 6

-63 + 18 = 6

-45 ≠ 6

Thus, (7,9) is not a solution

That is,

x = 0, y = 3

Putting the values into the first equation

Is -9(0) + 2(3) = 6

0 + 6 = 6

6 = 6

The ordered pair satisfies the first equation

Testing for the second equation

Is 5(0) - 3(3) = 8

0 - 9 = 8

-9 ≠ 8

Thus, (0, 3) is not a solution

That is,

x = 5, y = -4

Putting the values into the first equation

Is -9(5) + 2(-4) = 6

-45 - 8 = 6

-53 ≠ 6

Thus, (-5,4) is not a solution

That is,

x = -2, y = -6

Putting the values into the first equation

Is -9(-2) + 2(-6) = 6

18 - 12 = 6

6 = 6

The ordered pair satisfies the first equation

Testing for the second equation

Is 5(-2) -3(-6) = 8

-10 + 18 = 8

8 = 8

The ordered pair satisfies the second equation

∴ The ordered pair that is a solution to the system of equations is (-2, -6)

Hence, the only ordered pair that is a solution to the given system of equations is (-2, -6)

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The amplitude of function f(x)=cos(2x) is 1 and the period is 2.

Given that the function of x is f(x)=cos(2x).

We are required to find the value of amplitude and period of function f(x) which is given in the question.

Amplitude basically refers to maximum displacement from the equilibrium that an object in periodic motion show. It is a product analytics platform or term that helps businesses to track visitors with the help of collaborative analytics.

Period is basically the time interval between two waves. A function  that repeats its values at regular intervals or periods is known as periodic function.

The amplitude of f(x)=cos(2x) is 1 because the highest value that cos Θ can give 1. We can also see in graph that the value of cos 2x is going to 1 and starts decreasing again.

The period of f(x) is 2. From the graph we can say that the vertical distance between upper point and lower point is 2.

Hence the amplitude of function f(x)=cos(2x) is 1 and the period is 2.

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ANSWER: 480 out of 1200 were taken at the Honolulu Zoo.

The false statement is given by:

c. If b×b=c, then c is even integer.

Hence, since b is odd, b x b = c is odd, hence statement c is false.

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Answer:

Percent increase is 70%.

Step-by-step explanation:

The original price was $110. That will go on the bottom (denominator) in our calculation. On the top (numerator) we put the change in the dollar amount. The new price is $187. So we'll subtract:

187 - 110

= 77

The change in price was $77.

change/original

= 77/110

= 0.7

Change the decimal answer to a percent by multiplying by 100.

0.7 × 100

= 70%

The percent increase is 70%.

The mean average of push ups Sasha does in 5 days is 26.2.

Mean average = Total push ups done / number of days

= (22 + 36 + 21 + 25 + 27) / 5

= 131 / 5

= 26.2

Therefore, the mean average of push ups Sasha does in 5 days is 26.2.

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Step-by-step explanation:

there is a nice formula for the height in a right-angled triangle :

h = sqrt(p×q)

h being the height to the 90° angle, p and q being the segments (left and right of the height) of the Hypotenuse.

so, in our case

x = sqrt(25×144) = 5×12 = 60

Answer:

Step-by-step explanation:

If two triangles are similar, their corresponding sides will be k times greater or smaller, where k is the scale factor.

We have two corresponding sides given, 6 and 24 or 6k. Using this info, find the value of k:

The other sides of the larger triangle are:

The perimeter is the sum of sides:

Step-by-step explanation:

x+x+10+50=180

2x+60=180

2x=180-60

2x=120

x=120/2

x=60

144π cm²

Answer:

Solution given:

diameter (d)= 12cm

radius (r)=12/2=6 cm

slant height(l)=18cm

Now

Total surface area of cone=πr(r+l)π*6(6+18)=144π cm²

[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]

[tex]\qquad❖ \: \sf \:y + a = 180[/tex]

( linear pair )

[tex]\qquad❖ \: \sf \:y + 40 = 180[/tex]

[tex]\qquad❖ \: \sf \:y = 180 - 40[/tex]

[tex]\qquad❖ \: \sf \:y = 140 \degree[/tex]

And

[tex]\qquad❖ \: \sf \:x = a +( 180 - b)[/tex]

( Exterior angle = sum of opposite interior angles )

[tex]\qquad❖ \: \sf \:x = 40 + (180 - 61)[/tex]

[tex]\qquad❖ \: \sf \:x = 40 + 119[/tex]

[tex]\qquad❖ \: \sf \:159 \degree[/tex]

[tex] \qquad \large \sf {Conclusion} : [/tex]

Answer:

[tex]\sf 2\dfrac{1}{4}\ cups \ of \ sugar[/tex]

Explanation:

Let the full batch be x

Here given:

3/4 cup of sugar required to make 1/3 batch of cookies

Build equation:

[tex]\sf \rightarrow \dfrac{1}{3}x = \dfrac{3}{4} \ cup \ of \ sugar[/tex]

Solve:

[tex]\sf \rightarrow x = \dfrac{3(3)}{1(4)}[/tex]

[tex]\sf \rightarrow x = \dfrac{9}{4}[/tex]

[tex]\rightarrow \sf x = 2\dfrac{1}{4}[/tex]

Answer:

2 2\3 cups of sugar.

Step-by-step explanation:

Answer:

y = [tex]\frac{24}{\sqrt{x} }[/tex]

Step-by-step explanation:

given y varies inversely as [tex]\sqrt{x}[/tex] then th equation relating them is

y = [tex]\frac{k}{\sqrt{x} }[/tex] ← k is the constant of variation

to find k use the condition y = 8 when x = 9 , then

8 = [tex]\frac{k}{\sqrt{9} }[/tex] = [tex]\frac{k}{3}[/tex] ( multiply both sides by 3 to clear the fraction )

24 = k

y = [tex]\frac{24}{\sqrt{x} }[/tex] ← equation of variation

Answer:

  x-intercept: (4, 0)

  y-intercept: (0, 3)

Step-by-step explanation:

The intercepts of the equation can be found by setting each variable to zero and solving for the other. The graph will be a line through the intercept points.

Setting x=0 and solving for y, we have ...

  4y -12 = 0   ⇒   y = 12/4 = 3

Setting y=0 and solving for x, we have ...

  3x -12 = 0   ⇒   x = 12/3 = 4

The intercepts are ...

  x-intercept: (4, 0)

  y-intercept: (0, 3)

The line will go through these intercept points.

Answer:

cos(x)

Step-by-step explanation:

(1 + cos(x))(1 - cos(x)) = 1 - cos²(x) = sin²(x)

sqrt(sin²(x)) = sin(x)

sin'(x) = cos(x)

The expression is simplified to give 2 ( m² + m + 2Im ) = 0

Given the expression;

(1+m)²= (1-m)²+ 4lm,​

Expand the expression

( 1 +m) ( 1 + m) = ( 1 + m) ( 1 - m) + 4Im

1 + m + m + m² = 1 - m + m - m² + 4Im

collect like terms

1 + 2m + m² = 1 - m² + 4Im

1 - 1 + m² + m² + 2m + 4Im

2m² + 2m + 4lm = 0

simplify

2 ( m² + m + 2Im ) = 0

Thus, the expression is simplified to give 2 ( m² + m + 2Im ) = 0

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Answer:

Raphael's tomato sauce has too much garlic.

Step-by-step explanation:

We can use ratios to solve

Emily:

15 cloves

----------------

6L

2.5 Cloves per Liter

Raphael

25 cloves

----------------

9 L

2.7777(repeating) cloves per liter

Raphael has more garlic per liter

Answer:

B

Step-by-step explanation:

perfect tomato sauce

15 cloves → 6 L ( multiply both parts by 1.5 )

22.5 cloves → 9 L← Raphael's tomato sauce

since he used 25 cloves of garlic , then

Emily would think Raphael's sauce has too little garlic

The least number of colors needed to correctly color in the sections of the given picture so that no two touching sections have the same color is 5.

Let's say we begin with a single triangle. This triangle will be the first of a series of seven subsequent triangles, none of which will have any portions contact. If a square were the initial shape, then there are five shapes—three of which are squares and the other two are triangles—that don't have any touching portions. Given that a square takes up twice as much room, this value is probably lower, but location also matters. Therefore, for the given figure, the least number of colored areas you can color in that yet meet the required criteria is 5.

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Step-by-step explanation:

"congruent" for lines simply means they are equally long.

15. yes. AB = EF = 3

16. yes. BD = DF = 8

17. no. AC = 5, CD = 6

18. yes. AC = DE = 5

19. no. BE = 13, CF = 14

20. no. CD = 6, DF = 8

Answer: 111

Step-by-step explanation:

Angles in a quadrilateral add to 360 degrees, so:

[tex]121+58+70+x=360\\\\x=111[/tex]

Answer:

111

Step-by-step explanation:

The sum of interior angles in a triangle is equal to 360:

121 + 58 + 70 + x = 360 add like terms

249 + x = 360 subtract 249 from both sides

x = 111 is the measure of the angle represented with x

Answer:

converge

Step-by-step explanation:

the reason is : the individual terms of the series get smaller and smaller towards 0, and therefore the sum converges to a certain limit.

why do I know that the individual terms get smaller and smaller ?

because the terms are ultimately (with n getting very large the constant factors added constants become irrelevant)

n / (n^(3/2))

as sqrt(n³) = n^(3/2)

and n^(3/2) progresses much faster and stronger than n (or n¹), as 3/2 is larger than 1.

so, the denominator (bottom) of that fraction grows stronger than the numerator (top), and the terms go therefore against 0 with larger and larger n.

Answer:

300 tarts

Step-by-step explanation:

we must solve this equation by going backwards

3/4 of something (as 1/4 was given away) is 150

150 / 3/4 is what you must do

or

150 * 4/3

that is

200

3/5 was sold so 2/5 was left

2/5 of something is 200

200 / 2/5

200 * 5/2

that is

500

3/5 of that was sold

so

500 * 3/5 is 300

300 tarts were sold

The exponential equation modeling this relationship is given as follows:

f(x) = 8(0.5)^x.

An exponential equation is modeled by:

f(x) = a(b)^x

In which:

For this problem, we have that when x = 0, y = 8, hence a = 8. Then:

f(x) = 8(b)^x.

When x = 1, y = 4, hence b is found as follows:

f(x) = 8(b)^x.

4 = 8b

b = 0.5.

Hence the equation is:

f(x) = 8(0.5)^x.

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The examples of insurable interest is an employer under certain arrangements.

Insurable interest is a investment that protects anything subject to a financial loss. A person or entity has an insurable interest in an item, event, or action when the damage or loss of the object would cause a financial loss or other hardshapes. In order to have an insurable interest a person or entity would take out an insurance policy protecting the person,item, or event in question. The insurance policy is able to  mitigate the risk of loss if something happens to the asset-like becoming damaged or lost.

Examples of insurable interest are:

Hence the examples of insurable interest is an employer under certain arrangements.

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Answer: Insurable interest means you must have a financial stake in the risk being insured. You can’t claim insurance for a risk that you don’t face directly.

If Rob’s dad’s car is stolen, his father will receive the insurance money, not Rob.

Step-by-step explanation: Edmentum

Answer:

Step-by-step explanation:

3.5805

The length of the new base is 26.56 inches or [tex]26\frac{14}{25}[/tex] inches. Using the area of a right triangle, the required base is calculated.

The area of the right triangle is given by

A = [tex]\frac{1}{2}[/tex] × b × h sq. units

Where A -area; b -base; h -height;

It is given that,

The right triangle has a base of length b = 8 1/2 = 8.5 inches and a height of length h = 12 1/2 = 12.5 inches.

So, its area is

A = [tex]\frac{1}{2}[/tex] × 8.5 × 12.5 = 53.125 sq. inches

When the height of the right triangle is reduced to 4 inches,

53.125 = [tex]\frac{1}{2}[/tex] × b × 4

⇒ b = 53.125/2

∴ b = 26.56 or [tex]26\frac{14}{25}[/tex] inches

Thus, the length of the new base is 26.56 or [tex]26\frac{14}{25}[/tex] inches.

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Question 14

Part (a)

[tex]\frac{46800-41400}{4700} \approx \boxed{1.15}[/tex]

Part (b)

[tex]-2.57=\frac{x-41400}{4700} \\ \\ -2.57(4700)=x-41400 \\ \\ x=41400-2.57(4700) \\ \\ x \approx \boxed{29300}[/tex]

Answer:

c subtract 5 from both sides

Answer:

1.f(x)=2x-5

i will take the set {-2,-1,0,1,2}

f(-2)=2(-2)-5

=-4-5

=-9

f(-1)=2(-1)-5

=-2-5

=-7

f(0)=2(0)-5

=-5

f(1)=2(1)-5

=-3

f(2)=2(2)-5

=-1

so the coordinates of the function is {-9,-7,-5,-3,-1}

2.f(x)=-3x+6

i will the take the set {-2,-1,0,1,2} too

f(-2)=-3(-2)+6=6+6=12

f(-1)=-3(-1)+6=3+6=9

f(0)=-3(0)+6=6

f(1)=-3(1)+6=-3+6=3

f(2)=-3(2)+6=-6+6=0

{12,9,6,3,0}

3.f(x)=2/3.x+4

{-2,-1,0,1,2}

f(-2)=2/3(-2)+4=-4/3+4=(-4+12)/3=8/3

f(-1)=2/3(-1)+4=-2/3+4=(-2+12)/3=10/3

f(0)=2/3(0)+4=4

f(1)=2/3(1)+4=2/3+4=(2+12)/3=14/3

f(2)=2/3(2)+4=4/3+4=(4+12)/3=16/3

{8/3,10/3,4,14/3,16/3}

you're can graph those coordinates

actually you can take other coordinates...

CMIIW

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