1. Find the equation of the parabola satisfying the given conditions.

Focus: (3,6); Directrix: x=−1

A. (x−1)2=8(y−6)

B. (y−6)2=8(x−1)

C. (x−1)2=−8(y−6)

D. (y−6)2=−8(x−1)


2. Find the equation of the parabola satisfying the given conditions.

Focus: (−6,3); Directrix: y=1

A. (y−2)2=4(x+6)

B. (x+6)2=4(y−2)

C. (x+6)2=−4(y−2)

D. (y−2)2=−4(x+6)


3. Find the equation of an ellipse that has foci at (−1,0) and (4,0), where the sum of the distances between each point on the ellipse and the two foci is 9.

A. (x+1)2+y2−−−−−−−−−−−√+(x−4)2+y2−−−−−−−−−−−√=9

B. (x−1)2+y2−−−−−−−−−−−√+(x+4)2+y2−−−−−−−−−−−√=9

C. (x+1)2+y2−−−−−−−−−−−√+(x−4)2+y2−−−−−−−−−−−√=81

D. (x−1)2+y2−−−−−−−−−−−√+(x+4)2+y2−−−−−−−−−−−√=81


4. Find the equation of a hyperbola that has foci at (−1,0) and (4,0), where the difference of the distances between each point on the ellipse and the two foci is 5.

A. (x+1)2+y2−−−−−−−−−−−√−(x−4)2+y2−−−−−−−−−−−√=25

B. (x−1)2+y2−−−−−−−−−−−√−(x+4)2+y2−−−−−−−−−−−√=5

C. (x−1)2+y2−−−−−−−−−−−√−(x+4)2+y2−−−−−−−−−−−√=25

D. (x+1)2+y2−−−−−−−−−−−√−(x−4)2+y2−−−−−−−−−−−√=5

Answer:

[tex]\frac{4}{15}[/tex]  (4/15)

Step-by-step explanation:

[tex]\frac{4}{6}=\frac{2}{3}[/tex]

[tex]\frac{2}{5}*\frac{2}{3};[/tex]

1- Multiply the numerators:

[tex]2*2=4[/tex]

2- Multiply the denominators:

[tex]5*3=15[/tex]

3- Thus:

[tex]\frac{2}{5}*\frac{2}{3}= \frac{4}{15}[/tex]

Hope this helps ;)

Answer:  the answer is 9.9

Step-by-step explanation:

Answer:

[tex]4\frac{5}{12}[/tex]

Step-by-step explanation:

[tex]4\frac{3}{4} -\frac{1}{3} \\\\\frac{19}{4} -\frac{1}{3} \\\\\frac{57}{12} -\frac{4}{12} \\\\\frac{53}{12} \\\\4\frac{5}{12}[/tex]

Answer:

leon's older brother is 4 5/12 feet tall

Step-by-step explanation:

4 3/4 - 1/3

= 4 5/12

Answer:

3

Step-by-step explanation:

5/2 ÷ 5/6 = 5/2 × 6/5

5/2 × 6/5 = 30/10 or 3

Answer:

He should have done 8^2 + 15^2= x^2 because the hypotenuse is always the longest side and in Pythagorean theorem C represents the longest side

[tex] {x}^{2} = {(8)}^{2} + {(15)}^{2} [/tex]

[tex] {x}^{2} = 64 + 225[/tex]

[tex] {x}^{2} = 289[/tex]

[tex]x = \sqrt{289} [/tex]

[tex]x = 17[/tex]

Both the stores together donated 65.5 dozen cookies.

Answer:

the answer is B on USA Prep

Step-by-step explanation:

"A potential outlier at (50, 12)" is the statement that best describes the data shown in the scatter plot.

A straight line that minimizes the gap between it and certain data is called a line of best fit. In a scatter plot containing several data points, a relationship is expressed using the line of best fit. It is a result of regression analysis and a tool for forecasting indicators and price changes.

Given:

The scatter plot shows the relationship between backpack weight and student weight.

From the given choices:

An outlier is a value that nowhere near the range of the data set.

From the scatter plot:

A potential outlier at (50, 12).

Therefore, a potential outlier at (50, 12).

To learn more about the line of the best fit;

https://brainly.com/question/14279419

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Answer:

x = [tex]25.8^{o}[/tex] and y = [tex]51.4^{o}[/tex]

Step-by-step explanation:

Known that he sum of angles on a straight line is [tex]180^{o}[/tex]. From the diagram;

2y + x + y = [tex]180^{o}[/tex]

x + 3y = [tex]180^{o}[/tex] ................ 1

Also,

2x + x + 2y = [tex]180^{o}[/tex]

3x + 2y = [tex]180^{o}[/tex] .............. 2

Using the elimination method, multiply equation 1 by 3 and equation 2 by 1

3x + 9y = 540 ............ 3

3x + 2y = [tex]180^{o}[/tex] ............. 4

7y = 360

y = [tex]\frac{360}{7}[/tex]

y = [tex]51.4^{o}[/tex]

substitute the value of y in equation 1,

x + 3y = [tex]180^{o}[/tex]

x + 3(51.4) = [tex]180^{o}[/tex]

x + 154.2 = [tex]180^{o}[/tex]

x = [tex]180^{o}[/tex] - 154.2

x = [tex]25.8^{o}[/tex]

Thus, x = [tex]25.8^{o}[/tex] and y = [tex]51.4^{o}[/tex]

Answer:

5

Step-by-step explanation:

Sue in 5 years would 20, meaning Mike would be 10. Subtract 5 from Mike to get their current age.

Answer:

Mike= 10 years old

Sue= 25 years old

Step-by-step explanation:

Let the present age of Sue be s years old, while that of Mike be m years old.

Present

s= m +15 -----(1)

In 5 years

Sue's age= s +5

Mike's age= m +5

Given that Mike would be ½ of Sue's age in 5 years,

m +5= ½(s +5)

Multiply both sides by 2:

2(m +5)= s +5

Expand:

2m +10= s +5

2m +10 -5= s

s= 2m +5 -----(2)

Substitute (1) into (2):

m +15= 2m +5

2m -m= 15 -5

m= 10

Substitute m= 10 into (1):

s= 10 +15

s= 25

Thus, the present age of Mike is 10 years old and the present age of Sue is 25 years old.

Answer: 608

Step-by-step explanation: multiply by 2

Answer:

402.1 in^2

Step-by-step explanation:

Find the area of the circle with the 18 in. radius first.

Formula for a circle is πr^2

So the area of the circle with the 8 in. radius is 1017.9 in^2

Now do the same for the 14 in. radius circle.

The area for the 14 in. radius circle is 615.8

Now subtract:

1017.9 - 615.8 =

402.1 in^2

hope this helped!

Answer:

4x^2 - 4x - 19

Step-by-step explanation:

Given the following functions

f(x) = 2x^2 - 4x - 3

g(x) = 2x^2 - 16

f(x)+ g(x) =2x^2 - 4x - 3+ 2x^2 - 16

f(x)+ g(x) = 2x^2+2x^2 -4x - 3 - 16

f(x)+ g(x) =4x^2 - 4x - 19

Hence the required sum is 4x^2 - 4x - 19

Answer:

divide the figure into two parts.

area of square = side²

area of square =12²

area of square =144

area pf trapezium =1/2×(a+b)×h

area of trapezium =1/2×(12+6)×12

area of trapezium =108

area of polygon=144+108=252 unit²

Answer:

Second One-

[tex] {5}^{14}. {5}^{ - 2} [/tex]

Fifth One-

[tex] {5}^{6} \: . \: {5}^{6} [/tex]

Sixth One-

[tex] \sqrt{ {5}^{24} } [/tex]

Seventh One-

[tex] {5}^{11} \: . \: 5 [/tex]

1: no solution

2: infinitely many solutions

3: one solution

Answer:

35

Step-by-step explanation:

subtract highest and lowest numbers

Answer:

C) 5x-70=105

Step-by-step explanation:

As marked in the graph, angle 105 and angle (5x-70) equal to each other because they are vertically opposite angles therefore we have equation C)

Answer:

6 apples

Step-by-step explanation:

3 apples cost $1.00

so for $2.00, 2x3÷1=6

hope it helps. plz mark me as brainliest.

Answer:

6 apples

Step-by-step explanation:

if three apples are 1 dollar then every time you add a dollar you would get three more apples

so it would look somthing like

1$ = 3 apples

2$= 6 apples

3$= 9 apples  

4$= 12 apples

so on

Answer:

44

Step-by-step explanation:

14x3.14 is 43.96 and that after being rounded to the nearest tenth becomes 44

Answer:

Step-by-step explanation:

volume of cone formula: V = 1/3 πr²h

r = 1/2 d

r = 1/2 (17.5)

r = 8.75 in

V = 1/3 (π8.75²)(18.5)

V = 1483.26 in²

Set up a ratio of height over shadow for each :

12/8 = 4/x

Cross multiply:

12x = 32

Divide both sides by 12:

X = 2 2/3 feet

The shadow is 2 2/3 feet.

Answer:

She will make a total commission of $1130+$325=$1445

Then 5% of $1445= $1445×5%=$72,75

Answer:

If rounded to the nearest tenth of a cubic foot, would be: 927587.2

Step-by-step explanation:

The equation of finding the equation of the volume of a sphere is "4π[tex]\frac{radius^{3} }{3}[/tex]"

If values are inserted in for radius as 60.5, the answer will be 927587.2 when rounded to the nearest tenths.

Hope this helps!

Answer:

y=-1/2x+4 Is your answer

Step-by-step explanation:

y=mx+b

3=2x+4

-1=2x

x=-1/2

You already know y is 4 so y=-1/2x+4

Answer:

226.19 inches

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

2,400 divided by 4 = 6

Answer:

x = 0

Step-by-step explanation:

hi there!

im not sure if the x between the 2's is a x as in a variable or if it is multiplication sign. im going to solve the problem as if it is a multiplication sign but if that is wrong then please let me know!

2 * 2 + x - 4 = 0

is our equation that we are working with ^

first step is, following the pemdas we multiply *2 with its self

( ^ parentheses, exponents, multiplication/ division making sure to solve it left to right, addition and subtraction still making sure to follow the left to right rule )

2 * 2 + x - 4 = 0

2 * 2

= 4 + x - 4 + 0

then we add positive 4 and negative 4 together, canceling eachother out the giving us the answer of  x = 0

4 + x - 4 + 0

4 + - 4 = 0

x = 0

i hope this helps you! have a good rest of your day :)

There are no possible positions for Ismael's house.

In this case, we need the following geometrical constructions:

1) Given that Ismael's house has the same distance from towns A and B, we must create a line segment between A and B and perpendicular line passing through the midpoint of line segment AB.

2) Since Ismael's house is 20 miles away from town C, we must create a circle centered at C.

All possible positions of Ismael's house are the set of points where both the perpendicular line and the circle intercepts each other. After making all operations defined above, we conclude that there are no possible positions for Ismael's house.

We kindly invite to check this question on line segments: https://brainly.com/question/23297288

Answer:

the answer is 18

Step-by-step explanation:

9X6=54

54/3=18

Answer:

18

Step-by-step explanation: