what is the area of the shaded portion of the figure above

Answer:

(y-5)^2=14(x+7/2)

Step-by-step explanation:

The equation for a parabola with a focus at (0,5) and a directrix at x = -7 is (y - 5)² = 14 (x + 3.5).

A parabola is a two dimensional figure on a plane which is U shaped and any point on the parabola is at an equal distance from a fixed point called focus and a fixed line called directrix.

Given,

Focus of the parabola at (0, 5).

Directrix is x = -7.

The parabola is horizontal parabola since the directrix is a vertical line.

Equation of the parabola is of the form,

(y - k)² = 4p (x - h)

Here (h, k) is the vertex.

Vertex of the parabola is the mid point of focus (0, 5) and the point (-7, 5).

(h, k) = ([tex]\frac{0 + -7}{2}[/tex], 5) = (-7/2, 5)

Now, p is the distance from vertex to focus.

p = 0 - -7/2 = 7/2 = 3.5

So the equation is,

(y - 5)² = 4× 3.5 (x - -3.5)

(y - 5)² = 14 (x + 3.5)

Hence the equation is (y - 5)² = 14 (x + 3.5).

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Answer:

d=90°

e=81°

f=99°

Step-by-step explanation:

To find f

180-81

=99

Answer:

d = 90°

e = 81°

f = 99°

Step-by-step explanation:

Have a nice day!

Answer:

Papyrus

Step-by-step explanation:

the one that's not right is the 3rd one

Answer:

C) {6+√43, 6-√43}

Step-by-step explanation:

Applying,

x = [-b±√(b²-4ac)]/2a.................... Equation 1

From the question,

Given: a = 1, b = -12, c = 7

Substitute these values into equation 1

x = [-(-12)±√(-12²+4×1×7)]/2×1

x = [12±√(144+28)]/2

x = [12±√172]/2

either,

x = (12-√172)/2

x = (12-2√43)2

x = (6+√43)

or

x = (12+√172)/2

x = (12+2√43)/2

x = (6+√43)

Hence,

The right answer is C). {6+√43, 6-√43}

Step-by-step explanation:

18 and 5 are both missing if that's what you mean

Answer:

D. 360

Step-by-step explanation: It's being multiplied by plus one more every time you move on to a new term.

So 2*3=6, 6*3=18, 18*4=72, 72*5=360

Answer:

a

Step-by-step explanation:

[tex]\frac{3x}{x-1}[/tex] + [tex]\frac{8}{x-1}[/tex]

These fractions have a common denominator and so do not require to be altered.

The numerators can be added to simplify, that is

= [tex]\frac{3x+8}{x-1}[/tex]

The remaining fractions have different denominators and would require to be altered before they could be added.

Answer: if its 87% then its 0.87, but if its 87 then its 87.00

Step-by-step explanation: I'm doing these questions for a challenge :D

Answer:

Nelly should take out the pies after 64 mins or an hour and four minutes.

Step-by-step explanation:

Answer:

2 hours!

Step-by-step explanation:

Answer:

1. 22

2. 7*3=21

3. 2

4. 8

Step-by-step explanation: (I am not sure what level math you are as you put HS but I used simple algebra in my answers)

1. Using algebra I put the missing variable as x.

"add 5 to me" is x+5.

"divide by 9, you get 3"

[tex]\frac{x+5}{9}[/tex] = 3

Begin solving by multiplying 9 to the 3 on the other side

x+5 = 27

Subtract 5 to get x by itself

x = 22

2. An equivalent multiplication sentence can be found using algebra.  

21 ÷ 7 = 3 can be rewritten as [tex]\frac{21}{7} =3[/tex]

Using algebra we know if we multiply 7 onto both sides we end up with

7*3=21

3.

Combined total of 16 fumbles

8 players

Same amount of fumbles

How many fumbles per player?

I would draw this out. You have 8 players and 16 fumbles to allocate to them. You can draw tallies and allocate them to each player. You'll find that the first time they all have the equal amount is when they all have 1 fumble. The next time they all have an equal amount they'll have 2 per and all 16 will be used.

4. Algebra

[tex]\frac{x * 7 - 2}{6} =9[/tex]

First is multiplication: x*7 = 7x

[tex]\frac{7x - 2}{6} =9[/tex]

Then division: Multiply the 6 over because we don't like fractions

[tex]{7x - 2} = 54[/tex]

Next we add the 2 over

[tex]{7x } = 56[/tex]

Then divide by 7 to solve for x

x=8

About what percentage of people had a score between Janine's and Laura's scores?

Answer:

Its D) 36%

Answer: A

Step-by-step explanation:

I took the test

Answer: 106 km/h,2.5 hr

Step-by-step explanation:

Given

The train travels 315 km in the same time car travels 265 km

The average speed of the train is 20 kmph faster than car

Suppose, speed of the car is v and it travels 265 km in t hours

[tex]\therefore \dfrac{315}{v+20}=\dfrac{265}{v}\\\\\Rightarrow 315v=265\left (v+20\right)\\\\\Rightarrow 315v=265v+5300\\\Rightarrow 50v=5300\\\Rightarrow v=106\ km/h[/tex]

Time taken to travel is

[tex]\Rightarrow t=\dfrac{265}{106}}\\\\\Rightarrow t=2.5\ h[/tex]

Answer:

1. 2 runners

2. 25 runners

3. 24%

4. 15 runners

5. 60%

6. uh I think it's asking the same thing as 3, so 24%?

Answer:

120

Step-by-step explanation:

Answer:

Step-by-step explanation:

negative 5 is less then -3 is the statement. so saying that -3 is less than five, is false.

remember your number line.

-5_-4_-3_-2_-1_0_1_2_3_4_5_6

five sure is to the left of three, and saying that three is to the right of five is the exact same thing.

Answer:

- x= 10-6y+y²

Step-by-step explanation:

|x-1|=3-y

(|x-1|)²=(3-y)²

x-2x+1=9-6y+y²

-x=9-6y+y²+1

Answer:

I believe 188.68

Answer:

188.68

Step-by-step explanation:

first we divide 11/100 =0.11 then 0.11*212= 23.32

then 212-23.32= 188.68

Answer:

ioujyghfdgtrssssfhyjukh

Step-by-step explanation:

Answer:

A: x<7/12

Step-by-step explanation:

I hate math too :)

The sign wouldn't be flipped cause you don't have to divide, and 5/6 - 1/4 is 7/12. Hope this helps

Answer:

it's 10 cemetery in a two way too far and far from a lot for

The volume of irregular solid is 45239 mm^3

Given
 for cylinder,
radius = 6mm and length = 400 mm

Volume, is defined as the ratio of the mass of object to its density.

since if the cylinder is melted to sphere the volume remains the constant
so.
volume of an irregular solid = volume of cylinder
= πr^2l
= 3.14 x 6^2 x 400
= 45239 mm^3

Thus, the required volume of of irregular solid is 45239 mm^3

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Answer:

the term arc is used for a portion of a circle along its circumference. The size of the arc is usually given by the size of the angle subtended by the arc at the center or the length of the arc. The angle subtended at the center is also known as the angle measure of an arc or informally the arc measure.

Step-by-step explanation:

Answer:

A) 64°

Step-by-step explanation:

By intersecting secants theorem:

[tex] m\angle ACB = \frac{1}{2} (m\widehat {AS} - m\widehat {BD}) [/tex]

[tex] 35\degree = \frac{1}{2} (134\degree - m\widehat {BD}) [/tex]

[tex] 70\degree =134\degree - m\widehat {BD} [/tex]

[tex] m\widehat {BD} =134\degree - 70\degree[/tex]

[tex] m\widehat {BD} =64\degree[/tex]

Answer: C) The mean will increase more than the median, but both will increase.

Step-by-step explanation:

I got it right already! :)

The solution is, The mean will increase more than the median, but both will increase.

[third option listed]

In statistics and probability theory, the median is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution. For a data set, it may be thought of as "the middle" value.

here, we have,

the median of a data set is the number in the middle [when listed from lowest to highest in value]

1 2 3 4 5 6 7 8 9 10 11 12 13

is the current median

let's consider what adding 12 would mean--it would mean that we move the median slightly higher [further along in the data set] because there are more numbers (but let's try this out to confirm:)

1 2 3 4 5 6 7 8 9 10 11 12 12 13

[if a median placement is shared between two numbers, the mean/average of those two numbers is taken, and that is considered to be the median]

so, 7.5 is the current median

(this is an increase of 0.5)

the mean of a data set is what we commonly refer to as the "average"

[you find this value by adding all of the numbers in the data set together and dividing by the number of terms in the data set]

1 2 3 4 5 6 7 8 9 10 11 12 13

mean of original data set:

1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 [= 91]

_______________________________________

                                   13

[91 ÷ 13 = 7]

because our number is greater than our original mean [12 > 7], we know that the mean must increase:

[91 + 12 = 103]

[103 ÷ 14 ≈ 9.36]

[we had an increase of 2.36]

so, median increased by 0.5, mean increased by 2.36

so, both values increased, whilst the mean increased by more than the median [as to be expected]

so, we get,

"The mean will increase more than the median, but both will increase." [third option listed]

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Answer:

127.2

Step-by-step explanation:

The area of a semicircle is:

[tex]\frac{\pi r^{2} }{2}[/tex]

So to figure it out we first find the diameter:

18÷2=9

Then we plug it into the equation

[tex]\frac{9^{2}\pi }{2} = \frac{81\pi}{2}[/tex] Which we can put into a calculator to get 127.2345... so we round to 1 d.p to get our answer, 127.2 (the fifth digit, 3, rounds down)

Answer:

8x+14

Step-by-step explanation:

Answer:

The answer is 89.22

Step-by-step explanation:

Answer:1

Step-by-step explanation:

because 1 devided by 3 is 3 and 1 devided by 25 is 5

=======================================================

Work Shown:

A = pi*r^2

A = 3.14*8^2

A = 200.96

Note that the radius r = 8 is half of the diameter d = 16. I'm using the approximation pi = 3.14, which means the area is approximate. To get a more accurate answer, use more decimal digits of pi. The units of the area are in square feet, which can be written as "sq ft" or as "ft^2".