Garrett read 100 pages in his new mystery novel. The book has a total of 250 pages.
What percent of the book has Garrett read?

Answer:

The given equations are;

y = a·(x - h)² + k or y = a·x² + b·x + c

We have;

(x - h)² = 4·p·(y - k),

Where;

(h, k) are the x, and y coordinates of the vertex

p = The distance from the focus to vertex distance;

Comparing, we have;

y - k = a·(x - h)²

(y - k)/a = (x - h)²

(x - h)² = 4·p·(y - k)

4·p·(y - k) = (x - h)²

∴ 4·p = 1/a

p = 1/(4·a)

Therefore, the focus to vertex distance inversely proportional to the value of a

The distance of every point on the parabola is equidistant from the directrix and the focus

Therefore, the equation of the directrix is y = k - p

For example, we have;

y = 2·x² + 3·x + 1

h = -b/2a = -3/4

k = (4ac - b²)/4a = (4×2×1 - 3²)/(4×2) = -1/8

The coordinate of the focus is (h, k + p) = (-3/4, -1/8 + 1/8) = (-3/4, 0)

The directrix, y = k - p = -1/8 - 1/8 = -1/4

For a point x = 2, we have, y = 2·2² + 3·2 + 1 = 15

The coordinate of the point is (2, 15)

The distance of the point from the directrix = 15 - (-1/4) = 15 + 1/4 = 15.25

The distance of the point from the focus is √((2 - (-3/4))² + (15 - 0)²) = 15.25

Therefore, all points on the parabola have equal distances from the focus and the directrix

Step-by-step explanation:

Answer:

The answer is stan twice

Step-by-step explanation:

simple

Answer:

x=10

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Answer:

Yes. |8|+|-7| = 15

Step-by-step explanation:

the absolute cancels out the -, so it would mean that -7 is now positive 7, so yes it'd be 15

Answer:

Option (2)

Step-by-step explanation:

Arrow shown on the left hand side of the number line represents the inequality,

x < 5 [No sign of 'equal to' because arrow starts with a hollow circle]

Arrow given on the right hand side of the number line will represent,

x > 18

And these arrows represent the two solution areas of x, so the composite inequality that represents the graph will be,

x < 5 or x > 18

Option (2) will be the answer.

Answer:

3

Step-by-step explanation:

Let's isolate x on one side.

2x - x - 2/3x = -8+5+4

1/3x=1

x=3

Answer:

X = 3

Step-by-step explanation:

-8 + 2/3x + 4 = 2x - 5 - x

2/3x - 2x - x = -5 + 8 - 4

-1/3x = -1

x = -1 * -3

x = 3

Answer:

[tex]a=9[/tex]

Step-by-step explanation:

In this problem, you can use the Pythagorean Theorem ([tex]a^{2} +b^{2} =c^{2}[/tex]) to find what a is. The steps are shown below:

Steps (variables a, b, and c are in italics):

-You can rearrange the formula from the Pythagorean Theorem, which is[tex]a^{2} +b^{2} =c^{2}[/tex] to only get a because we want to know what a is.

Rearranged: [tex]a=\sqrt{c^{2}-b^{2} }[/tex] or [tex]a=-\sqrt{c^{2}-b^{2} }[/tex]  It has to ways/options for a because when finding the square root of a number, it can be either positive or negative. But in this problem, it’s going to be positive because we’re finding the length of something.

-Since we know what c and b are, you can plug them into the new formula:

[tex]a=\sqrt{15^{2}-12^{2} }[/tex]

-Simplify it:

[tex]a=\sqrt{225-144}[/tex]

-Subtract inside the radical:

[tex]a=\sqrt{81}[/tex]  Then simplify it to get [tex]a=9[/tex].

You can check your answer by putting a back into the original Pythagorean Theorem formula ([tex]a^{2} +b^{2} =c^{2}[/tex]):

Steps

-Plug a, b, and c into the formula [tex]a^{2} +b^{2} =c^{2}[/tex]:

[tex](9)^{2} +(12)^{2} =(15)^{2}[/tex]

-Simplify to get:

[tex]81+144=225[/tex]

-Add:

[tex]225=225[/tex]  This is very true. So our answer is correct.

ANSWER: [tex]a=9[/tex]

Sorry for the long explanation, but I hope you understand and that this helps with your question! :)

Answer:

Step-by-step explanation:

lets make is short and simple

Pythagorean theorem: a² + b² = c²

a² + 12² = 15²

a² = 15² - 12²

a = √81

a = 9

Answer:

$7 total

Step-by-step explanation:

$5 + $2 = $7

Answer:

$1368

Step-by-step explanation:

Income from dividends = price per share x number of dividends purchased

$3.42 x 400 = $1368

Answer:

The union of these sets is:

Step-by-step explanation:

Given the sets

The union of two sets K and L is the collection of elements that are in K or in L or in both K and L

The 'union' of two sets is denoted by the symbol 'U'.

Therefore, the union of these sets is:

Important Note: The duplicate or repeated elements of the sets are written only once.

Answer: (A)0.0024 Km (D) 240 cm, (E) 2,400 mm... Hope it helps, have a great day!

Step-by-step explanation:

The measurements that are equivalent to 2.4 meters are

0.0024km, 240cm and 2400mm.

The correct options are (A), (D) and (E).

Unit conversion is a process with multiple steps that involves multiplication or division by a numerical factor or, particularly a conversion factor.

A unit conversion expresses the same property as a different unit of measurement.

For instance, time can be expressed in minutes instead of hours, while distance can be converted from miles to kilometers, or feet, or any other measure of length.

Given,

measurement = 2.4 meters

1 meter = 1/1000 km

⇒ 2.4 meter = 2.4 /1000 = 0.0024 km

1 meter = 100 cm

⇒ 2.4 meters = 2.4×100 = 240 cm

1 meter = 1000 mm

⇒ 2.4 meters = 2.4×1000 = 2400 mm

Hence, 0.0024km, 240cm and 2400mm are the measurements that are equivalent to 2.4 meters.

Learn more about unit conversion here:

https://brainly.com/question/19420601

#SPJ2

come to your house to pick it lowest to go with D

Answer:

All of them have different answers so gonna say D because its only one number  

Step-by-step explanation:

Hope this helps

sorry If its wrong

Answer:n=-3.1

Step-by-step explanation:

2n + 3 = -3.2

Subtract 3 on both sides

2n+3-3=-3.2-3

2n=-6.2

Divide 2 on both sides

2n/2=-6.2/2

n=-3.1

Answer:

n= -3.1

Step-by-step explanation:

hope this helps have a nice day :)

Answer:

$31.56

Step-by-step explanation:

$9.85 × 4 = $39.40

$39.40 25% off is $29.55

6.75% rounded to the nearest cent 6.80%

Sales tax is $2.01

$29.55 + $2.01 = $31.56

Answer:

Step-by-step explanation:

2x^2-2x^3+3x

Answer:

Step-by-step explanation:

Add them together

-2[tex]X^3[/tex] + 2[tex]X^2[/tex] + 3x

Answer:

FV= $712.88

Step-by-step explanation:

Giving the following information:

Initial investment (PV)= $500

Number of periods (n)= 12 years

Interest rate (i)= 3% compounded annually

To calculate the future value, we need to use the following formula:

FV= PV*(1+i)^n

FV= 500*(1.03^12)

FV= $712.88

Answer:

25%

Step-by-step explanation:

Because she divided it

Answer:

[tex]c + h = 5[/tex] and

[tex]0.75c + 1.10h = 4.55[/tex]

Step-by-step explanation:

Assume that Mike bought only cookies and hot dogs.

The total can be represented as:

[tex]Cookies + Hot\ Dogs = 5[/tex] --- (1)

And the amount spent can be represented as:

[tex]Cost\ of\ cookies + Cost\ of\ hot\ dogs = 4.55[/tex] --- (2)

Required

Determine the system of equation

Let c represents the number of cookies and h, number of hot dogs.

[tex]Cookies + Hot\ Dogs = 5[/tex] implies [tex]c + h = 5[/tex]

And

[tex]Cost\ of\ cookies + Cost\ of\ hot\ dogs = 4.55[/tex]

Cost of cookies = 0.75 * c

Cost of hot dogs = 1.10 * h

So, we have:

[tex]0.75c + 1.10h = 4.55[/tex]

Hence, the equations are:

[tex]c + h = 5[/tex] and

[tex]0.75c + 1.10h = 4.55[/tex]

Solving for c and h

Make c the subject in [tex]c + h = 5[/tex]

[tex]c = 5 - h[/tex]

Substitute 5 - h for c in [tex]0.75c + 1.10h = 4.55[/tex]

[tex]0.75(5- h) + 1.10h = 4.55[/tex]

[tex]3.75- 0.75h + 1.10h = 4.55[/tex]

[tex]3.75 +0.35h = 4.55[/tex]

Collect Like Terms

[tex]0.35h = 4.55 - 3.75[/tex]

[tex]0.35h = 0.8[/tex]

Solve for h

[tex]h = 0.8/0.35[/tex]

[tex]h = 2.28571428571[/tex]

[tex]h =2[/tex] -- approximated

Recall that:

[tex]c = 5 - h[/tex]

[tex]c = 5 - 2[/tex]

[tex]c =3[/tex]

Answer:

Quadrant III and Quadrant I

Step-by-step explanation:

Answer:

Zero; 0

Step-by-step explanation:

(-5+5)/(18+2) = 0

Answer:

1,000,000 times larger

Step-by-step explanation:

2 x [tex]10^{8}[/tex] = 200,000,000

2 x [tex]10^{2}[/tex] = 200

200,000,000 divided by 200 is 1,000,000

It can also be solved by subtracting the exponents from 10. Then dividing the two number being put the scientific notation.

[tex]10^{8} - 10^{2}[/tex] = [tex]10^{6[/tex]

2 ÷ 2 = 1

Now solve:

1 x [tex]10^{6[/tex] = 1,000,000

Answer:

f(x)=x+6

-2+6

4

when x=0

0+6

6

when x=5

5+6

11

Step-by-step explanation:

Answer:

0+5

Step-by-step explanation:

Hope this helps. :)

Given:

Consider the pentagon MVEDR is dilated with the origin as the center of dilation using the rule [tex](x,y)\to(\dfrac{2}{3}x,\dfrac{2}{3}y)[/tex] to create pentagon M'V'E'D'R'.

To find:

The correct statement.

Solution:

If a figure dilated by factor k, then the rule of dilation is

[tex](x,y)\to (kx,ky)[/tex]

Here,

If k>1, then the image is larger than the original figure.

If k<1, then the image is smaller than the original figure.

We have,

[tex](x,y)\to(\dfrac{2}{3}x,\dfrac{2}{3}y)[/tex]

Here, M'V'E'D'R' is image and MVEDR is original figure. The scale factor is

[tex]k=\dfrac{2}{3}<1[/tex]

Pentagon M'V'E'D'R' is smaller than pentagon MVEDR because the scale factor is less than 1.

Therefore, the correct option is B.

  Option (B). Pentagon M'V'E'D'R' is smaller than pentagon MVDER because the scale factor is less than 1.

           image point formed will follow the rule,

           (x, y) → (kx, ky)

            If k < 1, image will be smaller than the preimage.

Given in the question,

Rule for the transformation → [tex](x,y)\rightarrow (\frac{2}{3}x,\frac{2}{3}y)[/tex]

Here, [tex]k=\frac{2}{3}[/tex] which is less than 1.

      Therefore, image pentagon M'V'E'D'R' will be smaller than the original pentagon MVDER.

      Option (B) will be the correct option.

Learn more about the transformation of a figure here,

https://brainly.com/question/2298651?referrer=searchResults

Answer:

The inches in height will be 18 inches.

Step-by-step explanation:

Okay so we know that the original width is 4 inches and she enlarged that to 12 inches

So what we first have to do is find out how much did the photograph "grow" per se. To find this we have to divide 12 by 4. 12 divided by 4 = 3.

So, the width of the photograph grew "times 3" inches

Now whatever you do to the width you have to do to the height. In this case, what is "3 times" 6 (which is the height). 3 times 6 = 18 inches

So in simpler words 12 divided 4 = 3 x 6 = 18 inches

The inches in height will be 18 inches.

Jill has a square with a width of 12 inches, and a height of 18 inches.

Have a wonderful day!

Answer:

287

Step-by-step explanation:

70/100*410

(cross out the zeroes then multiply 7 by 41 and you'll get 287)

Answer:

0.5

Step-by-step explanation:

The rate of change is the same as the slope. The equation y=0.5x+9 is written in slope intercept form, so 0.5 is the slope.

Answer:

Slope: 0.5

Y - Intercept: (0, 9)

x           y

-18        0

0           9

(pretend that's a graph)

Proportional: Ratios are equivalent.

Non-proportional: Ratos are not equivalent.

-18/ 0 is not equal to 0/9.

Undefined                  =0

Non-proportional

Answer:

1). Options (B) and (E)

2). First train is going faster than the second train.

Step-by-step explanation:

1). Rate of 2 gallons of vinegar = $3

   Therefore, per gallon rate of vinegar = [tex]\frac{3}{2}[/tex] = $1.5

   In $3 quantity of vinegar chef will get = 2 gallons

   Therefore, quantity of vinegar chef will get in $1 = [tex]\frac{2}{3}[/tex] gallons

Option (A).

Price of 4 gallons = 4 × $1.5 = $6.00

False.

Option (B)

Price of 1 gallon = $1.50

True

Option (C)

Price of 30 gallons = 30 ×$1.5 = $45    

False.

Option (D)

In $2 number of gallons of vinegar chef will get = [tex]\frac{2}{3}\times 2=\frac{4}{3}[/tex] gallons

False

Option (E)

Number of gallons of vinegar chef gets in $1 = [tex]\frac{2}{3}[/tex]

True

Therefore, Options (B) and (E) are the correct.

2). Speed = [tex]\frac{\text{Distance}}{\text{Time}}[/tex]

For first train,

Speed = [tex]\frac{30}{\frac{1}{3}}[/tex]

            = 90 miles per hour

For second train,

 Speed = [tex]\frac{20}{\frac{1}{2}}[/tex]

             = 40 miles per hour

 Since, 90 miles per hour > 40 miles per hour

 First train is going faster than the second train.

9514 1404 393

Answer:

  y = -3/4x -1

Step-by-step explanation:

The given equation is in the slope-intercept form, which lets you see that its slope is 4/3.

The slope of the perpendicular line will be the negative reciprocal of this:

  -3/4

Then the slope-intercept form equation will be ...

  y = -3/4x +b . . . . . . for some b

We can find the value of b that makes the line go through (4, -4) by using those values in this equation.

  -4 = -3/4(4) +b

  -4 +3 = b . . . . . . . . add 3

  -1 = b

Then the equation you're looking for is ...

  y = -3/4x -1

Answer:

0.86016949152

Step-by-step explanation:

This is the answer because 29 divided by 59 is 0.49152542372 and 42 divided by 24 is 1.75 and 0.49152542372 multiplied by 1.75 is 0.86016949152