Angelica reads 15 pages of a book each day. In 10 days, she reads 200 pages. Assume the relationship is linear. Find and interpret the rate of change and initial value.

help me please

Answers

Answer 1

Given:

Angelica reads 15 pages of a book each day.

In 10 days, she reads 200 pages.

Assume the relationship is linear.

To find:

The rate of change and initial value.

Solution:

The slope intercept form of a linear function is:

[tex]y=mx+b[/tex]            ...(i)

Where m is the slope and b is the y-intercept.

Angelica reads 15 pages of a book each day. So, the rate of change is 15 pages per day and [tex]m=15[/tex].

In 10 days, she reads 200 pages. It means the linear relation passes through the point (10,200).

Putting [tex]x=10,y=200,m=15[/tex] in (i), we get

[tex]200=15(10)+b[/tex]

[tex]200=150+b[/tex]

[tex]200-150=b[/tex]

[tex]50=b[/tex]

So, the y-intercept is 50. It means the initial number of pages angelica already read is 50.

Therefore, the rate of change is 15, it means Angelica reads 15 pages per day. The y-intercept is 50, it means the initial number of pages angelica already read is 50.


Related Questions

2kg 300g - 375g help

Answers

Answer:1925g=1kg 925g

Step-by-step explanation:

1kg=1000g

2kg=2000g

2kg 300g=2300g

2300-375=1925g=1kg 925g

if h(x) =5 for the function h(x) =2x+1 what is the value of x

Answers

Answer:

h (x) = 5

h (x) = 2x + 1

h (x) = 2 x 2 + 1 = 5

x = 2

Answer:

x = 2

Step-by-step explanation:

Its given that h(x) = 2x + 1

But its also given that h(x) = 5

[tex]=> h(x) = 2x + 1 = 5[/tex]

[tex]=> 2x + 1 = 5[/tex]

Solve the equation.

Substract 1 from both the sides.

[tex]=> 2x + 1 - 1 = 5 - 1[/tex]

[tex]=> 2x = 4[/tex]

Divide both the sides by 2.

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

[tex]=> x = 2[/tex]

hello i need help with these questions attached.

Answers

Answer:

Beep

Step-by-step explanation:

4 x − 3 x + 2 y (simplify)

Answers

[tex]\huge\text{Hey there!}\\\\\large\text{4x - 3x + 2y}\\\\\large\text{\underline{\underline{COMBINE the LIKE TERMS}}}\\\\\large\text{(4x - 3x) + 2y}\\\\\large\text{4x - 3x = \bf 1x }\large\text{(or you could simply say \underline{x} because a variable by itself}\\\large\text{is understood as an invisible 1)}\\\\\large\text{\bf x + 2y}\\\\\\\boxed{\boxed{\huge\text{Therefore your answer is: x + 2y}}}\huge\checkmark\\\\\large\text{Good luck on your assignment and enjoy your day!}\\\\\\\\\frak{Amphitrite1040:)}[/tex]

pls solve them all pls

Answers

Answer:

Step-by-step explanation:

Hope this helps u !!

The perimeter of a rectangle is 84 cm. If the length is 29 cm write an equation you can use to answer this question

Answers

Answer:

Width = 13

Equation: 2 × 29 + 2W = 84

Step-by-step explanation:

Ace here!

I'm going to assume that we have to find the width. In a rectangle, there are 4 sides and opposite sides are congruent.

Let L represent the length and W represent the width.

Since there are 4 sides, we know that to find the of a rectangle perimeter, we have to do:

L+L+W+W=Perimeter

Let's first simplify this equation by combining like terms:

2L+2W = Perimeter

Now, let's plug in known values:

2(29) + 2W = 84

Divide everything by 2:

29+W=42

Isolate W:

W=42-29

W=13

Keep in mind, I didn't have to divide by 2 at the step that I had. I could've also done this:

2(29) + 2W = 84

Simplify:

58+2W=84

Bring everything to one side:

2W=26

Isolate W by dividing 2:

W=13

Two different slightly approaches, same answer.

I hope that helped, let me know if you have any questions.

Find the exact value of sin2Θ if tanΘ=[tex]\frac{-2\sqrt{5} }{5}[/tex] and 90 < Θ < 180.

Answers

Answer:

[tex]sin 2 \theta = \frac{4 \sqrt5}{9}[/tex]

Step-by-step explanation:

Identities used :

[tex]1. sin^2 \theta = 1 - cos^2\theta\\\\2. tan^2 \theta + 1 = sec^2 \theta\\\\3.cos \theta = \frac{1}{sec \theta} \\\\4. sin 2 \theta = 2 sin\theta cos\theta[/tex]

[tex]Given \ tan \theta = -\frac{2 \sqrt5}{5}\\[/tex]

[tex]we \ know \ tan ^2 \theta + 1 = sec^2\theta[/tex]

            [tex](-\frac{2 \sqrt 5}{5})^2 + 1 = sec^2 \theta\\\\\frac{4 \times 5}{25 } + 1 = sec^2 \theta \\\\\frac{20 + 25}{ 25} = sec^2 \theta \\\\\frac{45}{25} = sec^2 \theta \\\\sec \theta = \sqrt{ \frac{45}{25}}\\\\sec \theta = \sqrt{ \frac{9 \times 5}{5 \times 5}} \\\\sec \theta = \frac{3 \sqrt {5}}{5}\\\\[/tex]

[tex]We \ know \ cos \theta = \frac{1}{ sec \theta}[/tex]

[tex]So , \cos \theta = \frac{5}{3 \sqrt5}[/tex]

[tex]Next \ sin^2 \theta = 1 - cos^2 \theta[/tex]

                 [tex]= 1 - (\frac{5}{3 \sqrt5})^2\\\\=1 - \frac{25}{9 \times 5}\\\\=1 - \frac{25}{45}\\\\=\frac{45 - 25}{45}\\\\=\frac{20}{45}\\\\=\frac{4}{9}[/tex]

    [tex]sin \theta = \sqrt{ \frac{4}{9}} = \frac{2}{3}[/tex]

[tex]Find \ sin 2 \theta[/tex]

[tex]sin 2 \theta = 2 (sin \theta \times cos \theta)[/tex]

        [tex]= 2 \times \frac{2}{3} \times \frac{5}{3\sqrt5}\\\\= \frac{4 \times \sqrt5 \times \sqrt5}{9 \times \sqrt 5}\\\\=\frac{4 \sqrt5}{9}[/tex]

Raffle tickets cost $6 for 5 tickets. What is the price of 1 ticket? How many tickets can you get for $90​

Answers

Answer:

1 ticket is worth 1.2$

90$ gets you 75 tickets

Step-by-step explanation:

t=ticket(s)

6=5t

6/5=t

90/(1.2)=75

Answer:

1 ticket = $1.2

Step-by-step explanation:

Can someone please help me out with this question

Answers

Answer:

C.

Step-by-step explanation:

Which of the following pairs of functions are inverses of each other?

Answers

Answer:

do you have a picture or something So I can answer your question?

Step-by-step explanation:

Option-A is accurate because f(x) = 9(x/2)-8 and g(x) = 2(x+8)/9 are the values we get when solving the function.

What is inverse function?

A function receives values, performs certain operations on them, and outputs a result. After acting and concurring with the result, the inverse function switches back to the original function.

The inverse function, which also returns the initial value, returns the result of a function.

this selection. Option-A is the proper choice, so

f(x)=9(x/2)-8

consider the f(x)=y

y=9(x/2)-8

y+8=9(x/2)

(y+8)/9=x/2

2(y+8)/9=x

g(x)=2(x+8)/9

As a result, Option-A, which states that when the function is solved, the output is the inverse function, is correct. Its values are f(x) = 9(x/2)-8 and g(x) = 2(x+8)/9.

To know more about inverse function check:

https://brainly.com/question/2541698

#SPJ7

8. Find the area of the regular polygon.​

Answers

Answer:

To find the area of a regular hexagon, or any regular polygon, we use the formula that says Area = one-half the product of the apothem and perimeter. As shown below, this means that we must find the perimeter (distance all the way around the hexagon) and the measure of the apothem using right triangles and trigonometry. Area of a Hexagon

Step-by-step explanation:

What’s the answer please.

Answers

Answer:

[tex]\frac{m^{3}n+5 }{m^{2}n^{2} }[/tex]

Explanation :

is down below in the picture

Please give me brainiest!!

whats the answer to this ​

Answers

Answer:

its the 2nd one

hope that helps<3

Answer:

jhkkkhj

Step-by-step explanation:

jkjkjkjkj

Jackie bought an iphone for $200. Find the total
cost including a 7% sales tax,

Answers

Find 7% of 200

7% = 7/100

Divide 7 by 100

7/100

= 7 ÷ 100

= 0.07

Multiply 0.07 to 200

0.07 × 200

= 14

Add 14 to 200

200 + 14

= 214

Therefore, the total cost of the iphone including sales tax is $ 214

Write the equation of the line that passes through the points (-8,-1) and (−2,9). Put your answer in fully reduced point-slope form, unless it is a vertical or horizontal line.

Answers

Answer:

not sure if understood you; slope: (-1-9)/(-8+2)=-10/-6=5/3, y-int: -1-(-40/3)=37/3; y=5/3x+37/3

What is the simplified form of [tex]3\sqrt{135}[/tex]?

Answers

The answer is: [tex]9\sqrt{15}[/tex]

=5.12992784
Rounded to the nearest 1d.p would be 5.1
And to the nearest whole number it would be 5

if gon had 40 tubs of orange juice then killua gave gon 29348211239587316837637869437637689767609 more tubs of orange juice, how many tubs of orange juice would gon have?

Answers

Answer:

It would be 2.9348211e+40

Step-by-step explanation:

Use a calculator

Bro no offense but use a calculator

Which solution finds the value of x in the triangle below?

Answers

Answer: B

Step-by-step explanation:

The answer would be B.

answer all the questions, just the answers, it's pythagorean theorem, plssss helpppp

Answers

Answer:

1. option c

2. option b

3. option b

Step-by-step explanation:

1 . option C

Square of longer side = sum of squares of other side

a)

5, 6 , 11

[tex]121 = 25 + 36\\does\ not \ satisfy[/tex]

b)

9, 12, 16

[tex]256 = 144 + 81\\Does\ not \ satisfy[/tex]

c)

7, 24, 25

[tex]625 = 576 + 49\\Does\ satisfy[/tex]

d)

12, 20, 25

[tex]625 = 400 + 144\\does \ not \ satisfy[/tex]

2. Option B

Square of longer side = sum of squares of other side

15 ² = 8 ² + r²

225 = 64 + r²

161 = r²

r = 12.688

r = 13ft

3 . Option b

To find length  of AB,  Use distance formula

[tex]AB = \sqrt{(x_2- x_1)^2 + (y_2 - y_1)^2}[/tex]

    [tex]= \sqrt{(14-3)^2 + (6-1)^2}\\\\=\sqrt{11^2 + 5^2}\\\\=\sqrt{121 + 25}\\\\= \sqrt{146} \\= 12 \ ft[/tex]

please help guys! i don’t wanna fail

Answers

Answer:

25: 6,000

26: 450

27: 70,000,000

28: 10,500

29: 3,052

30: (cant really see the exponent but I think its 10^5)  500,000

31: 9.87

32: 5.43

group the like terms separately? 3v^5-10v^2-12v^5+14v^2​

Answers

so here you just add them as if they were regular numbers. -9v^5+4v^2, hope it helped.

Use the drop-down menus to correctly relate each pair of numbers
manee help meh son

Answers

Answer:

Sorry for the late response, I had to have lunch.

1. >

2. =

3. <

4. >

Step-by-step explanation:

Have a great summer :)

Keisha runs 3 miles in 25 minutes. At the same rate, how many miles would she run in 20 minutes?

Answers

Answer:

2.4 miles

Step-by-step explanation:

Since Keishas rate is 3/25 miles per minute, we multiply the Rate with the Time (Rate * Time = Distance). So 20 * 0.12 = 2.4 miles

what is this app and why are you reading this

Answers

Brainly, I’m looking for questions to answerrrrrr

Point of intersection Question:

Mike has $9.85 in dimes and quarters. If there are 58 coins altogether,
how many dimes and how many quarters does Mike have? Use the point of intersection to find the answer. Explain how you used a formula to calculate the # of quarters and dimes

Answers

Answers:

He has  27   quarters and  31   dimes

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

Work Shown:

d = number of dimes

q = number of quarters

d+q = 58 since there are 58 coins of only these two types

d = 58-q

10d+25q = 985 .... note that 985 cents is $9.85

10(58-q)+25q = 985 .... replace d with 58-q

580-10q+25q = 985

15q+580 = 985

15q = 985-580

15q = 405

q = 405/15

q = 27 ..... Mike has 27 quarters

d = 58-q

d = 58-27

d = 31 .... Mike also has 31 dimes

-----------

As a way to check:

d+q = 31+27 = 58 so that works out

and

10d+25q = 10*31+25*27 = 310+675 = 985

so that works out as well. The answer is confirmed.

NEED HELP ASAP Let the function f(x) have the form f(x) = Acos(x+C). To produce a graph that matches the one shown below, what must the value of C be?

Answers

Answer:

[tex]C = 2[/tex] (A)

Step-by-step explanation:

We assume the constant A is different than 0

We notice that the graph of the function intercepts the x-axis when x = -0.5

we know that cos(x) = 0 when x = π/2 or x = -π/2

thus, [tex]-0.5 + C = \pi /2[/tex]    or  [tex]-0.5 + C = -\pi /2[/tex]

then [tex]C = \pi /2 + 0.5 = 2[/tex]  or [tex]C = -\pi /2 = 0.5 = -1[/tex]

so [tex]C = 2[/tex]

The button on David's coat has a radius of 4
millimeters. What is the button's diameter?

Answers

Answer:

0.013

I think.

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

So there are two things that must be remembered.

The radius is half of the diamater. It is the distance from the side of a circle to its center.

The diamater is two times the radius. It is the distance from one side of the circle to the opposite side of the circle.

In this case, we know the radius is 4.

The radius is half of the diamamter, or the diamater is two times the radius.

This can be though of as:

2r=d

Or

1/2d=r

So lets plug 4 in for r:

2*4=d = 8=d

1/2d=4 = 2*1/2=4*2 = 1d=8

So using either of these formulas, we find d is equal to 8.

Hope this helps!

Solve the equation 3u+6=22

Answers

Step-by-step explanation:

3u+6=22

3u=16

u=16/3

!!!!!!!!!!!

Solve c =(a² + 3b)/4 for b.

Bruv take all my points I literally blow at math :'(​

Answers

Answer:

[tex]b=\frac{4c-a^{2} }{3}[/tex]

Step-by-step explanation:

First: multiply both sides by 4. 4 times c is 4c and the other sides cancels out as you are doing the inverse operation of division

Then, you have [tex]4c=a^{2} +3b[/tex]

Subtract both sides by a squared

DO NOT TAKE THE SQUARE ROOT! This is because it is a squared plus 3b so you have to do the inverse of addition

From that you get [tex]4c-a^{2} =3b[/tex]

Finally, divide both sides by 3.

You get  [tex]b=\frac{4c-a^{2} }{3}[/tex]

Given ΔUTS with coordinates U(-4,-3), T(-2,1), S(0,-2), rotate the figure 90° Counterclockwise about the origin

Question 8 options:

U'(-2,1) T'(-4,-2) S'(0,0)

U'(4,3) T'(2,-1) S'(0,2)

U'(3,-4) T'(-1,-2) S'(2,0)

U'(-2,-2) T'(0,2) S'(2,-1)

Answers

Answer:

U'(3,-4) T'(-1,-2) S'(2,0)

Step-by-step explanation:

Firstly, we need the general rotation method

We have this as;

(x,y) to (-y,x)

So;

U (-4,-3) becomes U’ (3,-4)

T(-2,1) becomes T’(-1,-2)

S(0,-2) becomes S’ (2,0)

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