Jose and Gavin are reading the same book. At the beginning of the month, Jose was

on page 10 and Gavin was on page 37. Jose will read 17 pages per day and Gavin will

read 14 pages per day. Let J represent the page of the book that Jose is on at the end

oft days into the month, and let G represent the page of the book that Gavin is on at

the end oft days into the month. Write an equation for each situation, in terms of t,

and determine what page Jose and Gavin will be on on the day they are both on the

same page.

Answers

Answer 1

Using linear functions, it is found that:

Jose's equation is: [tex]J = 17x + 10[/tex].Gavin's equation is: [tex]G = 14x + 37[/tex].They will be on the same page on the 9th day.

Linear function:

A linear function is modeled by:

[tex]y = mx + b[/tex]

In which:

m is the slope, which is the rate of change.b is the y-intercept, which is the value of y when x = 0.

Jose:

Initially, he was on page 10, hence [tex]b = 10[/tex].He reads 17 pages per day, hence [tex]m = 17[/tex].Hence, Jose's equation is: [tex]J = 17x + 10[/tex].

Gavin:

Initially, he was on page 37, hence [tex]b = 37[/tex].He reads 14 pages per day, hence [tex]m = 14[/tex].Hence, Gavin's equation is: [tex]G = 14x + 37[/tex].

The day they will both be on the same page is x for which:

[tex]J = G[/tex]

Hence:

[tex]17x + 10 = 14x + 37[/tex]

[tex]3x = 27[/tex]

[tex]x = \frac{27}{3}[/tex]

[tex]x = 9[/tex]

They will be on the same page on the 9th day.

To learn more about linear functions, you can take a look at https://brainly.com/question/16302622


Related Questions

Help help math math

Answers

Answer:

y = 1/2x + 3

Step-by-step explanation:

Y= mx+b is slope-intercept form, m is for slope, and b is for my y-intercept. Also remember the pitch is the rise over the run or the y-direction over the x-direction.

In our case, they highlight 2 points to calculate the slope; looking at the graph, we can see it rises one and runs two to get to the second highlighted point at (2,4). And my slope is rise over run, so here it 1/2.

My b or y-intercept is simply three because that is where the line passes over or intercepts the Y-axis

Answer: y = 1/2 x + 3

Step-by-step explanation:

What is 8 hours and 37 minutes converted into minutes?

Answers

Answer:

517 minutes

Step-by-step explanation:

Hope this helps:))

Answer:

517 mins

Step-by-step explanation:

1hour=60min

8hour=480min

37min is the same because it is already in minutes

480+37=517mins

Which of the following is the graph of y=x+3

Answers

Answer:ITS THE SECOND ONE

Step-by-step explanation:

To solve for the hypotenuse of a right triangle, what information do you need?

Answers

To find the hypotenuse of any right triangle, you need to square and add the other two sides. We call those two sides LEGS.

(legs)^2 + (leg)^2 = (hypotenuse)^2

In your textbook, you will see it this way:

a^2 + b^2 = c^2, where a = b = legs.

Answer:

You can use Sin to solve that problem in it you should have Angle=theeta and perpendicular.

Step-by-step explanation:

First you should have Perpendicula and Then Angle Put That info in Sinɵ = perpendicular/base. Solve it and get your Answer

Given the system: 3x-3y=9 -9x+12y= -30

What number would you multiply the TOP equation by to eliminate your "x" values with addition?

Answers

Answer:

you would multiply by 3.

Step-by-step explanation:

Hi there!

In order to solve this system of equations through elimination, the sum of either the x or y values will have to equal 0. To eliminate x, you would have to find what, when added, will make the sum 0. In this case, a positive 9 will cancel out the -9 and give us 0. All we have to do is multiply the top equation by 3 so that the x value is equal to 9x!

I hope this helps!

a book is marked down by 28% from the original price of 19.50 what is the new price​

Answers

Answer:

$14.04

Step-by-step explanation:

to find the answer we can multiply 19.5 by 28% and use that answer to subtract to 19.5 or we can just directly multiply 19.5 by 72%

19.5 * 72% = 14.04

it costs $14.04 after a markdown of 28%

vnicn letter on the map indicates the location of the North China Plain?
AAA
o
О В
О С
OD
F

Answers

Answer:

The letter C

Step-by-step explanation:

North china plain runs along near the northern east border. It's territory has a noticeable river going through it, and is close to the Gulf of Jilin. A is most likely not correct, since North china plane doesn't go up that high the Yellow river. So it is safe to assume the answer is most likely C

Find the HCF of 150 and 250.

Answers

Answer:

It is 50

Step-by-step explanation:

Hope this helps

Answer:

50

Step-by-step explanation:

PLEASE HELP WILL MARK BRAINLIEST!

Answers

Answer:

Step-by-step explanation:

[tex]12000(1+\frac{.12}{4})^{4*45}=2454040.31463\\=2454040[/tex]

(1) Mr. Jones finished correcting 6 out of 7 homework assignments. Miss Smith finished
correcting 83% of that week's homework assignments. Which teacher corrected a greater
percentage of her homework assignments?

Answers

Answer:

Mr. jones

Step-by-step explanation:

6/7 is 85.71% which is greater than 83%.

Consider f and c below. f(x, y) = x2 i + y2 j c is the arc of the parabola y = 2x^2 from (−1, 2) to (0, 0)
(a) find a function f such that f = ∇f.
f(x, y) =
(b) use part (a) to evaluate c ∇f · dr along the given curve C.

Answers

(a) If there is a scalar function f(x, y) such that ∇ f(x, y) = x² i + y² j, then

∂f/∂x = x²

∂f/∂y = y²

Integrating both of these equations with respect to x and y (respectively) gives

f(x, y) = 1/3 x³ + g(y)

f(x, y) = 1/3 y³ + h(x)

Differentiating with respect to the other variable gives

∂f/∂y = g'(y) = y²

∂f/∂x = h'(x) = x²

so it follows that

f(x, y) = 1/3 x³ + 1/3 y³ + C

for some constant C.

(b) By the gradient theorem,

[tex]\displaystyle \int_C \nabla f \cdot d\vec r = f(0,0) - f(-1,2) = \boxed{-\dfrac73}[/tex]

Please look for the question in the picture.

Answers

Answer:

x = 8

Step-by-step explanation:

[tex]\frac{1}{4} x-\frac{3}{5} =1\frac{2}{5}[/tex]

[tex]\frac{1x}{4} -\frac{3}{5} =\frac{7}{5}[/tex]

[tex]\frac{1x}{4} =\frac{7}{5} +\frac{3}{5} \\[/tex]

[tex]\frac{1x}{4} =\frac{10}{5}[/tex]

Use cross multiplication.

[tex]5x=4*10[/tex]

[tex]5x=40[/tex]

[tex]\frac{5x}{5}=\frac{40}{5}[/tex]

[tex]x=8[/tex]

Hope this helps you.

Let me know if you have any other questions :-)

Hello There!

Question:-

[tex]\sf \longmapsto1/4x-3/5=1\dfrac{2}{5}[/tex]

We need to find the value of x.

Solution:-

Convert[tex] \dfrac{2}{5}[/tex] to improper fraction:-

[tex] \sf \longmapsto\dfrac{1}{4} x + \dfrac{ - 3}{5} = \dfrac{7}{5} [/tex]

Add 3/5 to both sides:-

[tex]\sf \longmapsto \: \dfrac{1}{4} x + \dfrac{ - 3}{5} + \red {\dfrac{3}{5}} = \dfrac{7}{5} + \red{\dfrac{3}{5}} [/tex]

On Simplification:-

[tex]\sf \longmapsto \: \dfrac{1}{4} x + \dfrac{ 3}{5} - \dfrac{3}{5} = \dfrac{7 + 3}{5} [/tex]

[tex]\sf \longmapsto \: \dfrac{1}{4} x - 0 = \cancel \dfrac{10}{5} [/tex]

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

Multiply both sides by 4 :-

[tex]\sf \longmapsto \: \red4 \times \bigg( \dfrac{1}{4} x \bigg) = \red 4 \times 2[/tex]

On Simplification:-

[tex]\sf \longmapsto \: \cancel 4 \times \dfrac{1}{ \cancel4}x = 4 \times 2[/tex]

[tex]\sf \longmapsto \: x = 8[/tex]

______________________________________

Henceforth,The value of x is :-

[tex] \boxed{ \huge\bf \: x = 8}[/tex]

________________________________

Please let me know if you have any questions.

~MisterBrian

Sierra left $4.50 as a tip for a waiter. This was 18% of the bill before the tip. How much was her bill before adding the tip?

Answers

Answer:

25

Step-by-step explanation:

what is 4.5 18% of

100 / 18 = 5.56

4.5 x 5.55... = 25

$25

4.50 = 18%
0.25 = 1%
25 = 100%

The local sales tax is 8% if a pair of shoes sells for $140 what is the cost after tax

Answers

Answer:

$151.2

Step-by-step explanation:

To find the price after the tax is implemented,

set a relationship x/140=8/100 (8/100) basically means 8%.

cross multiply (140)(8)=1120. Then divide it by 100x, you get $11.2.

But that's just 8 percent of the total amount. So you need to add onto the original price, 140+11.2=$151.2.

1. What kind of interest does credit card P illustrate? ​

Answers

Answer:

Interest rates can come in all sizes, but for credit cards they generally fall into one of three categories:

variable rate, fixed rate and promotional rate. Most companies issue cards tied to revolving credit. Users of these cards are allowed to carry a balance on their accounts at the end of every billing cycle.

Step-by-step explanation:

Hope this helps you !!

The mass of a sheet of metal varies jointly with its area and its thickness. A sheet of metal of area 250cm2 and thickness 1mm has a mass of 200g. Find the formula which connects the mass M g, the area A cm2 and the thickness 1mm. Hence find the mass of a piece of metal of area 400 cm2 and thickness 3mm​

Answers

The Formula of the relation is M = 8AT.

The mass of the metal sheet is 960 g.

The expression below shows the variation between the mass of the sheet (M), Area of the Sheet(A), and thickness (T).

Proportionality:

M ∝ AT

Removing the proportionality sign,

M = KAT

Where:

K = constant of proportionality.

make K the subject of the equation:

K = M/KT.................... Equation 1

From the question,

Given:

M = 200 gA = 250 cm²T = 1 mm = 0.1 cm

Susbtitute into equation 1

K = 200/(250×0.1)K = 8 g/cm³

Formula:

M = 8AT................. equation 2

Hence the formula of the relation is M = 8AT

If,

A = 400 cm²T = 3 mm = 0.3

Substitute these values into equation 2

M = 8(400)(0.3)M = 960 g

Hence,  the mass of the metal sheet is 960 g

Learn more about joint variation here: https://brainly.com/question/26047253

Find the vale of x need help

Answers

Answer:

x=45 degrees

Step-by-step explanation:

You can see based off of the markings on the 2 sides, that it is an isosceles triangle, so that means the 2 base angles are equal.

so 2x+90=180 degrees

so 2x=90 degrees

x=45  

Answer:

[tex]x=45[/tex]

Step-by-step explanation:

→a+b+c=180

→Angle a is given to be 90 degrees

→ Also the other to angles are the same length so the same angle

[tex]90+2x=180[/tex]

Step 1: Subtract 90 from both sides.  

[tex]2x+90-90=180-90[/tex]

[tex]2x=90[/tex]

Step 3: Divide both sides by 2.

[tex]\frac{2x}{2} =\frac{90}{2}[/tex]

[tex]x=45[/tex]

Answer:x=45

7. Derek has $20 to spend on used books. Hardcover books cost $5 each and paperbacks cost $2 ea Write an equation that models the situation.​

Answers

You could use 5x+2x=20

LCM of two numbers is 1134 and HCF is 18. if one of the numbers is 162, find the other. number.

Answers

Answer:  126

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

Work Shown:

Let x and y be the two numbers.

We're given x = 162 and the variable y is unknown.

We're also given LCM = 1134 and HCF = 18

So,

LCM = (x*y)/HCF

1134 = 162*y/18

1134 = (162/18)y

1134 = 9y

9y = 1134

y = 1134/9

y = 126

The other number is 126

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

Notice that

162 = 18*9126 = 18*7

showing that 18 is the highest common factor (HCF) of the numbers 162 and 126. This partially confirms the answer.

Now let,

A = multiples of 162B = multiples of 126

So,

A = 162, 324, 486, 648, 810, 972, 1134, 1296, ...B = 126, 252, 378, 504, 630, 756, 882, 1008, 1134, 1260, ...

We see that 1134 is in each list of multiples and the smallest such common item. So the lowest common multiple (LCM) of 162 and 126 is 1134. This helps fully confirm the answer.

Which type of correlation does this scatterplot show?

Answers

Answer:

i think the answer to this question is positive correlation

Step-by-step explanation:

this image below may help u

Positive correlation. It is a positive correlation if y increases when x increases or y decreases when x decreases.

can anyone pls help?

Answers

Answer:

5x+12+x'

_______

2x'-2x-4

'=2

Solve each inequality 5 + 5(x + 4) = 20

Answers

Answer:

5 x + 25 ≤ 20

Step-by-step explanation:

Simplify 5  +  5  (  x  +  4  ) .

5  + 5 x  +  20  ≤  20

Add  5  and 20 .

135% as a fraction or a mixed number fully simplified please 50 POINTS + BRAINILEST

Answers

Answer:

27/20

Step-by-step explanation:

135% = 135/100 = (27/20 × 5) = 27/20 = 1 7/20 I think

the distance between(3,-3) and (-3,5)

Answers

Answer:

10 units

Step-by-step explanation:

use distance formula to solve for this!

distance formula is

the square root of the change in x squared + the change in y squared.

sqrt (3+3)^2 + (|-3-5|)^2

sqrt 36 + 64

sqrt 100 = 10

the distance is 10 !

Answer:

the ditstance between (3,-3) and (-3,5) is 10

Step-by-step explanation:

we know the distance in a cartesian axis is

[tex] \sqrt{(x2 - x1) ^{2} + (y2 - y1) ^{2} }[/tex]

so the answer is calculated 10

A rectangle that measures 10 inches by 7 inches.

Which expression will determine the perimeter, in inches, of the rectangle?

Answers

Answer:

( 2 x 10 ) + ( 2 x 7)

Step-by-step explanation:

Hope this helped!

Answer: 34 inches  Perimeter = 2L + 2W

Step-by-step explanation:

A rectangle has two sets of equal side lengths.    We'll assign 10 inches to the length, L, and 7 inches to the width, W.

The perimeter of a rectangle is 2L + 2W

Perimeter, P = 2(10) + 2*(7)

P = 20 + 14

P = 34 inches

3.
In parallelogram ABCD, M m

Answers

Answer:

Please send a picture or explain properly

Find the Values of X and Y
X=
Y=

Answers

Answer:

14 and 12

Step-by-step explanation:

Find the x- and y-intercepts of the parabola y=x2+4x−6.

Answers

The x and y intercepts are as followed: where the parabola touches the X axis

Choose the function that the graph represents.
Click on the correct answer.

Answers

Answer:

y=log_2 (x)

Step-by-step explanation:

We see that the graph passes though the point (2,1). So we can write:

log_a (2) = 1  => a = 2

So it's a log in base 2.

b) Find the square root of 66.4225.

Answers

Answer:8.15

Step-by-step explanation: 8.15

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