Justin is planning to purchase books for $20 each month. How much money will he spend on the books in 2 years?

Answer:

Step-by-step explanation:

5r + 2b = 14 (5 lbs of oranges and 2 lbs of bananas = $14)

3r + 6b = 18 (3 lbs of oranges and 6 lbs of bananas = $18)

Let's use the elimination method. Multiply the first equation by -3:

-15r - 6b = -42

3r + 6b = 18

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

12r = 24

Divide by 12:

r = 2

Answer:

The price per pound of the oranges is $ 2.

The price per pound of the bananas is $ 2.

Step-by-step explanation:

A system of linear equations is a set of equations that have more than one unknown. The unknowns appear in several of the equations, but not necessarily in all. In these equations the unknowns are related to each other.

In this case a system of equations is applied. For that, you must first define the unknowns (or also called variable):

The price of the 5 pounds of oranges, whose price is "x", and 2 pounds of bananas, whose price is "y", bought by Gail must add $ 14. Then expressed in an equation this represents: 5*x+2*y=14 Equation (A)

The price of the 3 pounds of oranges, whose price is "x", and 6 pounds of bananas, whose price is "y", bought by her husband must add $ 18. Then expressed in an equation this represents: 3*x+6*y=18 Equation (B)

Equation A and equation B form the equation system, where the variables are "x" and "y", which are the price of an orange and a banana:

[tex]\left \{ {{5*x+2*y=14} \atop {3*x+6*y=18}} \right.[/tex]

One of the ways to solve a system of equations is through the substitution method.  This method consists of isolating one of the unknowns (for example, "x") and replacing its expression in the other equation. In this way, a first degree equation is obtained with the other variable, "y".

In this case, x is isolated from the first equation, obtaining:

5*x+2*y=14

5*x=14-2*y

[tex]x=\frac{14-2*y}{5}[/tex]

[tex]x=\frac{14}{5} -\frac{2}{5}*y[/tex] Equation (C)

Replacing this equation (C) in the other equation you get:

[tex]3*[\frac{14}{5} -\frac{2}{5} *y]+6*y=18[/tex]

Isolating the value of "y" you get:

[tex]3*\frac{14}{5} -3*\frac{2}{5} *y+6*y=18[/tex]

[tex]\frac{42}{5} -\frac{6}{5} *y+6*y=18[/tex]

[tex]-\frac{6}{5} *y+6*y=18-\frac{42}{5}[/tex]

[tex]\frac{24}{5} *y=\frac{48}{5} \\[/tex]

[tex]y=\frac{\frac{48}{5} }{\frac{24}{5} }[/tex]

[tex]y=\frac{48}{5} *\frac{5}{24} \\[/tex]

y=2

Remembering that "y" is the price per pounds of the banana, then it is possible to say that the price per pound of the banana is $ 2.

Replacing the value of the variable "y" in equation (c) and isolating the value of the variable "x" gives:

[tex]x=\frac{14}{5} -\frac{2}{5}*2[/tex]

[tex]x=\frac{14}{5} -\frac{4}{5}[/tex]

[tex]x=\frac{14-4}{5}=\frac{10}{5}[/tex]

x=2

Remembering that "x" is the price per pounds of the oranges, then it is possible to say that the price per pound of the oranges is $ 2.

Solution for an=19-7(n-1) equation:

Simplifying

an = 19 + -7(n + -1)

Reorder the terms:

an = 19 + -7(-1 + n)

an = 19 + (-1 * -7 + n * -7)

an = 19 + (7 + -7n)

Combine like terms: 19 + 7 = 26

an = 26 + -7n

Solving

an = 26 + -7n

Solving for variable 'a'.

Move all terms containing a to the left, all other terms to the right.

Divide each side by 'n'.

a = 26n-1 + -7

Simplifying

a = 26n-1 + -7

Reorder the terms:

a = -7 + 26n-1

Answer:

9

Step-by-step explanation:

the answer is 9 because 7 goes into 63 evenly 9 times

Answer: $9

Step-by-step explanation:

$63 for 7 people

63 ÷ 7 = 9

So that means that one person gets $9

The cafeteria sold 41 corn chips and 80 potato chips.

Step-by-step explanation:

Let,

Corn chips = x

Potato chips = y

Price of corn chips = $0.80

Price of potato chips = $0.60

According to given statement;

x+y= 121   Eqn 1

0.80x+0.60y=80.80   Eqn 2

Multiplying Eqn 1 by 0.80

[tex]0.80(x+y= 121)\\0.80x+0.80y=96.80\ \ \ Eqn\ 3[/tex]

Subtracting Eqn 2 from Eqn 3

[tex](0.80x+0.80y)-(0.80x+0.60y)=96.80-80.80\\0.80x+0.80y-0.80x-0.60y=16\\0.20y=16[/tex]

Dividing both sides by 0.20

[tex]\frac{0.20y}{0.20}=\frac{16}{0.20}\\y=80[/tex]

Putting y=80 in Eqn 1

[tex]x+80=121\\x=121-80\\x=41[/tex]

The cafeteria sold 41 corn chips and 80 potato chips.

Keywords: linear equation, subtraction

Learn more about linear equations at:

#LearnwithBrainly

There will be 133.33% increase of airplane passengers.

Step-by-step explanation:

Present value of passengers = 600

Expected value of passengers by 2020 = 1400

Increase = Expected value - present value

Increase = 1400 - 600 = 800

Increase percentage = [tex]\frac{increase}{present\ value}*100\\[/tex]

[tex]Increase\ percentage=\frac{800}{600}*100\\\\Increase\ percentage=\frac{80000}{600}\\Increase\ percentage=133.33\%[/tex]

There will be 133.33% increase of airplane passengers.

Keywords: percentage, division

Learn more about division at:

#LearnwithBrainly

The percent of increase in airplane passengers from 600 to 1400 is 133%, calculated using the formula for percentage increase.

To calculate the percent of increase of airplane passengers from 600 to 1400, we need to use the formula for percentage increase, which is: Percentage Increase = ((New Number - Original Number) / Original Number)  imes 100%.

Following the formula:

Therefore, the percent of increase in airplane passengers from 600 to 1400 is 133%.

The first group of points is not a function due to repetition of elements in domain while second group of points is a function because no element of domain is repeated in any ordered pair.

Step-by-step explanation:

Why {(0, 1), (0, 5), (2, 6), (3, 3)} is not a function?

A relation is said to be a function if there is no repetition in the first elements of each ordered pair. In this group of points, 0 is repeated in two ordered pairs (0, 1), (0, 5) so it is not a function.

Why {(1, 4), (2, 7), (3, 1), (5, 7)} is a function?

The given group of points is a function because there is no repetition in first elements of each ordered pair i.e. there is not repetition in domain so it is a function

Keywords: Functions, Domain

Learn more about functions at:

They both will finish the work in 3.07 hours

Step-by-step explanation:

Time taken by Rachel = 5 hours

Work done by Rachel in one hour = 1/5

Time taken by Carl = 8 hours

Work done by Carl in one hour = 1/8

Let x hours be the time taken by both to do work

Then 1/x will be the work done by both in one hour

So,

[tex]\frac{1}{5} + \frac{1}{8} = \frac{1}{x}[/tex]

Taking LCM

[tex]\frac{8+5}{40} = \frac{1}{x}\\\frac{13}{40} = \frac{1}{x}\\13x = 40\\x = \frac{40}{13}\\x = 3.07\ hours[/tex]

They both will finish the work in 3.07 hours

Keywords: Linear Equation

Learn more about linear equations at:

#LearnwithBrainly

Answer:

12 hrs

Step-by-step explanation:

X/30+x/48=1

common denominator

x/1440+x/1440

2x/1440=1

2x=1440

x=720

when you convert to hrs  you get 12

A valid reason is :opposite sides of a parallelogram are equal

Step-by-step explanation:

It is possible to notice that RUTS is a parallelogram where RU=TS and RS = UT.

When you introduce a diagonal RT you form triangles RUT and TSR.

∠URT = ∠STR ----alternate angles

∠UTR=∠SRT------alternate angles

RU║ST and RS║UT

RT=TR -----Common

ΔRUT ≡ ΔTSR by AAS theorem

hence RS=UT matching sides of congruent triangles

Learn More

Properties of a parallelogram : https://brainly.com/question/12780093

Keywords : proof, parallelogram, reason

#LearnwithBrainly

Answer:

opposite sides of a parallelogram are equal

Step-by-step explanation:

got it right on odyssey

Answer:

A

Step-by-step explanation:

(3a^4-2a^2+5a-10)-(2a^4+4a^2+5a-2)

a^4-6a^2-8

Answer:

The number which satisfy the given statement is 26 .

Step-by-step explanation:

Given as :

Twice a number is added to the number and the resultant is 78

Let The number is x

Now, According to statement

Two times x + x = 78

Or, 2 × x + x = 78

Or, 3 x = 78

So ,  x= [tex]\frac{78}{3}[/tex]

∴   x = 26

I.e The number is 26

Hence The number which satisfy the given statement is 26 .   Answer

Answer:

4(7 + 2v).

Step-by-step explanation:

The greatest common factor of 28 and 8v is 4 so we take 4 out:

28 + 8v

= 4(7 + 2v).

Answer:

B

Step-by-step explanation:

When we see "square inches" in a statement (or squared centimeters, meters, feet, etc) this refers to an area measure. So we need to find which of the options are areas.

A is not, as it is width, is a longitude measure. I could never be in square inches.

C is volume and it measure should be in cubic inches. So, not.

D is perimeter and is the sum if the lengths of different sides of a figure, so is also in inches, not square inches.

Finally, B is the area,  so is our only chance. B in correct.

Answer:

a) $25,261

b) $25,156

Step-by-step explanation:

I'm sorry but I don't know how to show my work because I just searched up "Car Loan Calulator" :|

So don't put me up for Brainlist

Answer:

Step-by-step explanation:

Just draw a number line and label three numbers, -4, -3.4 & -3. Mark -3.4 in the number line.

Answer:

[tex]y=10[/tex]

Step-by-step explanation:

we know that

The y-intercept is the value of y when the value of x is equal to zero

we have

[tex]-7x+3y=30[/tex]

so

For x=0

substitute the value of x in the linear equation and solve for y

[tex]-7(0)+3y=30[/tex]

[tex]3y=30[/tex]

Divide by 3 both sides

[tex]y=10[/tex]

Answer:

1.64 oz

Step-by-step explanation:

0.2 of the soap is 0.2 of 8.2 ounces which is

0.2 * 8.2 ounces

0.2 * 8.2 oz = 1.64 oz

She used 1.64 oz

0.2 is equal to 20% you can figure that out by multiplying 8.2 x20 and then diving that by 100

8.2x20=164

164/100=1.64

Answer:

Distance between points [tex]P(-12,-2)[/tex] and [tex]Q(3,6)[/tex] is 17 units

Step-by-step explanation:

Given points:

[tex]P(-12,-2)[/tex]

[tex]Q(3,6)[/tex]

To determine the distance between points P and Q.

Steps to be carried out:

1) Plot the points P and Q on graph.

2) Construct a line from P towards right horizontally and a line from Q downwards vertically such that they meet at point [tex]O(3,-2)[/tex]

3) Join PQ thus forming a right triangle POQ.

4) We can find the distance of sides OP and OQ by counting the units between the points.

OP=[tex]|-12-3|=|-15|=15\ units[/tex]

OQ=[tex]|6-(-2)|=|6+2|=8\ units[/tex]

4)Now, we can apply Pythagorean theorem for triangle POQ.

[tex]PQ^2=OP^2+OQ^2[/tex]   [ [tex]Hypotenuse^2=Leg1^2+Leg 2^2[/tex]]

[tex]PQ^2=15^2+8^2[/tex]

[tex]PQ^2=225+64[/tex]

[tex]PQ^2=289[/tex]

Taking square root both sides:

[tex]\sqrt{PQ^2}=\sqrt{289}[/tex]

[tex]PQ=17\ units[/tex] [We take only the positive value as distance is always positive.

∴ Distance between points [tex]P(-12,-2)[/tex] and [tex]Q(3,6)[/tex] is 17 units

Answer:

6

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

-22x=-4x+28

-18x=28

x=-28/18=-14/9

Answer: 0.5

Step-by-step explanation: In this problem, we're asked to solve the following equation for p. Let's first switch 14 and 14p around so we have 14p + 14 = 21.

To solve this equation for p, we must first isolate the term containing p which in this case is 14p.

Since 14 is being added to 14p, we need to subtract 14 from both sides of the equation.

14p + 14 = 21

        -14   -14

On the left side of the equation, the positive 14 and negative 14 cancel each other out and we have 14p. On the right side of the equation, we hav 21 - 14 which gives us 7.

Now we have the equation 14p = 7.

Since p is being multiplied by 14, to get p by itself, we divide both sides of the equation by 14.

On the left side of the equation the 14's cancel and we are left with p. On the right side of the equation, 7 divided by 14 is 0.5 which is our answer.

Therefore, p = 0.5 which is the solution for our equation.

Remember, you can always check your solution by substituting a number in for a variable to make sure the equation is true.

Answer:

A. 1/2

Step-by-step explanation:

Took test got right on edge 2021

Answer:

10 and 7

Step-by-step explanation:

10 + 7 = 17

10 - 7 = 3

Answer:

your answer is 10 and 7.

Step-by-step explanation:

because if you add 10 and 7 you get 17. them if you subtract them the answer is 3.

Answer:

1. The required slope m, for the context is[tex]m = 1.08[/tex]

2. The y-intercept in the context is [tex]a = y = 1052[/tex]

3. The graph is on Desmos.

Step-by-step explanation:

Given:

[tex]a = 1.08\times t + 1052[/tex]

Where,

a is the speed of sound wave.

t is the air temperature.

This is a linear model type equation.

Can be represented in the slope intercept form  which is equal to

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

Where,

m = Slope of the line.

c = y-intercept.

Now if we compare the given model by slope intercept formula we get

[tex]m = 1.08\\\\c = 1052[/tex]

So ,the slope in the context of the problem is [tex]m = 1.08[/tex].

and the y intercept in the context of the problem [tex]a = c = y = 1052[/tex]

For Sketching the graph we require two point

put t = 0

∴ a = 1052

Let A (1052, 0) be one point.

put a = 0

∴ t = -974.07

Let B (0, -974.07) another point.

So, the x intercept of the linear model is [tex]t = x = -974.07[/tex]

Here in the graph

X axis represent temperature in degree, Fahrenheit.(t)

Y axis represent Speed of sound wave in feet per second.(a)

Scale on both axes:

1 cm = 100 feet per second on y-axis

1 cm = 100 degree Fahrenheit on x-axis

Answer:

12/35 inches are in 1 mile.

Step-by-step explanation:

(3/10)/(7/8)=(3/10)(8/7)=24/70=12/35

1 mile=8/8

(8/8)(12/35)=1(12/35)=12/35

Answer:

Joe shoveled 6, Jill shoveled 9

Step-by-step explanation:

Answer:

Joe: 6

Jim: 9

Step-by-step explanation:

Joe: x

Jim: 2x - 3

x + 2x - 3 = 15

3x - 3 = 15

3x = 18

x = 6

Answer:

We can conclude that Δ ABC ≅ Δ DEF by SSS postulate.

Step-by-step explanation:

Δ ABC and Δ DEF are congruents because:

1. Their sides AB and DE are equal (9 units = 9 units)

2. Their sides BC and EF are equal (5 units = 5 units)

3. Their sides AC and DF are equal (10 units = 10 units)

Now, we can conclude that Δ ABC ≅ Δ DEF by SSS postulate.

Answer:

Interest =$7540

Step-by-step explanation:

p=$13000

r=5.8%

t=10yrs

i=p*r*t/100

=13000*5.8*10/1000

=130*58

= $7540

Answer:

is is 20

Step-by-step explanation:

Answer:

3, -3

Step-by-step explanation:

6x^2=54

x^2=54/6

x^2=9

x=sqrt(9)

x=3, -3

Answer:

n=0

Step-by-step explanation:

6=1-2n+5-4n

Combine like terms

6=-6n+6

now move the +6 to other side

0=-6n

so divide to remove the n from the -6

0=n

No worries I tested it it's right! I hope :/