Sam drives his car at a constant speed. He travels a distance (d) of 15 miles with 12 of a gallon of gas (g). Write an equation in the form of d=rg that represents the relationship between distance (d) and the number of gallons of gas (g), where r is the constant of proportionality.

Answer:

y = -3x + 2; y = ⅓x -14/3

Step-by-step explanation:

Step 1. Find the equation of the parallel line

Original line: y = -3x+ 7

Parallel line: slope = m₁ = -3

The line passes through (2, -4).

 y = m₁x + b      Insert the values

-4 = (-3)×2 + b

-4 = -6 + b        Add 6 to each side

b = 2

y = -3x + 2

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

Step 2. Find the slope (m₂) of the perpendicular line

m₂ = -1/m₁     Substitute the value of m₁

m₂ = -1/(-3)

m₂ = ⅓

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

Step 3. Find the equation for the perpendicular line

y = mx + b

y = ⅓x + b

The line passes through (2, -4).  

-4 = ⅓(2) + b      Substitute the values

-4 = ⅔ + b         Subtract ⅔ from each side

-4 - ⅔ = b

 b = -14/3

y = ⅓x - 14/3

In the image, below  the graph of your original equation is the red line.

The green line passing through (2, -4) is the parallel line.

The purple line passing through (2, -4) is the perpendicular to both lines.

Answer:

line 2

Step-by-step explanation:

#1 You got it right

When a you add a number you need to add to both sides

So line 2  was an error because it only added on the left side, not right side

This question was asked almost 3 years ago, there is a very good chance that they're not even in school anymore, it's crazy to think about. 3 years ago, I was living in Washington, and had joined online school for the first time, while this guy was here, begging people for answers to a question so he could pass highschool. Now, he's probably living his best life right now and doesn't even know what I'm typing right now, either that, or he's working at McDonald's. Honestly though, time flies by so fast though, it really is crazy.

Answer:

$3.15

Step-by-step explanation:

We start by dividing 4.5 by 100,(.045) to find what 1 percent is, once we have that we multiply by 30 (1.35)and get that and subtract it from 4.5

Answer:

The price of the coupon is $3.15.

Step-by-step explanation:

Boxes of sticky finger popsicles  are = $4.50

Supermarket is offering 30% coupon off.

We have to calculate the price with the coupon price of sticky finger popsicles will be given by

discounted price = original price - discount

                            = 4.50 - (30% of $4.50)

                           = 4.50 - (0.30 × 4.50)

                           = 4.50 - 1.35 = $3.15

The price of the coupon is $3.15.

Answer:

c ∛ (16)

Step-by-step explanation:

2 ^ (4/3)

We can separate this into 2 pieces using the power of power rule in reverse

x^a ^b = x^ (ab)

(2^4 ) ^ 1/3

2 to the 4th power is

16 ^ (1/3)

We now have the cubed root of 16

∛ (16)

Answer:

The answer is C :)

Answer:

Interest (I) = $ 900

Step-by-step explanation:

Formula for interest is given by:

Interest(I) = [tex]\frac{P \times R \times T}{100}[/tex]

where

P represents principal

R represents rate of interest

T represents the time in year.

Given : P = $ 12,000 , R =2.5% and  T = 3 years.

Interest(I) = [tex]\frac{12000 \times 2.5 \times 3}{100}[/tex]

On simplify:

[tex]I = \$ 900[/tex]

Therefore, the interest is , $ 900

Answer:

f^-1(x) = (x+2)/3

Step-by-step explanation:

To find the inverse of a function, exchange x and y and solve for y

y =3x-2

Exchange x and y

x =3y-2

Solve for y

Add 2 to each side

x+2=3y-2+2

x+2 = 3y

Divide each side by 3

(x+2)/3 =y

The inverse of the function is

f^-1(x) = (x+2)/3

Answer:

F-1(x)=(x+2)/3

Answer:

y = - 2x - 4

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y-intercept )

To calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (- 4, 4) and (x₂, y₂ ) = (2, - 8) ← 2 points on the line

m = [tex]\frac{-8-4}{2+4}[/tex] = [tex]\frac{-12}{6}[/tex] = - 2

the line crosses the y-axis at (0, - 4) → c = - 4

y = - 2x - 4 ← equation of line

Answer:

y= -2x-4

Step-by-step explanation:

Since, from the graph,we can see it is a straight line, therefore we apply the equation of the straight line that is:

y= mx+c where m is the slope and c is the intercept.

Since the points are(-4,4) and (2,8),

m= [tex]\frac{y_{2}-y_{1}  }{x_{2}-x_{1}  }[/tex]

 = [tex]\frac{-8-4}{2+4}[/tex]

 =[tex]\frac{-12}{6}[/tex]

 = -2

Therefore, m= -2

Now,since c is the intercept and the line cuts y- axis at (0,-4), therefore

 c= -4

⇒y= mx +c

  y= -2x+ (-4)

 y= -2x_4

Hello!! The answer is $22.08 Hope this helped!

$22.08 Would be the Answer for the price of a 20% off coupon on a $27.60 purchase.

Answer:

Part 1) Option D [tex]75=10d+5n[/tex]

Part 2) Option B [tex](4, -2), (0, -1), (-4, 0)[/tex]

Part 3) Option A [tex]50=2LW[/tex]

Part 4) Option A Ms. Monti bought [tex]4[/tex] adult tickets and [tex]3[/tex] children’s tickets

Part 5) Option D The kitten weighed [tex]14[/tex] ounces when it was [tex]4[/tex] weeks old

Step-by-step explanation:

Part 1)

we know that

[tex]1\ dime=\$0.10[/tex]

[tex]1\ nickel=\$0.05[/tex]

Let

d-------> the number of dimes

n-----> the number of nickels

so

[tex]0.10d+0.05n=0.75[/tex]

Multiply by [tex]100[/tex] both sides

[tex]10d+5n=75[/tex]

Part 2)

we have

[tex]y=(-\frac{1}{4})x-1[/tex]

To calculate the solutions of the equation for an x value, substitute the value of x in the equation and find the value of y

For [tex]x=4[/tex] -----> [tex]y=(-\frac{1}{4})(4)-1=-2[/tex] ----> [tex](4,-2)[/tex]

For [tex]x=0[/tex] -----> [tex]y=(-\frac{1}{4})(0)-1=-1[/tex] ----> [tex](0,-1)[/tex]

For [tex]x=-4[/tex] -----> [tex]y=(-\frac{1}{-4})(4)-1=0[/tex] ----> [tex](-4,0)[/tex]

Part 3)

we know that

The perimeter of a rectangle is equal to

[tex]P=2(L+W)[/tex]

we have

[tex]P=50\ ft[/tex]

substitute

[tex]50=2(L+W)[/tex] ------> [tex]50/2=(L+W)[/tex] -----> [tex]50=2L+2W[/tex]

Par 4)

Let

x------> the number of adult tickets

y------> the number of children tickets

we have

[tex]25x + 15y = 145[/tex]

The ordered pair [tex](4,3)[/tex] represent

[tex]x=4\ adult\ tickets[/tex]

[tex]y=3\ children\ tickets[/tex]

therefore

Ms. Monti bought [tex]4[/tex] adult tickets and [tex]3[/tex] children’s tickets

Part 5)  

Let

x------> the number of weeks after it was born

y-----> the kitten’s weight in ounces

we have

[tex]y=2.5x+4[/tex]  

The ordered pair [tex](4,14)[/tex] represent

[tex]x=4\ weeks[/tex]

[tex]y=14\ ounces[/tex]

therefore

The kitten weighed [tex]14[/tex] ounces when it was [tex]4[/tex] weeks old

Answer:

E = 216 joules

Step-by-step explanation:

The given equation is

E = [tex]\frac{m*v^{2} }{2}[/tex]                ............(i)

Here

m = 3 kg

v = 12 m/s

Putting the given values in equation (i)

E = [tex]\frac{3*12^{2} }{2}[/tex]

E = [tex]\frac{3*144}{2}[/tex]

E = [tex]\frac{432}{2}[/tex]

E = 216 kg m² /s²

or

E = 216 joules

Answer:

D

Step-by-step explanation:

the answer is d because the amount of speed changes the total amount of distance that he travels in time

Answer:

A motorcycle will complete the 540 mile trip in [tex]\frac{540}{48} = 11.25 hr[/tex]

And the car will complete it 2.25 hours less, i.e 11.25 -2,25 = 9 hours.

then,

Speed of the car is  [tex]\frac{540}{9} = 60 km/hr[/tex]

60t + 48t = 540

108t = 540

Divide both sides by 108 we get

t = 5

So, they will meet in 5 hours,

After 5 hours, the motorcycle will have traveled [tex]48 \times 5 = 240 miles[/tex]

and the car will have traveled = [tex]60 \times 5 = 300 miles[/tex]

Given is :

The distance between the cities Chicago and Toronto is = 540 miles

Speed of motorcycle = 48 mph

So, time taken by motorcycle to cover 540 miles = [tex]\frac{540}{48}=11.25[/tex] hours

Hence, the motorcycle will complete the 540 miles trip in 11.25 hours.

As given, the car takes 2.25 hours less to cover the same distance, so car takes [tex]11.25-2.25=9[/tex] hours

So,the speed of the car therefore is [tex]\frac{540}{9}=60[/tex] mph.

Let both the car and motorcycle meets is 't' time.

So, [tex]60t+48t=540[/tex]

[tex]108t=540[/tex]

t = 5

So, they will meet in 5 hours.

After 5 hours, the motorcycle will have traveled 48x5 = 240 miles

And the car will have traveled 60x5 = 300 miles.

Answer:

=110.8 percent

Step-by-step explanation:

We can use this formula to find the percent increase

percent increase = (new - original)/ original * 100

new = 363,844,490

original =172,602,624

Substitute these values in

percent increase = (363,844,490 - 172,602,624)/ 172,602,624 * 100

percent increase = 191241866/172602624 *100

                             = 1.107989332

                            =110.8 percent

Answer:

80

Step-by-step explanation:

A triangle always measures to be 180 degrees. 50+50=100 so 80 degrees is left

Answer:

This is the actual steps and answer.

Step-by-step explanation:

\text{Exponential Functions:}

Exponential Functions:

y=ab^x

y=ab  

x

a=\text{starting value = }5000

a=starting value = 5000

r=\text{rate = }4\% = 0.04

r=rate = 4%=0.04

\text{Exponential Growth:}

Exponential Growth:

b=1+r=1+0.04=1.04

b=1+r=1+0.04=1.04

\text{Write Exponential Function:}

Write Exponential Function:

y=5000(1.04)^x

y=5000(1.04)  

x

Put it all together

\text{Plug in time for x:}

Plug in time for x:

y=5000(1.04)^{7}

y=5000(1.04)  

7

y= 6579.6589

y=6579.6589

Evaluate

y\approx 6580

y≈6580

round

The population after 7 years at the rate of 4% growth every year would be 6580.

Exponential growth is a function that grows or decays at a constant percent rate.

The formula used is [tex]y = b(1 + r)^ t[/tex]. where, y is the exponential growth function, b is the initial amount, r rate, and t time interval.

From the information given,

b = 5000

r = 4% = 4/100

= 0.04

t = 7 years

Therefore

[tex]y = b(1 + r)^ t[/tex]

[tex]y = 5000(1 + 0.04)^7[/tex]

[tex]y = 5000(1.04)^7[/tex]

y = 6580

Thus, The population after 7 years at the rate of 4% growth every year would be 6580.

Learn more about exponential growth;

https://brainly.com/question/11487261

Answer:

B

Step-by-step explanation:

Answer:

The answer is B : Perpendicular

Step-by-step explanation:

Parallel lines are lines that never intersect as   or do not meet so this is  not the case. Skew lines are lines that neither intersect nor they are parallel. This are lines that are in separate planes in space so they never touch. Adjacent lines are lnes that meet at a specific point , but can form any type of angle. Perpendicular lines are lines that cross and form 4 right angleso rangles of 90 degrees so this is the answer,

Answer:

6 1\20 is the answer

Step-by-step explanation:

Answer:

6 to the power of 1 over 20

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

here's how I got it A and C are similar but C will have a different answer because you will multiply 12*7 then add 91 that will equal 175 but it wants the answer that is 12 larger than 7 + 91. when it is in parenthesis it goes first so then you do 7+91 first and that is 98. then multiply 12*98=1176 and that is the correct answer because it is 12 times the sum of 7 and 91.

The expression that is 12 times as large as the expression 7 plus 91 is A) 12 x (7+91). First, we solve the expression in parentheses, 7+91, to get 98. Then, we multiply 98 by 12 to get the final result of 1176.

The question is asking which expression results in a value that is 12 times as large as the expression 7 plus 91. The expression 7 plus 91 results in a value of 98. In order to find a value that is 12 times as large as 98, we need to multiply 98 by 12. That operation is represented by the expression 12 x (7+91), which is option A.

To break it down step by step:

In conclusion, the expression that is 12 times as large as the expression 7 plus 91 is A) 12 x (7+91).

https://brainly.com/question/29020789

#SPJ3

Answer:

0

Step-by-step explanation:

23/40 - 11/30

We are using the benchmarks 0, 1/2 ,1 to approximate our values

23/40 is close to 1/2

11/30 is close to 1/2

1/2 - 1/2 = 0

Answer:

4

Step-by-step explanation:

To figure out how many times the population of India  is as compared to the US, we take the population of India and divide by the population of the US

Population of India/population of US

1.2*10^9 /300000000

I will change 300000000  into scientific notation by moving the decimal 8 places to the left, so it becomes 3 *10^8

1.2*10^9 /3* 10^8

Now we divide the numerals and subtract the exponents

1.2/ 3  * 10^(9-8)

.4 * 10^1

.4*10

4

Answer: D

Step-by-step explanation:

D contains both (2,2) and (2,1), and fails the definition. D(2) would have to be 2 and 1 at the same time.

Set S is a function if and only if

x ∈ S implies x is an ordered pair,

and

(a,b) and (a,c) ∈ S implies b = c.

Answer:

set D

Step-by-step explanation:

For a function we need to have for evety x value, only one value of y.

in set D, we have the points (2, 2) and (2, 1)

this two points have one value of x: x=2

but for the same x we have two values of y: 2 and 1

so this does not obey the requirements to be a functios wich is that for every x, we cannot have more than one value of y.

Answer:

x=4 °

z = 77°

Step-by-step explanation:

We know vertically opposite angles are equal

HEre (5x+83)  and 103  are vertically opposite angles . so they are equal'

Set them equal and solve for x

5x+83= 103

subtract 83 on both sides

5x = 20

Divide both sides by 5

x= 4

103  and angle z  are in a straight line

Sum of angles in a straight line is 180 degrees

So 103 + z = 180

subtract 180 on both sides

z = 77°

If C is the cost and x the amount of cans.

C = 0.5x - 0.8

To round a number to the nearest hundredth, check the thousandth digit. If it's 4 or less, the hundredth digit doesn't change. If it's 5 or greater, round up the hundredth digit and increase it by 1.

To round a number to the nearest hundredth, you need to look at the thousandth place. If this digit is 4 or less, the hundredth digit remains the same. If the thousandth digit is 5 or greater, then you round up the hundredth digit by increasing it by 1. In this case,

Alex's batting average is 0.346, and the thousandth digit is 6, which is greater than 4. So, when rounded to the nearest hundredth, his batting average would be 0.35.

https://brainly.com/question/29022222

#SPJ3

Answer:

x - 6y = -9

Step-by-step explanation:

We are given two points (-3,1) and (3,2) on a line so we will use them to find the slope.

Slope ([tex]m[/tex]) = [tex]\frac{2-1}{3+3} =\frac{1}{6}[/tex]

The standard form of the equation is [tex]y=mx+c[/tex] so we will substitute the values of the coordinates of a point and slope (m) to find the y-intercept (c).

[tex]2=\frac{1}{6} +c\\\\c=\frac{3}{2}[/tex]

So the equation of the line which passes through the given points will be [tex]y=\frac{1}{6} x+\frac{3}{2}[/tex] which can be rearranged to write it as:

x - 6y = -9

Answer:

Option C.

Step-by-step explanation:

The standard form of a line is

[tex]Ax+By=C[/tex]

It a line passes through two points then the equation of line is

[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

It is given that the line passes through the points (-3,1) and (3,2). So the equation of line is

[tex]y-(1)=\dfrac{2-1}{3-(-3)}(x-(-3))[/tex]

[tex]y-1=\dfrac{1}{6}(x+3)[/tex]

Multiply both sides by 6.

[tex]6(y-1)=x+3[/tex]

[tex]6y-6=x+3[/tex]

Subtract 6y and 3 from both sides.

[tex]6y-6-6y-3=x+3-6y-3[/tex]

[tex]-6-3=x-6y[/tex]

[tex]-9=x-6y[/tex]

Interchange both sides.

[tex]x-6y=-9[/tex]

Therefore, the correct option is C.

Hi there! :) :D

Answer:

A. -9

*The answer must have a negative sign.*

Step-by-step explanation:

Lesson: Dividing integers

First, you divide by the numbers from left to right.

[tex]72/8=9[/tex]

It change positive to negative sign.

[tex]72/9=8[/tex]

Then, you can also multiply by the numbers from left to right.

[tex]9*8=72[/tex]

[tex]8*9=72[/tex]

Final answer is -9

Hope this helps!

Have a nice day! :)

:D

-Charlie

Thank you so much! :)

:D

Answer:

the answer is -9

Step-by-step explanation:

3 - 15 = -12

-12 - (-3) = 9 adding two negatives gives you a positive so its really, -12 + 3

Just substitute then solve

3-15-(-3)

Answer:

-9

If it helps draw a number line

<--------------------------------------------------------------------->

 -10            -5                 0              5                   10

start at 3, then left 15 spaces, then right 3 spaces

Answer:

The Science Center charge less than the Dino Discovery museum for more then 10 students

Step-by-step explanation:

Let us assume that the number of students are x .

Let us assume that the total charge for x students be y.

As given

Mrs. Williams is deciding between two field trips for her class.

The Science Center charges $120 plus $5 per student.

Than the equations becomes

y = 120 + 5x

The Dino Discovery Museum simply charges $7 per student.

y = 7x

Than

[tex]120 + 5x < 7x[/tex]

[tex]120 < 7x - 5x[/tex]

[tex]120 < 2x[/tex]

[tex]\frac{120}{12} < x[/tex]

[tex]10 < x[/tex]

Therefore the Science Center charge less than the Dino Discovery museum for more then 10 students.

Answer:

There are 10,000 1s in Ten Thousand

Hope this helped:)

Step-by-step explanation: