Rearranging Equations: Solve the equation for y: 8x + y = 14 Solve the equation for x: -9x + 3y = 18

Given:

Number of passengers seated in the roller coaster = 21

Empty seats = 3

Number of cars in roller coaster = 4 (each with the same number of seats)

To find:

An equation that can be used to determine the number of seats in each car.

Solution:

Let s be the number of seats in each car.

Total number of seats in 4 cars = 4s

Using the given information,

Total number of seats = Occupied seated + Empty seats

                                   = 21 + 3

                                   = 24

Now, the required equation is

[tex]4s=24[/tex]

Therefore, the required equation is [tex]4s=24[/tex].

Divide both sides by 4.

[tex]s=\dfrac{24}{4}[/tex]

[tex]s=6[/tex]

Therefore, the number of seats in each car is 6.

Answer:

Step-by-step explanation:

Given the function y= 2x if x>0 and x−3 if x≤0, to find the value of the function for x = 1, we will substitute x = 1 into the function y = 2x since x>0 at that point.

If x = 1;

y = 2(1)

y = 2

Hence when x = 1, y = 2

If x = 3, we will still use the function y = 2x since 3 is still grater than 0 satisfying the condition x>0.

y = 2(3)

y = 6

Hence when x = 3, y = 6

when x = 0, since x is zero, we will substitute x = 0 into the function x-3 because x≤0 at this point.

If y = x-3

y = 0-3

y = -3

Hence when x = 0, y = -3

when x = -2, we will substitute x = 0 into the function x-3 because -2 is also less than zero

If y = x-3 for x≤0

y = -2-3

y = -5

Hence when x = -2, y = -5

Answer:

B(4, -5)

Step-by-step explanation:

A(-8, 7)

M(-2, 1)

B(x, y)

x-coordinate:

(-8 + x)/2 = -2

-8 + x = -4

x = 4

y-coordinate:

(7 + y)/2 = 1

7 + y = 2

y = -5

B(4, -5)

Answer:

  69 miles

Step-by-step explanation:

Put the number in place of the variable representing it and do the arithmetic.

  L = 41 +28 = 69

After 28 days, the length of the road is 69 miles.

Answer:

4,000 is the integer representing the final balance of the bank account

Step-by-step explanation:

Here, we are told that Shiavni had a total of $9,000 in her bank account at the start of the week of which she spent $5,000 out of it on an antique clock.

Now, we want to know the integer that represents the amount which is the final balance of the bank account.

Mathematically, when we talk of an integer, we are simply referring to a whole number, be it negative or positive.

Thus, the integer is the case is the difference in what she had at the beginning of the week minus the cost of the clock

That would be; $9,000 -$5000 = $4,000

Answer:

Width = 44.45 inches

Height = 25.00 inches

Step-by-step explanation:

(16x)^2 + (9x)^2 = 51^2

256x^2 + 81x^2 = 2601

337x^2 = 2601

x^2 = 7.718

x = 2.778

Width = 44.45 inches

Height = 25.00 inches

I think this is right

The width and height of the given TV screen will be 44.45 inches and 25.00 inches.

A rectangle is a geometrical figure in which opposite sides are equal.

The angle between any two consecutive sides will be 90 degrees.

Area of rectangle = length × width.

Perimeter of rectangle = 2( length + width).

The length of any TV is measured diagonally.

So,

Diagonal = 51 inches

Now the ratio is ;

W/H = 16 / 9

Let's say both are fractions of x

So,

Width = 16x , Height = 9x

By Pythagoras theorem,

(16x)² + (9x)² = 51²

256x² + 81x² = 2601

337x² = 2601

x² = 7.718

x = 2.778

So width = 16(2.778) = 44.45 inches.

And height = 9(2.778) = 25.00 inches

Hence "The width and height of the given TV screen will be 44.45 inches and 25.00 inches".

For more about rectangles,

https://brainly.com/question/15019502

#SPJ2

Answer: 13

Step-by-step explanation:

cost for 3 hours: 7+2(3)=13

cost for t hours: 7+2t

Answer:

(x-12y)(x+y)

Step-by-step explanation:

Answer:

16

Step-by-step explanation:

I counted each of the cubes and got 64.

Then I divided it by 4 since you need to divide it be 1/4.

once I divided 4 for 64 I got 16.

Angle LMN

Angle NML

Angle M

These are the only ways to name this angle

Answer:

Angle NML, LMN, and the angle created by rays MN and ML intersecting at point M.

Step-by-step explanation:

The first two ways are just the points in order. The third can be written in multiple ways but I believe this one is quite explanatory.

Answer:

7

Step-by-step explanation:

Answer:

I

Step-by-step explanation:

J

Answer:

12.5 cm

Step-by-step explanation:

1,000 meters/ 80m is 12.5

if it was negitive I would be -2

Step-by-step explanation:

so 6-4=2 and if you make that negative it would be -2

Answer:

-$6 + $4 = -$2

Step-by-step explanation:

Since Morris borrowed 6 dollars to begin with, the first term in my equation is -6$, representing the debt he has incurred from taking a loan of 6 dollars from his mother. After paying $4 dollars, he would still be in debt of $2 to his mother. Since he is still in debt of 2 dollars, the furthest right term in my aforementioned equation is -$2.

Answer:

A negative number

Step-by-step explanation:

I know this is right. Negative numbers represent opposites. If positive represents a movement to the right, negative represents a movement to the left.In the context of negative numbers, a number that is greater than zero is referred to as positive. Thus every real number other than zero is either positive or negative, while zero itself is not considered to have a sign. Positive numbers are sometimes written with a plus sign in front, e.g. +3 denotes a positive three.

The solution to the equation W - 2 + 2w = 6 + 5w is W = -4.

To solve the equation W - 2 + 2w = 6 + 5w,  follow these steps:

Begin by gathering the terms with W on one side and the terms without W on the other side of the equation.

Start by subtracting 2w from both sides:

W - 2 + 2w - 2w = 6 + 5w - 2w

Simplify:

W - 2 = 6 + 3w

Next, move the constant term (6) to the left side by subtracting 6 from both sides:

W - 2 - 6 = 6 + 3w - 6

Simplify:

W - 8 = 3w

Now, let's isolate the variable W by subtracting 3w from both sides:

W - 3w - 8 = 3w - 3w

Simplify:

-2w - 8 = 0

Finally, solve for W by adding 8 to both sides:

-2w - 8 + 8 = 0 + 8

Simplify:

-2w = 8

Divide both sides by -2 to isolate w:

(-2w) / -2 = 8 / -2

Simplify:

w = -4

To know more about equation  here

https://brainly.com/question/29657983

#SPJ6

[tex]\text {Hi There! The answer to your problem is}[/tex]

[tex]\fbox {x=-3/13}[/tex]

[tex]\text {Your 1st Step will be to Simplify the Equation}[/tex]

[tex]\text {-5x+3=8x+9+-3}[/tex]

[tex]\text {-5x+3=(8x)+(9+-3) (Combine Like Terms)}[/tex]

[tex]\text {-5x+3=8x+6}[/tex]

[tex]\text {The Next Step is to Subtract 8x}[/tex]

[tex]\text {-13x+3-3=6-3}[/tex]

[tex]\text {-13x=3}[/tex]

[tex]\text {The Final Step is to Divide by -13}[/tex]

[tex]\text {-13x/13=3/-13}[/tex]

[tex]\text {x=-3/13}[/tex]

[tex]\text {Best of Luck!}[/tex]

[tex]\text {-LimitedX}[/tex]

In 3(x+2)=18,  X=4

Divide both sides by the numeric factor on the left side, then solve.

Answer: m=2

Use the slope-intercept form

y=mx+b to find the slope m

Step-by-step explanation:

Use the slope-intercept form

y=mx+b to find the slope m

Answer:

D. [tex]y = 2x[/tex]

Step-by-step explanation:

A proportional relationship is represented by the formula [tex]y = mx + b[/tex].

m = the slope, which is  [tex]\frac{y_{2}-y_{1} }{x_{2} - x_{1}}[/tex].

b = the y-intercept, the point where the line crosses the y-axis. We actually don't have to worry about the [tex]+ b[/tex] part of the formula because [tex]b = 0[/tex], so it can be left out.

To find the slope, use [tex]\frac{y_{2}-y_{1} }{x_{2} - x_{1}}[/tex]. Subtract the smaller y value (2) from the larger y value (6).

(6 - 2 = 4)

Then subtract the smaller x value (1) from the larger x value (3).

(3 -  1 = 2)

So it looks something like this now:

[tex]\frac{6-2}{3-1}[/tex] , which equals [tex]\frac{4}{2}[/tex]

Then you divide the top part of the fraction (4) by the bottom part. (2).

[tex]\frac{4}{2}[/tex] = 2. The slope (m) is 2.

So the final equation is [tex]y=2x[/tex].

Answer:

=10x2+3x+4

Step-by-step explanation:

I hope this helps you

Answer:

10x^2+3x+4 should be the correct answer