100 students attended a revision lesson at the weekend.

Graph on a coordinate plane each set of (x, y) values. Which set of values describes two quantities that are in a proportional r

natita [175]

Answer:

C

Step-by-step explanation:

4 : 9

2 : 4.5

y = kx

y = 2.25x

4 0

3 years ago

Two cars traveled equal distances in different amounts of time. Car A traveled the distance in 2.4 h, and Car B traveled the dis

Arte-miy333 [17]

One way to go about this is to first list everything we know in the form of variables. This will make it easier to see how these numbers correlate instead of trying to remember formulas to plug these numbers into.

TimeA = 2.4h (time of Car A to travel)
TimeB = 4h (time of Car B to travel)
SpeedA = SpeedB + 22mph (Speed of Car A)
SpeedB = SpeedA - 22mph (Speed of Car B)
Distance = x (the distance traveled by each car)

We are looking for SpeedA. How can we find this? Well, we know that speed multiplied by time is equal to distance, so let's start there.

SpeedA * 2.4h = x
(SpeedB + 22mph) * 2.4h = x
(2.4h * SpeedB) + 52.8miles = x

We also know that:
SpeedB * 4h = x

Since both of these equations are equal to x, we can combine them:
SpeedB * 4h = x = (2.4h * SpeedB) + 52.8miles
SpeedB * 4h = (2.4h * SpeedB) + 52.8miles
1.6h * Speed B = 52.8miles
SpeedB = 52.8/1.6 mph = 33 mph

SpeedA = SpeedB + 22mph = 33mph + 22mph = 55mph

Therefore, Car A was traveling at 55mph.

3 0

3 years ago

Does anyone understand how to do this

Lerok [7]

Answer:

Step-by-step explanation:

I understand it! (But I'm a high school math teacher so it might be unfair!) ; )

Anyway you have 2 numbers. You don't know what they are so we will call them x and y. Our first statement says that these numbers multiply to equal 120. So that first equation is

xy = 120

Our second statement says that they add to -22. So that second equation is

x + y = -22

Now we need to find the 2 numbers. We have 2 unknowns, x and y. That means that we have to have 2 equations. No more than 2 no less than 2. Solve the first equation for y. It doesn't matter which equation you pick and which variable you choose to solve for. If you do the work correctly, you will get the correct answers either way. Solving the first equation for y gives you:

$y=\frac{120}{x}$

Now tht we have a value for y, we can use the substitution property of equality to sub that value into the second equation for y:

$x+\frac{120}{x}=-22$

Instead of finding a common denominator, we are going to eliminate x in the denominator altogether. Do this by multiplying everything by x to get

$x^2+120=-22x$

Get everything on one side of the equals sign and factor:

$x^2+22x+120=0$

Because 12 * 10 = 120 and 12 + 10 = 22, our factors are 12 and 10:

$x^2+12x+10x+120=0$

Use factoring by grouping now.

$(x^2+12x)+(10x+120)=0$

From the first set of parenthesis you can factor out an x, and from the second set you can factor out a 10:

x(x + 12) + 10(x + 12) = 0

Now factor out the common x + 12 to get a factored quadratic:

(x + 12)(x + 10) = 0

By the Zero Product Property, either x + 12 = 0 or x + 10 = 0. Solving both for x gives you x = -12 or x = -10.

If x = -12, then

-12 + y = -22 so

y = -10

If x = -10, then

-10 + y = -22 so

y = -12.

The combinations of x and y are:

If x = -12, y = 10

If x = -10, y = -12

It doesn't matter which one is which. They are not asking you to specifically define x and y. They are asking you to find the numbers, and you did!

6 0

3 years ago

How do i solve 4g + 2 ≥ - 14

Kryger [21]

Answer:

g ≥ -4

Step-by-step explanation:

4g + 2 ≥ - 14

-2 -2 Subtract 2 from both sides

4g ≥ -16

g ≥ -4 Divide both sides by 4

5 0

3 years ago

Identify the terms,like terms,coefficient and constants

BartSMP [9]

Terms: -4j, -2, -5j, 6
Like Terms: -4j and -5j, -2 and 6
Coefficients: -4, -5
Constants: -2, 6

6 0

3 years ago