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2 years ago

Match each equation with its graph. y = 5x + 2, y = 3x + 3, y = 2x + 3

Mathematics

2 answers:

Licemer1 [7]2 years ago

4 0

Answer:

All the graphs for each problem

stiks02 [169]2 years ago

3 0

Answer:

Green line: y = 5x + 2

Red line: y = 3x + 3

Purple line: y = 2x + 3

Step-by-step explanation:

1) All the given equations are in slope-intercept form, or $y = mx + b$ format. When an equation is written in this form, the constant on the right side of the equation, or the $b$ , represents the y-intercept. The y-intercept is the point at which the line crosses the y-axis.

Knowing this, the y-intercept of $y = 5x + 2$ must be (0,2). The only graph in which the line crosses the y-axis at the point (0,2) is the one with the green line, thus the graph of $y = 5x + 2$ is the green one.

2) Now, since the other two equations share the same y-intercept, we have two graphs left. We can find out which graph belongs to which equation by taking a look at the slope of the line. The number in place of $m$ , or the coefficient of the x-term in an equation in slope-intercept format represents the slope. Thus, the slope of $y = 3x +3$ is 3 and the slope of $y = 2x + 3$ is 2.

Now, find the slope of one of the lines in the graphs. To do so, use the slope formula, $m = \frac{y_2-y_1}{x_2-x_1}$ . Substitute the x and y values of two points on the chosen line into the formula in order to figure out the line's slope. I chose to find the slope of the red line, using the points (0,3) and (-1,0):

$m = \frac{(0)-(3)}{(-1)-(0)} \\m = \frac{0-3}{-1-0}\\m = \frac{-3}{-1} \\m = 3$

So, the slope of the red line is 3. Its equation must be $y = 3x + 3$ since it has the matching slope. By process of elimination, the purple line must have the equation of $y = 2x + 3$ .

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Simplify the polynomial by combining like terms

Veseljchak [2.6K]

Answer:

22 x^2

Step-by-step explanation:

Simplify the following:

11 x^2 + 11 x^2

Hint: | Add like terms in 11 x^2 + 11 x^2.

11 x^2 + 11 x^2 = 22 x^2:

Answer: 22 x^2

none of your answers are correct.

8 0

3 years ago

Please help with this

KonstantinChe [14]

I believe the answer is 32

4 0

2 years ago

A model rocket is launched with an initial velocity of 200 ft per second. The height h, in feet, of the rocket t seconds after t

Solnce55 [7]

Answer:

2.10 s, 10.40 s.

Step-by-step explanation:

We know that the height of the rocket is given by the function:

$h=-16t^2+200t$

We are asked to find the time for which the height of the rocket will be 350 ft. So, for that moment, we know the height but we don't know the time; however, we know that the equation can help us to find the time, doing h=350:

$350=-16t^2+200t$

The last is a quadratic equation, which can be put in the form $at^2+bt+c=0$ and solved applying the formula:

$t=\frac{-b+-\sqrt{b^2-4ac} }{2a}$

So, let's put the equation on the form $at^2+bt+c=0$ adding $16t^2$ and subtracting $200t$ to each side of the equation; the result is:

$16t^2-200t+350=0$

So, we note that a=16, b=-200, and c=350.

Then,

$t_1=\frac{200-\sqrt{200^2-4*16*350} }{2*16}=2.10$

$t_2=\frac{200+\sqrt{200^2-4*16*350} }{2*16}=10.40$

According to the equation, that are the times for which the height will be 350 ft; that is because the rocket is going to ascend and then to fail again to the ground.

4 0

3 years ago

Two competitive neighbours build rectangular pools that cover the same area but are different shapes. Pool A has a width of (x +

GenaCL600 [577]

<u>Answer: </u>

a)Dimensions of pool A are length = 6.667m and width = 3.667 m and dimension of pool B are length = 7.333m and width = 3.333m.

b) Area of pool A is equal to area of pool B equal to 24.44 meters.

<u> Solution: </u>

Let’s first calculate area of pool A .

Given that width of the pool A = (x+3)

Length of the pool A is 3 meter longer than its width.

So length of pool A = (x+3) + 3 =(x + 6)

Area of rectangle = length x width

So area of pool A =(x+6) (x+3) ------(1)

Let’s calculate area of pool B

Given that length of pool B is double of width of pool A.

So length of pool B = 2(x+3) =(2x + 6) m

Width of pool B is 4 meter shorter than its length,

So width of pool B = (2x +6 ) – 4 = 2x + 2

Area of rectangle = length x width

So area of pool B =(2x+6)(2x+2) ------(2)

Since area of pool A is equal to area of pool B, so from equation (1) and (2)

(x+6) (x+3) =(2x+6) (2x+2)

On solving above equation for x

(x+6) (x+3) =2(x+3) (2x+2)

x+6 = 4x + 4

x-4x = 4 – 6

x = $\frac{2}{3}$

Dimension of pool A

Length = x+6 = ( $\frac{2}{3}$ ) +6 = 6.667m

Width = x +3 = ( $\frac{2}{3}$ ) +3 = 3.667m

Dimension of pool B

Length = 2x +6 = 2( $\frac{2}{3}$ ) + 6 = $\frac{22}{3}$ = 7.333m

Width = 2x + 2 = 2( $\frac{2}{3}$ ) + 2 = $\frac{10}{3}$ = 3.333m

Verifying the area:

Area of pool A = ( $\frac{20}{3}$ ) x ( $\frac{11}{3}$ ) = $\frac{220}{9}$ = 24.44 meter

Area of pool B = ( $\frac{22}{3}$ ) x ( $\frac{10}{3}$ ) = $\frac{220}{9}$ = 24.44 meter

Summarizing the results:

(a)Dimensions of pool A are length = 6.667m and width = 3.667 m and dimension of pool B are length = 7.333m and width = 3.333m.

(b)Area of pool A is equal to Area of pool B equal to 24.44 meters.

5 0

3 years ago

How are the shapes alike

Andrews [41]

Answer:

Each circle (A, B, and C) contain shapes that all share at least one characteristic. Some shapes are contained in more than one circle because they share more than one characteristic. For example, shape 3 fits the rule for circles A and B, but not circle C. It lies within circles A and B, but not circle C.

Step-by-step explanation:

3 0

2 years ago