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nalin [4]
2 years ago
12

Find the slope and the y-intercept of the following graph

Mathematics
1 answer:
spin [16.1K]2 years ago
5 0

Answer:

The slope of the graph is 5, and the y-intercept is (0, -3).

Step-by-step explanation:

Let's start by finding the y-intercept.

The y-intercept is the point where the line intercepts the y-axis.

Looking at the graph, we can determine that the y-intercept is (0, -3).

The slope of a graph can be found using two points on the line.

Let's use (0, -3) and (1, 2):

Slope=\frac{Rise}{Run}=\frac{y_2-y_1}{x_2-x_1}=\frac{2-(-3)}{1-0}=\frac{5}{1}=5

Therefore the slope of the graph is 5, and the y-intercept is (0, -3).

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Samantha threw an apple out of a window from the tenth floor of her apartment building.The equation y=-16t^2+120 can be used to
Savatey [412]
If the apple is on the ground, then the height y is 0. To find t, just plug in 0 for y:
0=-16t^{2}+120
-120=-16t^{2}
t^{2} =7.5
t=2.74

So the answer is 2.74 seconds.

Note that taking the square root of 7.5, mathematically, gives you both 2.74 and -2.74. But because we know that time did not go backwards, only the positive value for t was considered.
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The point U (-2,0) is translated 1 unit up. What are the coordinates of the resulting point, U’?
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Point U' (-2, 1)

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If the perimeter of square region S and the perimeter of rectangular region R are equal and the sides of R are in the ratio 2:3
horrorfan [7]

Answer:  The correct option is (B) 24 : 25.

Step-by-step explanation:  Given that the perimeter of square region S and the perimeter of rectangular region R are equal and the sides of R are in the ratio 2 : 3.

We are to find the ratio of the area of R to the area of S.

Let 2x, 3x be the sides of rectangle R and y be the side of square S.

Then, according to the given information, we have

\textup{Perimeter of rectangle R}=\textup{Perimeter of square S}\\\\\Rightarrow2(2x+3x)=2(y+y)\\\\\Rightarrow 5x=2y\\\\\Rightarrow \dfrac{x}{y}=\dfrac{2}{5}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)

Therefore, the ratio of the area of R to the area of S is

\dfrac{2x\times3x}{y\times y}\\\\\\=\dfrac{5x^2}{y^2}\\\\\\=6\left(\dfrac{x}{y}\right)^2\\\\\\=6\times\left(\dfrac{2}{5}\right)^2~~~~~~~~~~~[\textup{Using equation (i)}]\\\\\\=\dfrac{24}{25}\\\\=24:25.

Thus, the required ratio of the area of R to the area of S is 24 : 25.

Option (B) is CORRECT.

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