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2 years ago

Write the systems of equations from the table below and find the solution?

Mathematics

1 answer:

Alecsey [184]2 years ago

5 0

The system of equations is y = 4x - 3 and y = -1/3x + 4 and the solution is (21/13, 45/13)

<h3>How to determine the system of equations?</h3>

From the question, we have the table of values as the parameters that can be used in our computation:

From the table, we have

Table 1

(x, y) = (0, -3) and (4, 13)

A linear equation is represented as

y = mx + c

Where

Slope = m

c = y when x = 0

This means that

c = -3

So, we have

y = mx - 3

The point (4, 13) implies that

13 = m * 4 - 3

So, we have

4m = 16

m = 4

So, the equation is

y = 4x - 3

Table 2

(x, y) = (0, 4) and (4, 6)

A linear equation is represented as

y = mx + c

This means that

c = 4

So, we have

y = mx + 4

The point (4, 6) implies that

6 = m * 4 + 4

So, we have

4m = -2

m = -1/3

So, the equation is

y = -1/3x + 4

Substitute y = -1/3x + 4 in y = 4x - 3

-1/3x + 4 = 4x - 3

So, we have

-x + 12 = 12x - 9

Evaluate the like terms

13x = 21

Divide

x = 21/13

y = -1/3x + 4 implies that

y = -1/3 x 21/13 + 4

So, we have

y = -7/13 + 4

Evaluate

y = 45/13

So, the solution is (21/13, 45/13)

Read more about system of equations at

brainly.com/question/13729904

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Is 3/8 squared irratonal

givi [52]

the correct answer is yes. 3/8 is the irrational.

step by step explaination: Assuming you meant, then it's irrational. The square root of any Natural Number which is not a perfect square is irrational. 8 is not a perfect square so is irrational.

I am glad to help you!!!!!!!!!!!!

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4 years ago

Points (−7, 5) and (7, 5) on the coordinate grid below show the positions of two players of a football team:

MAXImum [283]

Given:

Player 1 is at (-7,5).

Player 2 is at (7,5).

To find:

The relationship between the positions of the two players.

Solution:

The two points are (-7,5) and (7,5).

Here, x-coordinates are different but y-coordinates are same. The absolute values of x-coordinates are equal but the signs are different.

The transformation is defined as

$(x,y)\to (-x,y)$

It means, the points are mirror image of each other with respect to y-axis.

Player 1's position is Player 2's position reflected across the y-axis; only the signs of the x-coordinates of Player 1 and Player 2 are different.

Therefore, the correct option is C.

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3 years ago

A ball is thrown upward with an initial velocity of 16 ft/sec from a height of 32 ft above the ground. The height, in feet, of t

GaryK [48]

Answer: 2 seconds.

Step-by-step explanation:

Given : A ball is thrown upward with an initial velocity of 16 ft/sec from a height of 32 ft above the ground.

The height, in feet, of the ball t sec after it is thrown can be represented by

$s=-16t^2+16t+32.$

When ball reaches the ground , s= 0.

$\Rightarrow -16t^2+16t+32=0$

Divide both sides by 16 , we get

$-t^2+t+2=0\\\\\Rightarrow\ t^2-t-2=0\\\\\Rightarrow\ t^2-2t+t-2=0\\\\\Rightarrow\ (t-2)(t+1)=0 \\\\\Rightarrow\ t=2,-1$

But time cannot be negative , so t= 2.

Hence , it will take 2 seconds for the ball to reach the ground.

8 0

3 years ago

A parabola can be drawn given a focus of (5, -3) and a directrix of y=1. Write the equation of the parabola in any form.

Anna71 [15]

Answer:

(x²-10x+33)/(-8) = y

Step-by-step explanation:

The distance between any point on a parabola from both its focus and directrix are the same.

Let's say we have a point (x,y) on the parabola. We can then say that using the distance formula,

$\sqrt{(x-5)^2+(y-(-3))^2}$ is the distance between (x,y) and the focus. Similarly, the distance between (x,y) and the directrix is |y-1| (I use absolute value here because distance is always positive). We can find this equation by taking the shortest distance from the point to the line. Because the closest point to the line will be the same x value as the point itself, the distance is simply the distance between the y value of the point and the y value of the directrix.

Equating the two equations given, we have

$\sqrt{(x-5)^2+(y-(-3))^2} = |y-1|$

square both sides to get

(x-5)²+(y+3)²=(y-1)²

expand the y components

(x-5)² + y²+6y+9 = y²-2y+1

subtract y²+6y+9 from both sides

(x-5)² = -8y - 8

expand the x components

x²-10x+25 = -8y - 8

add 8 to both sides to isolate the -8y

x²-10x+33 = -8y

divide both sides by -8 to isolate y

(x²-10x+33)/(-8) = y

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3 years ago

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spin [16.1K]

hello i would not know to be honest

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3 years ago