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Bumek [7]
3 years ago
13

Which equation describes the relation indicated by the table? x = -2,0,4,6 y = 3,2,0, -1

Mathematics
1 answer:
Brilliant_brown [7]3 years ago
5 0
<span>Answer: - (1/2)x + 2

Solution:

1) Table
</span>
<span><span> </span><span><span> x    y

</span> <span> -2   3 </span> <span>
0    2 </span> <span>
4    0
</span> <span> 6   -1

The first thing that you must probe is whether the relation is linear.

When the relation is linear the rate of change is constant.

The rate of change is Δy / Δx

2) Let's calculate that rate for all the points given:

</span></span></span><span><span> x    y

</span> -2   3 <span>
0    2 </span> <span> ---> Δx = 0 -(-2) = 2, Δy = 2 - 3 = - 1 => Δy / Δx = - 1/2
4    0 ---> Δx = 4 - 0 =4, Δy = 0 - 2 = -2 => Δy / Δx = -2/4 = - 1/2
</span> <span> 6   -1</span></span> ---> Δx = 6 - 4 = 2, Δy = - 1 - 0 = -1 => Δy / Δx = - 1/2
<span> </span>
So, we have shown that the relation is linear.

3) Now, you can use the equation of the line: y = mx + b, where m is the slope (rate of change Δy / Δx) and b is the y-intercept.

We already found m = -1/2

The y-intercept is the value of y when x = 0, which you can get from the table; b = 2.

Therefore the equation is: y = (-1/2)x + 2.
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The area of a rectangle is 256.5m.  If the length is 18m what is the perimeter of the rectangle?
irga5000 [103]
The area of a rectangle equals length times height. (A=LH)

A=256.5 L=18

Plugging in the numbers into the equation, you get 256.5=18H. (like I substituted the numbers in)

next if you divided both sides by 18, it will cancel out the 18 in the 18H side of the equation.

So, it is 256.5/18 equaling H

256.5 divided by 18 is... 14.25

That means the height is 14.25 an the length is 18.

the perimeter is all of the sides added together. in a rectangle, the sides opposite each other are the same.

So you have two sides that are 14.25 and two that are 18 meters long.

14.25+14.25+18+18 equals the perimeter then.

So the answer would be... 64.5!
5 0
3 years ago
Read 2 more answers
What is the solution to the system of equations? y = 2x – 3.5 x – 2y = –14 (–7, 3.5) (3.5, –7) (7, 10.5) (10.5, 7)
Mandarinka [93]

y = 2x-3.5 ----->1

x-2y=-14. ----->2

1 into 2

x-2(2x-3.5)=-14

x-4x+7=-14

-3x=-14-7

-3x=-21

x=-21/-3

x=7 --- -->3

3 into 1

y = 2x-3.5

y=2(7)-3.5

y=10.5

:)

6 0
3 years ago
One factor of the function f(x) = x3 − 6x2 + 11x − 6 is (x − 3)
arlik [135]
Let f(x)= y = x3 - 6x2 + 11x - 6
X intercept means a point on the graph which intercepts the x axis
And Y-intercept mean a point on the graph which intercepts the y axis
Meaning at the x intercept the component of y is zero because there is no y on the x axis


And at the y intercept the x component of the coordinate is zero because on the y axis there is no x value
So in finding the y intercept of the graph wherever u see x place zero there (ie x= 0 on the y axis)
So with x = 0
y = (0)3- 6(0)2 + 11(0) - 6
y = -6

Therefore the y intercept is (0,-6) in coordinate form or -6

X-intercept
y = x3 - 6x2 + 11x - 6
After factorization and simplification
y = (x-1)(x-2)(x-3)
On the x axis y= 0
0= (x-1)(x-2)(x-3)
Either x-1=0
x=1
(1,0)
Or x-2=0
x=2
(2,0)
Or x-3=0
x=3 (3,0)
Therefore the x intercepts are 1,2 and 3
And they are expressed in coordinate form as (1,0) ,(2,0) and
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3 years ago
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olga55 [171]
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4 0
3 years ago
cheryl used 40% of her money to buy a dress and 1/5 of the remainder to buy a pair of shoes. She then donated $60 to charity and
Ede4ka [16]
Let x be total amount of money

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left: x - 0.4x = 0.6x

shoes: 1/5x 0.6x = 0.12x

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donate: $60

$132 left over

0.48x - 60 = 132

solve for x:

0.48 - 60 = 132

0.48x = 192

x = $400

8 0
3 years ago
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