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Ber [7]
3 years ago
13

What is the slope of the line passing through the point(2,-1) and the origin.

Mathematics
1 answer:
tiny-mole [99]3 years ago
7 0

Answer:

- 1/2

Step-by-step explanation:

(0,0) (2,-1)

m = difference of y/difference of x = (-1 - 0) / (2 - 0) = - 1/2

y = - 1/2 x

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The area of a rectangular piece of cardboard is represented by
Liula [17]

This question is solved applying the formula of the area of the rectangle, and finding it's width. To do this, we solve a quadratic equation, and we get that the cardboard has a width of 1.5 feet.

Area of a rectangle:

The area of rectangle of length l and width w is given by:

A = wl

w(2w + 3) = 9

From this, we get that:

l = 2w + 3, A = 9

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

ax^{2} + bx + c, a\neq0.

This polynomial has roots x_{1}, x_{2} such that ax^{2} + bx + c = a(x - x_{1})*(x - x_{2}), given by the following formulas:

x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}

x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}

\Delta = b^{2} - 4ac

In this question:

w(2w+3) = 9

2w^2 + 3w - 9 = 0

Thus a quadratic equation with a = 2, b = 3, c = -9

Then

\Delta = 3^2 - 4(2)(-9) = 81

w_{1} = \frac{-3 + \sqrt{81}}{2*2} = 1.5

w_{2} = \frac{-3 - \sqrt{81}}{2*2} = -3

Width is a positive measure, thus, the width of the cardboard is of 1.5 feet.

Another similar problem can be found at brainly.com/question/16995958

5 0
3 years ago
How do you solve each system of equations?
stiv31 [10]

Answer:

x=1,y=3,z=1

Step-by-step explanation:

4x-4y+4z=-4

4x=-4+4y-4z

x=-1+y-z

Substitute  x=-1+y-z into second equation:

4\left(-1+y-z\right)+y-2z=5

-4+4y-4z+y-2z=5

5y-6z-4=5

y=\frac{6z+9}{5}

Substitute x=-1+y-z and y=\frac{6z+9}{5} into the third equation:

\frac{-41z-54}{5}+3=-16

-41z-54=-95

z=1

Substitute z=1 into y=\frac{6z+9}{5}:

y=3

Plug in y and z values into x=-1+y-z:

x=1

4 0
3 years ago
Write a story that could represent this math problem. A rectangle partitioned into thirds five times. The first part, the second
SSSSS [86.1K]

Answer:

The problem is 5 × 2/3 so

Billy paycheck every week was 2/3 a dollar which is approximately 66 cents but one day he did fantastic and got a raise and the raise was 5 times his last paycheck how much money is Billy new paycheck? So we do 5 × 2/3 and that equals 10/3, or 3 1/3, or 3 dollars and 30 cents.

Step-by-step explanation:

just copy and paste it.

7 0
3 years ago
PLEASE HELP
postnew [5]

Answer:

Below

Step-by-step explanation:

Substituting the given values:

f(6) = 6(2/3) - 2 =   cube root of 6^2 - 2 = cube root 36 - 2

f(-6)=  (-6)(2/3) - 2 =   cube root of(-6)^2 - 2 = cube root 36 - 2

So This is true,

f(6) =   cube root of 6^2 - 2 = cube root 36 - 2 = 1.3019

2 * f(3) = 2 *  (cube root of 3^2 - 2 )  =  2 * (cube root of 9 - 2) = 0.1602

So False,

4 0
3 years ago
The Sun hits a 30 foot flagpole at a 60° angle and casts an unobstructed 52 foot shadow. If a building is built 32 feet away, wh
Over [174]
<span>11.5 Not sure but it should be the answer!!

</span>
4 0
3 years ago
Read 2 more answers
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