Find the slope of the line that passes through each pair of points a. (-4, 5), (1, 1)

Kendra earns $11.60 per hour working at the movie theater. Each week, she donates of

stich3 [128]

Answer:

$9.86

Step-by-step explanation:

First, write both numbers in the same form. Convert 8

1

2

to a decimal.

8

1

2

= 8+

1

2

= 8+

1×5

2×5

= 8+

5

10

= 8+0.5

= 8.5

Multiply.

11.6

× 8.5

580

+ 9280

98.60

Kendra earned $98.60 last week.

Now multiply to find how much money Kendra donated to the charity last week. She earned $98.60, and she donates

1

10

of her earnings each week.

First, write both numbers in the same form. Convert

1

10

to a decimal.

1

10

=0.1

Multiply.

98.6

× 0.1

9.86

Kendra donated $9.86 to the charity last week.

7 0

4 years ago

Each year, Kipp raises money by participating in the Walk for Breast Cancer. Last year, Mr. Madrid walked at a pace of 12 miles

Ilia_Sergeevich [38]

A.

The rate is 12:2

B.

Set up a proportion:

12/2 = x/5

Multiply 5 to both sides:

60/2 = x

Divide:

30 = x

So he will walk 30 miles in 5 hours.

C.

To find out, we can divide 12 / 2.

12 / 2 = 6 miles per hour

8 0

4 years ago

2x^3-x^2-3x=210<br> the answer is 5 but I want to know why.

mel-nik [20]

Answer:

$x=5,\frac{-9+\sqrt{255}i }{4} ,\frac{-9-\sqrt{255}i }{4}$

Step-by-step explanation:

1) Move all terms to one side.

$2x^{3} -x^{2} -3x-210=0$

2) Factor $2{x}^{3}-{x}^{2}-3x-210$ using Polynomial Division.

1 - Factor the following.

$2x^{3} -x^{2} -3x-210$

2 - First, find all factors of the constant term 210.

$1,2,3,4,5,6,7,10,14,15,21,30,35,42,70,105,210$

3) Try each factor above using the Remainder Theorem.

Substitute 1 into x. Since the result is not 0, x-1 is not a factor..

$2*1^{3} -1^{2} -3*1-210=-212$

Substitute -1 into x. Since the result is not 0, x+1 is not a factor..

$2(-1)^{3} -(-1)^{2} -3*-1-210=-210$

Substitute 2 into x. Since the result is not 0, x-2 is not a factor..

$2*2^{3} -2^{2} -3*2-210=-204$

Substitute -2 into x. Since the result is not 0, x+2 is not a factor..

$2{(-2)}^{3}-{(-2)}^{2}-3\times -2-210 = -224$

Substitute 3 into x. Since the result is not 0, x-3 is not a factor..

$2\times {3}^{3}-{3}^{2}-3\times 3-210 = -174$

Substitute -3 into x. Since the result is not 0, x+3 is not a factor..

$2{(-3)}^{3}-{(-3)}^{2}-3\times -3-210 = -264$

Substitute 5 into x. Since the result is 0, x-5 is a factor..

$2\times {5}^{3}-{5}^{2}-3\times 5-210 =0$

------------------------------------------------------------------------------------------

⇒ $x-5$

4) Polynomial Division: Divide $2{x}^{3}-{x}^{2}-3x-210$ by $x-5$ .

$2x^{2}$ $9x$ $42$

-------------------------------------------------------------------------

$x-5$ | $2x^{3}$ $-x^{2}$ $-3x$ $-210$

$2x^{3}$ $-10x^{2}$

-----------------------------------------------------------------------

$9x^{2}$ $-3x$ $-210$

--------------------------------------------------------------------------

$42x$ $-210$

-------------------------------------------------------------------------

5) Rewrite the expression using the above.

$2x^2+9x+42$

$(2x^2+9x+42)(x-5)=0$

3) Solve for $x.$

$x=5$

4) Use the Quadratic Formula.

1 - In general, given $a{x}^{2}+bx+c=0$ , there exists two solutions where:

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

2 - In this case, $a=2,b=9$ and $c = 42.$

$x=\frac{-9+\sqrt{9^2*-4*2*42} }{2*2} ,\frac{-9-\sqrt{9^2-4*2*42} }{2*2}$

3 - Simplify.

$x=\frac{-9+\sqrt{255}i }{4} ,\frac{-9-\sqrt{255}i }{4}$

5) Collect all solutions from the previous steps.

$x=5,\frac{-9+\sqrt{255}i }{4} ,\frac{-9-\sqrt{255}i }{4}$

4 0

3 years ago

Read 2 more answers

Identify the domain and range of each relation. Use a mapping diagram to determine whether the relation a function.

Xelga [282]

Answer:

Domains- 6, 5, 1, 7

Ranges- -7, -8, 4, 5

6 0

3 years ago

3x+122=22x-11<br>i need help!

nasty-shy [4]

3x + 122 = 22x - 11

+11 + 11

3x + 133 = 22x

-3x -3x

133 = 19x

x = 7

5 0

3 years ago

Read 2 more answers