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2 years ago

15

a runner warms up for ten minutes and then takes seven minutes to run each mile. the total time after r miles in 45 minutes. how

manymiles are run

1 answer:

Alika [10]2 years ago

6 0

45=10+7x
35=7x
5=x

Answer: they ran 5 miles

Hope this helps:)

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The ordered pairs (3,2) and (-2,13) are points on a linear function. Which equation best describes this function?

Mars2501 [29]

Answer:

The equation which describe this function is 5x + 11y = 37

Step-by-step explanation:

<u>To find the slope</u>

slope = (y₂ - y₁)/(x₂ - x₁)

slope = (13 - 2)/(-2 - 3) = 11/-5

<u>To find the equation</u>

(x - 3)/(y - 2) = -11/5

5(x - 3) = -11(y - 2)

5x -15 = -11y + 22

5x + 11y = 22 + 15

5x + 11y = 37

Therefore the equation which describe this function is

5x + 11y = 37

7 0

3 years ago

Read 2 more answers

3. Lonnie has a gift card worth $600 for a local entertainment store. Movies cost $20 each and newly released video games cost $

Mandarinka [93]

Answer:

8 movies and 6 video games

<em></em>

Step-by-step explanation:

Given

$Gift\ Card = \$600$

$Movies =\ $20$

$Video\ Game = \$50$

$Minimum\ Items = 13$

Required

Determine the items Lonnie can afford

To solve this question, we make use of trial by error method by taking the options one at a time:

Option 1: 6 movies and 4 video games

<em>This option can not be considered because the number of items is not up to the minimum Lonnte must purchase.</em>

<em />

Option 2: 14 movies and 7 video games

$Cost = 14 * \$20 + 7 * \$50$

$Cost = \$280 + \$350$

$Cost = \$630$

<em>This option can not be considered because the cost of purchase is greater than Lonnte's worth of Gift card.</em>

<em />

Option 3: 2 movies and 10 video games

<em>This option can not be considered because the number of items is not up to the minimum Lonnte must purchase.</em>

<em />

Option 4: 8 movies and 6 video games

$Cost = 8 * \$20 + 6 * \$50$

$Cost = \$160 + \$300$

$Cost = \$460$

Hence, the correct option is <em>8 movies and 6 video games </em>

4 0

2 years ago

HELP PLEASE!!!!!!!! ASAP!!!!!!!!

Serjik [45]

37 degrees Ill explain in a second but thats it!

6 0

3 years ago

Read 2 more answers

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 $x-5$ .

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

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

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

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

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

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

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

$42x$ $-210$

$42x$ $-210$

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

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

2 years ago

Read 2 more answers

Can someone plug some numbers into a small equation real quick for me?:)

Arada [10]

-13 times -7 equals -91

5 0

2 years ago