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erma4kov [3.2K]

3 years ago

9

Which of the following graphs shows the solution to the system of equations y=5x-1 and y= x+3

1 answer:

lubasha [3.4K]3 years ago

6 0

Where are the graphs?

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this year benny is 12 years old and his mom is 48 years old, what percent of Benny's age is his mom's age?

jolli1 [7]

25% should be correct

3 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

Evaluate -16 - 9x<br> When x= 3

vfiekz [6]

Answer:

-43

Step-by-step explanation:

first we need to do 9x witch would be 9x3 so 9x3 is 27 now its down to -16 - 27 and that is -43

8 0

2 years ago

Help ASAP for BRAINLIEST!!!!

xenn [34]

Answer:

1/2

Step-by-step explanation:

1/4 (4x - 8) + 3x =0

distribute the 1/4

x-2+3x=0

combine like terms

-2+4x=0

move -2 to the other side [by ADDing +2 to each side

4x=2

divide [by 4 on both sides]

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2 years ago

Johnny bought an oil painting originally priced at $80 but on sale for for 50% off. After 10% sales tax, what was the total cost

Alecsey [184]

Answer:

$44

Step-by-step explanation:

Original price = $80

Discount on sale = 50%

Discounted price = (1 - 50%) * original price

Discounted price = 0.5 * $80 = $40

Sales tax = 10%

Sales tax amount = 0.1 * $40 = $4

Total cost = discounted price + sales tax amount

Total cost = $40 + $4 = $44

5 0

2 years ago