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3 years ago

7

In f(x) = a(x - p)(x - 9), what does "a" tell us?

1 answer:

ANTONII [103]3 years ago

4 0

Answer:

Step-by-step explanation:

f(x) = a(x-p)(x-9) is the equation of a vertical parabola.

If a>0, the parabola opens upwards.

If a<0, the parabola opens downwards.

Also, the focal length of the parabola is 1/|4a|.

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Solve the system of equations.

Brums [2.3K]

Solve the system of equations.
12x + 3y = 12
-6x +y = -26

A) (-3,9)
B (-6, -9)
© (-3,8)
D (3, -8)

12x + 3y = 12
2(-6x +y = -26)

12x + 3y = 12
-12x + 2y = -52

—-now x cancels out

5y/5 = -40/5

y = -8

The answer should be D. Let me know if you got it right.

7 0

2 years ago

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Find the cost of 5 Kgs of apples using the data given in the graph.

zzz [600]

Answer: 2.50 dollars

Explanation:

Locate 5 on the x axis, which corresponds to buying 5 kgs of apples.

Draw a vertical line through 5 on the x axis until you reach the blue line. Mark this as point P.

From point P, draw a horizontal line until you reach the y axis. You should arrive at y = 2.5

This tells us that buying x = 5 kgs of apples will cost a total of y = 2.50 dollars.

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3 years ago

What is the product of (4y-3)(2y^+3y-5)

MAVERICK [17]

the answer is

8y^3y−4 −6y^3y−5

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3 years ago

Mike played a game and earned 25 points if he then lost 30 points what was his final score?

Vlad1618 [11]

Answer:

5

Step-by-step explanation:

I subtracted

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2 years ago

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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

3 years ago

Read 2 more answers