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kaheart [24]
3 years ago
10

PLEASE HELP ASAP!!!

Mathematics
2 answers:
Mariana [72]3 years ago
4 0

Answer:

<h3>C. (a, b)</h3>

Step-by-step explanation:

The formula of a midpoint:

M\left(\dfrac{x_1+x_2}{2};\ \dfrac{y_1+y_2}{2}\right)

We have A(0, 0) and C(2a, 2b). Substitute:

x=\dfrac{0+2a}{2}=\dfrac{2a}{2}=a\\\\y=\dfrac{2b+0}{2}=\dfrac{2b}{2}=b

M(a, b)

pogonyaev3 years ago
3 0

Answer:

Choice C is correct.

Step-by-step explanation:

The  formula to find mid-point of a line segment is:

M= (x_{1}+x_{2}/2,y_{1} +y_{2}/2)

where  (x_{1} ,y_{1}) and (x_{2} ,y_{2}) are end-points  of a line segment.

we have to find mid-point of AC.

A is located at the center of xy-graph.

hence, A(x_{1} ,y_{1}) is given as (0,0) and C(x_{2} ,y_{2}) is given as (2a,2b).

put above values in the formula of mid-point formula:

M=(0+2a/2,0+2b)

M=(2a/2,2b/2)

M=(a,b) is mid-point of AC.




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erma4kov [3.2K]

Answer:

The ratios are equivalent.

Step-by-step explanation:

If you multiply both 5 and 6, the ratio stays the same.

5:6 = 10:12 = 15:18 = 20:24 etc.

You can try this by dividing the larger number by the smaller number. You'll always get 1.2 as the "relationship", or ratio, is preserved.

24/20 = 1.2

15/18 = 1.2

10/12 = 1.2

6/5 = 1.2

6 0
3 years ago
What are the factors of 5x2 + 39x − 8?
prisoha [69]

Answer:

C. (5x - 1)(x + 8)

Step-by-step explanation:

In a factoring problem by hand, the common steps to solve would be the "AM" method, or (Add-Multiply). Simply stated, finding what adds to the x-coeficient and what multiplies to the constant. In this case, what adds to 39(x) and what multiplies to 8. Just reading that, we can see that there aren't any numbers that can do that, so we have to improvise. Set up the problem equal to something that it can factor into:

  1. <em>Multiply the 5 and -8</em> = -40: <em>this is what we will factor</em>
  2. <em>The factors with add to 39 are 40 and -1</em>.
  3. <em>Set up the problem:</em>

5x^{2}+39x-8 = 5x^{2}+40x-x-8

Now, we can fo the math:

5x^{2} -8 = 5x^{2} -8

8(5x - 1) + x(5x - 1)

<em>Factor (5x - 1) from this:</em>

(5x - 1)(x + 8)

And we have our answer.

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3 years ago
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What is the equation of the quadratic graph with a focus of (4, −3) and a directrix of y = −6?
Artyom0805 [142]

Answer:

y=\frac{1}{6} (x-4)-\frac{9}{2}

Step-by-step explanation:

∵ The quadratic equation form is :

y = [1/2(b - k)] (x - a)² + (b + k)/2

Where (a , b) is the focus and directrix y = k

∵ The focus is (4 , -3) and directix is y = -6

∵ y=\frac{1}{2(-3-(-6))} (x-4)^{2}+\frac{(-3)+(-6)}{2}

∴ y=\frac{1}{6} (x - 4)^{2}+\frac{-9}{2}

∴ y=\frac{1}{6} (x-4)-\frac{9}{2}

another way:

Assume that (x , y) is the general point on the parabola

∵ The distance between the directrix and (x , y) = the distance between the focus and (x , y)

By using the distance rule:

∵ (y - -6)² = (x - 4)² + (y - -3)² ⇒ (y + 6)² = (x - 4)² + (y + 3)

∴ y² + 12y + 36 = (x - 4)² + y² + 6y + 9

∴ 12y - 6y = (x - 4)² + 9 - 36

∴ 6y = (x - 4)² - 27 ⇒ ÷ 6

∴ y = 1/6 (x - 4)² - 9/2

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serg [7]
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