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mars1129 [50]
3 years ago
13

Fully Factor 3x^2 – 16x + 20

Mathematics
1 answer:
ryzh [129]3 years ago
4 0

Answer:

C. (3x2 - 10) (x - 2)

Step-by-step explanation:

3x^2 - 16x +20

Step 1: Sum = - 16x

Product = 60x^2

Step 2: Find 2 numbers that their sum is -16 and their product is 60. If you do that correctly, then you will get two numbers: 10 and -6

Step 3: Replace -16x with the two numbers found in step 2, then you will have; 3x^2 - 6x - 10x + 20

Step 4: Factorise the equation in step 3, like so;

(3x^2 - 6x)(- 10x + 20)

3x(x - 2) -10(x - 2)

(3x - 10)(x - 2)

To check if the answer is correct, expand the bracket: (3x - 10)(x - 2)

If the bracket is opened properly, you will get 3x^2 - 16x + 20

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Answer:

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There are two buildings that you want to have in the amusement park, but the size hasn’t been determined yet. Although you don’t
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A = lw\\
A = (20x + 24)(36x - 20)\\
A = (20x)(36x) + (20x)(-20) +  (24)(36x) + (24)(-20)\\
A = 720x^{2} - 400x + 864x - 480\\
A = 720x^{2} + 464x - 480

The expression for the area of the gift shop is 720x^{2} + 464x - 480.

B) The equation for the perimeter of the gift shop is P = 2(l+w), where l = length and w = width. Plug your values for l and w into this equation:
P = 2(l+w)\\
P = 2(20x + 24 + 36x - 20)\\
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The expression for the perimeter of the gift shop is 112x + 8

C) Since you know the perimeter is going to be 176 ft, that means P = 176. Plug that into the equation you found in part B, P = 112x + 8, and solve for x.
P = 112x + 8\\
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x = 1.5

Once you solve for x, you can plug x into your equations for width and length to find the dimensions. x = 1.5, so:
1) L<span>ength = 20x+24 feet 
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2) Width = <span>36x-20 feet
Width = 36(1.5)-20 feet = 34 feet

Your dimensions are 54 feet (length) by 34 feet (width).
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Given parameters:

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Unknown:

Equation of the line with the given slope = ?

Solution:

Let us find the coordinates of the mid-point of the line given.

   Since the end points are (2, -3) and (-6,5);

   Midpoint;

            x, y = \frac{x_{1} + x_{2} }{2} , \frac{y_{1} + y_{2} }{2}  

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                  y = mx + c

x and y are the coordinates

     m is the slope

     c is the y intercept

We need to find c in order to fully develop our equation;

             y = mx + c

              y = 1 , x = -2 and m = \frac{9}{7}

So,

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Multiply through by 7,

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The equation of the line is 7y = -14x + 25

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