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kati45 [8]
2 years ago
13

Given x^2 -4x+4 is a factor of the polynomial 2x^4 - 11x^3 +68x-80, completely factor the polynomial using algebraic methods.​

Mathematics
1 answer:
asambeis [7]2 years ago
4 0
Answer:

2x^4-11x^3+68x-80

2x^4-4x^3-7x^3+14x^2-14x^2+28x+40x-80

2x^3(x-2)-7x^2(x-2)-14x(x-2)+40(x-2)

(x-2)(2x^3-7x^2-14x+40)

(x-2)(2x^3-4x^2-3x^2+6x-20x+40)

(x-2)(2x^2(x-2)-3x(x-2)-20(x-2))

(x-2)(x-2)(2x^3-3x-20)

(x-2)(x-2)(2x^2+5x-8x-20)

(x-2)(x-2)(x(2x+5)-4(2x+5))

(x-2)(x-2)(2x+5)(x-4)

(x-2)^2(2x+5)(x-4)
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Find the equation of the line passing through (1,4) with a gradient of 3
tatiyna

I really don't know, this is to difficult

8 0
3 years ago
OMG PLEASE HELP ME ASAP!!!!!!! A local charity sponsors a 5K race to raise money. It receives $55 per race entry and $10,000 in
Dominik [7]
Start with how much profit they are making off each race entry. People pay $55 to race, but $15 of that is expenses so they are only profiting $40 for each entry. Now write one side of the equality. They start with $10,000 in donations, and then have a $40 profit for each race entry. So 10,000+40x. X will represent the unknown number of race entries. What do we want that expression to be equal to? We want 10000+40x>55000. It can also be greater than or equal to, not just greater than. Solve for x. Subtract 10000 from each side resulting in 40x>45000. Divide each side by 40 to solve for x. X>1125. X needs to bbe greater than or equal to 1125. If there are 1125 race entries, the charity will profit exactly $55000, so the lowest number of race entries is 1125
3 0
2 years ago
The Garden Task
Igoryamba

If the perimeter of the garden is (14x - 32) ft and has a side length of (x + 2) ft:

  • the perimeter = 24 ft
  • the area = 36 sq. ft
  • if the perimeter of the garden is doubled, the perimeter of the new garden = 48 ft
  • if the area of the garden is doubled, the area of the new garden = 72 sq. ft

<em><u>Recall</u></em>:

  • A square has equal side lengths
  • Perimeter of a square = 4(side length)
  • Area of a square = (side $ length)^2

<em><u>Given:</u></em>

Perimeter of square (P) = (14x - 32) $ ft

Side length (s) = (x + 2) $ ft

<em><u>First, let's find the </u></em><em><u>value of x</u></em><em><u> by creating an </u></em><em><u>equation </u></em><em><u>using the </u></em><em><u>perimeter </u></em><em><u>formula:</u></em>

  • Perimeter of a square = 4(side length)

  • Plug in the values

(14x - 32) = 4(x + 2)

  • Solve for x

14x - 32 = 4x + 8\\\\14x - 4x = 32 + 8\\\\10x = 40\\\\x = 4

<em><u>Find how much fencing would be needed (</u></em><em><u>Perimeter </u></em><em><u>of the fence):</u></em>

  • Perimeter of the fence = (14x - 32) $ ft

  • Plug in the value of x

Perimeter of the fence = 14(4) - 32 = 24 $ ft

<em><u>Find the </u></em><em><u>area </u></em><em><u>of the garden:</u></em>

  • Area of the garden = (side $ length)^2

Area = (x + 2)^2

  • Plug in the value of x

Area = (4 + 2)^2 = 6^2 = 36 $ ft^2

<u><em>Find the </em></u><u><em>perimeter </em></u><u><em>if the garden size is doubled:</em></u>

  • Perimeter of the new garden = 2 x 24 = 48 ft

<em><u>Find the </u></em><em><u>area </u></em><em><u>if the garden size is doubled:</u></em>

  • Perimeter of the new garden = 2 x 36 = 72 sq. ft

In summary, if the perimeter of the garden is (14x - 32) ft and has a side length of (x + 2) ft:

  • the perimeter = 24 ft
  • the area = 36 sq. ft
  • if the perimeter of the garden is doubled, the perimeter of the new garden = 48 ft
  • if the area of the garden is doubled, the area of the new garden = 72 sq. ft

Learn more here:

brainly.com/question/13511952

4 0
2 years ago
Craig and Alissa are building a sandcastle on the beach. They each have a bucket. Craig's bucket holds 1/2 pound of sand and Ali
Nitella [24]
<h3>Amount of sand craig and Alissa collect together at one time is 1.4 pounds</h3>

<em><u>Solution:</u></em>

Given that,

Craig and Alissa are building a sandcastle on the beach. They each have a bucket

Craig's bucket holds 1/2 pound of sand and Alissa's bucket holds 9/10 pound of sand

Therefore,

Craig\ bucket = \frac{1}{2}\ pound\\\\Alissa\ bucket = \frac{9}{10}\ pound

<em><u>How much sand can craig Alissa collect together at one time</u></em>

Add both, we get

Collect\ together = \frac{1}{2} + \frac{9}{10}\\\\Collect\ together = \frac{1 \times 5}{2 \times 5} + \frac{9}{10}\\\\Collect\ together = \frac{5}{10} + \frac{9}{10}\\\\Collect\ together = \frac{9+5}{10}\\\\Collect\ together = \frac{14}{10} = \frac{7}{5} = 1.4\\\\In\ mixed\ fractions,\\\\Collect\ together = 1\frac{2}{5}

Thus, amount of sand craig and Alissa collect together at one time is 1.4 pounds

4 0
3 years ago
Score: 0 of 1 pt
cupoosta [38]

Answer:

70

Step-by-step explanation:

21/.3

5 0
3 years ago
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