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tester [92]
3 years ago
14

Simplify and verify the results for

Mathematics
1 answer:
KatRina [158]3 years ago
3 0

Answer:

21440

Step-by-step explanation:

<h2>Simplify:</h2>
  • (7x³ + 8x² - 3)(x² - 5)

Start by multiplying 7x³ by x² and -5.

  • 7x⁵ - 35x³ + (8x² - 3)(x² - 5)    

Multiply 8x² by x² and -5.

  • 7x⁵ - 35x³ + 8x⁴ - 40x² + (-3)(x² - 5)

Multiply -3 by x² and -5.

  • 7x⁵ - 35x³ + 8x⁴ - 40x² -3x² + 15

Combine like terms together.

  • 7x⁵ - 35x³ + 8x⁴ - 43x² + 15

Rearrange the terms in descending power order.

  • 7x⁵ + 8x⁴ - 35x³ - 43x² + 15  
<h2>Verify (I): </h2>

Substitute x = 5 into the above polynomial.

  • 7(5)⁵ + 8(5)⁴ - 35(5)³ - 43(5)² + 15

Evaluate the exponents first.

  • 7(3125) + 8(625) - 35(125) - 43(25) + 15

Multiply the terms together.

  • 21875 + 5000 - 4375 - 1075 + 15

Combine the terms together.

  • 21440

This is the answer when substituting x = 5 into the simplified expression.

<h2>Verify (II):</h2>

Substitute x = 5 into the expression.

  • [7(5)³ + 8(5)² - 3][(5)² - 5]

Evaluate the exponents first.

  • [7(125) + 8(25) - 3][(25) - 5]

Multiply the terms in the first bracket next.

  • [875 + 200 - 3][25 - 5]

Evaluate the expressions inside the brackets.

  • [1072][20]

Multiply these two terms together.

  • 21440

This is the answer when substituting x = 5 into the original (unsimplified) expression.

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Answer:

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Step-by-step explanation:

4 0
2 years ago
A right triangle has a hypotenuse C=12cm and a an angle A= 30°. find the length of side a, witch is opposite angle A
Alisiya [41]
Use the sin identity to find that side.  Sin(30) = a/12...12 sin(30) = a, and a = 6
7 0
3 years ago
The total cost for tuition plus room and board at State University is $2,584.00. Tuition costs $100 more than twice room and boa
liq [111]

Answer:

$1756

Step-by-step explanation:

1.  More = Addition

2. Twice = Multiplication by 2

3. Tuition costs $100 more than twice room and board

   Tuition = 2x + 100

   $2584 = (2x + 100) + x

   $2584 = 3x + 100

4. Subtract 100 on both sides: $2484 = 3x

5. Divide both sides by 3: $828 = x

6. Plug it in to the tuition equation: Tuition = 2(828) + 100

                                                                       = $1756

Check Work: (828*2) + 100 = $1756

                      $1756 + 828  = $2584

7 0
2 years ago
A coin is tossed 20 times. It lands heads four times. Compare the experimental probability to its theoretical probability. If th
MrRa [10]

Theoretical probability is based on the likelihood of events.

if a coin is flipped 20 times, and it has landed on heads 4 times, theres a 50% chance it would land on heads the 5th time.

it could be that heads gets more than tails or it could be vise versa.

The probability of getting two heads is 1 in 4.

5 0
3 years ago
The perimeter of a square is 96m.Find its area.
nadya68 [22]
<h3>Solution</h3>

P = 4a

96 = 4a

a = 24 m

so, the area is

A = a²

A = 24²

A = 24 × 24

A = 576 m²

4 0
2 years ago
Read 2 more answers
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