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IgorC [24]
1 year ago
13

Find the product, using suitable properties:

Mathematics
1 answer:
Ray Of Light [21]1 year ago
8 0

Answer: a) 6700    b) 2233

Step-by-step explanation:

a)

(-67)*(-99)+(-67)*(-1)=\\(-67)*((-99)+(-1))=\\(-67)*(-100)=\\6700

b)

29*(80-3)=\\(30-1)*(80-3)=\\30*80+(-1)*80+(-3)*30+(-1)*(-3)=\\2400-80-90+3=\\2403-170=\\2233

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2/x2-9 - 3x/ x2-5x+6 please show work
Luda [366]

Answer: -3x^3 - 7x^2 - x + 39

Step-by-step explanation:

2/(x^2 -9) - 3x/(x^2-5x+6)

get those denominators factored out

2/(x-3)(x+3) - 3x/(x-3)(x-2)

Multiply both by both denominators

2(x-3)(x-2) - 3x(x-3)(x+3)

Multiply it out

(2x^2 - 10x + 12) - (3x^3 + 9x^2 -9x - 27)

Simplify and it becomes

-3x^3 -7x^2 -x + 39

5 0
2 years ago
Help pleasee ill give u the crown or whatever its called
Gnom [1K]

Answer:

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Step-by-step explanation:

Hope this will help!!!

5 0
2 years ago
Help would be truly appreciated. Write the polynomial in standard form from the given zeroes of lest degree that has rational co
pishuonlain [190]

Answer:

1) The polynomial in standard form is f(x) = x³ - 9·x² + 23·x - 15

2) The polynomial in standard form is f(x) = x³ - (2 - 2·i)·x² + 4·i·x

3) The polynomial in standard form is f(x) = x² + (3·i - 3)·x + 2 - 6·i

4) The polynomial in standard form is f(x) = x² - (5 + √5)·x + 6 + 3·√5

Step-by-step explanation:

Given that that the polynomial is of least degree, we have;

The standard form is the form, f(x) = a·xⁿ + b·xⁿ⁻¹ +...+ c

1) The zeros of the polynomial are x = 5, 3, 1

Which gives the polynomial in factored form as_f(x) = (x - 5)·(x - 3)·(x - 1)

From which we have;

f(x) = (x - 5)·(x - 3)·(x - 1) = (x - 5)·(x² - 4·x + 3) = x³ - 4·x² + 3·x - 5·x² + 20·x - 15

f(x) = x³ - 9·x² + 23·x - 15

The polynomial in standard form is therefore f(x) = x³ - 9·x² + 23·x - 15

2) The zeros of the polynomial are x = 2, 0, 2·i

Which gives the polynomial in factored form as_f(x) = (x - 2)·(x)·(x - 2·i)

From which we have;

f(x) = (x - 2)·x·(x - 2·i) = (x² - 2·x)·(x - 2·i) = x³ - 2·i·x² + 2·x² + 4·ix

The polynomial in standard form is therefore f(x) = x³ - (2 - 2·i)·x² + 4·i·x

3) The zeros of the polynomial are x = 2, 1 - 3·i

Which gives the polynomial in factored form as_f(x) = (x - 2)·(x - 1 - 3·i)

From which we have;

f(x) = (x - 2)·(x - (1 - 3·i)) = x² - x + 3·i·x - 2·x + 2 -6·i = x² + 3·i·x - 3·x + 2 - 6·i

The polynomial in standard form is therefore f(x) = x² + (3·i - 3)·x + 2 - 6·i

4) The zeros of the polynomial are x = 3, 2 + √5

Which gives the polynomial in factored form as_f(x) = (x - 3)·(x - (2 + √5))

From which we have;

f(x) = (x - 3)·(x - (2 + √5)) = x² - 2·x - x·√5 - 3·x + 6 + 3·√5

f(x) = x² - 5·x - x·√5 + 6 + 3·√5 = x² - (5 + √5)·x + 6 + 3·√5

The polynomial in standard form is therefore f(x) = x² - (5 + √5)·x + 6 + 3·√5.

5 0
2 years ago
Is the simplified form of 2 square root of 3 ⋅ 2 square root of 6 rational?
alina1380 [7]
√3(√6)
= √3(6)
=√3(3·2)
=3√2

B. No the product will not be rational as 3√2 cannot be expressed as a simple fraction
7 0
3 years ago
Read 2 more answers
10e=1 what does e equal need this asap
Dahasolnce [82]

Answer:

To solve for e, divide 10 from each side.. 1 divided by 10 e=0.1

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2 years ago
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