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2 years ago

Without actual division prove that x4 +2x3 -2x2 +2x -3 is exactly divisible by x2 +2x-3

Mathematics

1 answer:

Brut [27]2 years ago

7 0

Answer:

Step-by-step explanation:

$\displaystyle\Large\boldsymbol{} x^4+2x^3-2x^2+2x-3= \\\\\\x^4+2x^2(x-1)+2x-\underbrace{2-1}_{-3}= \\\\\\x^4-1+2x^2(x-1)+2x-2 = \\\\\\(x^2-1)(x^2+1)+2x^2(x-1)+2(x-1) = \\\\\\\underline{(x-1)}(x+1)(x^2+1)+2x^2\underline{(x-1)} +2\underline{(x-1)} =\\\\\\(x-1)((x+1)(x^2+1)+2x^2+2)=\\\\\\(x-1)(x^3+x^2+2x^2+x+2+1)=\\\\\\(x-1)(x^3+3x^2+x+3) =\\\\\\(x-1)( \underline{(x+3)}x^2+\underline{(x+3)})=(x^2+1)\underbrace{(x-1)(x+3)}_{x^2+2x-3}= \\\\\\(x^2+1)(x^2+2x-3) : (x^2+2x-3)=x^2+1$

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Find the quotient. Do not round. 55.328 ÷ 3.8

enot [183]

Hello

the answer is 14.56

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2 years ago

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What is 6.9 × 107 written in standard form?

mihalych1998 [28]

6.9 x 10⁷ is a scientific notation.

6.9 x 10⁷ in standard form is 69,000,000

Scientific notation is used to represent very large numbers or very small numbers.

Scientific notation has three parts. Its parts are the coefficient, base of ten, and the exponents.

6.9 is the coefficient
10 is the base of 10
7 is the exponent

The must always be 1 digit before the decimal point in the scientific notation.
The exponent tells us the number of places the decimal point has moved. Its sign tells us the direction of the decimal point's movement.

Since the exponent is positive, it tells us that the decimal point moved from right to left.

69000000. to 6.9000000

If the exponent had a negative sign, it means that the decimal point moved from left to right.

example: 6.9 x 10⁻⁷
its standard form would have been .00000069

3 0

2 years ago

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Kelly tells you that when variables are in the denominator, the equation one over two plus three over x equals three over four b

ki77a [65]

3/4=1/2+3/x

1/4=3/x

x/4=3

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6 0

3 years ago

The number of "destination weddings" has skyrocketed in recent years. For example, many couples are opting to have their wedding

Andru [333]

Answer:

There is no sufficient evidence to support the claim that wedding cost is less than $30000.

Step-by-step explanation:

Values (x) ∑(Xi-X)^2

----------------------------------

29.1 0.1702

28.5 1.0252

28.8 0.5077

29.4 0.0127

29.8 0.0827

30.1 0.3452

30.6 1.1827

----------------------------------------

236.1 3.4088

Mean = 236.1 / 8 = 29.51

$S_{x}=\sqrt{3.4088/(8-1)}=0.6978$

Statement of the null hypothesis:

H0: u ≥ 30 the mean wedding cost is not less than $30,000

H1: u < 30 the mean wedding cost is less than $30,000

Test Statistic:

$t=\frac{X-u}{S/\sqrt{n}}=\frac{29.51-30}{0.6978/\sqrt{8}}= \frac{-0.49}{0.2467}=-1.9861$

Test criteria:

SIgnificance level = 0.05

Degrees of freedom = df = n - 1 = 8 - 1 = 7

Reject null hypothesis (H0) if

$t$

Finding in the t distribution table α=0.05 with df=7, we have

$t_{0.05,7}=2.365$

$t>-t_{0.05,7}$ = -1.9861 > -2.365

Result: Fail to reject null hypothesis

Conclusion: Do no reject the null hypothesis

u ≥ 30 the mean wedding cost is not less than $30,000

There is no sufficient evidence to support the claim that wedding cost is less than $30000.

Hope this helps!

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3 years ago

Please help me I need help with my test review I can’t figure out m<1 and m<2

aksik [14]

Answer:

m1=12 and m2=168

Step-by-step explanation:

$m1 + m2 = 180 \: (straight \: angle) \\ then \\ x - 12 + 7x = 180 \\ 8x - 12 = 180 \\ 8x = 180 + 12 = 192 \\ x = 192\div 8 \\ x = 24\\ hence \\ m1 = 24 - 12 = 12 \\ m2 = 7 \times 24 = 168.$

6 0

3 years ago