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3 years ago

Please help!!! Thank you

Mathematics

2 answers:

HACTEHA [7]3 years ago

6 0

Answer: x = 8, x = 5

Step-by-step explanation:

first problem: first, we collect like terms

3x + 3 = 2x + 11

then, we move the terms around.

3x - 2x = 11 - 3

finally, we collect those like terms and calculate.

x = 8

second problem: first, we rewrite the expression

2 x 3x + 1 = 2x + 21

then, we calculate.

6x + 1 = 2x + 21

next, we move the terms,

6x - 2x = 21 - 1

then, we collect the like terms.

4x = 20

finally, we divide both sides.

x = 5

Sedbober [7]3 years ago

3 0

Answer:

5. =8

6= x=20 ur welcome

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Write a polynomial function of least degree with integral coefficients that has the given zeros. -5, 3i

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Solving for the polynomial function of least degree with integral coefficients whose zeros are -5, 3i

We have:
x = -5

Then x + 5 = 0

Therefore one of the factors of the polynomial function is (x + 5)

Also, we have:
x = 3i
Which can be rewritten as:
x = Sqrt(-9)
Square both sides of the equation:
x^2 = -9
x^2 + 9 = 0

Therefore one of the factors of the polynomial function is (x^2 + 9)

The polynomial function has factors: (x + 5)(x^2 + 9)
= x(x^2 + 9) + 5(x^2 + 9)

= x^3 + 9x + 5x^2 = 45

Therefore, x^3 + 5x^2 + 9x – 45 = 0

f(x) = x^3 + 5x^2 + 9x – 45

The polynomial function of least degree with integral coefficients that has the given zeros, -5, 3i is f(x) = x^3 + 5x^2 + 9x – 45

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3 years ago

Angles α and β are the two acute angles in a right triangle. Use the relationship between sine and cosine to find the value of α

8_murik_8 [283]

Answer:

The value of angle α is 18 degree.

Step-by-step explanation:

Given information: Angles α and β are the two acute angles , α < β.

Given equation is

$\sin (2x-8)=\cos (6x-6)$

$\cos (90-(2x-8))=\cos (6x-6)$ $[\because \sin (90-x)=\cos x]$

Equating both sides.

$90-2x+8=6x-6$

$98+6=6x+2x$

$104=8x$

$13=x$

The value of x is 13.

The measure of angles is

$2x-8=2(13)-8=18$

$6x-6=6(13)-6=72$

Since 18<72, therefore the value of angle α is 18 degree.

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4 years ago

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Answer:

We cannot say that the mean wake time are different before and after the treatment, with 98% certainty. So the zopiclone doesn't appear to be effective.

Step-by-step explanation:

The goal of this analysis is to determine if the mean wake time before the treatment is statistically significant. The question informed us the mean wake time before and after the treatment, the number of subjects and the standard deviation of the sample after treatment. So using the formula, we can calculate the confidence interval as following:

$IC[\mu ; 98\%] = \overline{y} \pm t_{0.99,n-1}\sqrt{\frac{Var(y)}{n}}$

Knowing that $t_{0.99,15} = 2.602$ :

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