Hello... HELP PLEASE
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The factored form of the cubic equation x³ + 27 is equal to (x + 3) · (x - 3 / 2 - i 3√3 / 2) · (x - 3 / 2 + i 3√3 / 2). The roots of the cubic equation are - 3, 3 / 2 + i 3√3 / 2 and 3 / 2 - i 3√3 / 2.

In this problem we find a cubic equation of the form x³ + a³, whose factor form can be found by using algebra properties:

f(x) = x³ + 27

f(x) = (x + 3) · (x² - 3 · x + 9)

f(x) = (x + 3) · (x - 3 / 2 - i 3√3 / 2) · (x - 3 / 2 + i 3√3 / 2)

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The length of the rectangle is 45 yard and the width of the rectangle is 9 yard.

WE have Given that the length of a rectangle is 5 times its width, and the perimeter is 108 yd.

Let the width of rectangle be 'x' yard and the length of the rectangle is '5x' yd . also the length is five times the width.

we know that,

The Perimeter of the rectangle = 2(length + width)

The perimeter of rectangle is 108 yd.

Therefore the perimeter = 2( 5x + x )

                              108    = 2( 6x )

                              108    = 12x

                         108/12    = x

                               x      = 9

Therefore, the width of given rectangle is 9 yard, and

The length of the rectangle is 5x = 5 * 9 = 45 yd.

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8272936388272o274o4i49484i484748474

Step-by-step explanation:

2-2=Fish

Answer:

The correct answer is B - 327 ft.

Step-by-step explanation:

t+d = is equal to 8+6=14

14divided by 8-6 equal to 14 divided by 2

Answer is 7

Answer:

no

Step-by-step explanation

an example of vertical angles would be 6 and 8

pls give brainliest :)

Applying the definition of supplementary angles, the measure of angle A is: 47°

The definition of supplementary angles states that two angles are referred to as supplementary angles if they give a sum of 180 degrees when added together.

Given that angle A and angle B are supplementary angles, therefore, based on the definition of supplementary angles, measure of angle A + measure of angle B = 180 degrees.

Measure of angle A = 3x - 10

Measure of angle B = 8x - 19

Substitute

3x - 10 + 8x - 19 = 180

Combine like terms

11x - 29 = 180

11x = 180 + 29

11x = 209

11x/11 = 209/11

x = 19

Measure of angle A = 3x - 10

Plug in the value of x

Measure of angle A = 3(19) - 10

Measure of angle A = 57 - 10

Measure of angle A = 47°

Thus, applying the definition of supplementary angles, the measure of angle A is: 47°

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Answer:Measure of angle A = 3x - 10

Measure of angle B = 8x - 19

Substitute

3x - 10 + 8x - 19 = 180

Combine like terms

11x - 29 = 180

11x = 180 + 29

11x = 209

11x/11 = 209/11

x = 19

Measure of angle A = 3x - 10

Plug in the value of x

Measure of angle A = 3(19) - 10

Measure of angle A = 57 - 10

Measure of angle A = 47°

Thus, applying the definition of supplementary angles, the measure of angle A is: 47°

Step-by-step explanation:

The function is f (x) = 3/4 x - 1.

What is Linear equation?

A linear equation is an algebraic equation with slope m is defined as,

y = mx + b

Where, b is the y - intercept.

Given that;

Slope of function (m) = 3/4

f (-12) = -10

Now,

A linear equation with slope m is defined as,

f (x) = mx + b

Substitute m = 3/4,

f (x) = 3/4 x + b

Apply the condition f (-12) = -10 we get,

f (-12) = 3/4 * (-12) + b

- 10 = 3 * (-3) + b

- 10 = - 9 + b

b = - 10 + 9

b = - 1

Substitute value of m and b in linear equation we get;

The function is,

⇒ f (x) = 3/4 x - 1.

Hence, The function is f (x) = 3/4 x - 1.

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Answer:

237500000000

Step-by-step explanation:

1.14 × [tex]10^{6}[/tex] = 1140000

4.8 × [tex]10^{-6}[/tex] = 0.000005

1140000 ÷ 0.000005 = 237500000000

9*1/6

Step-by-step explanation:

1= 6/6 and there are 9 boxes so multiply 9*1/6

Answer:

f−1(x)=3√4(x+3)/2 :)

Answer:

x = -5

Step-by-step explanation:

[tex]2x + 32 + x = 17[/tex]

[tex]3x + 32 = 17[/tex]

[tex]3x = - 15[/tex]

[tex]x = - 5[/tex]

Answer:

Slope is 0.

Step-by-step explanation:

If you graph these points, it is a horizontal line. Horizontal lines have ZERO slope.

Using slope formula:

subtract y's and put that on top of a fraction. Subtract x's and put that on the bottom of the fraction.

6-6 goes in top and 10-6 goes on the bottom.

slope = m = 0/4 = 0

Slope is zero.

The whole number for the value (x + 21) is 41.

All integers starting from 0 are called whole numbers. The opposite of their corresponding positive numbers, the negative numbers are additive. The blackboard bold math Z or boldface Z is a common way to represent the set of integers in mathematical terminology.

given,

       x = 20

then by putting the value of x = 20 in

       (x + 21)°      we get,

     = (20 + 21)°

     = 41°

Hence, the whole number of (x + 21) is 41

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The average rate of change of [tex]f[/tex] over an interval [tex][a,b][/tex] is the difference quotient

[tex]\dfrac{f(b) - f(a)}{b - a}[/tex]

Over the interval [tex]3\le x\le5[/tex], we have

[tex]\dfrac{f(5) - f(3)}{5 - 3} = \dfrac{27 - 3}{5 - 3} = \dfrac{24}2 = \boxed{12}[/tex]

There is no Real number whose square is −16.

If

a∈R then a2≥0. So there is no real square root of −16

If i is the imaginary unit, then i

i^2=-1

and we find that:

(4i)2=2⋅i2=16⋅−1=-16

So 4i is a square root of −16.

(−4i)2=(−4)2i2=16⋅−1=−16

So, −4i is a square root of −16√−16=i√16=4i

There is no Real number whose square is −16.

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Answer:

Step-by-step explanation:

63
because 9x7=63

and 7x9=63

The proof is shown below:

Angle sum property of triangle states that the sum of interior angles of a triangle is 180°.

Given:

CB || HE

Now using the property of parallel lines.

So,

<HAC = <ACB (alternate interior angles)

<EAB= <ABC (alternate interior angles)

Now, HAE is a straight line then

<HAC + <CAB + <EAB = 180 ( linear pair)

<ACB + <CAB + <ABC = 180

Hence, the sum of the three interior angles of a triangle is 180.

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Answer:

5/6 cup

Step-by-step explanation:

[tex] \frac{1}{3} \times 2 \frac{1}{2} = \frac{1}{3} \times \frac{5}{2} = \frac{5}{6} [/tex]

The solved logarithmic function is log (2x + y) = 4 log (2) and log (4x - y) = 0 for 2x + y = 2⁴ and 4x - y = 1 respectively.

What is a logarithmic and exponential function?

Logarithmic functions and exponential functions are inverses of each other. The logarithmic function is denoted by using the word log while exponential by using the alphabet,  e. For example log 10 = 1 and e^2.

Solving the given expressions: 2x + y = 16 and 4x - y = 1

Applying given properties of logarithmic and exponential function;

log a + log b = log (ab)

4 log x = log x⁴

e^(log x) = 1

e^(x + y) = (e^x) × (e^y)

Take the expression, 2x + y = 16

Applying log on both sides, we get,

log (2x + y) = log (16)

log (2x + y) = log (2⁴)

log (2x + y) = 4 log (2)

To Check Results,

Taking exponential on both sides,

e^[log (2x + y)] = e^(4 log 2)

2x + y = e^(log 2⁴)

2x + y = 2⁴

2x + y = 16

Thus, the answer is verified.

Take expression, 4x - y = 1

Applying log on both sides, we get,

log (4x - y) = log 1

log (4x - y) = 0

To Check Results,

Taking exponential on both sides,

e^[log (4x - y)] = e^0

4x - y = 1

Thus, the answer is verified.

Hence, the solved expression is log (2x + y) = 4 log (2) and log (4x - y) = 0 for 2x + y = 2⁴ and 4x - y = 1 respectively.

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The answer is = 3

The phrase simplifies the way to make something less challenging to do or understand. So, by lowering or simplifying the fractions approach we make the fraction as easy as possible. We do this by dividing the numerator and the denominator by using the most important number which could divide into both numbers precisely.

Cross-cancellation is a simplification that may be executed earlier than. that is wonderful because simplifying earlier than the method while you do multiply, you'll have smaller numbers, and smaller numbers are easier to paint with.

Simplifying a rectangular root just means factoring out any best squares from the radicand, shifting them to the left of the unconventional image, and leaving the opposite factor within the radical image. If the variety is an ideal square, then the novel signal will disappear when you write down its root.

[tex]\sqrt[n]{a}[/tex][tex]\sqrt[n]{b}[/tex]=[tex]\sqrt[n]{ab}[/tex] , a[tex]\geq[/tex]0, b[tex]\geq[/tex]0

[tex]\sqrt[3]{9}[/tex][tex]\sqrt[3]{3}[/tex] = [tex]\sqrt[3]{9.3}[/tex]

[tex]\sqrt[3]{9.3}[/tex]

multiply the number 9.3 = 27

[tex]\sqrt[3]{27}[/tex]

[tex]\sqrt[3]{27}[/tex] =3

=3

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The average rate of change of the function between the points is -4/7

The constant average rates of change of a function is also regarded as the slope or the gradient of the function

Here, we have the points to be

(-3, 16) and (4, 12)

The average rates of change between these points is calculated as

Average rate of change = [f(b) - f(a)]/[b - a]

So, we have

Average rate of change = [12 - 16]/[4 + 3]

Evaluate the sum and the difference

So, we have

Average rate of change = -4/7

Hence, the average rate of change between the points is -4/7

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The number line (d) represents the location of the fraction -3/8 on the number line

A number line is a  vertical or horizontal line that has endpoints and it is used to represent numbers at a constant interval

The fraction is given as

-3/8

The above number is a negative number and it is greater than -1

This means that the location of the number line is between 0 and -1

To plot the number line, we make use of 8 intervals between 0 and -1 ( as represented by the number lines in the options)

The third point to the left of 0 represents -3/8

This means that the number line (d) represents the location of the fraction -3/8 on the number line

Hence, the number line (d) represents the location of the fraction -3/8 on the number line

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Answer:

1152

Step-by-step explanation:

32 * 36 lol

every yard is 36 inches

Answer:

Step-by-step explanation:

A measure of central tendency is a summary statistic that represents the center point or typical value of a dataset. These measures indicate where most 

Given that E is the midpoint of DF, the numerical values of DE, EF, and DF are 31, 31, and 62 respectively.

A midpoint is simply a point that divides a segment into two equal halves.Given the data in the question;E is the midpoint of D

Since E is the midpoint of DF, DE is equal to EF.

Segment DE = Segment EF

6x + 1 = 7x - 4

Solve for x:

6x - 7x = - 4 - 1

-x = -5x = 5

Now, the numerical values of DE, EF, and DF will be;

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The cost of one packet of biscuit is £1.60.

The total amount that Aisha paid for the items she purchased is a function of the total cost of bread rolls, ketchup and biscuits.

Total cost of the items purchased = total cost of bread rolls + total cost of biscuits + total cost of ketchup

Total cost of bread rolls = cost per packet x number of packets bought

2 x £1.20 = £2.40

Total cost of ketchup = cost of one bottle x number of bottles bought

1 x £2.10 = £2.10

Total cost of biscuits = cost of one packet  x number of packets bought

3 x b = 3b

Total cost = £2.40 + £2.10 + 3b = £4.50 + 3b

Total amount paid by Aisha = note given - change received

£10 - 70p

£10 - £0.70 = £9.30

Total amount paid by Aisha =  total cost

£9.30 = £4.50 + 3b

£9.30 - £4.50 = 3b

£4.80 = 3b

b = £4.80 / 3

b = £1.60

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Answer:9.3

Step-by-step explanation:

Area= length times width

132.99= 14.3xw

Divide by 14.3

W= 9.3

Answer: 1.12

Step-by-step explanation:

Answer:

1

1.12 is the exact value. 1 is an estimate.

Step-by-step explanation:

[tex]1.79 = 2\\0.67 = 1\\2 - 1 = 1\\\mathrm{(Estimate)~1 < 1.12~but > 0~and~1}\\\mathrm{Therefore,}\\= 1.12[/tex]