factor completely x^3 + 1/8

Answer:

• 9(sin 42°)

_______

sin 29°

Step-by-step explanation:

The value of x is calculated by the sine rule is 9(sin 42°)/sin 29°. Then the correct option is B.

Trigonometry deals with the relationship between the sides and angles of a triangle.

We know that the sine rule is given as

[tex]\rm \dfrac{a}{sin A} =\dfrac{b}{sin B}=\dfrac{c}{sin C}[/tex]

Then put the values and we have

[tex]\begin{aligned} \rm \dfrac{x}{sin 42^o} &= \rm \dfrac{9}{sin 29^o}\\\\\\\rm x &= \rm \dfrac{9*sin 42^o}{sin 29^o} \end{aligned}[/tex]

More about the trigonometry link is given below.

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Answer:

DF = 458

Step-by-step explanation:

In statistics, T-test have an extensive application. T-tests are used in hypothesis testing or inference about the population mean when the population standard deviation is not known. Nevertheless, they are used in making inference in paired samples or dependent samples t-test as well as independent samples.

The degrees of freedom, DF, is a characteristic of the student's t distribution which is used in T-tests. In a simple T-test;

DF = n - 1

where n is the sample size

Given n is 459, DF = 459 - 1 = 458

Therefore, DF = 458

Answer:

She decorated 4 faces.

Explanation:

A rectangular pyramid has 5 faces in total. There are 4 lateral faces and a base. If the baker only decorated the lateral faces, then she decorated 4 faces.

Rectangular Pyramid:

Answer:

The factorization of [tex]x^{3}+8[/tex] is [tex](x+2)(x^{2} -2x+4)[/tex]

Step-by-step explanation:

The problem is a sum of cubes factorization, this type of factorization applies only in binomials of the form [tex](a^{3} +b^{3} )[/tex] which means numbers that have exact cubic root and the exponents of the letters a and b are multiples of three.

Sum of cubes equation

[tex](a^{3} +b^{3} )= (a+b)(a^{2} -ab+b^{2})[/tex]

So, let's factor [tex]x^{3}+8[/tex]

we have to bring the equation to the form [tex](a^{3} +b^{3} )[/tex]

[tex]x^{3}+8=x^{3}+2^{3}[/tex] con [tex]a=x[/tex] y [tex]b=2[/tex]

Solving using sum of cubes equation

[tex](x^{3} +2^{3} )= (x+2)(x^{2} -(x)(2)+2^{2})[/tex]

[tex](x^{3} +2^{3} )=(x+2)(x^{2} -2x+4)[/tex]

.

Answer:

a: (x+2)(x^2-2x+4)

Step-by-step explanation:

i just did on edgen 2020

The coefficient of 'a' is 5.

The coefficient of 'b' is 9.

The coefficient of the constant term '-4' is -4 (or you can think of it as -4 times '1').

The coefficient in the expression 5a + 9b - 4 is the number that multiplies or is associated with a variable. In this expression:

The coefficient of '5a' is 5.

The coefficient of '9b' is 9.

The constant term '-4' does not have a variable and can be considered as a coefficient of '1' for the constant.

So, in summary:

The coefficient of 'a' is 5.

The coefficient of 'b' is 9.

The coefficient of the constant term '-4' is -4 (or you can think of it as -4 times '1').

for such more question on coefficient

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In the expression 5a+9b-4, 5 and 9 are the coefficients, representing the magnitude and direction of the variables 'a' and 'b'. The '-4' is a constant.

In the algebraic expression 5a+9b-4, the coefficients are the numbers in front of the variables. So in this case, 5 is the coefficient of a and 9 is the coefficient of b. A coefficient provides information about the magnitude and direction of a certain variable. In the absence of a variable, such as with the -4 in this expression, we don't refer to it as a coefficient, but rather as a constant.

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Answer:

80%

Step-by-step explanation:

4/5 is equal to 0.8, and 0.8 is equal to 80%

Answer:

[tex]\large\boxed{\dfrac{4}{5}=80\%}[/tex]

Step-by-step explanation:

[tex]n\ to\ a\ percent:\ n=n\cdot100\%\\\\======================\\\\\dfrac{4}{5}=\dfrac{4}{5}\cdot100\%=\dfrac{400}{5}\%=80\%[/tex]

Answer:

120 pounds

Step-by-step explanation:

1. divide 45 by 15

45 / 15 = 3

2. Each box costs 3 pounds each

3. multiple 3 by 40.

4. 40 x 3 = 120

The range of the piecewise defined function is:

                  y= -6 , y= -4 , y= -3 , y=0

The piecewise function is defined by:

f(x)  =    2x+2   when  x < -3

              x       when  x = -3

  and  -x-2      when  x > -3

Then the graph of the function is a strictly increasing function and is a line with a slope of 2.

The function increases continuously from -∞ to -4

i.e. it takes all the value in the interval (-∞,-4)

There is a open circle at (-3,-4)

The graph of the function f(x) is strictly decreasing .

Since the graph is a line with slope -1.

Also, there is a open circle at (-3,1)

and the function starts decreasing continuously and will take all the values strictly less than 1.

i.e. the range for x > -3 is:  (-∞,1)

The range of the whole function f(x) is:

                            (-∞,1)

Answer:

(-6,-4)

Step-by-step explanation:

The first endpoint of the line is (-6,8), we can call

x_1 = -6

and

y_1 = 8

Let the last endpoint have coordinates (x_2,y_2)

Also, the midpoint formula is:

(x_1+x_2)/2 , (y_1+y_2)/2

Now, plugging these values is the formula, we get:

(-6+x_2)/2 = -6

-6+x_2=-12

x_2=-12+6 = -6

x_2 = -6

Also

(8+y_2)/2=2

8+y_2=4

y_2=4-8=-4

y_2 = -4

The coordinates of the other endpoint is (-6,-4)

Answer:

12

Step-by-step explanation:

He can take one of the 2 shirts, so he has 2 choices.

He can take any one of the 3 pair of pants, so he has 3 choices.

He can choose any one of the 2 caps he has, thus he has 2 choices.

To find the number of different outfits possible, we simply multiply the number of choices available for each.

2 * 3 * 2 = 12 different outfits

Answer:

he can only make 2 outfits and have 1 pair of pants and one cap left byebye tell me if i am rightor wrong plz

stay safe

Step-by-step explanation:

2\xy³z⁴ is the simplification.

Answer:

96   sq.cm.

Step-by-step explanation:

area =16*12/2

are= 192/2 = 96

The area of the logo = area of kite = 96 sq. cm

Area of a kite = 1/2(product of its diagonals).

Thus:

The logo in form of Kite has the following diagonals measuring 12 cm and 16 cm.

Therefore:

Area of a kite = 1/2(12)(16)

Area of a kite = 1/2(192)

Area of a kite = 96 sq. cm

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For this case we must find the value of the variable "x" of the following equation:

[tex]y = 10^{x}[/tex]

We rewrite the equation as:

[tex]10 ^ {x} = y[/tex]

We take the logarithmic base 10 from both sides of the equation to remove the variable from the exponent.

[tex]log (10 ^ {x}) = log (y)\\x (log (10)) = log (y)[/tex]

The logarithmic base 10 of 10 is 1.

[tex]x * 1 = log (y)\\x = log (y)[/tex]

ANswer:

[tex]x = log (y)[/tex]

1,2 cause of the o and y axis

The vertex is where the parabola changes directions, or in simpler terms, at the parabolas lowest point. Unless the parabola is upside down, then the vertex is where the highest point is.

The acid of symmetry is the line where the parabola can be divided evenly. This is almost always where the vertex is, except it continues on.

The y-intercept is where the parabola intersects with the y-axis.

I’ve answered the question below in the picture (my graph is not to scale but the answers are correct for yours)

Hope this helped and good luck!!

Answer:

5 + 5 + 5 + 5 + 5 + 5 = 30

6 + 6 + 6 + 6 + 6 = 30

5 = 30 ÷ 6

6 = 30 ÷ 5

Answer:

1/182 or 0.55%

Step-by-step explanation:

There are 2 ways to approach this problem (and both give the same answer!).

First method: probability for each test.

First test, worms: There's 1/14 chances for bear #3 to be selected, since there are 14 bears total.

Second test, ticks: There's 1/13 chances for bear #5 to be selected, since only 13 bears remain (#3 cannot be tested for both ticks and worms).

So, to obtain the total probability, we multiply 1/14 with 1/13 = 1/182

Second method: permutations

We can see the problem from a permutations perspective.  How many permutations can we have for 2 bears to be tested? It's a permutation since the order is important. (#3 ticks + #5 worms ≠ #3 worms + #5 ticks)

[tex]P(14,2) = \frac{14!}{(14 - 2)!} = 182[/tex]

There are 182 permutations possible, ONE of which is bear #3 is tested for worms and bear #5 is tested for ticks.

So, once again, 1/182.

The phrase 'Eight less than the product of two and a number x' translates to the algebraic expression 2x - 8.

The student's question is about writing an algebraic expression to represent a phrase. In this case, 'Eight less than the product of two and a number x' can be translated into algebraic expression. The 'product of two and a number x' is simply, 2x. 'Eight less than' is subtracting 8 from something. Therefore, this phrase is written as 2x - 8 in algebraic expression.

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Answer:

15,000m or if you want it in km it is 15km

Step-by-step explanation:

1 minutes = 60 seconds

250 × 60 = 15,000 m

Answer:

15,000 m.

Step-by-step explanation:

There are 60 seconds in one minute.

Therefore the distance the plane travels in one minute = 250*60

=  15,000 m answer.

Answer:

false

Step-by-step explanation:

tangent always touch to the circle

so....

Answer:

False

I got it right!!

Step-by-step explanation:

For this case we have that Allison traveled 9x miles, while Adrian traveled 4x + 5 miles. The variable "x" represents the number of days.

We want to know how many miles of Allison toured Adrian, for this we subtract:[tex]9x- (4x + 5) =[/tex]

We take into account that:[tex]- * + = -[/tex]

[tex]9x-4x-5 =\\5x-5[/tex]

ANswer:

[tex]5x-5[/tex]

Answer:

Expression to show how many more miles Allison hiked than Adrian is:

5x-5

Step-by-step explanation:

Number of miles Allison hiked = 9x

Number of miles that Adrian hiked = 4x+5

Miles Allison hiked more  than Adrian

= 9x-(4x+5)

=9x-4x-5

=5x-5

Hence, expression to show how many more miles Allison hiked than Adrian is:

5x-5

Answer:

Step-by-step explanation:There's 4 people so you would multiply 6×4=24 and now add 20+24=48

30, because there are 4 people and their total age is 20 divide it by 4 you get 5 then you multipy by 6 to find their ages.

Answer:

8.6

Step-by-step explanation:

Answer:

b. 1.5 hope it helps

The answer is:

The simplified form of the given expression is 7.

[tex]49^{\frac{1}{2}}=\sqrt[2]{49^{1}}=\sqrt[2]{49}=7[/tex]

To simplify the given expression, we must remember the following property of roots:

[tex]a^{\frac{m}{n}}=\sqrt[n]{a^{m} }[/tex]

We are given the expression:

[tex]49^{\frac{1}{2}}[/tex]

Which can be also written as:

[tex]49^{\frac{1}{2}}=\sqrt[2]{49^{1}}=\sqrt[2]{49}[/tex]

Then, simplifying we have:

[tex]\sqrt[2]{49}=7[/tex]

Hence, the simplified form of the given expression is 7.

Have a nice day!

Answer: 7

Step-by-step explanation: To simplify [tex]49^{1/2}[/tex], it's important to understand that an exponent of 1/2 means that we take the square root of the base. In other words, [tex]49^{1/2}[/tex] means the same thing as the square root of 49 or [tex]\sqrt{49}[/tex] and the square root of 49 is 7.

This means that [tex]49^{1/2}[/tex] is 7.

Answer:

Step-by-step explanation:

Definition of absolute value:

|a| = a if a ≥ 0

|a| = -a if a < 0

Examples:

|2| = 2

|-2| = -(-2) = 2

|0.45| = 0.45

|-0.45| = -(-0.45) = 0.45

|1000| = 1000

|-1000| = 1000

Therefore

|12| = 12

Answer:

27 years old

Step-by-step explanation:

let Sydney's age be x, then

Devaughn's age is 3x ( three times Sydney's )

The sum of their ages is 108, thus

x + 3x = 108

4x = 108 ( divide both sides by 4 )

x = 27

Sydney is 27 years old

Answer:

I think it would be 27

Answer:

The percent of the cost tax is:

                                8.5%

Step-by-step explanation:

Cost of shoe before tax= $ 78

Cost of shoe after tax= $ 84.63

This means that the cost of tax is:

Cost of shoe after tax-cost of shoe before tax

= $ 84.63-$ 78

= $ 6.63

Now, the percent of tax is calculated as:

[tex]Percent\ tax=\dfrac{Cost\ of\ tax}{Cost\ of\ shoe\ before\ tax}\times 100\\\\\\Percent\ tax=\dfrac{6.63}{78}\times 100\\\\\\Percent\ tax=8.5\%[/tex]

                     Hence, the percent tax is:

                              8.5%

Answer:

[tex](-5,0)[/tex] and [tex](3,0)[/tex]

Step-by-step explanation:

Think about it.

What two numbers multiply to -15 and add up to 2?

The answers are 5 and -3.

So plug that into the factored form of a parabola.

[tex]y=(x+5)(x-3)[/tex]

To find the x-intercepts, plug in 0 for [tex]y[/tex].

[tex](x+5)(x-3)=0[/tex]

Since we are multiplying, at least one of the terms has to equal 0.

[tex]x+5=0 \\ x-3=0 \\ \\ x=-5,3[/tex]

So the x-intercepts are [tex](-5,0)[/tex] and [tex](3,0)[/tex].

Rounding to the nearest tenth, the area of the regular pentagon is approximately 175.1 square centimeters.

To find the area of the regular pentagon, we can use the formula:

Area = (5/2) * s * r

Where s is the length of one side of the pentagon and r is the distance from the midpoint of the pentagon to one of its vertices.

We are given that s = 8.37 cm and r = 8.37 cm.

Plugging these values into the formula, we get:

Area = (5/2) * 8.37 * 8.37

Area = (5/2) * 70.0569

Area = 175.14225

Rounding to the nearest tenth, the area of the regular pentagon is approximately 175.1 square centimeters.

Well if you were to do 18 ÷ 2 it would be 8. But since this is 8 and a half let's use 2.5. So, let's do this.

18 ÷ 2.5 = 7.2.

But since cake can't be exactly that we can estimate to 7 since it is the closest so, the answer is 7 pieces of cake.