The volume of a rectangular prism is represented by the function x3 9x2 6x − 16. the length of the box is x 2, while the height is x 8. find the expression representing the width of the box. x − 4 x − 1 x 1 x 4

Answer:

[tex]x=1+5\sqrt{2}, 1-5\sqrt{2}[/tex]

Step-by-step explanation:

[tex](x-1)^2=50 \\ \\ x-1=\pm 5\sqrt{2} \\ \\ x=1 \pm 5\sqrt{2}[/tex]

The next term of the given geometric series is the fifth term which is; a₅ = 4

We are given the geometric series as;

1024, -256, 64, -16,.....

The formula to find the nth term of a geometric series is;

aₙ = ar^(n - 1)

where;

a is first term

r is common ratio

n is position of term

Thus, from the given series, we have that;

a = 1024

r = -256/1024

r = -1/4

Thus, the formula for the nth term of the series is;

aₙ = 1024(-¹/₄)^(n - 1)

Next term is the fifth term and so we have;

a₅ = 1024(-¹/₄)^(5 - 1)

a₅ = 1024(-¹/₄)^(4)

a₅ = 4

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Answer:1/6.4, and there are 5.4 times as many pigs as cows.

Step-by-step explanation: In this scenario there are 64 animals, 54 pigs and ten cows. So the ration is 10/64, which can be simplified if you like to 1/6.4

There are 54 pigs for every 10 cows, which is the same as 5.4/1.

For every cow there is 5.4 pigs, so however many cows there are you can take that number and multiply it by 5.4 to get the number of pigs.

Answer:

5/32

5.4

Step-by-step explanation:

54:10 is the ratio of pigs to cows.

It could be assumed that there are 54 pigs and 10 cows.

Problem is asking for the ratio of cows to all animals. So,

Add up the pigs and cows to get 64 total animals.

Input the numbers to the ratio cows:all animals

10:64

Change to a fraction

5/32

How many times the number of cows is the number of pigs. This can be found by dividing the number of pigs by the number of cows.

54 / 10 = 5.4

The number of pigs is 5.4 times more than the number of cows.

Step-by-step explanation:

so, it is

3³ × (3⁴)^(0.5) ?

remember, when multiplying exponents of the same base, we add the exponents : e.g.

a⁵ × a³ = a⁸

when we have exponents in exponents we multiply the exponents : e.g.

(a³)⁴ = a¹²

now, also remember the priorities of mathematical operations :

1. brackets

2. exponents

3. multiplications and divisions

4. additions and subtractions

now, let's look at our expression again :

3³ × (3⁴)^(0.5)

since we only want to simplify and not to calculate, we leave (3⁴) alone, because the only thing we could do would be to actually calculate 3⁴.

so,

(3⁴)^(0.5) = 3^(4×0.5) = 3²

and then,

3³ × 3² = 3^(3+2) = 3⁵

so, the simplified expression is 3⁵.

which is 243 ...

Answer: 1.72

Step-by-step explanation:

[tex]2\div \cfrac{3}{7}\implies \cfrac{2}{1}\div \cfrac{3}{7}\implies \cfrac{2}{1}\cdot \cfrac{7}{3}\implies \cfrac{14}{3}\implies 4\frac{2}{3}[/tex]

The quotient for the expression is 4.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

2 ÷ [tex]\frac{3}{7}[/tex]

= 2 / (3/7)

= (2 x 7) / 3

= 14/3

Now,

3 ) 14 ( 4

    12

      2

Remainder = 2

Quotient = 4

Thus,

The quotient is 4.

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In exponential relations, we can represents given values like this:

[tex]f(x)=a*c^x[/tex]

We're given:

⇒ Plug this information into [tex]f(x)=a*c^x[/tex]:

[tex]f(x)=27,100*(0.93)^x[/tex]

Why input 0.93 and not 0.07? Let's think of it this way: To calculate the new price of the car after one year, we find 93% of 27,100.

The dependent variable is the price (y) and the independent variable is the time in years (x).

Therefore, to find the value of the car after 6 years, we plug in 6 as x:

[tex]f(x)=27,100*(0.93)^6[/tex]

[tex]V=27,100*(0.93)^6[/tex]

The values of x, y and z in the angles are as follows

When parallel lines are cut by a transversal line, angle relationship are formed such as corresponding angles, alternate angles, linear angles, vertically opposite angles.

The parallel lines forms angles relationships.

Therefore,

x = 2y (alternate angles)

z = 2x + 90 (alternate angles)

Using substitution,

z = 2(2y) + 90

z = 4y + 90

x + 2x + 90 = 180 (sum of angles on a straight line)

3x  = 180 - 90

3x = 90

x = 90 / 3

x = 30°

Hence,

30 = 2(y)

y = 30 / 2

y = 15

z = 4(15)+ 90

z = 60 + 90

z = 150°

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[tex](\stackrel{x_1}{9}~,~\stackrel{y_1}{1})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{1}{9} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{1}=\stackrel{m}{ \cfrac{1}{9}}(x-\stackrel{x_1}{9}) \\\\\\ y-1=\cfrac{1}{9}x-1\implies {\Large \begin{array}{llll} y=\cfrac{1}{9}x \end{array}}[/tex]

Answer:

D

Step-by-step explanation:

500 user in a day that mean in 2 days you get 1000 user cause the double of 500 is 1000

The vertex form of the quadratic equation is f(x) = -3(x - 2)² + 5. The coordinates of the vertex are (2, 5).

We are given a quadratic function. The equation of the quadratic function is f(x) = -3x² + 12x - 7. We need to convert the equation to vertex form. We can convert a quadratic equation to its standard vertex form by "completing the square" method. The calculations are done below.

f(x) = -3x² + 12x - 7

f(x) = -3(x² - 4x) - 7

f(x) = -3(x² - 4x + 2² - 2²) - 7

f(x) = -3(x² - 4x + 2²) - 7 + 3*2²

f(x) = -3(x - 2)² - 7 + 12

f(x) = -3(x - 2)² + 5

The coordinates of the vertex are (2, 5).

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Volume of the cone is 628 In^3

What is cone?

A cone can be seen as a set of non-congruent circular disks that are stacked on one another such that the ratio of the radius of adjacent disks remains constant.

Cones typically have pyramidal shapes with circular cross sections. A right cone is a cone with the vertex located above the base's middle. Right circular cone is another name for it. If you know the height and radius of a cone and plug those values into a formula, you can quickly determine the volume of a cone.

The volume of a cone defines the space or the capacity of the cone. A cone is a three-dimensional geometric shape having a circular base that tapers from a flat base to a point called apex or vertex. A cone is formed by a set of line segments, half-lines or lines connecting a common point, the apex, to all the points on a base that is in a plane that does not contain the apex.

According to the question

The volume of a cone = (1/3) πr2h cubic units

r=10 inch

h=6 inch

π=3.14

Volume=0.33(3.14)(10)(10)(6)

volume=628 [tex]inch^3[/tex]

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Answer:

I think it would be 12^1/4

Step-by-step explanation:

I hope this is what you were asking for :)

The absolute value equation representingnumbers all x whose distance from is 11 units is

Without taking direction into account, absolute value describes how far away from zero a certain number is on the number line.

A number can never have a negative absolute value.

The equation is written in the form below

|1 - x| = 11

removing the absolute value sign

1 - x = ± 11

solving for x for positive value

1 - x = 11

1 - 11 = x

x = -10

solving for x for negative value

1 - x = -11

1 + 11 = x

12 = x

The absolute value equation as required is |1 - x| = 11 the values of is 12 or -10

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Answer: $3.01

Step-by-step explanation:

1. You first have to find out how much she spent for ALL the jellybeans, you find this by multiplying the pounds by the cost per pound.

(7/2)*(2.58)

Kelsey spent $9.03 for the 3 1/2 pound bag of jellybeans

2. You now have to find out how much she spent for 1/3 if the bag. You do this by multiplying the total cost by 1/3.

(1/3)(9.03)

3.01

ANSWER: Kelsey spent $3.01 on the amount of jellybeans she gave away.

The expression that is equivalent to x is ∛4/s

In this question, the mathematical statement of the equation is given as

5x to the power of 7 times s = 20x to the power of 4

When the mathematical statement is represented as an equation, we have the following representation

5x⁷ * s = 20x⁴

Divide both sides by x⁴

So, we have the following representation

5x⁷/x⁴ * s = 20x⁴/x⁴

Evaluate the quotients

This gives

5x³ * s = 20

Divide both sides by 5

x³ * s = 4

So, we have

x³ = 4/s

Take the cube root of both sides

x = ∛4/s

Hence, the solution is x = ∛4/s

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Pressure = Force/Area

According to question, we have

18 = Force/4

force = 72 N

Answer:

Step-by-step explanation:

The Cyclical Unemployment rate is 3%.

Unemployment simply means a scenario where those who are willing and able to work can't find suitable jobs.

Actual Unemployment Rate = 8%

Natural Unemployment Rate = 5%

The Actual Unemployment rate will be:

= Cyclical Unemployment Rate + Natural Unemployment Rate

8% = 5% + C

C = 8% - 5%

C = 3%

C = Cyclical Unemployment rate

The unemployment is 3%.

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Answer:

1. 190 degrees

2.

For the red triangle

-2,4, -4,2 -2,1

For the blue triangle

-2,-5 -5,-5 -7,-4

I don't know if this is correct but I hope this helps :)

1/2 x + 8 = 15  Grace will pay for a student ticket

the question requests the cost of a "student ticket." Because we don't know, let's assume the student ticket price is "x" dollars.

Because we know from the question that "the price of an adult ticket is half the price of a student ticket plus $8.00," we can represent the adult ticket price as follows:

1/2 x + 8

If we also get "An adult ticket costs $15.00" from the question, we can write the equation as:

1/2 x + 8 = 15

Grace will pay for a student ticket

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Answer:

8 hours

Step-by-step explanation:

if it takes 2hrs to do 4 pages it takes an hour to do 2 pages

2*8=16

1*8=8

8 hours

hope it helps

Answer:

9/14 (9 over 14)

Step-by-step explanation:

Answer:

0.001? or -299.7

Step-by-step explanation:

so i don't have idea what do you meaning so

0,3:300=0.001 or 0,3-300=-299.7

so i think i help

The two related linear equations for |x – 2| = 5 are x - 2 = 5 and x - 2 = -5

From the question, we have the equation to be

|x - 2| = 5

This equation is an absolute value function

The general rule of an absolute value function is that:

An equation represented as y = |x| can be expressed as y = x or y = -x

Using the above guideline as a guide, we have the following representation of |x – 2| = 5

x - 2 = 5 and x - 2 = -5

Hence, the equations are x - 2 = 5 and x - 2 = -5

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An equation for the trend line shown on the scatter plot is y = 5x + 15.

In order to determine a linear equation for the trend line (line of best fit) that models the data points described in the scatter plot above, we would have to calculate the slope of this line.

By critically observing the scatter plot, we can reasonably and logically deduce the following points through which the trend line passes through:

Points (x, y) = (2, 25)

Points (x, y) = (6, 45)

Mathematically, the slope of any straight line can be calculated by using this formula;

Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope, m = (y₂ - y₁)/(x₂ - x₁)

Slope, m = (45 - 25)/(6 - 2)

Slope, m = 20/4

Slope, m = 5.

At point (2, 25), a linear equation for the trend line can be calculated by using the point-slope form:

y - y₁ = m(x - x₁)

Where:

Substituting the given parameters into the formula, we have;

y - y₁ = m(x - x₁)

y - 25 = 5(x - 2)

y - 25 = 5x - 10

y = 5x - 10 + 25

y = 5x + 15.

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The area of the rectangle is, 24 square centimeter.

What is area?

Area is a mathematical concept that expresses the size of a region on a planar or curved surface. The area of an open surface or the boundary of a three-dimensional object is referred to as the surface area, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.

Let, the perimeter of the rectangle is 20 centimeter.

The length is 6 centimeter.

Suppose the width of the rectangle is y.

So,

Perimeter = 2(6) + 2(y)

           20 = 12 + 2y

             8 = 2y

             y = 4

Hence, the width of the rectangle is 4 centimeter.

Since,

Area of rectangle = length x width

                          A =  6 x 4

                          A = 24

Therefore, the area of the rectangle is, 24 square centimeter.

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Answer:

132

Step-by-step explanation:

240/5=48

48*2=96

240-15%=204

240-204=36

96+36=132

The number of pupils who came by bus is 108.

Total number of kids in school = 240

Fraction of pupils who came to school by car = 2/5

Number of pupils who came to school by car = [tex]\frac{2}{5}[/tex] × 240

                                                                           = 96

Percentage of pupils who came to school by walk = 15 %

Number of pupils who came to school by walk = [tex]\frac{15}{100}[/tex] × 240

                                                                              = 36

Number of people who came by bus  

                    =Total number of kids in school - number of pupils who         came by car - number of pupils who came by walk

                    = 240 - 96 - 36

                    = 108

Therefore, the number of pupils who came to school by bus = 108.

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The statement that "the sample is set of all people or objects whose properties ,  are to be described and analyzed by the data collector " is False .

In the question ,

it is given that ,

The sample is the set of all the people or objects whose properties are to be described and analyzed by the data collector .

But we know that the Population is defined as "set of all people or objects whose properties are to be described and analyzed by the data collector"

and the Sample is the Subset or subgroup of the population .

Therefore , the given statement is False .

The given question is incomplete , the complete is

State whether the statement is True or false "a sample is the set of all the people or objects whose properties are to be described and analyzed by the data collector " .

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