a rectangular piece of marble is cut such that the width is triple the length and the height is double the width. write a polynomial function v (x) in standard form for the volume of the piece of marble, where a is the length of the marble. v(x) =

Answer:

x = 5

Step-by-step explanation:

-3x = -15  Divide both sides by -3

[tex]\frac{-3x}{-3}[/tex] = [tex]\frac{-15}{-3}[/tex]    A negative divided by a negative is a positive.

x = 5

Answer:

radius = 13 cm

Step-by-step explanation:

the segment OT bisects the chord RS , then

RT = 12 cm

the radius of the circle is the line OR

using Pythagoras' identity in the right triangle RTO

OR² = RT² + OT² = 12² + 5² = 144 + 25 = 169 ( take square root of both sides)

OR = [tex]\sqrt{169}[/tex] = 13

that is the radius = 13 cm

Answer:

1) y=5/2x +2

2) y=1/2x+4

Step-by-step explanation: Slope intercepts equation is y=mx+b. After solving your slopes for each problem would be 5/2x and 1/2x, then you would solve to find B, which for this problem is 2, and 4. You would leave the y as just a regular y for this problem.

The volume of the solid is 207.23 cm³.

Volume of the Solid:

Volume is the area occupied by an object/matter (solid, liquid, gas) within a 3D object. Alternatively, the volume of a three-dimensional object is generally defined as the capacity of the object that matter can hold.

For example, the volume of a cubic box indicates how much water or other substance it can contain. For ice cream cups, the amount of ice cream that can fit in the cup without gaps corresponds to the volume of the ice cream cup.

Now, based on the question:

Volume of Solid = Volume of Cylinder + Volume of Cone

Volume of Cylinder = πr²h

v= 3.14 * (3)² * 6

v = 169.56

Volume Of Cone:

Cone volume defines the space or volume of the cone. A cone is a three-dimensional geometric shape with a circular base that tapers from a flat base to a point called an apex or vertex. A cone is formed by a series of line segments, half-lines, or lines connecting vertices that are common to all points on the base in a plane that does not contain vertices. A cone can be thought of as a series of noncongruent disks that overlap each other such that the ratios of the radii of adjacent disks are kept constant.

We know that :

Volume of Cone = πr² h/3

v = 3.14 * (3)² * 4/3

v = 37.7

Now,

Volume of Solid = 169.56 + 37.7

              = 207.26 cm³

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Answer:

25%

Step-by-step explanation:

Because the thing is divided in to fourths the is 1/4 chance of getting any of those four numbers. Also 1/4 as a percentage is 25%

Answer:

84

Step-by-step explanation:

To find the length of the image [tex]\overline{G'H'}[/tex], multiply the length of the preimage [tex]\overline{GH}[/tex] by the scale factor of [tex]4[/tex].

Answer:

162

Step-by-step explanation:

1 hundred (100) + 5 tens (50) + 12 ones (10+2)

100+50+12 = 162

-1016 is a rational number and integer

Integers are basically the whole numbers that can be positive, negative, or zero. In integers, fractional numbers are not included. For instance, -2, -3,0,1,5, and so on are integers.

A rational number, in Mathematics, can be defined as any number which can be represented in the form of p/q where q ≠ 0.

Example of rational numbers are 1/2 , 2/1 , 3/5 e.t.c.

All positive and negative integers are also rational numbers.

Therefore the number -1016 is a both a rational number and an integer.

This is because all positive and negative numbers are integers.

And -1016 can be written as -1061/1 which makes it a rational number.

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On solving the provided question, we can say that as we have a hexagon here, each angle = x = 120

A hexagon is a six-sided polygon or hexagon in geometry that makes up the cube's outline. A straightforward hexagon's internal angles add up to 720°. A closed two-dimensional polygon with six sides is what is known as a hexagon in geometry. Additionally, a hexagon has 6 corners on each side. Hexa signifies six, and gona denotes an angle. Soccer balls, honeycombs, floor tiles, and surfaces of pencils are all hexagonal in shape. A hexagon is a polygon with six sides in geometry. A hexagon is referred to as a regular hexagon if all of its sides and angles have the same length.

as we have a hexagon here,

so sum of angles = 720

x+x+x+x+x+x = 720

6x = 720

x = 720/6

x = 120

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The third variable should be solved for by substituting the system accordingly within one of the original equations.

The number is said to be in its simplest form when divided into its smallest equivalent fraction. What to do to find the most basic form. Verify a fractional integer to verify if it qualifies as a prime number. A statement having two spherical geometry and an equal sign in the middle is called an equation in mathematics. The general form of any equation contains the degrees of all the variables in descending order. The conventional form of the a linear equation is an x + b = 0. The general form of a linear equation with two variables is an x + b y + c = 0. (or something similar).  An identity holds true regardless of the value given to the variables.

given

From the system, choose any two equation pairings. The Addition/Subtraction technique should be used to remove so same element from each pair.

Apply the addition and subtraction method to the two new equations' system of problems.

The third variable should be solved for by substituting the system accordingly within one of the original equations.

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The complete question is :-

How to solve three system of equations ?

Since, f(0)=0, hence the given x-5 is the factor of given function.The slope-intercept form of the linear function equation. As a result, it is written as f(x) = mx + b, where m denotes the slope and b the line's y-intercept. Recognize a linear function's standard form. Usually, linear functions are written

The graph of a linear function is a straight line. The following is the form of a linear function. a + bx = y = f(x). One independent variable and one dependent variable make up a linear function. X and Y are the independent and dependent variables, respectively.

Given, equation

[tex]f(x)=2x^3+7x^2-15x[/tex]

putting x=-5 in above equation

[tex]f(-5)=2*(-5)^3+7*(-5)^2-15*(-5)\\f(-5)=0[/tex]

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Since, f(0)=0, hence the given x-5 is the factor of given function.The slope-intercept form of the linear function equation. As a result, it is written as f(x) = mx + b, where m denotes the slope and b the line's y-intercept. Recognize a linear function's standard form. Usually, linear functions are written

The graph of a linear function is a straight line. The following is the form of a linear function. a + bx = y = f(x). One independent variable and one dependent variable make up a linear function. X and Y are the independent and dependent variables, respectively.

Given, equation:

f(x) = 2x³ + 7x² - 15x

Putting x = -5 in above equation:

f(-5) = 2 * (-5)³ + 7 * (-5)² - 15 * (-5)

f(-5) = 0

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Absolute functions and inequality signs are both included in an expression to be considered an absolute value inequality.

The absolute value inequality is demonstrated by the values of z.

The z values that can be used

Z's polar opposite is bigger than 5.

the following absolute value inequality results.

[tex]$|z| > 5$[/tex]

Expand

[tex]$z > 5$ or $z < -5$[/tex]

The number five is a good one.

So, we use the inequality to our advantage.

[tex]$z < -5$[/tex]

According to the inequality above, z might have a value between -6 and -7.

There are more z values to be aware of.

The values that z cannot exist in (a) are as follows:

[tex]$z > 5$ or $z < -5$[/tex]

Inequality is a representation of the values that z cannot be.

[tex]$z > 5$[/tex]

Z cannot be 6 or 7 given the inequality above.

They are all negative numbers less than -5, which is the accurate statement about the values of z.

The complete question is:

The opposite of z is greater than 5. a. What are two possible values of z? What are two values that z cannot be? What must be true about all possible values of z? Show your work.​

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An example of substitution property is finding the solution of an algebraic expression.

The substitution property is a notion in algebra that is used for substituting the value of a given variable or a quantity into an expression to find the value of the unknown.

In other words, we can express that the substitution property is utilised to replace the value of a quantity in an equation or an expression to solve a mathematical problem.

For example, Find the value of the algebraic expression x² - 3x + 8 if x = 1.

Using the substitution property, we will substitute x with 1 in the given expression to find its value.

x² - 3x + 8 if x = 1

= 12 - 3(1) + 8

= 1 - 3 + 8

= -2 + 8

= 6

So, the value of the given algebraic expression x² - 3x + 8 is 6 when x = 1.

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Answer:

24wx + x

Step-by-step explanation:

3( wx8) + x

3(8wx) +x

3 × 8wx + x

\ /

24wx + x

The null and the alternative hypothesis are:

H0 : µ = 444

Ha : µ < 444 (Left tail test)

We have the following data to solve the problem with

level of significance is given as 0.1

standard deviation = 10

Sample Size , n = 20

Sample Mean, x = 447.0000

solve for the degree of freedom

degree of freedom

DF

20-1= 19

find the  Standard Error

= s/√n

= 10 / √ 20 = 2.2371

find the test statistic

t-test statistic= (x - µ )/SE =

( 447 - 444 ) / 2.2371 = 1.341

find the p value using df = 19

p value = .097866.

0.1 > .097866.we have to reject the null hypothesis

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Answer:

a= 92.7

Step-by-step explanation:

Assuming the width and height are 5 and the length is 6

The expected profit in the long run can be determined by calculating the expected value of the total revenue from selling the lobsters. The expected total revenue is the sum of the expected revenue from selling the lobsters to the restaurant and the from selling the lobsters to the grocery store.

The expected value of the revenue from selling the lobsters to the restaurant can be calculated by multiplying the expected price per pound from the restaurant by the expected amount of lobsters caught in a day. The expected price per pound from the restaurant follows a triangular distribution with minimum value $1.50, maximum value $5.50, and likeliest value $3.50. The expected amount of lobsters caught in a day follows a normal distribution with mean 1,500 pounds and standard deviation sqrt(12,500) pounds.

The expected value of the revenue from selling the lobsters to the grocery store can be calculated by multiplying the expected price per pound from the grocery store by the expected amount of lobsters caught in a day. The expected price per pound from the grocery store is decreasing with more lobsters: $3.85 - 50.0005 * y, where y is the total lobster amount sold in pounds. The expected amount of lobsters caught in a day follows a normal distribution with mean 1,500 pounds and standard deviation sqrt(12,500) pounds.

Given the expected values of the total revenue from selling the lobsters to the restaurant and the grocery store, Amir can use simulation to determine the optimal percentage of lobsters to sell to the restaurant in order to maximize his expected profit in the long run. He can run several simulations with different percentages of lobsters to be sold to the restaurant and compare the expected profits for each simulation. The percentage that produces the highest expected profit is the optimal percentage for Amir to maximize his expected profit in the long run.

Amir can use simulation to determine the optimal percentage of lobsters to sell to the restaurant in order to maximize his expected profit in the long run. He can calculate the expected value of the total revenue from selling the lobsters to the restaurant and the grocery store, and then run several simulations with different percentages of lobsters to be sold to the restaurant to compare the expected profits for each simulation. The percentage that produces the highest expected profit is the optimal percentage for Amir to maximize his expected profit in the long run.

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Answer:

Step-by-step explanation:

Answer:

[tex]x=6.40[/tex] (to 3sf)

Step-by-step explanation:

Height of triangle = 14 - 10

                             = 4

Following the Pythagoras' Theorem,

[tex]x^{2} =5^{2} +4^{2} \\x^{2} =41[/tex]

∴ [tex]x=6.40[/tex] (to 3sf)

The additive inverse of (-3 9) is (3 -9). This means that if you add the two numbers together, the result is zero.

(-3 9) + (3 -9) = 0

The additive inverse of a number is a number that when added to the original number produces a result of zero. In other words, the two numbers have the same absolute value, but one is the opposite sign of the other.

For example, the additive inverse of (-3 9) is (3 -9). This means that if you add the two numbers together, the result is zero. To demonstrate this mathematically, (-3 9) + (3 -9) = 0.

The concept of additive inverse is important in mathematics because it is used to solve equations. By understanding the concept, you can quickly find the solution to an equation by adding the opposite of the number in question.

Furthermore, additive inverse is also important in understanding the concept of subtraction. Subtraction can be thought of as addition of the inverse of the number being subtracted. For example, if you subtract 3 from 9, you can also think of it as adding the inverse of 3 to 9, which would be (-3). Therefore, 9 - 3 = 9 + (-3) = 6.

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Dilation is a transformation that changes the size of an object while keeping its shape the same.

In this case, the scale factor of 3 tells us that the triangle will be three times larger than the original triangle.

To perform the dilation, you would take each vertex of the triangle and multiply the x-coordinate and y-coordinate by 3. For example, if one vertex of the original triangle had coordinates (x, y), the coordinates of that same vertex in the dilated triangle would be (3x, 3y).

It's also worth noting that the dilation is done with respect to a fixed point called the center of dilation. You can think of this point as the "pivot" around which the dilation occurs.

The center of dilation is typically represented by the letter "O".

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Answer:

$1080

Step-by-step explanation:

F = P + Prt

r = 5% = 0.05; t = 4

F = $900 + $900 × 0.05 × 4

F = $1080

The compound inequality that represents each phrase is x=-3. An inequality expression is 25 < x < 30.

An inequality that combines two other inequalities by using either "and" or "or" is referred to as a compound inequality. In some cases, "and" won't be stated explicitly, but it is still understood. For instance, 1 x 3 simply means "x > 1 and x 3". However, a compound inequality using "or" is always explained in detail using "or." Conjunction and disjunction are the two forms of compound inequalities, and the following are their distinctions:

All real numbers that are less than -3 => x < -3

or greater than or equal to 5 => x≥5

Compounded inequalities :   x < -3 or  x≥5

From the graph, there is a hole at x = -3.

2. If you want to say that a cake needs to bake for between 25 and 30 minutes, you can use the inequality phrase 25 x 30. Option is the response that is appropriate (A).

What do math operations consist of?

The built-in functions for multiply, divide, and subtract can also be used to specify arithmetic operations.

Describe inequality.

Mathematical statements are considered to be unequal if at least two of the terms contain variables or integers that are not equal.

It has been stated that a cake should bake for a minimum of 25 minutes and a maximum of 30 minutes.

The time needed to bake a cake is between 25 and 30 minutes, which may be expressed as an inequality statement, where x

⇒ 25 < x < 30.

Therefore, the inequality expression is 25 < x < 30.

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Lisa also cleans windows on the weekend. The correct answer is c = 10w + 5

So, she charges $10 a window plus a $5 flat supply fee, we are going to add 10 and 5 to find are answer and we are going to use c:

→ w = 10

→ 10w

$5 in the other hand, is independent.

→ + 5

→ c = 10w + 5

Therefore, Lisa also cleans windows on the weekend. The correct answer is c = 10w + 5

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Answer: [tex]\frac{(\sqrt{10} +3)^{2}+1 }{\sqrt{10}+3 }[/tex]

Step-by-step explanation：

The system of equations is y = 35 - 2.2x and y = 1.7x.

The solution of the system of equations is (8.97,15.25).

At about 8.97 seconds, both elevators will be about 15.25 feet above the ground.

What is an elevator?

An elevator, often known as a lift, is a car that moves vertically in a shaft to transport passengers or freight between the levels of a multistory building. Most modern elevators are propelled by electric motors via a system of wires and sheave with the assistance of a counterweight (pulleys).

Given that there are two elevators in an office. The 4th floor of the office at 35 feet above the ground and is descending at a rate of 2.2 feet per second.

The equation represents the height of the elevator above the ground after x seconds is y = 35 + (-2.2)x. Since the elevator is descending at a rate of 2.2 feet per second.

The other elevator starts out at ground level and rises at a rate of 1.7 feet per second.

The equation represents the height of the elevator above the ground after x seconds is y = 1.7x. Since the elevator is rising at a rate of 1.7 feet per second.

The system of equations is

y = 35 + (-2.2)x .....(i)

y = 1.7x   ........(ii)

Solve the equations substitution method.

Putting y = 1.7x in equation (i)

1.7x = 35 + (-2.2)x

1.7x = 35 - 2.2x

Add 2.2x on both sides:

1.7x + 2.2x = 35

3.9x = 35

Divide both sides by 3.9:

x = 35/3.9

x = 8.97

Putting x = 8.97 in equation (ii)

y = 1.7 × 8.97

y = 15.25

After 8.97 seconds, the elevators will be 15.25 feet above the ground.

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The measure of the missing angle is 21°.

1. Measure the length of each side of the triangle.

2. Using the triangle inequality theorem, determine the angles of the triangle.

3. Use the formula to calculate the measure of each interior and exterior angle.

Solution:

To measure a missing angle of triangle,

∠ABC + ∠ACB + ∠CAB = 180°

x + 132° + 27° = 180°

x + 159°  = 180°

x = 180° - 159°

x = 21°

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If Triangle ABC ~ triangle DEF then the measurement of EF is 2.37

A triangle is a three-sided polygon that consists of three edges and three vertices.

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .

Triangle ABC ~ triangle DEF

The sides of triangle ABC are proportional to sides of triangle DEF

ED/AB=EF/7.9

3.3/11=EF/7.9

0.3=EF/7.9

Apply cross multiplication

EF=2.37

Hence, if Triangle ABC ~ triangle DEF then the measurement of EF is 2.37

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The r in math example is a real number .

What is an integer ?

integer can be defined as a whole number but not a fraction number in which it can be positive , negative or zero and integer is denoted by the letter Z , integers additionally does now not include the fractional part. for that reason, we are able to say, integers are numbers that can be positive, negative or 0, but cannot be a fraction. we will carry out all the arithmetic operations, like addition, subtraction, multiplication and division, on integers.

The examples of integers are, 1, 2,-4,-8 and etc.

Real number can be any number, fraction, decimal, whole, positive, negative

So the examples for the real numbers are 1/2 , 2.3 , +4 , -69 and etc .

Hence, The r in math example is a real number .

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