A line includes the points (0, -8) and (3, 3) find the rate of change of the line

The use of x^2^k is a more efficient way to multiplying than starting with x and successively squaring.

according to question,

real number = x

positive integer = k

x^2^k

Starting with x and squaring to find x², x⁴, xⁿ

The efficient way of multiplying is

x^2^k

where, k = 1, 2, 3, 4,.....…

check:

when k = 1

x^2^1

= x²

when k = 2

x^2^2

= x⁴

when k = 3

x^2^3

= x^2*2*2

= x^8

Therefore,

x^2^k

is a more efficient way to multiplying.

Integer

An integer is a number with no decimal or fractional part and it includes negative and positive numbers, including zero.

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The amount of gravel needed to cover the floor of the cube shaped tank to a depth of 1 inch is 0.38 ft^3.

The area that any three-dimensional solid occupies is known as its volume. These solids can take the form of a cube, cuboid, cone, cylinder, or sphere. Various forms have various volumes.

Given that the fish tank is a cube that holds 10 ft^3 of water.

The volume of the cube is given by:

V = a³

Substituting the value of 10 in V we have:

a³ = 10

a = 2.15

Now, to gravel at the bottom of the tank will have the following dimensions as height will be 1 inch.

1 inch = 0.083

V = (a)(a)(a)

V = (2.15) (2.15) (0.083)

V = 0.38 ft^3

Hence, the amount of gravel needed to cover the floor of the tank to a depth of 1 inch is 0.38 ft^3.

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Answer: C 150-99

Step-by-step explanation:

Answer:

0.02

Step-by-step explanation:

hope it helped

Answer:

0.0266666667 or 0.02

Step-by-step explanation:

Answer:

4632/8=579

Step-by-step explanation:

MARK ME BRAINLISIST.

Answer: 579

Hope I'm right

The quotient of the expression is 7x² + 8x +  1

From the question, we have the following expression that can be used in solving the quotient

(7x^3-13x^2-23x-5)/(x-3)

Express properly

So, we have

(7x³ - 13x² - 23x - 5)/(x-3)

Set the divisor to 0

x - 3 = 0

So, we have

x = 3

Using a synthetic setup, we have

3 | 7 - 13 - 23 - 5

The synthetic division is then carried out as follows

3 | 7 - 13 - 23 - 5

        21   24    3

    7   8     1    -2

So, we have

Quotient = 7   8   1

Remainder = 2

Introduce the variable

Quotient = 7x² + 8x +  1

Remainder = 2

Hence, the result is 7x² + 8x +  1 remainder 2

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Answer:

  D(3.4, 20.8)

Step-by-step explanation:

Given points B(-2, 10) and C(8,7), you want the coordinates of point D such that BD has a slope of 2 and CD has a slope of -3.

The equation for the slope between two points is ...

  m = (y2 -y1)/(x2 -x1)

Using this formula and the given points, we can find D(x, y) to satisfy ...

  2 = (y -10)/(x +2)

  -3 = (y -7)/(x -8)

Putting each of these equations in general form, we have ...

  2(x +2) -(y -10) = 0

  2x -y +14 = 0

and

  -3(x -8) -(y -7) = 0

  3x +y -31 = 0

Adding the two equations eliminates the y-variable:

  (2x -y +14) +(3x +y -31) = 0

  5x -17 = 0 . . . . . . simplify

  x -3.4 = 0 . . . . . . divide by 5

  x = 3.4 . . . . . . . . . add 3.4

Substituting for x in the first equation gives ...

  2(3.4) -y +14 = 0

  y = 6.8 +14 = 20.8 . . . . add y

The point D has coordinates (3.4, 20.8).

__

Additional comment

The graph shows the equations of the lines written in point-slope form.

Answer: We can start by solving for one variable in one of the equations and then substituting that value into the other equation.

Solve for y in the first equation: y = 1 - 3x

Substitute this value of y into the second equation: 4(1 - 3x) + 4x = -20

Solve for x: -4x = -24

x = 6

Substitute this value of x into the first equation to find the value of y: y = 1 - 3(6) = -17

So the solution is x = 6 and y = -17.

Step-by-step explanation:

The ratio of x:y in simplest form is 5 : 2

From the question, we have the following parameters that can be used in our computation:

3.5y = 1.4x

Divide both sides of the equation by 1.4

So, we have

3.5y/1.4 = x

Divide both sides of the equation by y

So, we have

3.5/1.4 = x/y

Express as ratio

x : y = 3.5 : 1.4

Divide by 0.7

x : y = 5 : 2

Hence, the ratio is 5 : 2

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The shape of the histogram is expected to be symmetric.

A histogram is a graphical representation of the distribution of a dataset. It is an estimate of the probability distribution of a continuous variable. The histogram is plotted with bin ranges on the x-axis and the frequency (count) of data points that fall within each bin on the y-axis.

The shape of the histogram can give you a sense of the underlying distribution of the data, such as whether it is symmetric or skewed.

Standardized test scores, like the SAT, are typically designed to have a normal distribution, meaning that the majority of scores fall in the middle range, with fewer scores at the extremely high or low ends.

Additionally, because the data is being collected from a large and diverse population of students from one state, it is unlikely that there would be a significant skew in one direction or another.

However, some factors such as socioeconomic status, family background, school district, and student ethnicity may affect the distribution.

Therefore, The shape of the histogram is expected to be symmetric.

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The graph of the polynomial function is given by the following option:

Not C or D.

At z = -3, the function has a zero with an even multiplicity of 2, meaning that the graph of the function turns at z = -3, due to the even multiplicity.

At z = 2, the function has a zero with an odd multiplicity of 3, meaning that the graph of the function crosses the x-axis at z = 2, due to the odd multiplicity.

At z= -4, the function is negative, hence it becomes positive at z = 2 and goes towards infinity.

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Answer: 391.92ft²

Step-by-step explanation:

Answer: 391.92

Step-by-step explanation:

All you simply do in multiply the two numbers together.

Answer: $840

If it's 20% off, it's 80% of it's original price.

80% = 0.8

$1,050 x 0.8 = $840

Answer:

6931.73

Step-by-step explanation:

π =3

cone base diameter = 6 so r=3

it's given height is 11

so use formula given V = π/3*3²*11 =99

sphere r =3

so use formula given V = 4/3*π*3³ = 4*81 = 324

total 99+324 =423 cubic INCHES!!!

1" = 2.54 cm

so you'll have to multiply 2.54³ to covert it to

cubic CMS = 6931.73 cubic CMS

Answer:

10 Slices

Step-by-step explanation:

6x5=30

30 slices in total

We are trying to find 2/3 of 30 slices so we multiply them.

(2x30)/3

=60/3

=20

20 slices were sold out of 30 total slices

This means that 10 slices are left

30-20=10

The measure of PQ is approximately 57.8 units.

Now, According to the question:

A proportion is an equality of two ratios. We write proportions to help us establish equivalent ratios and solve for unknown quantities.

Quadrilateral JKLM is similar to quadrilateral NOPQ .

We have the sides are:

JK = 9, LM = 13.7, NO = 38,

and To find the measure of PQ.

Corresponding sides in similar figures are proportional in length:

PQ/LM = NO/JK

PQ/13.7 = 38/9

PQ = 13.7(38/9) = 2603/45 ≈ 57.8

Hence, The measure of PQ is approximately 57.8 units.

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If a red balloon costs $0.80, then 9 red balloons costs would be $7.20.

What is an algebraic manipulation?

Algebraic manipulation is the process of rearranging mathematical expressions in order to solve equations or to make them easier to understand. It involves the use of mathematical operations and properties such as addition, subtraction, multiplication, division, and the commutative, associative, and distributive properties.

To find out how much 9 red balloons cost, you need to multiply the cost of one red balloon by the number of red balloons.

So 9 red balloons cost $0.80 * 9 = $7.20

Hence, If a red balloon costs $0.80, then 9 red balloon costs would be $7.20.

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Answer:

Step-by-step explanation:

7

The correct option is C. ((6, 5), (3,2), (2, 4), (6, 3), (1, 0))

Reason: This relation has two y-values of 6 which violates the vertical line test and therefore is not a function.

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If a bicycle is of worth $500 and decreases in value by 7.8% per year , then the function to model this situation is P(n) = 500(0.922)ⁿ  and the value of bicycle after 5 years is  $333.14    .

The price of  bicycle is = $500 ;

the percent decrease in the value per year is = 7.8% = 0.078   ;

let number of years be = "n" years ;

So , the Price of bicycle after "n" years is written as :

⇒ P(n) = 500(1 - 0.078)ⁿ ;

⇒ P(n) = 500(0.922)ⁿ ;

to find the value of bike after 5 years , we substitute n = 5 ;

⇒ P(5) = 500(0.922)⁵  ;

⇒ P(5) = 500 × 0.66627

⇒ P(5) = 333.138334052816

⇒P(5) ≈  $333.14

Therefore , the value of bike after 5 years is $333.14   .

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The measure of one interior angle in the regular polygon is 180° degrees.

Polygon:

A polygon is a shape that is made of straight line segments that are connected to each other.

The polygons are named according to their properties and the number of sides they have which have a minimum of three sides.

A polygon cannot have curved sides they are all straight line segments and can measure each side equal to one other.

The formula to find the interior angles of a regular polygon is required.

The required formula is     [tex]\frac{(n-2)*180}{n}[/tex]

where n = Number of sides of the polygon.

given to measure one interior angle n=1

Substitute the n value in the above formula, and we get

[tex]A=\frac{(2-1)*180}{1}[/tex]

A=180°

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The volume of the cabinet where Samantha stores all her important documents would be given as = 7.2 ft

A cabinet is defined as an equipment usually located in offices or laboratory which is used for the storage of documents that are of high importance to an organisation.

The shape of the cabinet is the shape of a cube and the volume of a cube is the product of all the sides given

That is = 2⅙ × 1¼ × 2⅔ ( change to single fraction)

= 13/6 × 5/4 × 8/3

= 520/72

= 7.2 ft

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The scale factor of a model is, 30 feet in a inch.

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

We have to given that;

A model of Seattle, Washington space Needle is 20 inches tall The actual Space Needle is approximately 600 feet tall.

Hence, The scale factor of a model is,

⇒ 600 feet / 20 inches

⇒ 30 feet per inches

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Answer:

group has raised $1680 in the first three months.

Step-by-step explanation:

The students group has raised $1680 in the first three months.

Due of this, The Helping Hands Student Club decided to fundraise $4,000 by the end of the academic year.

How much is a percentage?

A percentage is a certain number or part in every hundred. It is a fraction with the denominator 100, and the symbol for it is "%."

It accomplishes 42% of its goal after three months.

The money raised over the initial three months is

42% of 4000

= 42/100 × 4000

= 42×40

= $1680

Thus, the students' group has raised $1680 in the first three months.

The step that can be used to draw an Inscribed Circle of A ABC is to draw the perpendicular bisectors of AB, BC, and AC that pass through point D

Inscribed Circle is a circle that touches each of the three sides of the triangle at exactly one point. Inscribed Circle is the largest circle that can be made in a triangle. The center of the Inscribed Circle is also the center of the triangle, that is, the point where the angle bisectors of the triangle meet.

Steps to draw an Inscribed Circle:

a. construct an angle bisector of each vertex (<ABC, <BAC, <ACB) of the triangle to determine the center of the triangle.

b. draw a line perpendicular to one side of the triangle that passes through its center.

c. draw an Inscribed Circle that passes through the point where the sides of the triangle intersect and the perpendicular from above.

As in the question, it was stated that the center of the Inscribed Circle is point D, so the step that can be used to draw an Inscribed Circle of A ABC is to draw the perpendicular bisectors of AB, BC, and AC that pass through point D

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The equation to represent the coldest temperature recorded at Vostok Station in °F is 4*(−22.3)°F = 89.2°F.

The solution is obtained by using the arithmetic operations.

What are arithmetic operations?

In mathematics, mainly there are four basic operations upon which all the calculations are done. The operations are:

1. Addition(‘+’) wherein the sum of the numbers is obtained.

2. Subtraction(‘-’) wherein the difference of the numbers is obtained.

3. Multiplication(‘×’) wherein the product of the numbers is obtained.

4. Division(‘÷’) wherein the quotient of the numbers is obtained.

We are given that the coldest temperature recorded in a city in Texas was −22.3°F and the coldest temperature recorded at Vostok Station in Antarctica was 4 times as cold.

This means that the coldest temperature recorded at Vostok Station in Antarctica was

4*(−22.3)°F = 89.2°F

Hence, the equation to represent the coldest temperature recorded at Vostok Station in °F is 4*(−22.3)°F = 89.2°F.

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The y-intercept of the line 11x + 10y = 2 is equal to 1/5.

In Mathematics, the slope-intercept form of a line can be calculated by using this linear equation:

y = mx + c

Where:

Based on the information provided about the line, it is represented by this equation;

11x + 10y = 2

By making "y" the subject of formula in the above equation, we have the following:

10y = -11x + 2

By dividing both sides of the equation by 10, we have the following:

y = -11x/10 + 2/10

y = -11x/10 + 1/5.

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The solution is Option B.

The rotation of the line JK around the point P by 180° will be J'K'

The measure of the amount a figure is rotated about the center of rotation is called the angle of rotation. The angle of rotation is usually measured in degrees. We specify the degree measure and direction of a rotation.

90° clockwise rotation: (x,y) becomes (y,-x)

90° counterclockwise rotation: (x,y) becomes (-y,x)

180° clockwise and counterclockwise rotation: (x, y) becomes (-x,-y)

270° clockwise rotation: (x,y) becomes (-y,x)

270° counterclockwise rotation: (x,y) becomes (y,-x)

Given data ,

Let the rotation angle be represented as A

Now , the value of A is 180°

Let the points be represented as J and K

Let the rotated point be represented as J'K'

And , when a point is rotated by and angle 180° , the x and y coordinates of the point will become their additive inverse

For a 180° clockwise and counterclockwise rotation: (x, y) becomes (-x,-y)

And , the figure which represents the coordinates of the point J' and K' is when K' is below and J' is above

Hence , the solution is Option B.

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