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Answer: 3x² - 27y² = (3x²) - (27)(y²) = 3(x² - 9y²) = 3(x - 3y)(x + 3y), and 2014² - 2013² = (2014 + 2013)(2014 - 2013) = (3127)(1) = 3127

Im not 100% sure of this answer cause I'm not that good at stuff like this but I still think this is right fr fr

The volume of water that the pool can hold is  150.72 cubic centimeters.

Remember that the volume of a cylinder of radius R and height H is:

V = pi*R²*H

Where pi = 3.14

For the pool we know that the height is H = 3ft, and the diameter is 8ft, then the radius is R = 8ft/2 = 4ft

Replacing that in the volume formula we will get:

V = 3.14*(4cm)²*3cm

V = 150.72 cubic centimeters.

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A simplification of the given expression is 1/m¹⁶.

In Mathematics, an exponent is a mathematical operation that is commonly used in conjunction with an algebraic equation or expression, in order to raise a given quantity to the power of another.

Mathematically, an exponent can be represented or modeled by this mathematical expression;

bⁿ

Where:

By applying the division and multiplication law of exponents for powers of the same base to the given algebraic expression, we would have the following simplified expression:

[tex](m^{\frac{4}{5}} \cdot m^{\frac{4}{5}} )^{-10}\\\\(m^{\frac{4}{5} +\frac{4}{5} } } )^{-10}\\\\(m^{\frac{8}{5} } )^{-10}\\\\(m^{\frac{8 \times -10}{5} } )\\\\(m^{\frac{-80}{5} } )\\\\m^{-16}[/tex]

1/m¹⁶

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Answer:

50) Midpoint: (5.5, 0)

51) Midpoint:  (6, -8)

Step-by-step explanation:

We can find the midpoint between two points using the midpoint formula, which is m = (x1 + x2) / 2, (y1 + y2) / 2, where

50) We can allow (10, 10) to be our (x1, y1) point and (1, -10) to be our (x2, y2) point:

x-coordinate of midpoint of (10, 10) and (1, -10):

(10 + 1) / 2

11 / 2

5.5

y-coordinate of midpoint of (10, 10) and (1, -10):

(10 + (-10)) / 2

(10 - 10) / 2

0 / 2

0

Thus, the midpoint of the line segment with the endpoints (10, 10) and (-1, 10) is (5.5, 0).

51) We can allow (3, -6) to be our (x1, y1) point and (9, -10) to be our (x2, y2) point:

x-coordinate of midpoint of (3, -6) and (9, -10):

(3 + 9) / 2

12 / 2

6

y-coordinate of midpoint of (3, -6) and (9, -10):

(-6 + -10) / 2

(-16) / 2

-8

Thus, the midpoint of the line segment with the endpoints (3, -6) and (9, -10) is (6, -8).

The equation of the parabola in vertex form is y = (x - 0)² + 8, which simplifies to y = x² + 8.

We have,

The vertex form of a parabola is given by the equation y = a(x - h)² + k, where (h, k) represents the vertex of the parabola.

Now,

Given that the parabola passes through (-2, 4) and has a vertex (0, 8), we can substitute these values into the equation to find the value of 'a'.

Using the vertex (0, 8):

8 = a(0 - 0)² + 8

8 = a(0) + 8

8 = 8

Since the coefficient of the squared term is 'a', which remains unchanged, we can conclude that a = 1.

Therefore,

The equation of the parabola in vertex form is y = (x - 0)² + 8, which simplifies to y = x² + 8.

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The z- score of a person who scored 280 on the exam can be found to be - 0. 5.

A z-score indicates how many standard deviations an element is from the mean.

The formula is:

Z = ( X - μ ) / σ

The details here are:

X = 280, μ = 300, and σ = 40

The z - score is therefore :

Z = (280 - 300) / 40

= -20 / 40

= -0.5

In conclusion, the z - score of a person who scored 280 on the exam is -0.5. This means that their score is half a standard deviation below the mean.

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The constant term of the polynomial 2x³-5x²+8x+3 is 3.

A polynomial is a mathematical expression consisting of variables (also called indeterminates) and coefficients, which are combined using addition, subtraction, and multiplication, but not division by a variable.

The variables in a polynomial are typically denoted by x, y, or z, and the coefficients can be constants or other polynomials.

The constant term of a polynomial is the term that doesn't have any variable attached to it. In this case, the constant term is the one that only has a number, which is 3.

Therefore, the constant term of the polynomial 2x³-5x²+8x+3 is 3.

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The ratios for the rectangles and the ovals is 4 : 3

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

Rectangle = 4

Oval = 3

The ratio can be represented as

Ratio = Rectangle : Oval

When the given values are substituted in the above equation, we have the following equation

Rectangle : Oval = 4 : 3

The above ratio cannot be further simplified

This means that the ratio expression would remain as 4 : 3

Hence, the solution is 4 : 3

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The proof of ΔRUV ≅ ΔSUT is shown below.

Given that:

RSTV is a rectangle and U is the midpoint of VT.

Here, We have to Prove:

⇒ ΔRUV ≅ ΔSUT

Now, We can prove as;

Statement                               Reason

1) RSTV is a rectangle               Given

2) Angle V and T are                Because every angle in a rectangle is 90

right triangle.

3) ∠V ≅ ∠T                               Because both are right angle.

4) U is the midpoint of VT.        Given

5) VU = UT                                By midpoint theorem.

6) VR ≅ TS                                Opposite sides of rectangle.

7) ΔRUV ≅ ΔSUT                       By SAS congruency theorem.

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Answer:

512

Step-by-step explanation:

To determine how many 1" x 1" x 1" cubes can fit into an 8" x 8" x 8" box, we need to calculate the volume of the box and then divide it by the volume of a single cube.

The volume of the box is calculated by multiplying its length, width, and height:

Volume of the box = 8" x 8" x 8" = 512 cubic inches.

The volume of a single cube is 1" x 1" x 1" = 1 cubic inch.

To find out how many cubes can fit, we divide the volume of the box by the volume of a single cube:

Number of cubes = Volume of the box / Volume of a single cube

Number of cubes = 512 cubic inches / 1 cubic inch

Number of cubes = 512

Therefore, 512 cubes that are 1" x 1" x 1" can fit into an 8" x 8" x 8" box.

If rectangle has an area of 114cm squared and a perimeter of 50 cm, the dimensions of the rectangle are approximately 5 cm by 22.8 cm.

Let's assume the length of the rectangle is "l" and the width is "w". We can start by using the formula for the area of a rectangle, which is A = lw. From the given information, we know that the area is 114cm².

So, we have:

lw = 114

Next, we can use the formula for the perimeter of a rectangle, which is P = 2l + 2w. From the given information, we know that the perimeter is 50cm.

So, we have:

2l + 2w = 50

We now have two equations with two variables, which we can solve using substitution or elimination. Let's use substitution by solving the first equation for l:

l = 114/w

We can then substitute this expression for l in the second equation:

2(114/w) + 2w = 50

Multiplying both sides by w to eliminate the fraction, we get:

228 + 2w² = 50w

Rearranging and simplifying, we get a quadratic equation:

2w² - 50w + 228 = 0

We can solve for w using the quadratic formula:

w = [50 ± √(50² - 4(2)(228))]/(2(2)) ≈ 11.4 or 5

Since the length and width must be positive, we can discard the solution w = 11.4. Therefore, the width of the rectangle is approximately 5 cm. We can then use the equation lw = 114 to solve for the length:

l(5) = 114

l ≈ 22.8

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The coordinates of the vertices after a dilation of the scale factor would be:

To perform a dilation with a scale factor of 1/2 centered at the origin, we multiply the coordinates of each vertex by the scale factor.

Given the vertices:

W = (5, 10)

V = (0, -10)

U = (5, -10)

After applying the dilation with a scale factor of 1/2, the new coordinates of the vertices would be:

W' = (5 * 1/2, 10 x 1/2) = (2.5, 5)

V' = (0 * 1/2, -10 x 1/2) = (0, -5)

U' = (5 * 1/2, -10 x 1/2) = (2.5, -5)

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The greatest common factor of two terms given as 21x⁴ and 49x³ is equal to  7x³.

To find the greatest common factor (GCF) of two terms, we need to find the highest factor that is common to both terms. In this case, we have 21x⁴ and 49x³.

To find the factors, we can break each term down into its prime factors:

21x⁴ = 3 * 7 * x * x * x * x

49x³ = 7 * 7 * x * x * x

The common factors are 7 and x³. To find the GCF, we multiply these common factors together:

GCF = 7  * x³

GCF = 7x³

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The equation y = 3x - 2. can be placed in table as shown below. For example, when x = -2, y = 3(-2) - 2 = -8. Similarly, when x = -1, y = 3(-1) - 2 = -5, and so on.

In this table, each row represents a pair of values (x, y) that satisfy the equation y = 3x - 2. For example, when x is -2, y is calculated as 3(-2) - 2 = -8. Similarly, for the other values of x, the corresponding values of y are calculated accordingly.

Here's a table showing the values of x and the corresponding values of y for the equation y = 3x - 2:

x y

-2 -8

-1 -5

0 -2

1 1

To fill in the table, substitute each value of x into the equation and calculate the corresponding value of y. For example, when x = -2, y = 3(-2) - 2 = -8. Similarly, when x = -1, y = 3(-1) - 2 = -5, and so on.

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The set of 3 lengths that make a right triangle is {8, 15, 17}

Remember that for any right triangle, the sum of the squares of the two shorter sides must be equal to the square of the longer side.

So if the 3 sides are A, B, and C, such that:

A < B < C

We will have:

A² + B² = C²

Now you only need to try sets of 3 values in that equation, if we use: 8, 15, and 17 we will have:

8² + 15² = 17²

289 = 289

That equationis true, thus, these 3 lengths make a right triangle.

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Answer:

d = [tex]\sqrt{58}[/tex]

Step-by-step explanation:

calculate the distance d using the distance formula

d = [tex]\sqrt{x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]

with (x₁, y₁ ) = (2, 5 ) and (x₂, y₂ ) = (- 5, 8 )

d = [tex]\sqrt{(-5-2)^2+(8-5)^2}[/tex]

   = [tex]\sqrt{(-7)^2+3^2}[/tex]

   = [tex]\sqrt{49+9}[/tex]

   = [tex]\sqrt{58}[/tex]

The total distance she cover after running is 9600 meters

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

Number of times = 12 times

Dimensions of the playground = 240 m by 160 m

The perimeter of the playground is calculated as

Perimeter = 2 * sum of dimensions

substitute the known values in the above equation, so, we have the following representation

Perimeter = 2 * (240 + 160)

The total distance she cover is calculated as

total distance = 12 * 2 * (240 + 160)

Evaluate

total distance = 9600 meters

Hence, the total distance she cover is 9600 meters

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By ASA congruency triangle KBH is congruent to triangle NWH.

Given that, KBWN is a parallelogram with diagonals KW and BN intersecting at point H.

From the given figure,

Consider ΔKBH and ΔNWH,

∠KHB=∠NHW (Vertically opposite angles)

∠HKB=∠HWN (Interior alternate angles parallelogram)

KH=HW (Diagonals bisect each other)

By ASA congruency ΔKBH ≅ ΔNWH

Therefore, by ASA congruency triangle KBH is congruent to triangle NWH.

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If f(x) = 1/343, then x = -3. The point on the graph of f when f(x) = 1/343 is (-3, 1/343).

A point is the basic relationship displayed on a graph. Each point is defined by a pair of numbers containing two coordinates. A coordinate is one of a set of numbers used to identify the location of a point on a graph. Each point is identified by both an x and a y coordinate.

If f(x) = 1/343, then x = -3. This is because 343 = 7³, therefore the inverses is 1/343. The point on the graph of f when f(x) = 1/343 is (-3, 1/343

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The ridgeline will be 18.67 feet above the house.

Generally, a height refers to the measurement of someone or something from head to foot or from base to top.

To find the height of the ridgeline, we will use the formula: Height = (Pitch / 12) * Span

Given data:

Pitch = 7

Span = 32 feet

Inputting the values, we have:

Height = (7 / 12) * 32

Height = 0.5833 * 32

Height = 18.6656

Height = 18.67 feet.

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The difference between the record high and low temperatures is 149 degrees.

A negative number is a number that is less than zero. A negative number usually has a minus sign in front of it. An example of a negative number is -35. A positive number is a number that is greater than zero. An example of a positive number is 10.

In order to find the difference between two or more numbers, subtract the numbers from each other.

Difference between the temperature = record high temperature - record low temperature

114 - -35

114 + 35 = 149 degrees

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The probability that it is raining if the flight has been delayed is 0.07, or 7%.

We can use the following formula to calculate the probability that it is raining if the flight has been delayed:

P(Rain|Delayed) = P(Rain and Delayed) / P(Delayed)

We are given that P(Rain) = 0.07 and P(Delayed) = 0.18. We can also use the fact that P(Rain and Delayed) = P(Rain) * P(Delayed):

= 0.07 * 0.18

= 0.0126.

Substituting these values into the formula, we get:

P(Rain|Delayed) = 0.0126 / 0.18 = 0.07

Therefore, the probability that it is raining if the flight has been delayed is 0.07, or 7%.

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Answer:

----------------------

Use the compound interest formula:

Where:

Plugging in the values, we get:

The  quotient of 302 ÷ (9.1 x [tex]10^4)[/tex] in scientific notation is approximately 3.31868131868 x [tex]10^1[/tex]

Dividing 302 by 9.1 gives:

302 ÷ 9.1 ≈ 33.1868131868

Now, to express this result in scientific notation, we need to move the decimal point to the appropriate position to create a number between 1 and 10. In this case, we move the decimal point two places to the left:

33.1868131868 ≈ 3.31868131868 x[tex]10^1[/tex]

Therefore, the quotient of 302 ÷ (9.1 x [tex]10^4[/tex]) in scientific notation is approximately 3.31868131868 x[tex]10^1[/tex]

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The points (1,0) (8,0). and. (3,0) are not the solution of system of inqualities

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

The graph

Also, we have the following ordered pairs

(1,0) (8,0). (0,4). (3,0)

From the graph, we have the following ordered pairs in the shaded region

(0, 4)

Other points (1,0) (8,0). and. (3,0) are not in the shaded region

This means that (1,0) (8,0). and. (3,0) are not the solution of system of inqualities

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Answer:

Domain:  {-24, -12, -8, 9, 14, 50}

Range:  {23, 69, 83, 92, 97, 32}

Step-by-step explanation:

For a function like f(x), each coordinate is in the form (x, f(x)) aka (x, y)

Since our x-coordinates are -24, -12, -8, 9, 14, and 50, the domain of f(x) is {-24, -12, -8, 9, 14, 50}

Since our f(x) or y-coordinates are 23, 69, 83, 92, 97, and 32, the range is {23, 69, 83, 92, 97, 32}

Answer: E. 25%

Step-by-step explanation: There are 12 circles in total. 3 out of those twelve are shaded in, making it in fraction form 3/12. dividing both the numerator in the denominator by 3 simplifies it into 1/4. which is subsequently, 25%