When solving with radical exponents, what has to be true in order for you to solve them?

1. Parallelogram: Opposite sides are congruent, Opposite angles are congruent, Consecutive angles are supplementary, Diagonals bisect each other, Diagonals are congruent, Diagonals are perpendicular.

Congruence is a term used in mathematics to describe the relationship between two geometric figures or objects. When two geometric figures are said to be congruent, it means that the two figures have the same size and shape.

2. Rectangle: Two pairs of consecutive congruent sides, but opposite sides are not congruent, Diagonals are perpendicular, Exactly one pair of congruent angles, Diagonals bisect one pair of angles.

3. Rhombus: Opposite sides are congruent, Opposite angles are congruent, Consecutive angles are supplementary, Diagonals bisect each other, Diagonals are congruent, Diagonals are perpendicular.

4. Kite: Opposite sides are congruent, Opposite angles are congruent, Consecutive angles are supplementary, Diagonals bisect each other, Diagonals are perpendicular, Diagonals bisect angles.

5. Square: Opposite sides of a are congruent, Opposite angles of are congruent, Consecutive angles are supplementary, The diagonals of bisect each other, All four sides are congruent.

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Answer:

9

Step-by-step explanation:

5'4 to 6'0 is 8

6'0 to 6'1 is 9

i think im right i dont use inches tho

The height difference between 5’4 and 6’1 is 9 inches.

Measurement is the method of comparing the properties of a quantity or object using a standard quantity.

Measurement is essential to determine the quantity of any object.

There are two heights given.

5’4 and 6’1.

5'4 means that 5 feet and 4 inches.

1 feet = 12 inches

5 feet = 60 inches

5'4 = 60 inches + 4 inches = 64 inches

Similarly,

6'1 = 6 feet + 1 inch

    = (6 × 12) inches + 1 inch

    = 73 inches

Height difference = 73 inches - 64 inches = 9 inches

Hence the height difference is 9 inches.

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Using angle theorems the value of x = 67.5°

Angle theorems are rules that govern the properties of angles.

Given that we have the figure and we desire to find angle x, we proceed as folllows.

Now, we notice that one angle is a right angle and it is equal to 90°.

Also, we notice that all the angles meet at the same point.

So, we have that

x + 3x + 90° = 360° (sum of angles at a point)

Solving for x, we have that

x + 3x + 90° = 360°

4x + 90° = 360°

4x = 360° - 90°

4x = 270°

x = 270°/4

x = 67.5°

So, the value of x = 67.5°

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In given graph, Points that meet the condition X>-2 are A, B, C, and D. and Points that are below the line y=1 are points A, B, C, and E.  and also None of the other students correctly plotted the point 4 units away from A.

What is graph?

A set of vertices or nodes connected by edges or arcs is known as a graph. Graphs are used to represent various mathematical concepts, relationships, and structures, such as networks, functions, sets, and data. Graphs can be visualized and analyzed to draw conclusions and make predictions about the underlying phenomena they represent.

For question 17:

a. Points that meet the condition X>-2 are A, B, C, and D.

b. Points that are below the line y=1 are points A, B, C, and E.

c. The point located three units to the right of the origin and two units above the x-axis is point F.

For question 18:

a. The labeled points are:

A: (3,0)

B: (4,3)

C: (-4,-2)

D: (1/12, 1/12)

E: (-3/2, 2/12)

F: (-4,-2)

b. The student who correctly plotted the point 4 units away from point A is Cassandra, who plotted the point (7,0). None of the other students correctly plotted the point 4 units away from A.

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By 12.57 feet the circumference of outer circle greater than the circumference of the inner​ circle

The circle's boundary is the length of the circle's circumference, sometimes referred to as its perimeter. whereas the size of a circle determines the space it occupies.

The formula for calculating a circle's circumference is written as

Circumference = πD

where D stands for the circle's diameter.

The inner circle is 44 feet in diameter. It means that

22/7 × D = 44

22D = 7 × 44 = 308

D = 308/22

D = 14 ft

The inner circle and the outer circle are separated by 2 feet. This implies that the outer circle's diameter would be

14 + 2 + 2 = 18 ft

Circumference of the outer circle is

22/7 × 18 = 56.57 ft

The distance in feet that the circumference of the outer circle exceeds that of the inner circle is

56.57 - 44 = 12.57 feet

Hence, By 12.57 feet the circumference of outer circle greater than the circumference of the inner​ circle

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Answer: B. h=192÷ (6⋅4)

Step-by-step explanation:

B. h=192÷ (6⋅4)

This equation can be used to find the height of the prism because the volume of a rectangular prism can be represented by the equation V = l*w*h, where l and w are the length and width, respectively, and h is the height. In this case, given that V=192, the equation h=192÷ (l*w) can be used to find the height, where l=6 and w=4.

The population after 4 years will be 12,155.06. It will take approximately 22.52 years for the population to triple.

The population of a town grows proportionally to its current population. This means that the larger the population, the more it will grow. To determine the population after 4 years, we can use the formula:

P = P0 * (1 + r)^t

Where P is the final population, P0 is the initial population, r is the growth rate, and t is the time in years. Plugging in the values given in the question, we get:

P = 10,000 * (1 + 0.05)^4

P = 10,000 * 1.21550625

P = 12,155.06

Therefore, the population after 4 years will be 12,155.06.

To determine how long it will take the population to triple, we can use the same formula, but set P to 3 * P0 and solve for t:

3 * 10,000 = 10,000 * (1 + 0.05)^t

3 = (1 + 0.05)^t

ln(3) = t * ln(1.05)

t = ln(3) / ln(1.05)

t = 22.52

Therefore, it will take approximately 22.52 years for the population to triple.

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For the function f(x)=(x-2)^(2)-4, the transformation(s) done to the parent function are a horizontal shift to the right by 2 units and a vertical shift downward by 4 units.

The parent function of the function f(x)=(x-2)^(2)-4 is the quadratic function f(x)=x^(2).

The transformation(s) done to the parent function are a horizontal shift to the right by 2 units and a vertical shift downward by 4 units.

This can be seen by comparing the given function to the parent function. The (x-2) in the given function indicates the horizontal shift to the right, and the -4 at the end of the function indicates the vertical shift downward.

Therefore, the transformation(s) done to the parent function are a horizontal shift to the right by 2 units and a vertical shift downward by 4 units.

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Answer:

Step-by-step explanation:

The altitude of an equilateral triangle is basically the height of the triangle. We can find this using trigonometry, even though I'm sure there's a beautiful little formula that can find this.

If you cut an equilateral triangle in half, you get two special 30-60-90 triangles. The base of each triangle is 3.5 cm in length, and the height (not the hypotenuse!) is equal to:

[tex]base*\sqrt{3}[/tex]

So basically we have 3.5(sqrt(3)), or our altitude! Wow, how easy!

[tex]3.5(\sqrt{3})=6.06[/tex]

Hope this helps!

Answer: It is not possible to use only translations and dilations to map one circle to another unless the two circles are identical in size and shape.

A translation is a transformation that moves an object without changing its size, shape, or orientation. It involves moving every point on the object the same distance in the same direction. Since a circle is defined by all the points that are equidistant from its center, a translation will simply move the entire circle in the same direction, but will not change its size or shape.

A dilation is a transformation that changes the size of an object, but not its shape or orientation. It involves multiplying the distance of every point on the object from a fixed center point by a scale factor. While a dilation can change the size of a circle, it will also change the distance between points on the circle, and thus change its shape.

Therefore, if the two circles are not identical in size and shape, it would be necessary to use other transformations, such as rotations or reflections, to map one circle to the other.

Step-by-step explanation:

The length of the missing side is 15.

What is a theorem?

A statement that can be proven true using well-known mathematical procedures and arguments is known as a theorem. A theorem, in general, is an application of a general principle that joins it to a larger theory. Proof is a procedure used to demonstrate a theorem's correctness.

A right triangle's three sides are related in Euclidean geometry by the Pythagorean theorem, also known as Pythagoras' theorem. According to this statement, the areas of the squares on the other two sides add up to the area of the square whose side is the hypotenuse.

The hypotenuse is 17. The length of one leg is 8.

The length other leg is

√(17² - 8²)

= √(289 - 64)

= √(225)

= 15

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F(prime) = 30

Given the information in the question, we can calculate \(F^{\prime}(2)\) using the chain rule. The chain rule states that \(F^{\prime}(x) = f^{\prime}(g(x))\cdot g^{\prime}(x)\). Thus, \(F^{\prime}(2) = f^{\prime}(-5)\cdot g^{\prime}(2)\). Plugging in the given values, we get \(F^{\prime}(2) = 6 \cdot 5 = 30\). Therefore, \(F^{\prime}(2) = 30\).

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The number of people we would expect to be found within an area of 1400 m by 1.3 km is approximately 25.

The mass of the cube for the object that has the side lengths of 56 cm is 0.043904 g.

1. To find the number of people in an area of 1400 m by 1.3 km, we need to first convert the measurements to the same unit. Since the population density is given in people/km2, we will convert the measurements to kilometers.
1400 m = 1.4 km
Now we can multiply the two measurements to find the area:
1.4 km x 1.3 km = 1.82 km2
Next, we can use the population density to find the number of people in this area:
14 people/km2 x 1.82 km2 = 25.48 people
Therefore, we would expect to find approximately 25 people in an area of 1400 m by 1.3 km.

2. To find the mass of the cube, we first need to find the volume. Since the side lengths are given in centimeters, we will convert them to meters:
56 cm = 0.56 m
Now we can find the volume of the cube by multiplying the side lengths:
0.56 m x 0.56 m x 0.56 m = 0.175616 m3
Next, we can use the density to find the mass of the cube:
0.25 g/m3 x 0.175616 m3 = 0.043904 g
Therefore, the mass of the cube is 0.043904 g.

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The area of a trapezoidal region is 1/2h(a+b), where a and b are the lengths of the two parallel sides, and h is the height.

The area of a trapezoidal region is given by the formula A = 1/2h(a+b), where a and b are the lengths of the two parallel sides, and h is the height. This formula can be derived by dividing the trapezoid into two right triangles and a rectangle, and finding the area of each of these shapes.

First, let's consider the two right triangles. The height of each of these triangles is h, and the lengths of their bases are (a-b)/2 and (b-a)/2, respectively. The area of each of these triangles is therefore 1/2h(a-b)/2 = 1/4h(a-b).

Next, let's consider the rectangle. The length of this rectangle is b, and the height is h. The area of this rectangle is therefore bh.

The area of the trapezoidal region is the sum of the areas of the two right triangles and the rectangle. This gives us:

A = 1/4h(a-b) + 1/4h(b-a) + bh

Simplifying this equation gives us:

A = 1/2h(a+b)

Therefore, the area of a trapezoidal region is 1/2h(a+b), where a and b are the lengths of the two parallel sides, and h is the height.

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The value of g(f(x)) is  3x^(2)+23x+44.

To find g(f(x)), we need to substitute the expression for f(x) into the expression for g(x). This means that wherever we see an "x" in the expression for g(x), we will replace it with the expression for f(x).

g(f(x)) = 3(f(x))^(2)-7(f(x))+4

Now we can substitute the expression for f(x) into the equation:

g(f(x)) = 3(x+5)^(2)-7(x+5)+4

Next, we need to simplify the expression by expanding the squared term and distributing the -7:

g(f(x)) = 3(x^(2)+10x+25)-7x-35+4

g(f(x)) = 3x^(2)+30x+75-7x-35+4

Finally, we can combine like terms to get the polynomial in standard form:

g(f(x)) = 3x^(2)+23x+44

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The given statement [tex]x = \frac76[/tex] can be proved by using the given equation.

Algebra, a discipline of mathematics where abstract symbols rather than concrete numbers are subjected to arithmetic operations and formal transformations. The idea that there is such a separate branch of mathematics, as well as the term algebra to identify it, came about gradually through time. tries to find solutions to equations that contain one or more unknown quantities. Although early mathematicians would not have been familiar with such a concept, the word "equation" is frequently employed to conveniently represent these operations when discussing the early history of algebra.

As per the given data:

[tex]\frac{2x+6}{5} = 4x -3[/tex]

Simplifying to evaluate the expression:

[tex]\frac{2x+6}{5} = 4x -3[/tex]

[tex]= 2x+6 = 5(4x -3)\\= 2x + 6 = 20x - 15\\= 18x = 21\\= x = \frac{21}{18}\\\\= x = \frac76[/tex]

Hence, the given statement [tex]x = \frac76[/tex] can be proved by using the given equation.

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Answer:

- 10

Step-by-step explanation:

If y =12 when x is 18

Find x when y =-16

What the relationship between x and y

y = x - 6 and x = y +6

Insert y(-16) into equation above

Y = X - 6

-16= X - 6

Collect like terms

Add 6 to both sides

-10 = X

The given statement in the problem (f/g)(-2) = -6/5 is true.

A linear equation is an equation that has the variable of the highest power of 1. The standard form of a linear equation is of the form Ax + B = 0.

We are given that;

f(x) = 3x²

g(x) x - 8 ; (f/g)(-2) = -6/5

Now,

To evaluate (f/g)(-2), we need to divide f(-2) by g(-2).

We have f(x) = 3x², so f(-2) = 3(-2)² = 12.

We also have g(x) = x - 8, so g(-2) = (-2) - 8 = -10.

(f/g)(-2) = f(-2) / g(-2) = 12 / (-10) = -6/5.

So the statement (f/g)(-2) = -6/5

Therefore, the answer according to the given equation will be true.

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The inverse of the function f(x) = x² + 3 is, f⁻¹(x) = ± √(3 - x) and it is not a function.

First to be an inverse function that function needs to one to one function, meaning every different preimage must correspond to a different image.

We can obtain the inverse of a function by switching the variables x and y with their respective positions and solving for y in terms of x.

Given, A function f(x) = x² + 3.

Let, y = x² + 3.

x² = 3 - y.

x = ± √(3 - y).

f⁻¹(x) = ± √(3 - x).

The inverse of the function is not a function as two distinct outputs have the same intput.

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In order to validate these outliers and their possible influence on any following analysis or modelling, additional research and analysis of the data set may be required.

Data points that differ from the distribution's norm are considered outliers. a figure that falls "outside" of the normal range for the record (either significantly lower or substantially greater). For instance, when the scores are 25, 29, 3, 32, 85, 33, 27, 28, etc., both 3 and 85 are "outliers". Step aside. To spot outliers, look for numbers that are noticeably greater or lower than all other values. Value 4 is an outlier since it is much smaller than all other values. An outlier is a finding in a population sample selected at random that deviates unusually from other values.

There seem to be two possible outliers in the data, according to the scatter diagram you gave.

The data point located at about is the first outlier (60, 30).

The second anomaly is a data point that is situated at around (20, 120). At the upper right corner of the plot, this data point appears to be substantially higher than the other data points.

It's important to keep in mind that identifying outliers from a single scatter plot can be difficult and highly influenced by the surrounding data. In order to validate these outliers and their possible influence on any following analysis or modelling, additional research and analysis of the data set may be required.

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The polynomial with the given information can be represented as: P(x) = a(x-3)3(x-2)2(x-4). Where a is the leading coefficient. Since the leading coefficient is negative, we can assume that a = -1. Therefore, the polynomial can be written as: P(x) = -(x-3)3(x-2)2(x-4)

This polynomial satisfies all the given conditions:

- The leading coefficient is -1, which is negative.

- The zero of 3 has a multiplicity of 3, as indicated by the exponent of (x-3)3.

- The zero of 2 has a multiplicity of 2, as indicated by the exponent of (x-2)2.

- The zero of 4 has a multiplicity of 1, as indicated by the exponent of (x-4).

Therefore, the polynomial P(x) = -(x-3)3(x-2)2(x-4) is the correct answer.

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Step-by-step explanation:

5% Tip = $4.80

1% = $4.80/ 5

Cost of procedure = $4.80/5 x 100% (Equation)

b = $4.80 x 20.0 or 20($4.80)

b =$96

Answer:

1.7 × .5 = .85

15% smaller than the original

Answer: $12.45.

Without a calculator, we can first round a dinner bill of $83.44 to the closest whole figure and estimate a 15% tip. In this instance, $83.44 can be rounded up to $83.

Then, we can calculate 15% of $83 by using a quick technique. In order to do this, we must first calculate 10% of $83, or $8.30. After that, we can calculate 5% of $83 by subtracting 50% of 10%, or $4.15.

Finally, we can add 10% and 5% together to get an estimate of 15% of $83:

$8.30 (10%) + $4.15 (5%) = $12.45

So, a 15% tip on a dinner bill of $83.44 would be approximately $12.45.

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The value of x is 20 and the given two angles are adjacent .

What are parallel lines ?

Parallel lines are lines that are always the same distance apart and never intersect. They have the same slope but different y-intercepts. In other words, they have the same rate of change but different starting points. Parallel lines can be described by linear equations of the form y = mx + b, where m is the slope and b is the y-intercept.

From the given figure

we can say that,

the two angles 7x and x+20 are adjacent

and sum of two angles is 180 degrees.

SO,

7x+x+20 = 180

8x + 20 = 180

8x = 160

x = 160 / 8

x = 20

Therefore, The value of x is 20 and the given two angles are adjacent .

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In order to answer these questions, we need to have data on Mr. Reede's laptimes. Without this information, it is impossible to accurately calculate the proportions and laptime necessary for Mr. Reede to be in the fastest 3% of all his laps. Please provide the data so that we can accurately answer the questions.

Once we have the data, we can use the following steps to answer the questions:

1. To find the proportion of laptimes between 1.75 and 1.85 minutes, we can count the number of laptimes in this range and divide it by the total number of laptimes.
2. To find the proportion of laptimes that took more than 2 minutes, we can count the number of laptimes that took more than 2 minutes and divide it by the total number of laptimes.
3. To find the laptime necessary for Mr. Reede to be in the fastest 3% of all his laps, we can first calculate the 97th percentile of the data (since the fastest 3% of laptimes would be in the top 3% of the data). Then, we can find the laptime that corresponds to this percentile.
4. To redo the problems using the Applet, we can input the data into the Applet and use the built-in functions to calculate the proportions and percentile.

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The area of the village green is 3552 square meters.

What is area ?

Area is a measure of the size or extent of a two-dimensional surface. It is the amount of space inside a closed figure or shape, and is typically measured in square units such as square meters (m²), square centimeters (cm²), square feet (ft²), square inches (in²), and so on.

To calculate the area of the village green, we can use Heron's formula which is given as:

[tex]Area of triangle = \sqrt{(s(s-a)(s-b)(s-c))}[/tex]

where s is the semi - perimeter (half the perimeter) of the triangle, and a, b, and c are the lengths of its sides.

The semi - perimeter of the triangle can be calculated as:

s = (AB + BC + AC)/2

s = (92 + 75 + 105)/2

s = 136

Using this value of s, we can calculate the area of the triangle as:

Area of triangle = [tex]\sqrt{(136(136-92)(136-75)(136-105))}[/tex]

Area of triangle = [tex]\sqrt{(136(44)(61)(31))}[/tex]

Area of triangle = [tex]\sqrt{(12655264)}[/tex]

Area of triangle = 3552

Therefore, the area of the village green is 3552 square meters.

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Answer:

1) To calculate how much it would cost Abi to buy 24 sodas at the vending machines at work, we can multiply the cost of one can ($0.75) by 24 (24 sodas):

Cost at vending machine = $0.75 x 24 = $18

2) To calculate how much Abi can save each day by buying the 24 pack of soda and taking one with her to work, we can subtract the cost of one can at the vending machine ($0.75) from the cost of the 24 pack at Foodtown ($3.25):

Savings each day = $3.25 - $0.75 = $2.50

The number of games in which the player scored more than 25 points is: A. 25%.

In Mathematics, a boxplot is sometimes referred to as box-and-whisker plot and it can be defined as a type of chart that can be used to graphically or visually represent the five-number summary of a data set with respect to locality, skewness, and spread.

Based on the information provided about the given box-and-whisker plot (see attachment), the five-number summary for the given data set include the following:

By critically observing the box-and-whisker plots or boxplot (see attachment), we can logically deduce that in 25% of games the player score more than 25 points.

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