Determine if the two triangles in the following diagram are congruent. If so, select the correct way they can be proven congruent.

SSS - Side, Side, Side

SAS - Side, Angles, Side

ASA - Angle, Side, Angle

AAS - Angle, Angle, Side

HL - Hypotenuse, Leg

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Therefore, x = 0, x = 4, and x = -5/3 are the answers to the equation 3x(x-4)(3x+5) = 0.

An equation in mathematics is a claim that two expressions are equivalent. An equals sign (=) separates the left and right sides of an equation, which usually has two sides. Variables, constants, and mathematical operations like addition, subtraction, multiplication, division, exponents, and roots may be used in the formulas on either side of the equals sign. Finding the number of the variable or variables that make an equation true is the goal of an equation.

given

The zero product property, which asserts that at least one of the factors must be zero if the product of two or more factors equals zero, can be used to solve the equation 3x(x-4)(3x+5) = 0.

We then solve for x by setting each component equal to zero:

3x = 0, 3x + 4, or 3x + 5 = 0.

When we factor x into each solution, we obtain:

3x = 0 --> x = 0

x-4 = 0 —> x = 4

Therefore, x = 0, x = 4, and x = -5/3 are the answers to the equation 3x(x-4)(3x+5) = 0.

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Answer:

The one selected is correct

Step-by-step explanation:

The constant of proportionality of the graph is k = 3/2.

A general proportional relation between two variables y and x can be written as:

y = k*x

Were k is the constant of proportionality.

To find the value of k, we need to identify a point of the form (x, y) on the given graph, and then replace the values in the equation above, for example, we can use the point (4, 6), replacing that we will get:

6 = k*4

6/4 = k

3/2 = k

That is the constant of proportionality.

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Therefore , the solution of the given problem of mean comes out to be one team's data values are closer to the median mean than that of the other.

The result from a set, also known as the arithmetic mean, is the sum of all values split by all of the values. It is frequently referred to as "mean" and is thought to be among the most commonly employed primary trend average. To obtain this answer, multiply the total number of numbers in the collection by the total number of values present.

Here,

The closer the data values are to the mean, the less variable they are, and the smaller the MAD.

A higher MAD shows that the data values are more variable and dispersed from the mean.

In this instance, the Bears' MAD of the amount of victories is 1, while the Saints' MAD is unspecified.

We cannot compare the distinctions of the two teams based solely on MAD since the Saints' MAD is not stated.

Since we cannot tell which team has a larger or smaller MAD, we cannot draw the conclusion that one team's data values are closer to the median mean than that of the other.

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The probability that Mike becomes the champion given that he has won the first game is 7/12.

To find the probability that Alain wins the championship given that Mike won the first game, we can repeat the same reasoning as before, but with Alain as the starting player.

P(Mike wins championship | Mike won first game) = 1 - P(Alain wins championship | Mike won first game)

This leads to:

P(Alain wins championship | Alain won first game) = 5/8

Therefore, we can conclude that:

P(Mike wins championship | Mike won first game) = 1 - P(Alain wins championship | Mike won first game) = 1 - 5/8 = 3/8 + 1/8 = 4/8 = 1/2

Thus, The probability that Mike becomes the champion given that he has won the first game is 7/12.

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If the diameter of the pie is 12 inches, then the area of pie is 113.04 in² and 113 in² after rounding to the nearest tenth.

The formula for the area of a circle is: A = π × r²

where A is the area, pi is a mathematical constant approximately equal to 3.14, and r is the radius of the circle.

In this case, we are given the diameter of the pie, which is 12 inches. To find the radius, we need to divide the diameter by 2:

r = 12 / 2

= 6 inches

Now we can use the formula for the area of a circle to find the area of the pie:

A = π × r²

A = 3.14 × 6²

A = 113.04 square inches

Rounding to the nearest tenth gives:

A ≈ 113.0 square inches

Therefore, the area of the pie is approximately 113.0 square inches.

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The next picture in the sequence of pictures is a picture that has 16 cells

A pattern is a recurring design, shape, or arrangement that has a regular or logical repetition.

From the figure, we can see that teh pattern is

Picture = 2^n

Where n is the position

For the next picture, we have

n = 4

This means that

Picture = 2^4

So, we have

Picture = 16

Hence, the next picture would have 16 cells

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Answer:

a) 6x10^-6 b) 0.000006 c) I would not be concerned

Step-by-step explanation:

a)

50% is just half and more just means added onto.

Half of 4x10^-6 is 2x10^-6

If you add that onto the original value, you will have:

6x10^-6 (standard form)

b)

0.000006 (ordinary number)

c)

I would not be concerned about the increase in probability of a side effect while using the new medicine. The probability to begin with is extremely low, almost insignificant. While the 50% increase may sound intimidating, it is just a 50% increase on a number that is already very very small. Honestly, it makes almost no difference.

Answer:

diameter = 34 radius = 17

Step-by-step explanation:

Look at the line in the middle of the circle that is the diameter, diameter is a straight line passing from side to side through the center of a circle.

radius is the distance from the center of the circle to any point on its circumference.

Answer: 64x^6y^15

Step-by-step explanation:

If the packaging box is in the shape of a cube, then all its sides are equal in length. Let's call the length of each side "s".

We know that the length of the packaging box is 4x^2 y^5, so:

s = 4x^2 y^5

To find the volume of the packaging box, we need to calculate s^3 (since the box is a cube).

s^3 = (4x^2 y^5)^3

s^3 = 4^3 (x^2)^3 (y^5)^3

s^3 = 64x^6 y^15

Therefore, the volume of the packaging box in terms of x and y is 64x^6 y^15.

Answer: A rotation of 270° clockwise is equivalent to a rotation of 90° counterclockwise, because a full rotation is 360° and 270° clockwise is the same as 90° counterclockwise in terms of direction.

Therefore, the answer is: counterclockwise 90°.

Step-by-step explanation:

Answer: 33.33%

Step-by-step explanation:

5/15 divided

Answer:

Step-by-step explanation:

wios,wal

Answer:27.5

Step-by-step explanation:

i did this with a calculator, but the answer is

27.5

Penelope jogs a distance of 2898 meters in three laps around the rectangular playground.

To solve this problem, we need to first find the perimeter of the rectangle. For a rectangle with a length of L and a width of W, the perimeter P can be found using the following formula:

P = 2L + 2W

In this case, the length of the playground is 320 m and the width is 163 m. So, the perimeter of the playground is:

P = 2(320 m) + 2(163 m)

P = 966 m

This means that if Penelope jogs around the entire playground once, she will run a distance of 966 meters.

Since Penelope jogs three laps around the playground, we need to multiply the perimeter by 3 to find out how far she runs in total. So, the distance that Penelope jogs in three laps is:

Distance = 3 x P

Distance = 3 x 966 m

Distance = 2898 m

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Complete Question:

Every day, Penelope jogs three laps around the playground to keep in shape. The playground is rectangular with a width of 163 m and a length of 320 m.

Determine how many meters Penelope jogs in three laps.

A transformation is said to be not rigid because the segments is preserved.

A transformation is a function that maps one set of points to another set of points. There are different types of transformations, including translation, rotation, reflection, dilation, and combinations of these. Each type of transformation preserves certain properties of the shape or object.

The properties that are preserved during a transformation depend on the type of transformation

Similarly, a rotation is a transformation that rotates a shape or an object around a fixed point. During a rotation, the distance between any two points on the shape or object is preserved, but the direction may change. A reflection is a transformation that flips a shape or an object across a line. During a reflection, the distance between any two points on the shape or object is preserved, but the orientation may change.

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1. nonrigid

2. segment lengths are not

We need to calculate the z-test score. It is a statistical test for inference that tests the null hypothesis that the mean of a sample from a normal population equals a specified value, and it is a test of statistical significance. Z-score: Z = (x - μ) / (σ / √n)μ = 3000, x = (2176 + 2784) / 2 = 2480, σ is the standard error of the mean, and n is the number of data points.

Z = (2480 - 3000) / (3000 / √n). The standard error of the mean (SEM) is calculated as follows: SEM = σ / √nσ = (2784 - 2176) / (2 × 1.96) = 303.64. Therefore, SEM = σ / √n=303.64 / √n(303.64 / √n) = (3000 - 2176) / 1.96n = 141.56n = 142Z = (2480 - 3000) / (303.64 / √142)Z = -12.95.

Since Z is less than -1.96, the test is significant at the 5% level of significance. Therefore, we can refuse the null hypothesis, and the alternative hypothesis is accepted. Therefore, the data support the alternate hypothesis that the number of burglaries per month is not equal to 3000.

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Answer: 25 dollars and 52 cents

Step-by-step explanation:

Bill = $22

Tip = 16/100 X 22 = $3.52

Total = 22 + 3.52 = $25.52

Answer:

$25.52

Step-by-step explanation:

16% × 22= $3.52

3.52 + 22= $25.52

Answer:

6.

[tex]2x - 1 = x + 3[/tex]

[tex]x = 4[/tex]

[tex] y = 4 + 3 = 7[/tex]

So the solution is (4, 7).

7. Substituting 4x into the second equation:

[tex]4x + x = 5[/tex]

[tex]5x = 5[/tex]

[tex]x = 1[/tex]

[tex]y = 4(1) = 4[/tex]

So the solution is (1, 4).

Answer:

$1.90

Step-by-step explanation:

16.80 - 1.60 = 15.20, since we are finding the price of each bottle of juice.

1) Set up and equation equated to 15.20.

8x = 15.20

x = 15.20/8

x = 1.90

Therefore, each bottle of juice costs $1.90.

A = 40,000(1 + 0.07)^3

A = 40,000(1.07)^3

A = 47,676.08

Therefore, the population of the town in 3 years will be approximately 47,676.

We can find the equation of the line passing through the given two points (-4, 7) and (2, -2) using the slope-intercept form of a linear equation:

slope (m) = (change in y) / (change in x) = [tex](-2 - 7) / (2 - (-4)) = -9/6 = -3/2[/tex]

Using point-slope form with the first given point (-4, 7), we get:

[tex]y - 7 = (-3/2)(x - (-4))\\y - 7 = (-3/2)x - 6\\y = (-3/2)x + 1[/tex]

Now we can plug in the x-coordinates of the other points given and check if they satisfy the equation.

[tex](−2, −6):\\y = (-3/2)x + 1\\-6 = (-3/2)(-2) + 1\\-6 = 3 + 1\\-6 ≠ 4 (not on the line)[/tex]

[tex](−2, −5):\\y = (-3/2)x + 1\\-5 = (-3/2)(-2) + 1\\-5 = 3 + 1\\-5 ≠ 4 (not on the line)(4, −6):\\y = (-3/2)x + 1\\-6 = (-3/2)(4) + 1\\-6 = -6 + 1\\-6 ≠ -5 (not on the line)(4, −5):\\y = (-3/2)x + 1\\-5 = (-3/2)(4) + 1\\-5 = -6 + 1\\-5 = -5 (on the line)[/tex]

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Answer:

25%

Step-by-step explanation:

30/120 = 1/4

1/4 = 25%

The mean of the unintentional drug overdose deaths per 100,000 population from 1986-1996 is 2.18. (option 2).

To find the mean of a set of numbers, we add up all the numbers in the set and then divide by the total number of items in the set. In this case, we have the following numbers: 2, 1, 2, 2, 1, 2, 2, 3, 3, 3, and we want to find the mean.

To do so, we first add up all the numbers:

2 + 1 + 2 + 2 + 1 + 2 + 2 + 3 + 3 + 3 = 21

Then we divide by the total number of items in the set, which is 10:

21 / 10 = 2.1

Therefore, the mean of the unintentional drug overdose deaths per 100,000 population from 1986-1996 is 2.18.

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The phrase that reflects the amount of recordings, in thousands, owned by the collector 4 years later if it continues to expand at this rate is:   [tex]O 12 • (1.02)^48[/tex] Thus, option C is correct.

o calculate the number of records that will increase by a factor, you first need to know the initial number of records. Let's call this number "N".

To increase the number of records by a factor of "F", you can simply multiply the initial number of records by the factor:

New number of records = N x F

For example, if you have 100 records and you want to increase the number of records by a factor of 3, the new number of records would be:

New number of records  [tex]= 100 x 3 = 300[/tex]

So, the new number of records would be 300.

The growth rate is 2% per month, which means that the number of records will increase by a factor of 1.02 each month. After 4 years (48 months), the number of records owned by the collector can be calculated using the formula:

[tex]12,000 x (1.02)^48[/tex]

Simplifying this expression, we get:

[tex]12,00x0 1.02^48[/tex]

Therefore, the expression that represents the number of records, in thousands, owned by the collector 4 years later if it continues to grow at this rate is: O 12 • (1.02)^48

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Answer: The given function is:

A(x) = 140 + 25x

We need to find the value of A(215), which means we need to substitute x = 215 in the function and simplify:

A(215) = 140 + 25(215)

A(215) = 140 + 5375

A(215) = 5515

Therefore, the correct answer is (c) A(215) = 5515. The interpretation of this result is that if the accountant works for 215 hours to prepare the taxes, the cost will be $5,515, which includes the flat fee of $140 and an additional hourly rate of $25 for each hour worked.

Step-by-step explanation:

The value of A(215) and its interpretation are captured thus:

A(215) = 5515; If the accountant takes 215 hours to prepare the taxes, the cost will be $5,515

The function given as A(x) = 140 + 25x, represents the total cost of using the services of the accountants for tax computation and preparation, bearing in mind that the 140 means $140 which is the fixed charged irrespective of the number of hours it takes to prepare the tax returns whereas the 25x means that $25 is charged as variable fee for  every hour the accountant works on the tax computation

A(x) = 140 + 25x

In this case, A(215) means that 215 hours were made use of by the accountants, hence, to determine the total fees, we simply substitute for x

A(215) = 140+(25*215)

A(215) = 140+5375

A(215)=$5,515

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Answer:

95/63 or 1 32/63

Step-by-step explanation:

turn the fraction into a mixed number/improper fraction

65/9-40/7

find a common denominator which in this case is 63

so, the first fraction you will multiply the numerator and denominator by 7 to get

455/63

then the second fraction multiply the numerator and the denominator by 9

360/63

then you would subtract the two numerators KEEP THE DENOMINATOR THE SAME

455/63-360/63=95/63

The top of the ladder is coming down the wall at a rate of 15.39 ft/s

Let's assume that the ladder makes a right angle with the wall and the ground. Let's call the distance between the bottom of the ladder and the wall "x" and the height of the ladder at a given time t "y". We want to find the rate of change of "y" with respect to time "t", or dy/dt, when y = 8 ft.

We can use the Pythagorean theorem to relate "x" and "y":

x^2 + y^2 = 17^2

Taking the derivative of both sides with respect to time "t", we get

2x(dx/dt) + 2y(dy/dt) = 0

We want to find dy/dt when y = 8 ft and dx/dt = 2 ft/s. We can solve for dy/dt

2x(dx/dt) + 2y(dy/dt) = 0

2y(dy/dt) = -2x(dx/dt)

dy/dt = -x/y(dx/dt)

Substituting x = sqrt(17^2 - y^2) and dx/dt = 2 ft/s, we get:

dy/dt = -(17^2 - y^2)/y

When y = 8 ft, we get

dy/dt = -(17^2 - 8^2)/8 = -15.39 ft/s

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