The vertices of AABC are A(- 5,4), B(-2,5), and C(- 2,2). If AABC is reflected across the line y = 1 to produce the image AA'B'C', find the coordinates of the vertex B'.

Answer:

Step-by-step explanation:

1+1=4x2=8/2=

answer: 4

Answer:

the surface area of the prism is22

Answer:

Step-by-step explanation:

Ms Pace:   [tex]\frac{6}{24} \times 100=\frac{1}{4} \times 100=25\%[/tex]

Ms Lee:     [tex]\frac{14}{28} \times 100=\frac{1}{2} \times 100=50\%[/tex]

Difference [tex]=50-25=25[/tex]

The future value οf the accοunt after 2 years is $1,830.28. If Alice depοsits $1,500 intο an accοunt with an interest rate οf 2.5 percent, cοmpοunded quarterly.

An algebraic expressiοn is a mathematical phrase that cοntains variables, cοnstants, and mathematical οperatiοns such as additiοn, subtractiοn, multiplicatiοn, and divisiοn.

Tο calculate the future value οf the accοunt after 2 years, we can use the fοrmula fοr cοmpοund interest:

[tex]FV = PV * (1 + r/n)^{(n*t)[/tex]

where:

FV is the future value οf the accοunt

PV is the present value (initial depοsit)

r is the annual interest rate (2.5%)

n is the number οf cοmpοunding periοds per year (4, since it is cοmpοunded quarterly)

t is the number οf years (2)

Plugging in the values, we get:

[tex]FV = 1,500 * (1 + 0.025/4)^{(4*2)[/tex]

[tex]FV = 1,500 * 1.02891^8[/tex]

FV = 1,500 * 1.22019

FV = 1,830.28

Therefοre, the future value οf the accοunt after 2 years is $1,830.28.

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There are a total of 90 possible outcomes in this experiment involving three steps.

To find the total number of possible outcomes, you should multiply the number of outcomes for each step because each outcome for step 1 corresponds to each outcome for step 2 and so on. This experiment requires a sequence of three steps. First step can result in 5 possible outcomes, second step can result in 6 possible outcomes, third step can result in 3 possible outcomes. The total number of possible outcomes is the product of the possible outcomes of each step:

Total possible outcomes = 5 x 6 x 3

Total possible outcomes = 90

Therefore, the total number of possible outcomes in this experiment involving three steps is 90.

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The probability that a randomly selected region had exactly three hits is approximately 0.139.

In this problem, we can use the Poisson probability distribution formula to find the probability of a randomly selected region having exactly three hits.

The Poisson probability distribution formula is:

P(x) = (e^(-μ) * μ^x) / x!

Where:

P(x) is the probability of x occurrences of an event.

μ is the mean number of occurrences of the event in a given interval.

x is the number of occurrences of the event.

e is the mathematical constant e, approximately equal to 2.71828.

To apply this formula to the problem at hand, we need to determine the values of μ and x.

Since there were a total of 515 bombs that hit the 573 regions, we can calculate the average number of bombs that hit each region:

μ = total number of bombs / number of regions

μ = 515 bombs / 573 regions

μ = 0.8993

Therefore, the mean number of hits per region is 0.8993.

To find the probability that a randomly selected region had exactly three hits, we can plug in x = 3 into the Poisson probability distribution formula:

P(3) = (e^(-0.8993) * (0.8993)^3) / 3!

P(3) ≈ 0.139

Therefore, the probability that a randomly selected region had exactly three hits is approximately 0.139.

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Answer: There are 2 common tangents, they are external

Step-by-step explanation:

I just learned this lesson in my Geometry class trust

The amount of sand Jamilla have to order to fill the square sandbox with sides 8 1/2 feet long and 2 1/2 feet deep is 180.625 cubic feet of sand.

To calculate the amount of sand that Jamilla should order, you need to calculate the volume of the sandbox. Given that Jamilla is building a square sandbox with sides 8 1/2 feet long and wants to put sand 2 1/2 feet deep in the box. Thus, the volume of the sandbox is calculated as follows:

Volume of the sandbox = Length * Width * Depth

Volume of the sandbox = (8 1/2 feet) * (8 1/2 feet) * (2 1/2 feet)

Converting each mixed fraction to its corresponding improper fraction, we get:

8 1/2 feet = 17/2 feet

2 1/2 feet = 5/2 feet

On simplifying the above equation we get:

Volume of the sandbox = (17/2 feet)² * (5/2 feet)

Volume of the sandbox = (289/4) * (5/2) cubic feet

Volume of the sandbox = 1445/8 cubic feet

Volume of the sandbox = 180.625 cubic feet

Therefore, Jamilla should order 180.625 cubic feet of sand.

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Answer:

4,25

Step-by-step explanation:

[tex]3 \frac{5}{4} = \frac{17}{4} = 4 \frac{1}{4} = 4.25[/tex]

To solve this expression, we can use the order of operations, also known as PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (performed left to right), and Addition and Subtraction (performed left to right).

Following this order, we first need to evaluate the exponent, which gives:

1000^3 = 1,000,000,000

Then, we can substitute this value back into the expression:

1000 + 1000^3 = 1000 + 1,000,000,000 = 1,000,000,000 + 1000 = 1,000,001,000

Therefore, 1000 + 1000^3 equals 1,000,001,000.

Answer: 8000000000

Step-by-step explanation:

The composition of transformations that map ABCD to EHGF is: reflect over the x-axis, then translate (x + 3. y + 1).

In Mathematics and Geometry, a reflection over the x-axis is modeled by this transformation rule (x, y) → (x, -y). This ultimately implies that, a reflection over the x-axis would maintain the same x-coordinate while the sign of the x-coordinate changes from positive to negative or negative to positive.

Since triangle ABCD was reflected over the x-axis, the coordinate A of triangle ABCD can be calculated as follows;

(x, y)            →      (x, -y)

A (-5, 2)      →      (-5, -(2)) = (-5, -2)

For the translation, we have:

(x, y)            →       (x + a, y + b)

A (-5, -2)           →      E (-2, 1)

-5 + a = -2

a = -2 + 5

a = 3

-2 + b = -1

b = -1 + 2

b = 1

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Answer:

Step-by-step explanation:

they wrote the answer already^

Answer:A

Step-by-step explanation:

It would have the greatest chance to be the line on the graph

Therefore, the angle V in parallelogram WXUV is 100 degrees. Therefore, the angle L in parallelogram LMJK is 98 degrees. Therefore, the length of side SP in parallelogram SRQP is 26 units. Therefore, the length of side FC in parallelogram FCDE is 12.6 units.

A parallelogram is a quadrilateral (a four-sided polygon) with two pairs of parallel sides. In other words, the opposite sides of a parallelogram are parallel and congruent (equal in length). The properties of a parallelogram include:

Opposite sides are parallel and congruent

Opposite angles are congruent (equal in measure)

Consecutive angles are supplementary (add up to 180 degrees)

Diagonals bisect each other (divide each other into two equal parts)

Some common examples of parallelograms include rectangles, rhombuses, and squares. A rectangle is a parallelogram with four right angles, a rhombus is a parallelogram with four congruent sides, and a square is a parallelogram with four congruent sides and four right angles.

Here,

1. In a parallelogram, opposite angles are equal. Therefore, if angle U is 80 degrees, then angle W must also be 80 degrees.

We know that the sum of the angles in a quadrilateral is 360 degrees, so the sum of the angles at vertices V and U is 360 - 2*80 = 200 degrees.

Since opposite angles in a parallelogram are equal, the angle at vertex V must also be 100 degrees.

2. In a parallelogram, opposite angles are equal. Therefore, if angle J is 98 degrees, then angle L must also be 98 degrees.

We know that the sum of the angles in a quadrilateral is 360 degrees, so the sum of the angles at vertices J and K is 360 - 2*98 = 164 degrees.

Since opposite angles in a parallelogram are equal, the angle at vertex M must also be 98 degrees.

3. In a parallelogram, opposite sides are equal in length. Therefore, if side RQ is 26 units, then side SP must also be 26 units.

This is because SRQP is a parallelogram, so side SR is equal in length to side PQ, and side RQ is equal in length to side SP.

4. In a parallelogram, opposite sides are equal in length. Therefore, if side DE is 12.6 units, then side FC must also be 12.6 units.

This is because FCDE is a parallelogram, so side FC is equal in length to side DE, and side DE is equal in length to side FC.

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The skyscraper will have 78 floors when it is finished.

What is a fraction?

A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.

We have two types of fractions.

Proper fraction and improper fraction.

A proper fraction is a fraction whose numerator is less than the denominator.

An improper fraction is a fraction where the numerator is greater than the denominator.

Example:

1/2, 1/3 is a fraction.

3/6, 99/999 is a fraction.

1/4 is a fraction.

We have,

Let's assume that the total number of floors in the skyscraper is "x".

According to the problem, the builder has built 1/6 of the floors.

So the number of floors built by the builder is:

= (1/6)x

The problem also tells us that the builder has built 13 floors.

So we can set up the equation:

(1/6) x = 13

To solve for "x", we can multiply both sides by 6:

x = 78

Therefore,Therefore, The skyscraper will have 78 floors when it is finished.

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The probability that the mean gain for the sample was between 400 and 800 is approximately 1 or 100%.

What is probability?

Probability is the study of the chances of occurrence of a result, which are obtained by the ratio between favorable cases and possible cases.

We can use the central limit theorem to approximate the sampling distribution of the sample mean as normal, with a mean of 651 and a standard deviation of (standard deviation of the population)/√(sample size) = 6/√(34) ≈ 1.03.

Then, we can standardize the values of 400 and 800 using the formula z = (x - μ) / σ, where x is the value of interest, μ is the mean of the sampling distribution, and σ is the standard deviation of the sampling distribution.

For 400:

z = (400 - 651) / 1.03 ≈ -241.75

For 800:

z = (800 - 651) / 1.03 ≈ 143.69

We want to find the probability that the sample mean falls between 400 and 800, which is the same as finding the probability that the standardized value falls between -241.75 and 143.69. We can use a standard normal distribution table or a calculator to find this probability:

P(-241.75 < z < 143.69) ≈ P(z < 143.69) - P(z < -241.75) ≈ 1 - 0 ≈ 1

Therefore, the probability that the mean gain for the sample was between 400 and 800 is approximately 1 or 100%.

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Step-by-step explanation:

law of cosine :

c² = a² + b² - 2ab×cos(C)

c being the side opposite of the angle C. a and b are the other 2 sides.

a)

x² = 7² + 9² - 2×7×9×cos(102) = 49 + 81 - 126×cos(102) =

= 130 - 126×cos(102) = 156.196873...

x = 12.49787474... ≈ 12.5

b)

9² = 5² + 12² - 2×5×12×cos(theta)

81 = 25 + 144 - 120×cos(theta)

81 = 169 - 120×cos(theta)

120×cos(theta) = 88

cos(theta) = 88/120 = 11/15 = 0.733333333...

theta = 42.83342807...° ≈ 42.8°

Using the system of inequalities y ≥ 0, x ≥ 0, y ≤ -2x + 4 the minimum value of f(x,y) = 3x + y for the feasible region is d) 0.

We need to find the minimum value of the function

f(x,y) = 3x + y

we can use Lagrange multipliers method defining

F(x,y) = f(x,y) - λx g(x,y)  , where g(x,y) = x²+36 x y² - 1, such that

Fx(x,y) = fx(x,y) - λx gx(x,y) = 0

Fy(x,y) = fy(x,y) - λx gy(x,y) = 0

g(x,y)=0

where the sub-indices x and y represent the partial derivatives with respect to x and y, then

fx(x,y) - λx gx(x,y) = 3 - λx(2x) = 0 → x =3/(2xλ)

fy(x,y) - λx gy(x,y) = 1 - λx(36x2xy) = 0 → y =1/(72xλ)

x²+36xy² - 1 = 0 → [3/(2xλ)]²+36*[1/(72xλ)]² - 1 = 0

therefore, Using the system of inequalities y ≥ 0, x ≥ 0, y ≤ -2x + 4 the minimum value of f(x,y) = 3x + y for the feasible region is d) 0.

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The area of the given figure consisting of rectangle and triangles is 51.5 square feet.

Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape. The area of a plane figure is the area that its perimeter encloses. The quantity of unit squares that cover a closed figure's surface is its area. Square units like cm² and m² are used to measure area.

We must first calculate the areas of each form in the figure in order to obtain the total area.

Let's start by calculating the rectangle's area:

Area = length x width

Area = 11ft x 4ft

Area = 44ft²

The area of the two right triangles should now be determined.

Triangle 1:

Area = (base x height) / 2

Area = (2ft x 3ft) / 2

Area = 3ft²

Triangle 2:

Area = (base x height) / 2

Area = (3ft x 3ft) / 2

Area = 4.5ft²

The total area of the figure can now be calculated by adding the areas of the three shapes:

Total Area = Area of Rectangle + Area of Triangle 1 + Area of Triangle 2

Total Area = 44ft² + 3ft² + 4.5ft²

Total Area = 51.5ft²

Therefore, the area of the figure is 51.5 square feet.

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The area of the rectangle is 41 square units

The area of a composite figure, you must first break it down into simpler shapes. Then, you can find the area of each shape and add them together to get the total area of the composite figure.
Let's say our composite figure consists of a rectangle and a triangle. To find the area, we need to find the area of the rectangle and the area of the triangle separately, and then add them together.
To find the area of the rectangle, we need to know its length and width. Let's say the length is 8 units and the width is 4 units. The formula for the area of a rectangle is length x width, so the area of our rectangle is:
[tex]8 x 4 = 32 square units[/tex]
Now, let's find the area of the triangle. To do this, we need to know its base and height. Let's say the base is 6 units and the height is 3 units. The formula for the area of a triangle is 1/2 x base x height, so the area of our triangle is:
[tex]1/2 x 6 x 3 = 9 square units[/tex]
Now that we have the area of both the rectangle and the triangle, we can add them together to find the total area of the composite figure:
[tex]32 + 9 = 41 square units[/tex]
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A number line is a graphical representation of numbers in a linear format. It is a useful tool to help visualize the relative positions of numbers, especially fractions.

To place the fractions 2/3, 1/10, and 7/8 on a number line, we need to first identify their relative positions in terms of magnitude.

Starting at 0 on the number line, we can place 1/10 to the right of 0, followed by 2/3 and then 7/8, in order from left to right. Since 2/3 is greater than 1/10 but less than 7/8, it is placed between these two fractions on the number line. The resulting number line would show the relative positions of these three fractions in relation to each other and to the whole numbers. This can help in comparing and ordering fractions, as well as in visualizing their relative magnitudes.

1/10 = 0.1

2/3 = 0.667

7/8 = 0.875

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