Use the graph to answer the question.

Determine the coordinates of polygon A′B′C′D′ if polygon ABCD is rotated 180°.

A′(0, 0), B′(−2, 5), C′(5, 5), D′(3, 0)
A′(0, 0), B′(2, −5), C′(−5, −5), D′(−3, 0)
A′(0, 0), B′(−5, −2), C′(5, −5), D′(3, 0)
A′(0, 0), B′(−5, −2), C′(−5, 5), D′(0, 3)

The fraction of the rectangles shaded blue in the row containing the blue shaded rectangles is 4/5. The correct option is option A

A. 4/5

A fraction is a representation of a part of a whole amount.

The number area of the rectangle = 5 × 6 = 30

The number of blue shaded rectangles = 4

The number of rectangles in the row containing the blue shaded rectangles = 5

The fraction of the rectangles  shaded blue in the row containing the blue rectangles is therefore;

Fraction = 4/5

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The area of grass the groundkeepers need to cover is  10, 343. 74 square meters

To determine the area of the rectangle, we have;

Area = length × width

Now, substitute the values, we have;

Area = 73 (84.39)

Multiply the values

Area = 6160. 47 m²

The remaining part is a circle

radius = 73/2 = 36. 5

Area of a circle = πr²

Substitute the values

Area = 3.14 × 36.5²

find the square

Area = 4183. 27 m²

Add the areas = 10, 343. 74 square meters

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Answer:

2nd choice down

Step-by-step explanation:

Domain is the set of all real numbers (no restrictions on x).

The vertex of the solid-line open-down parabola is at (-1, 16), therefore the range is y≤16 (maximum value of y is 16, at the vertex point (-1, 16).  Range is {y|y≤16}

Answer:

Triangle A is correct since 87° + 23° + 70° = 180°.

The table of distance of points from the origin is:

Less than 13 units       Equals to 13 units        Greater than 13 units

          M                                  N, P                                Q, R

We know that in Cartesian Coordinate Plane, the distance between the point (a, b) and the origin (0, 0) is given by,

D = √(a² + b²)

Coordinates of Point M = (12, -5)

So the distance of the point M to the origin

= √(12² + (-5)²)

= √(144 + 25)

= √169

= 13 units

Coordinates of Point N = (6, 11)

So the distance of the point N to the origin

= √(6² + 11²)

= √(36 + 121)

= √157

= 12.53 units (approximated to two decimal places)

< 13 units

Coordinates of Point P = (-9, 9)

So the distance of the point P to the origin

= √((-9)² + 9²)

= √(81 + 81)

= √162

= 12.73 units (approximated to two decimal places)

< 13 units

Coordinates of Point Q = (10, 9)

So the distance of the point Q to the origin

= √(10² + 9²)

= √(100 + 81)

= √181

= 13.45 units (approximated to two decimal places)

> 13 units

Coordinates of Point R = (-1, -13)

So the distance of the point R to the origin

= √((-1)² + (-13)²)

= √(1 + 169)

= √170

= 13.04 units (approximated to two decimal places)

> 13 units

hence the table is,

Less than 13 units       Equals to 13 units        Greater than 13 units

          M                                  N, P                                Q, R

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The option that could be the side lengths of a dilation of HUK is (C) 18cm, 39cm, 21cm and 45cm.

From the question, the quadrilateral HIJK has sides measuring 12 cm, 26 cm, 14 cm, and 30 cm.

If HIJK is said to be dilated with a scale factor of 1.5, the side lengths will thus be:

12 x 1.5 =18 cm

26 x 1.5 =39 cm

14 x 1.5 =21 cm

30 x 1.5 =45 cm

A dilation of HIJK with a scale factor of 1.5 will make us have the side lengths: 18cm, 39cm, 21cm and 45cm.

Therefore, The correct option is C.18cm, 39cm, 21cm and 45cm.

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See full text below

Quadrilateral HUK has sides measuring 12 cm, 26 cm, 14 cm, and 30 cm. Which could be the side lengths of a dilation of HUK?

(A)24cm,50cm,28cm, 60cm (B)6cm,15cm,7cm,15cm (C)18cm,39cm,21cm,45cm (D)30cm,78cm,35cm,75cm

Answer: 60

Step-by-step explanation: 18 x 3 = 54

54 +6 = 60

The given function is in vertex form, which is:

f(x) = a(x - h)^2 + k

where (h, k) is the vertex of the parabola.

Comparing the given function to the vertex form, we can see that a = -1, h = 3, and k = 8.

Therefore, the vertex of the graph is at the point (h, k) = (3, 8).

So the coordinates of the vertex of the graph are (3, 8).

Answer:

OB. (3, 1)

Step-by-step explanation:

The rule for translating 1 unit left and 3 units up is (x-1, y+3)

So we just apply that to B

B(4, -2)

B'(4-1,-2+3) or B'(3,1)

Answer:

Nicole bought 4 fancy shirts and 3 plain shirts.

Step-by-step explanation:

I multiplied 28 x 4 to get $112

then I multiplied 8 x 3 to get $24

You add $112 and $24 to get $136.

Answer:

the question is not complete

The statement that is true of the information given is that C. Angle AEC measures 90°.

The picture of the diagram obtained from other sources shows aline CE that stands at a perpendicular angle to another line AED. These two lines meet at a point that corresponds to the summation of two 45° angles. Now we do our summation as follows:

45° + 45° = 90°.

So, we can arrive at the conclusion that angle AEC is a right-angle triangle with a dimension of 90°. Therefore, option C is correct.

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Answer:

s = 150m + 650

Step-by-step explanation:

Putting it all together, we get: A which is an orthogonal matrix with the first row being a multiple of (3, 3, 0).

An orthogonal matrix is a square matrix whose columns and rows are orthonormal vectors, i.e., each column and row has unit length and is orthogonal to the other columns and rows.

Let's start by finding a vector that is orthogonal to (3, 3, 0). We can take the cross product of (3, 3, 0) and (0, 0, 1) to get such a vector:

(3, 3, 0) x (0, 0, 1) = (3*(-1), 3*(0), 3*(0)) = (-3, 0, 0)

Note that this vector has length 3, so we can divide it by 3 to get a unit vector:

(-3/3, 0/3, 0/3) = (-1, 0, 0)

So, the first row of the orthogonal matrix A can be (-3, 0, 0) or a multiple of it. For simplicity, we'll take it to be (-3, 0, 0).

To find the remaining two rows, we need to find two more orthonormal vectors that are orthogonal to each other and to (-3, 0, 0). One way to do this is to use the Gram-Schmidt process.

Let's start with the vector (0, 1, 0). We subtract its projection onto (-3, 0, 0) to get a vector that is orthogonal to (-3, 0, 0):

v1 = (0, 1, 0) - ((0, 1, 0) dot (-3, 0, 0)) / ||(-3, 0, 0)||^2 * (-3, 0, 0)

= (0, 1, 0) - 0 / 9 * (-3, 0, 0)

= (0, 1, 0)

We can then normalize this vector to get a unit vector:

v1' = (0, 1, 0) / ||(0, 1, 0)|| = (0, 1, 0)

So, the second row of the orthogonal matrix A is (0, 1, 0).

To find the third row, we take the cross product of (-3, 0, 0) and (0, 1, 0) to get a vector that is orthogonal to both:

(-3, 0, 0) x (0, 1, 0) = (0, 0, -3)

We normalize this vector to get a unit vector:

v2' = (0, 0, -3) / ||(0, 0, -3)|| = (0, 0, -1)

So, the third row of the orthogonal matrix A is (0, 0, -1).

Putting it all together, we get:

A:

[-3 0 0]

[ 0 1 0]

[ 0 0 -1]

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Using differentials, the approximate value of (4.99)³ is 124.25, and using a calculator, the value is 124.251.

To use differentials to approximate the value of the expression (4.99)3, we can use the formula:

Δy ≈ dy = f'(x)Δx

Where f'(x) is the derivative of the function f(x) = x3 evaluated at x = 5, since we are approximating around x = 5, and Δx is the change in x from 5 to 4.99, which is -0.01.

f'(x) = 3x2
f'(5) = 3(5)2 = 75

Δy ≈ dy = 75(-0.01) = -0.75

So, the approximate value of (4.99)3 using differentials is:

(4.99)3 ≈ (5 + Δx)3 ≈ 53 + 3(53)(-0.01) = 124.2575

Rounding to four decimal places, we get:

(4.99)3 ≈ 124.2575

Using a calculator, we get:

(4.99)3 = 124.251

Comparing the two values, we see that the approximation using differentials is very close to the value obtained using a calculator. The difference is only in the third decimal place, which is likely due to rounding errors in both calculations.

Step 1: Choose a base point
Since 4.99 is close to 5, we will choose 5 as our base point (x = 5).

Step 2: Find the expression's value at the base point
At x = 5, the expression is (5)³ = 125.

Step 3: Calculate the derivative of the expression
For the expression x³, the derivative is 3x².

Step 4: Find the derivative's value at the base point
At x = 5, the derivative is 3(5)² = 3(25) = 75.

Step 5: Calculate the differential
Δx = 4.99 - 5 = -0.01.

Step 6: Approximate using differentials
Δy ≈ dy = (derivative) * Δx = 75 * (-0.01) = -0.75.

Step 7: Add the differential to the base point value
Approximate value = 125 + (-0.75) = 124.25.

Now, let's compare this with a calculator result.

Using a calculator:
(4.99)³ ≈ 124.251

In conclusion:
Using differentials, the approximate value of (4.99)³ is 124.25, and using a calculator, the value is 124.251. Both values are rounded to four decimal places.

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Point (-4, -5) is located in quadrant III.

The correct option is C.

We have the point (-4, -5)

The following are the symbol of coordinate as

Here, the x and y both coordinate are Negative which shows the point lie in III Quadrant.

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For 63 pounds of the bag, Eileen will have to pay $10.71.

Given is that the fee to check luggage with a new airline is based on the weight of each bag. Brett paid $7.14 to check a 42 pound.

Brett paid $7.14 to check a 42 pound.

Then, for 1 pound, Brett will have to pay $(7.14/42) or $0.17.

So, for 63 pounds of the bag, Eileen will have to pay -

63 x 0.17

10.71

Therefore, for 63 pounds of the bag, Eileen will have to pay $10.71.

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The compound inequality can be written as 83 ≤ x ≤ 91

we can write a compound inequality to represent this situation as:

83 ≤ (92 + 87 + 85 + 88 + 2x) / 6 ≤ 91

where x represents Marcus's score on the final exam (which counts as two tests).

To solve for x, we can start by multiplying both sides of the inequality by 6 to eliminate the denominator:

498 ≤ 352 + 2x ≤ 546

Next, we can subtract 352 from all sides of the inequality:

146 ≤ 2x ≤ 194

Finally, we can divide all sides of the inequality by 2:

73 ≤ x ≤ 97

Therefore, Marcus must score between 73 and 97 on his final exam to earn a "B" in the course.

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The simple interest on given principal, rate of interest and time period is $23.25.

Given that, principal=$310.00, rate of interest=2.5% and time period=3 years.

Simple interest is calculated with the following formula: S.I. = (P × R × T)/100, where P = Principal, R = Rate of Interest in % per annum, and T = Time.

Here, simple interest = (310×2.5×3)/100

= $23.25

Therefore, the simple interest on given principal, rate of interest and time period is $23.25.

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Answer:

1/y^2

Step-by-step explanation:

y^8/y^10 = 1/y^2 ( y^-2 )

True. Paired analysis is a statistical technique used to compare two related samples. In this method, we take the difference between each pair of observations in the two samples and then perform inference on these differences.

Paired analysis is used when the samples are not independent, but instead each observation in one sample is related to a corresponding observation in the other sample. For example, if we want to compare the performance of students before and after a training program, we can use a paired analysis to compare the differences in scores before and after the training.

The differences between the paired observations allow us to reduce the variability in our data and increase the power of our statistical tests. We can perform inference on these differences using methods such as a paired t-test or a Wilcoxon signed-rank test to determine if there is a significant difference between the two samples. Thus, the statement "in a paired analysis we first take the difference of each pair of observations, and then we do inference on these differences" is true.

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The commission percentage for the sales is 3%.

A mathematical statement known as an equation, typically with an equal sign, illustrates the relationship between two expressions. To determine the values of the variables that make an equation true, equations can be solved.

On the other hand, a function is a collection of ordered pairs where each input value (also known as the independent variable) and each output value (also known as the dependent variable) have a precise correspondence. Although equations are frequently used to write functions, this is only one approach to express a function.

Given, your commission percentage is x​.

Now, for commission x percent of the sales we have:

$140 = ($13 x 8) + (x/100 x $1200)

$140 = $104 + 12x

$36 = 12x

x = 3

Hence, the commission percentage for the sales is 3%.

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Answer:

B. 4/(3') 1/2 * pi sqrt(2) , 99%

To compare these numbers, we need to convert them to a common format. We know that 99% is equivalent to the fraction 0.99.

Converting the other numbers:

4/3 = 1.3333...

1/2 * pi ≈ 1.5708

sqrt(2) ≈ 1.4142

Now we can see that the order from greatest to least is: 4/(3') > 1/2 * pi > sqrt(2) > 99%

And in the given options, only option b has these numbers in the correct order.

The true statement is that D. On average, Rosalie scored higher on her maths test that Marvin.

Mean = (68+73+76+76+83+83+86)/7 = 77.14%

Therefore, this claim is untrue.

Rosaline's test results fall within a range of scores that is 11.

Q3 - Q1 = 16% is the interquartile range (IQR).

Therefore, this claim is untrue.

C) Marvin and Rosalie both had a wider range of test results.

The gap between the greatest and lowest scores is known as the range.

Range = 86 - 68 = 18% for Marvin.

Range = 97 - 70 = 27% for Rosalie

Therefore, this claim is untrue.

Rosalie performed better than Marvin on math exams on average.

Rosalie's test results' average were calculated as follows: Mean = (70+84+86+89+93+95+97)/7 = 87.14%

So, this assertion is accurate.

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Step-by-step explanation:

volume = L x W x H

 180 ft^3  =  L x 6 x 6   ft

    180 / ( 6x6) = L = 5ft

Determining which plot element is the most challenging to write can pose difficulties for writers, largely depending on their individual style and the story they are crafting.

One of the more difficult plot elements can be the climax, which requires careful buildup and execution to deliver on achieving a satisfying payoff for readers due to escalating tensions throughout the narrative.

Writers tend to employ two common narrative approaches in their writing- dialogue and sensory details. Dialogue helps establish characters' drive, emotions, and motivations, while also advancing the plot and providing critical information to readers. Sensory details create immersive scenes with vivid imagery that allow readers to become invested into the story's ambiance and location.

In sum, by utilizing sensory details, authors capture readers' senses and render stories more tangible, while dialogue helps readers grasp characters' actions and feelings.

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On plotting the equation on the graph the value of x is -1.25. The correct option is C.

A function is a rule in mathematics that links every element of one set, known as the domain, with precisely one element of another set, known as the range.

A function is, to put it simply, a relationship between two sets of numbers in which each input (domain value) has exactly one corresponding output (range value).

One method is to graph both sides of the equation and find the point of intersection. We can graph y = -4x-1  [tex]y = 5^x+4[/tex] on the same set of axes. The point of intersection will give us an approximate solution.

When the graph is plotted on the x-y axis the value of the x coordinate will be -1.28. Which is approximately equal to -1.25.

Therefore, the value of x will be -1.25. The correct option is C.

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Answer: N/A

Step-by-step explanation: In a race between Rich and Marcus, Rich is given a 10-yard head start. Assuming that Rich runs at a constant speed and Marcus runs at a faster constant speed, we can write their positions as functions of time:

Rich's position function is R(t) = 10 + r*t, where r is Rich's speed in yards per second.

Marcus's position function is M(t) = m*t, where m is Marcus's speed in yards per second.

We can use these functions to fill in a table of approximate values for the distance each runner travels at different times:

Time (t) Rich's Distance (R(t)) Marcus's Distance (M(t))

0 10 0

1 10 + r m

2 10 + 2r 2m

3 10 + 3r 3m

4 10 + 4r 4m

5 10 + 5r 5m

To graph these functions, we can plot the points from the table and connect them with a straight line. The graph shows the distance each runner travels as a function of time. Note that the value of r is not given in the problem, so we cannot calculate the exact positions of Rich at each time interval.