Which is the value of x?

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).

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 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:

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 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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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

The function that best models the data is r(x) = 480(1.093)^x

We have,

We can use the exponential function to model the data since the net revenue increases rapidly with time.

Let's try to find the general form of the exponential function:

r(x) = ab^x

where a and b are constants to be determined.

To find the value of b, we can use the information that the revenue doubles every 15 months.

So, we have:

r(15) = 2r(0)

where r(0) is the initial revenue.

Substituting the values from the table, we get:

960 = 2r(0)

r(0) = 480

Therefore,

r(x) = 480b^x

To find the value of b, we can use any two data points from the table.

Let's use the first and fifth data points:

r(3) = 274 = 480b³

r(15) = 960 = 480b^15

Dividing the second equation by the first equation, we get:

960/274 = (480b^15)/(480b³)

3.5036 = b^12

b = 1.093

Therefore,

The function that best models the data is r(x) = 480(1.093)^x

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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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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 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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Answer:

the question is not complete

Answer:

1/y^2

Step-by-step explanation:

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

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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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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The height on the wall that the ladder reaches is approximately 21.04feet.

Angle made by ladder against the wall = 68 degrees.

Distance between foot of the ladder and wall = 8.5 feet

Use trigonometry function  ,

Let us consider the height on the wall that the ladder reaches as 'h'.

Use the tangent function,

tan α = height on wall ladder reaches / distance between wall and foot of the ladder

⇒ tan(68°) = h / 8.5

Solving for h, we get,

⇒h = 8.5 × tan(68°)

⇒h = 8.5 × 2.475

⇒ h = 21.04 feet (Rounding to the nearest hundredth)

Therefore, ladder reaches a height of approximately 21.04 feet on the wall.

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Answer:

s = 150m + 650

Step-by-step explanation:

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:

55 Units Squared

Step-by-step explanation:

Since the area of a rectangle is length multiplied by width, you can go about solving this by multiplying 5 by 11, which gives us 55.

Answer:

Step-by-step explanation:

The area of a rectangle that’s 11 units long and 5 units wide can be calculated by multiplying 11 x 5.

Option C is the correct answer.We have,

To find the area of a rectangle, you need to multiply its length by its width.

In this case,

The length is 11 units and the width is 5 units.

So,

The area of the rectangle is:

= 11 x 5

= 55 square unitsA rectangle is a 2-D shape with length and width.

The length and width are different.

If the length and width are not different then it is a square.

The area of a rectangle is given as:

Area = Length x width

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:

105

Step-by-step explanation:

we can draw the line (9 cm) perpendicular to the line (11 cm)

so we get a rectangle and a right triangle

the area of the rectangle :

A = length * width

A = 15 * 6

A = 90

the base of the right triangle = 15 - 9 = 6

the height of the right triangle = 11 - 6 = 5

the area of the right triangle :

A = 1/2*base*height

A = 1/2*6*5

A = 15

the Area of the shape = area of rectangle+area of right triangle

the Area of the shape = 90+15

A = 105

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: 60

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

54 +6 = 60

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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Answer:

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

The measure of angle ZXY is given as follows:

m < ZXY = 58º.

The value of x is obtained applying the angle bisection theorem, which divides an angle into two angles of equal measure, hence the opposite segments also have equal length.

For this problem, we have that angle ZXY is bisected as follows:

Hence the measure of angle ZXY is given as follows:

m < ZXY = 2 x 29º = 58º.

(the bisection divides the angle into two parts of equal measure, hence the total measure is given by the sum of these measures).

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Answer:the best predicted value of ý when the twin born first has an IQ of 109 is 107.50

Step-by-step explanation:

Given the regression equation:

ŷ = -2.59 + 1.01x

We need to predict the value of ý when x (IQ score of the twin born first) is 109.

So we substitute x = 109 into the regression equation:

ŷ = -2.59 + 1.01(109)

ŷ = -2.59 + 110.09

ŷ = 107.50

Therefore, the best predicted value of ý when the twin born first has an IQ of 109 is 107.50.

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.

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}

The coefficient of static friction is typically larger than the coefficient of kinetic friction. This is because static friction needs to be overcome to initiate motion, while kinetic friction acts during the motion, which usually requires less force to maintain.

1. Difference between static and kinetic friction: -

Static friction occurs when two surfaces are not moving relative to each other. It opposes the force that is trying to make the objects move. -

Kinetic friction, on the other hand, occurs when two surfaces are moving relative to each other. It acts against the direction of motion.

2. Normal force: - The normal force is a perpendicular force exerted by a surface on an object resting on it. It acts perpendicular to the contact surface and balances the weight of the object.

3. Relationship between friction and normal force: - The frictional force (both static and kinetic) is directly proportional to the normal force acting on an object.

Mathematically, F_friction = μ * F_normal, where F_friction is the frictional force, μ is the coefficient of friction, and F_normal is the normal force.

4. Wheel friction type: - A wheel experiences static friction at the point of contact with the surface because there's no relative motion between the wheel's contact point and the surface. The rest of the wheel experiences kinetic friction as it moves in relation to the surface.

5. Comparison between coefficients of static and kinetic friction: - The coefficient of static friction is typically larger than the coefficient of kinetic friction. This is because static friction needs to be overcome to initiate motion, while kinetic friction acts during the motion, which usually requires less force to maintain.

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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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