Find the product of all integers between -11 and 13.

The length of each of the remaining sides of the isosceles trapezoid is 11 meters.

Let's denote the length of the remaining sides of the isosceles trapezoid as "x" meters each.

The perimeter of the trapezoid is the sum of all its side lengths. In this case, we have:

Shorter base + Longer base + Side 1 + Side 2 = Perimeter

Plugging in the given values:

4 + 6 + x + x = 32

Simplifying the equation:

10 + 2x = 32

Subtracting 10 from both sides:

2x = 22

Dividing both sides by 2:

x = 11

Therefore, the length of each of the remaining sides of the isosceles trapezoid is 11 meters.

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Based on the analysis, we can summarize the intervals as follows:

Increasing: (-∞, 0)

Decreasing: (2, ∞)

Constant: [0, 2]

To determine the intervals on which the function is increasing, decreasing, or constant, we need to analyze the behavior of the function in each interval.

For the given function:

F(t) =

t + 2, t < 0

2, 0 ≤ t ≤ 2

-t + 4, t > 2

Let's consider each interval separately:

For t < 0:

In this interval, the function F(t) = t + 2 is a linear function with a positive slope. As t decreases, the function value increases.

Therefore, the function is increasing on the interval (-∞, 0).

For 0 ≤ t ≤ 2:

In this interval, the function F(t) is constant, as it is defined as F(t) = 2. The function value remains the same regardless of the value of t.

Therefore, the function is constant on the interval [0, 2].

For t > 2:

In this interval, the function F(t) = -t + 4 is a linear function with a negative slope. As t increases, the function value decreases.

Therefore, the function is decreasing on the interval (2, ∞).

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The measure of the angle CDE is 170 degrees

To determine the value, we have that;

The formula for calculating the sum of the interior angles of a polygon is expressed as;

(n -2)180

Where 'n' is the number of the sides of the polygon

Substitute the values

5(180) = 900 degrees

Equate the angles

2x + 9 + 2x + 11 + 3x - 1 + 2x - 7 + 2x - 3 + 3x -8 + 2x - 13 = 900

collect the like terms, we get;

16x = 900 + 12

16x = 912

Divide by the coefficient

x = 57

Angle CDE = 3x -1 = 3(57) - 1 = 171 -1 = 170 degrees

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To map Figure T to Figure U, we can use the following sequence of transformations:

Translation: Move the figure 10 units to the right and 12 units down.

This will shift all the points in Figure T by the specified distances.

Reflection: Reflect the figure across the vertical axis.

This will reverse the order of the points horizontally.

Translation: Move the figure 5 units to the right and 10 units up.

This will shift all the points in Figure T (which is now reflected) by the specified distances.

The resulting sequence of transformations would be:

Translation (10 units right, 12 units down) -> Reflection (across the vertical axis) -> Translation (5 units right, 10 units up)

Applying these transformations to Figure T should result in Figure U.

Answer:

[tex]\mathrm{x=34^o}[/tex]

Step-by-step explanation:

[tex]\mathrm{Since\ A\ and\ B\ are\ complementary\ angles,}\\\mathrm{\angle A+\angle B=90^o}\\\mathrm{or,\ (x+22)^o+x^o=90^o}\\\mathrm{or,\ 2x+22^o=90^o}\\\mathrm{or,\ 2x=68^o}\\\mathrm{or,\ x=34^o}[/tex]

The value of x is :

Solution:

If two angles are complementary, their sum is 90°.

Since A and B are complementary, we know that :

[tex]\rm{A+B=90}[/tex]

The values are x + 22 and x, respectively.

[tex]\rm{x+22+x=90}[/tex]

Combine like terms.

[tex]\rm{2x+22=90}[/tex]

[tex]\rm{2x=68}[/tex]

Divide each side by 2.

[tex]\rm{x=34}[/tex]

The value of the other angle is:

[tex]\rm{x=34+22}[/tex]

[tex]\rm{x=56}[/tex]

Answer:

5*9=45

9\45=5

5/45=9

Step-by-step explanation:

It is essential for a table to meet both criteria to represent a valid function.

Based on the given information, it appears that the table in question does not represent a function. This is because a function requires each element in the domain to be associated with exactly one element in the range (Statement B).

If any element in the domain has more than one corresponding element in the range, it violates the definition of a function.

Additionally, the table fails to show a function because each output does not have exactly one input (Statement D). In a true function, every output value should be associated with only one input value. If any output has multiple inputs, it indicates that the table is not a function.

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The minimum distance between the two balls is: 5 + (Robinson's vertical velocity) * t - (1/2) * g * [tex]t^2[/tex] = 6 + (Derek's vertical velocity) * t - (1/2) * g * [tex]t^2[/tex]

Using the given information, we can calculate the horizontal and vertical components of Robinson's initial velocity:

Robinson's horizontal velocity: 45 ft/sec * cos(44 degrees)

Robinson's vertical velocity: 45 ft/sec * sin(44 degrees)

Using the given information, we can calculate the horizontal and vertical components of Derek's initial velocity:

Derek's horizontal velocity: 41 ft/sec * cos(39 degrees)

Derek's vertical velocity: 41 ft/sec * sin(39 degrees)

For Robinson's ball:

Robinson's y-coordinate at time t = 5 ft + (Robinson's vertical velocity) * t - (1/2) * g * [tex]t^2[/tex]

For Derek's ball:

Derek's y-coordinate at time t = 6 ft + (Derek's vertical velocity) * [tex]t - (1/2) * g * t^2[/tex]

Set these two equations equal to each other and solve for t:

5 + (Robinson's vertical velocity) *[tex]t - (1/2) * g * t^2 = 6[/tex] + (Derek's vertical velocity) * t - (1/2) * g * [tex]t^2[/tex]

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The equation is 13x + 2 = 15x - 2.

The value of x is 2.

The measure of the angles are:

BGF is 28.

EHC is 28.

EGB is 152.

FHD is 28.

We have,

From the figure,

BGF and EHC are alternate angles.

Since AB and CD are parallel lines.

Now,

FHC and EHD are opposite angles.

Since they share the same common point.

Now,

The equation is:

BGF and EHC are alternate angles.

This means,

13x + 2 = 15x - 2

2 + 2 = 15x - 13x

4 = 2x

x = 2

Now,

BGF = 13x + 2 = 13 x 2 + 2 = 26 + 2 = 28

EHC = 15x - 2 = 15 x 2 - 2 = 30 - 2 = 28

Now,

BGF + EGB = 180

EGB = 180 - 28 = 152

And,

EHC and FHD are alternate angles.

so,

FHD = 28

Thus,

The equation is 13x + 2 = 15x - 2.

The value of x is 2.

The measure of the angles are:

BGF is 28.

EHC is 28.

EGB is 152.

FHD is 28.

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Answer:

x = 1

Step-by-step explanation:

To solve the given equation, we'll start by setting up the equation and simplifying it step by step:

The product of (x + 3) and (2x + 3) is 14 more than the product of (x + 1) and (2x + 1).

(x + 3)(2x + 3) = (x + 1)(2x + 1) + 14

Expanding both sides of the equation:

2x^2 + 3x + 6x + 9 = 2x^2 + x + 2x + 1 + 14

Combining like terms:

2x^2 + 9x + 9 = 2x^2 + 3x + 15

Subtracting (2x^2 + 3x + 15) from both sides:

2x^2 + 9x + 9 - 2x^2 - 3x - 15 = 0

Simplifying:

6x - 6 = 0

Adding 6 to both sides:

6x = 6

Dividing both sides by 6:

x = 1

Therefore, the value of x that satisfies the equation is x = 1.

Hope this helps!

i think option c must be the answer

The scale factor used in the dilation is 3.

First, the distance between points A and B in triangle ABC is:

AB = √[(x₂ - x₁)² + (y₂ - y₁)²]

AB = √[(1 - (-1))² + (1 - (-1))²]

AB = √[(2)² + (2)²]

AB = √[4 + 4]

AB = √8

The distance between points A' and B' in triangle A'B'C' is:

A'B' = √[(x₂' - x₁')² + (y₂' - y₁')²]

A'B' = √[(3 - (-3))² + (3 - (-3))²]

A'B' = √[(6)² + (6)²]

A'B' = √[36 + 36]

A'B' = √72

The scale factor can be determined by dividing the corresponding side lengths:

Scale factor = A'B' / AB

Scale factor = √72 / √8

Scale factor = (√(72/8))

Scale factor = √9

Scale factor = 3

Therefore, the scale factor used in the dilation is 3.

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The perimeter of a rectangle with a length of Eight and one-sixth feet and a width of Six and two-thirds feet is  twenty-nine and four-sixths

The length of the rectangle is [tex]8\frac{1}{6}[/tex] feet, which can be written as a mixed number: 8 + 1/6 = 49/6 feet.

The width of the rectangle is [tex]6\frac{2}{3}[/tex]  feet, which can also be written as a mixed number: 6 + 2/3 = 6 2/3 = 20/3 feet.

To find the perimeter, we add twice the length and twice the width:

Perimeter = 2(length) + 2(width)

Perimeter = 2(49/6) + 2(20/3)

Perimeter = (98/6) + (40/3)

Perimeter = 98/6 + 80/6

Perimeter = 178/6

To simplify the fraction, we can divide the numerator and denominator by their greatest common divisor, which is 2:

Perimeter = (178/6) ÷ 2

Perimeter = 89/3

So, the perimeter of the rectangle is 89/3 feet. To express it as a mixed number:

Perimeter =[tex]29\frac{2}{3}[/tex] feet

Therefore, twenty-nine and four-sixths feet is the  perimeter of a rectangle with a length of Eight and one-sixth feet and a width of Six and two-thirds feet

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The critical value, given the sample size of 5 and the confidence level of 99. 0 percent would be 16. 812.

The critical values for the chi-squared (χ^2) distribution depend on the degree of freedom and the level of significance.

The degree of freedom for a chi-squared distribution typically equals the sample size minus 1 so the degrees of freedom here is:

= 5 - 1

= 4

The level of significance would be:

= 1 - 99. 0 %

= 0. 01

The critical value of the sample would therefore be found on a chi -squared distribution table for df = 4 and α = 0.01 to be 16. 812.

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The  local minima at (-2, 0) and (-3, 0), and the local maxima at (1, 3) and (0, 3).

To determine the local minima and maxima of the polynomial function based on the given points:

Since the point (-2, 0) is on the graph, it represents a local minimum.

Since the point (1, 3) is on the graph, it represents a local maximum.

Since the point (-2, 0) is on the graph, it represents a local minimum.

Since the point (0, 3) is on the graph, it represents a local maximum.

Since the point (-3, 0) is on the graph, it represents a local minimum.

Since the point (1, 3) is on the graph, it represents a local maximum.

Since the point (-3, 0) is on the graph, it represents a local minimum.

Since the point (0, 3) is on the graph, it represents a local maximum.

Therefore, based on the given points, the local minima at (-2, 0) and (-3, 0), and the local maxima at (1, 3) and (0, 3).

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Rounded to the nearest tenth, a 4-inch segment of the chain weighs approximately 53.3 ounces.

To find the weight of a 4-inch segment of the chain, we need to convert the given weight in pounds per foot to ounces per inch. Here's the solution:

1 foot = 12 inches
1 pound = 16 ounces

Given: The chain weighs 10 pounds per foot.
First, convert this weight to ounces:
10 pounds/foot × 16 ounces/pound = 160 ounces/foot

Now, we need to convert the weight from ounces per foot to ounces per inch:
160 ounces/foot ÷ 12 inches/foot = 13.33 ounces/inch (approximately)

Finally, calculate the weight of a 4-inch segment of the chain:
4 inches × 13.33 ounces/inch ≈ 53.32 ounces

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Answer:

The selling price of the car is $152,220.

Step-by-step explanation:

To find the selling price of a car that is sold at a loss of 14% on the cost price, we can follow these steps:

Calculate the amount of the loss:

Loss = 14% of the cost price

Loss = 14/100 * $177,000

Subtract the loss from the cost price to find the selling price:

Selling Price = Cost Price - Loss

Selling Price = $177,000 - (14/100 * $177,000)

Simplify the expression:

Selling Price = $177,000 - ($24,780)

Selling Price = $152,220

The  length of boundary ABCD is 23.1

The length BC is the length of an arc subtended by angle 120 degrees at the center of a circle of radius 5.

The length of an arc, l, subtended by an angle, x degrees, in the center is given by l = 120 / 360 x pi x 2r

Thus, BC = 120 / 360 x 3.14 x 2 x 5 = 10.4667

Similarly, length DA is the length of an arc subtended by angle 30 degrees at the center of a circle of radius 5.

DA = 30/360 x 3.14 x 2 x 5 = 2.6167

Therefore, the approximate length of boundary ABCD

= 5 + 10.4667 + 5 + 2.6167

= 23.0834

= 23.1

Hence, the approximate length of boundary ABCD is 23.1

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The Price per gram is $60, you will receive 2/3 of a gram of the product.

The product get $40 out of the $60 cost, we can set up a proportion based on the price per gram.

1. Let's denote the amount of product you will receive as x grams.

2. According to the given information, the price per gram is $60.

3. The total cost of the product can be calculated by multiplying the price per gram by the amount of product: $60/gram * x grams.

4. The amount of money you have available is $40.

5. We can set up a proportion to find the amount of product you will receive:

  ($60/gram * x grams) / $40 = 1

6. To solve for x, we can cross-multiply and solve for x:

  ($60/gram * x grams) = $40 * 1

7. Simplifying the equation, we have:

  $60x = $40

8. To isolate x, we divide both sides of the equation by $60:

  x = $40 / $60

9. Calculating the right side of the equation, we find:

  x = 2/3

Therefore, if you only have $40 and the price per gram is $60, you will receive 2/3 of a gram of the product.

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The two Skyscrapers are approximately 7670.51 feet apart.

The distance between the two skyscrapers, we can use trigonometry and the given information about the angle of inclination and the height of skyscraper B. Let's break down the problem step by step.

1. Let's denote the distance between the bases of the two skyscrapers as d.

2. We can visualize the situation as a right triangle, where the height of skyscraper B (1463 feet) represents the opposite side and the distance between the two buildings (d) represents the adjacent side. The angle of inclination (10.5°) is the angle between the adjacent side and the hypotenuse.

3. The trigonometric function that relates the opposite side, adjacent side, and the angle of inclination is the tangent (tan) function: tan(angle) = opposite/adjacent.

4. Plugging in the known values, we have tan(10.5°) = 1463/d.

5. To solve for d, we can rearrange the equation: d = 1463 / tan(10.5°).

6. Evaluating the tangent of 10.5° using a calculator, we find that tan(10.5°) is approximately 0.1908.

7. Now, substituting this value into the equation, we have d = 1463 / 0.1908.

8. Calculating the right side of the equation, we find that d is approximately 7670.51 feet.

Therefore, the two skyscrapers are approximately 7670.51 feet apart.

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[tex]2^3 + 3^3 - 5[/tex] :

[tex]\sf\:2^3 + 3^3 - 5 = 8 + 27 - 5 \\ = 35 - 5 \\ = 30[/tex]

Therefore, [tex]2^3 + 3^3 - 5[/tex] equals 30.

Answer:

5 weeks

Step-by-step explanation:

the two linear equations are:

sibling (A)      and  sibling (B)

y = 10x + 25   and y = 5x + 50

where y = mx + c

and x represents the number of weeks

after how many weeks will their savings accounts have the same amount of money i.e. for which value of x will both equations have the same value

inserting the value of x in both equations:

for x = 2.5  A = 50 and B = 62.5

for x = 5     A = 75  and B = 75

for x = 15    A = 175 and B = 125

for x = 75   A = 775 and B = 425

thus, after 5 weeks both siblings A and B will have the same amount of money in their accounts

The value of x (the perpendicular side) in the given triangle is 6√5 cm.

Let's denote the length of the perpendicular side as x.

Given that the hypotenuse is 14 cm and the base is 4 cm.

As per the Pythagoras's theorem, we can set up the equation:

x² + 4² = 14²

x² + 16 = 196

To solve for x, we subtract 16 from both sides of the equation:

x² = 180

Taking the square root of both sides, we get:

x = √180

Simplifying the square root:

x = √(36 × 5)

x = 6√5

Therefore, the value of x (the perpendicular side) is 6√5 cm.

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I) 1. The slope (m) of a line is 150.

2. The equation of the line is y = 150x.

II) 1. The slope (m) of a line is 100.

2. The equation of the line is y = 100x.

To estimate the line of best fit using the given points (1, 150) and (6, 900), we can follow these steps:

1. The slope (m) of a line passing through two points (x₁, y₁) and (x₂, y₂) is given by the formula:

m = (900 - 150) / (6 - 1)

m = 750 / 5

m = 150

2. We can use the point-slope form of a linear equation to write the equation of the line:

y - y₁ = m(x - x₁)

So, y - 150 = 150(x - 1)

y - 150 = 150x - 150

y = 150x

So, the equation of the line is y = 150x.

3. The slope of the line represents the change in y (sales) for each unit increase in x (TV ads). In this case, the slope is 150, which means that for every TV ad, CD sales increase by about 150 units.

Similarly, using the points (1, 100) and (8, 800) to estimate the line of best fit:

II) 1. the slope of the line:

m = (800 - 100) / (8 - 1)

m = 700 / 7

m = 100

and, the equation of the line:

y - 100 = 100(x - 1)

y - 100 = 100x - 100

y = 100x

So, the equation of the line is y = 100x.

and, the slope of the line represents the change in y (sales) for each unit increase in x (magazine ads). In this case, the slope is 100, which means that for every magazine ad, CD sales increase by about 100 units.

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Answer:

The domain of a radical function is the set of all real numbers for which the function is defined. In this case, we have the function f(x) = √(x + 1) - 3.

For the function to be defined, the value inside the square root (√) must be non-negative, since the square root of a negative number is undefined in the real number system.

So, to determine the domain, we set the expression inside the square root greater than or equal to zero:

x + 1 ≥ 0

Solving for x:

x ≥ -1

Therefore, the domain of the given radical function is all real numbers greater than or equal to -1. In interval notation, the domain can be expressed as (-1, +∞).

The value of x from equation 2 doesn't satisfy equation 1. Thus, there is no solution for this system of equations, meaning the given equations are inconsistent.

To solve the given system of equations, we have:

1) -x^2 + 12x + 14 = 0
2) 2x + 30 = 0

First, solve equation 2 for x:
2x = -30
x = -15

Now, substitute the value of x in equation 1:
-(-15)^2 + 12(-15) + 14 = 0
-225 - 180 + 14 = 0
-391 ≠ 0
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Answer:

(12 × 3) × 8 = 12 × (3 × 8)

Step-by-step explanation:

The associative property of multiplication states that the way in which factors are grouped in a multiplication expression does not change the product. In other words, if we have three or more numbers to multiply, it doesn't matter which order we multiply them in.

Out of the given number sentences, the example of the associative property of multiplication is:

(12 × 3) × 8 = 12 × (3 × 8)

This is because we can group the factors in either of the two ways and get the same product.

Hope this helps!