Use the trapezoid shown to mark each statement below as true or false. If false, rewrite the statement correctly in the space below the statement.

1. The length of line AB can be found using 3^2 + b^2 = 4^2.

2. The perimeter of the trapezoid shown is 22 units.

Answer:

B.......................

The range of the function is the set of all real numbers greater than or equal to -2, because the lowest possible value of the function is -2, which occurs at x = 2.

What is a piecewise function ?

A piecewise function is a function that is defined by different equations on different parts of its domain. The graph of a piecewise function consists of several distinct parts, each corresponding to a different equation.

The graph shown is an example of a piecewise function. The function is defined using different equations on different intervals of the domain.

On the interval from negative infinity to negative 2, the function is defined by the equation y = 2. This means that the value of the function is always 2 on this interval, regardless of the value of x.

On the interval from negative 2 to 2, the function is defined by the equation y = -x. This means that the value of the function is equal to the negative of x on this interval.

On the interval from 2 to positive infinity, the function is defined by the equation y = 2. This means that the value of the function is always 2 on this interval, regardless of the value of x.

At the point x = -2, the function experiences a discontinuity, because the two equations that define it have different values at this point. The function is not differentiable at this point, because it does not have a well-defined tangent line.

The domain of the function is the set of all real numbers, because there are no restrictions on the values of x that are allowed.

Therefore, The range of the function is the set of all real numbers greater than or equal to -2, because the lowest possible value of the function is -2, which occurs at x = 2.

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Using the product rule of logarithms, we can condense the expression as follows:

log(x/3 * y/3 * z/3)

= log((xyz) / 27)

So, the condensed form of the given expression is log((xyz) / 27).

The skater's total score would be 58 points (7.25 x 8 = 58).

Just dividing the total number of values in a data set by the sum of all of the values yields it. A frequency table of data or raw data can both be used for the calculation.

The following equation can be used to determine each skater's overall score, s, assuming that they each receive evaluations from eight judges and have a mean score of 7.25 points:

s = 7.25 x 8

The total score is determined by multiplying the average score by the quantity of judges in this equation. In this instance, the skater would have earned 58 points overall (7.25 x 8 = 58).

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In a skating competition each skater receives scores from eight judges a skater has a mean (average) of 7.25 points. Write an equation to find the skaters total score?

a. 7.25 × 8

b. 7.25⁸

c. 7.25 - 8

d. 7.25/8

Answer:The leading term in a polynomial is the term with the highest degree.

Step-by-step explanation:

Step-by-step explanation:

y = 3 x^2 - 4 x - 1

leading coefficient is 3  and its sign is ' + '   or positive

Answer:

260

Step-by-step explanation:

First you find the area of the triangle

1/2×base×height

1/2×20×10

=100

Then you find the area of the rectangle

A=l×b

=20×8

=160

Then you add the area of the triangle with the area of the rectangle

160+100=260

The value of x that makes A parallel to B is 15.

Alternate exterior angles are a pair of angles that lie outside of two parallel lines and are on opposite sides of the transversal. In other words, they are a pair of non-adjacent angles that are formed when a transversal intersects two parallel lines. The angles are congruent, meaning that they have the same measure.

The term "alternate" refers to the fact that they are on opposite sides of the transversal and "exterior" indicates that they are outside of the parallel lines. Alternate exterior angles are important in geometry because they can be used to prove that two lines are parallel. If the alternate exterior angles are congruent, then the lines are parallel.

Since the alternate exterior angles are equal, we can set them equal to each other:

8x + 30 = 10x

Subtracting 8x from both sides, we get:

30 = 2x

Dividing both sides by 2, we get:

15 = x

So the value of x that makes A||B is 15.

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Answer:

Matt's typing speed increased by 18.75%.

Step-by-step explanation:

To find the percent increase, we can use the following formula:

percent increase = (new value - old value) / old value x 100%

Using this formula, we can calculate the percent increase in Matt's typing speed as follows:

percent increase = (38 - 32) / 32 x 100%

percent increase = 6 / 32 x 100%

percent increase = 0.1875 x 100%

percent increase = 18.75%

Answer:

168 cm^2

Step-by-step explanation:

This rhombus is made up of two triangles. To find triangle area, base x height/2 (but bc there are two triangles we don’t need to divide by 2). To do this, 14 x 12 to get 168cm^2

Answer:

85 degrees.

Step-by-step explanation:

These are parallelograms, meaning the opposite sides are parallel. Since they are parallel, that the line EA becomes a transversal and a bisector for the angle CEK. That means the angle 8 and 3 are equivalent and 7 and 4 are equivalent. This is due to Same Side Interior Angles. These are two halves of the big angle. If the halves are equal, so are the angles. Therefore, CEK = CAK.

Answer: what shape?

Step-by-step explanation:

More info please

The values of x that could make the triangle into different types of triangles are:

For a triangle to be valid, the sum of the lengths of any two sides must be greater than the length of the third side.

Right Triangle:

A triangle is a right triangle if it satisfies the Pythagorean theorem: a² + b² = c², where c is the longest side (hypotenuse).

6² + 8² = x²

36 + 64 = x²

100 = x²

x = 10

Acute Triangle:

A triangle is acute if the sum of the squares of the two shorter sides is greater than the square of the longest side. Since we already know that the right triangle has x = 10, we can choose a value for x that is less than 10 to form an acute triangle.

Let's take x = 9:

6² + 8² > 9²

36 + 64 > 81

100 > 81

Obtuse Triangle:

A triangle is obtuse if the sum of the squares of the two shorter sides is less than the square of the longest side. We can choose a value for x that is greater than 10 to form an obtuse triangle.

Let's take x = 11:

6² + 8² < 11²

36 + 64 < 121

100 < 121

The possible values of x for each triangle type are:

Right Triangle: x = 10

Acute Triangle: x = 9

Obtuse Triangle: x = 11

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(a) The relative rate of growth of the bacterium population is 15% per unit time; (b) the initial population of the culture is 90 bacteria; (c) the culture will contain approximately 239 bacteria at time t=5.

(a) The relative rate of growth of the bacterium population can be calculated by taking the derivative of the function n(t) with respect to t and then dividing it by the value of n(t) at that point, which gives:

relative rate of growth = (dn/dt) / n(t)

= (0.15 * 90[tex]e^0.15t[/tex]) / (90[tex]e^0.15t[/tex])

= 0.15

Therefore, the relative rate of growth is 15%.

(b) The initial population of the culture at t=0 is given by plugging in t=0 in the function n(t):

n(0) = 90[tex]e^0.15[/tex]*0

= 90

Therefore, the initial population of the culture is 90.

(c) The number of bacteria in the culture at time t=5 can be found by plugging in t=5 in the function n(t):

n(5) = 90[tex]e^0.15[/tex]*5

= 385.97 (rounded to two decimal places)

Therefore, the culture will contain approximately 385.97 bacteria at time t=5.

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Answer:2.04

Step-by-step explanation:

Answer:

26° 180 -81 - 73 = 26

Step-by-step explanation:

Answer:

26

Step-by-step explanation:

triangle= 180

81 + 73 = 154

180 - 154= 26

The blanks of the number pyramid puzzle can be filled with numbers calculated below.

A number pyramid puzzle is a type of mathematical puzzle where a pyramid-shaped grid of numbers is given, with some of the numbers missing.

Check the attached image for labeling. Since each number is the product of the two numbers directly beneath it. We can say:

m = -4 * 0.5 = -2

k = 0.5 * 1/8 = 1/16

x * (-1/8) = 8

x = 8/(-1/8)

x = -64  

y = x * 1/8

y = -64 * 1/8

y = -8

j = m * k

j =  -2 * 1/16 = -1/8

p = -48 * m

p = -48 * (-2) = 96

n = y * 8

n = -8 * 8 = -64

t = p * j

t = 96 * (-1/8) = -12

w = -1/2 * n

w = -1/2 * (-64) = 32

c = t * 1/16

c = -12 * 1/16 = -3/4

u = 1/16 * w

u = 1/16 * 32 = 2

d = c * u

d = -3/4 * 2 = -3/2

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Because the x2 term's coefficient is positive, the function will rise without  equation bound as x approaches infinity or negative infinity. As a result, no horizontal asymptote exists.

An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x + 3" equals the number "9".

The y-intercept of the equation y = (0,0) is the point on the line where it meets the y-axis and corresponds to the value of y when x equals 0. As a result, the equation y = 0's y-intercept is (0,0).

An equation's domain is the set of all possible values of x for which the equation is defined.

a) Because there are no constraints on the potential values of x, the domain of the equation y = x2 - 4x is all real integers.

b) The domain of the equation y = 1/(x-4) includes all real numbers except x = 4, which is undefined since division by zero is undefined.

c) Because the term within the square root must be non-negative, the domain of the equation y = sqrt(x-3)(x-4) is x >= 3.

As x approaches a specific value, the graph of the function approaches but never reaches vertical asymptotes. As the denominator of a rational function hits 0, they arise.

Because y = (x-3)(x-4) is not a rational function, it lacks vertical asymptotes.

A function's horizontal asymptote is a horizontal line that it approaches when x approaches infinity or negative infinity.

The dominant term in the formula as x gets extremely large or very tiny is x2, thus we can rewrite the equation as [tex]y = x2 - 7x + 12[/tex]  .

Therefore, Because the x2 term's coefficient is positive, the function will rise without bound as x approaches infinity or negative infinity. As a result, no horizontal asymptote exists.

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The angles and lines that match the angles and lines in the diagram consisting of two lines and their common transversal to the correct description  are;

Alternate Interior Angles; 2. ∠4 and ∠8

Consecutive Exterior  Angles; 5. ∠1 and ∠6

Alternate Exterior Angles; 3. ∠1 and ∠5

Transversal; line l

Consecutive Interior Angles; 4. ∠3 and ∠4

Corresponding Angles; 1. ∠1 and ∠7

A transversal is a line that intersects two or more other lines.

The description of the relationship between the angles in the question are;

Alternate Interior Angles

Alternate interior angles are a pair of angles formed when a transversal intersects two lines. They are located between the two lines on opposite side of the transversal.

Consecutive Exterior Angles

Consecutive Exterior Angles are a pair of angles formed when a transversal intersects two lines. They are located outside the two lines on the same side of the transversal

Alternate Exterior Angles

Alternate exterior angles are a pair of angles formed when a transversal intersects two lines. They are located outside the two lines on the opposite sides of the transversal.

Consecutive Interior Angles

Consecutive Interior Angles, also known as Same-Side Interior Angles are a pair of angles formed when a transversal intersects two parallel lines. They are located between the two parallel lines on the same side of the transversal.

Corresponding Angles

Corresponding angles are a pair of angles formed when a transversal intersects two lines. They are located on the same relative positions with respect to the transversal and the two lines.

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Answer: it depends; if exam day, no

Step-by-step explanation:

In the equation y = 10 - 0.1x, the coefficient 0.1 represents the slope of the line.

it represents the rate of change of y with respect to x, which is the amount by which y changes for every unit increase in x.

In this case, the slope is negative (-0.1), which means that as the number of minutes on hold (x) increases by 1 unit, the level of satisfaction (y) decreases by 0.1 units.

In other words, the longer a customer spends on hold, the lower their level of satisfaction is likely to be. The slope is a key parameter in the equation and provides valuable information about the relationship between the two variables.

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Answer:

There is 5% of the juice left.

Step-by-step explanation:

We know that originally, the container had 80 oz of orange juice, this is 100% in our case.

Then we can write a relation:

80 oz = 100%

Now there are 4 ounces left, in the same way as before, we can write this as:

4 oz = X%

We want to find X%

First, let's write our equations:

4 oz = X%

80 oz = 100%

We can take the quotient between these two equations to get:

(4oz/80oz) = (X%/100%)

We need to solve this for X%, then we get:

(4oz/80oz)*100% = X% = 5%

This means that 4 oz is 5% of the initial volume of the juice container.

Then we can conclude that there is 5% of the juice left.

The graph is increasing from 0 minutes to 40 minutes, decreasing from 40 minutes to 80 minutes, and constant from 80 minutes to 200 minutes.

The rate of global warming is increasing. Every year, average global temperatures continue to rise, leading to more extreme weather events and disruptions to the environment. This has been caused by human activities, such as burning fossil fuels, which release carbon dioxide and other greenhouse gases into the atmosphere. These gases trap heat, leading to a rise in temperatures.

The domain of the relation is the set of all time values, ranging from 0 minutes to 200 minutes. The range of the relation is the set of all depth values, ranging from 0 feet to 8 feet.

The graph represents a function because for every value of time, there is exactly one corresponding value of depth.

The graph shows the depth of water in a horse trough over a certain amount of time. The graph starts at 0 feet and increases to a maximum of 8 feet over the first 40 minutes. After 40 minutes, the depth of the water starts to decrease until it reaches a minimum of 2 feet at 80 minutes. After 80 minutes, the depth of the water remains constant at 2 feet until the end of the graph at 200 minutes.

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All corresponding side lengths have a ratio of [tex]\frac{1}{3}$[/tex] or less, we can conclude that the scale factor of the dilation is less than or equal to [tex]\frac{1}{3}$[/tex]

We can use the distance formula to find the length of the sides of both quadrilaterals, and then find the ratio of corresponding side lengths to determine the scale factor of the dilation.

Let's start with the original quadrilateral ABCD. The length of AB is:

[tex]$\sqrt{(9 - (-3))^2 + (3 - 0)^2} = \sqrt{12^2 + 3^2} = \sqrt{153}$[/tex]

Similarly, the lengths of BC, CD, and DA are:

[tex]BC: $\sqrt{(9 - 9)^2 + (9 - 3)^2} = 6$[/tex]

[tex]CD: $\sqrt{(-3 - 9)^2 + (3 - 9)^2} = \sqrt{144 + 36} = \sqrt{180} = 6\sqrt{5}$[/tex]

[tex]DA: $\sqrt{(-3 - (-3))^2 + (3 - 0)^2} = 3$[/tex]

Now, let's find the corresponding side lengths of the dilated quadrilateral A'B'C'D'. The length of A'B' is:

[tex]$\sqrt{(3 - (-1))^2 + (1 - 0)^2} = \sqrt{16 + 1} = \sqrt{17}$[/tex]

Similarly, the lengths of B'C', C'D', and D'A' are:

[tex]B'C': $\sqrt{(3 - 3)^2 + (3 - 1)^2} = 2$[/tex]

[tex]C'D': $\sqrt{(-1 - 3)^2 + (1 - 3)^2} = \sqrt{16 + 4} = \sqrt{20} = 2\sqrt{5}$[/tex]

[tex]D'A': $\sqrt{(-1 - (-3))^2 + (1 - 0)^2} = \sqrt{4 + 1} = \sqrt{5}$[/tex]

Now we can find the ratio of corresponding side lengths:

[tex]$\frac{\text{length of A'B'}}{\text{length of AB}} = \frac{\sqrt{17}}{\sqrt{153}} = \frac{\sqrt{17} \cdot \sqrt{153}}{153} \approx 0.821$[/tex]

[tex]$\frac{\text{length of B'C'}}{\text{length of BC}} = \frac{2}{6} = \frac{1}{3}$[/tex]

[tex]$\frac{\text{length of C'D'}}{\text{length of CD}} = \frac{2\sqrt{5}}{6\sqrt{5}} = \frac{1}{3}$[/tex]

[tex]$\frac{\text{length of D'A'}}{\text{length of DA}} = \frac{\sqrt{5}}{3}$[/tex]

Since all corresponding side lengths have a ratio of [tex]\frac{1}{3}$[/tex] or less, we can conclude that the scale factor of the dilation is less than or equal to [tex]\frac{1}{3}$[/tex]. To find the exact scale factor, we can choose any two corresponding side lengths and take their ratio.

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Answer:

Step-by-step explanation:

To find the LCM of the given expressions, we need to factor each expression completely and then find the product of the highest powers of all the factors.

ax² - (a² + ab)x + a²b can be factored as:

ax² - (a² + ab)x + a²b = a(x - b)(x - a)

bx² - (b² + bc)x + b²c can be factored as:

bx² - (b² + bc)x + b²c = b(x - c)(x - b)

cx² - (c² + ac)x + c²a can be factored as:

cx² - (c² + ac)x + c²a = c(x - a)(x - c)

Now, the LCM is the product of the highest powers of all the factors.

The highest power of a is a², the highest power of b is b², and the highest power of c is c². So, the LCM is:

LCM = a²b²c²(x - a)(x - b)(x - c)

Therefore, the LCM of ax² - (a² + ab)x + a²b, bx² - (b² + bc)x + b²c and cx² - (c² + ac)x + c²a is a²b²c²(x - a)(x - b)(x - c).

Step-by-step explanation:

y = x^2 / z      now triple x and z

y = (3x)^2 / 3z = 9x^2 / 3z = 3 * x^2 / z  <==== this is 3 times the original

    y is tripled

The constant of proportionality of this table  is: k = 1/7.

The ratio between two quantities that are directly proportional is the constant of proportionality.

When y and x are two values that are direct proportion to one another, the proportionality constant k is defined as k=y/x.

Thus, using the x and its respective y values.

As the values are in direct proportion.

The constant of proportionality is:

k = 1/7

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Answer:

1039.23 square inches

Step-by-step explanation:

                      a = 20 inches

    [tex]\sf \boxed{\text{\bf Area of regular hexagon = $\dfrac{3\sqrt{3}}{2}a^2$}}[/tex]

                                                   [tex]= \dfrac{3\sqrt{3}}{2}*20*20\\\\= 3\sqrt{3}*200\\\\= 1039.23 \ inches^2[/tex]

Answer:

  -15

Step-by-step explanation:

You want the average rate of change of g(x) = 3x² +3 on the interval [-9, 4].

The average rate of change is defined as ...

  AROC(g) = (g(b) -g(a))/(b -a)

We can evaluate this directly, or we can simplify it a bit first.

 AROC = ((3b² +3) -(3a² +3))/(b -a)

  = (3b² -3a²)/(b -a)

  = 3(b -a)(b +a)/(b -a)

  = 3(b +a)

The AROC on the interval [a, b] = [-9, 4] is then ...

  AROC = 3(4 +(-9)) = 3(-5)

  AROC = -15

__

Additional comment

In the attachment, a graphing calculator is used to evaluate the rate of change directly from the definition. It gives the same value, as expected.