Which of the following statements must be true based on the diagram below?
Select all that apply. (Diagram is not to scale.)

The probability that the area of the triangle is at most 20 is 5/9

Probability is a measure of the likelihood of an event occurring. The probability formula is defined as the possibility of an event happening is equal to the ratio of the number of favorable outcomes and the total number of outcomes. Probability of event to happen P(E) = Number of favorable outcomes/Total Number of outcomes.

Given here: Right triangle XYZ has legs of length XY = 12 and YZ = 6. Point D is chosen at random within the triangle XYZ. Thus area of triangle XYZ is

1/2×12×6=36

Now if the area of the triangle is at most 20 then the required probability is = 20/36

                      =5/9

Hence, The probability that the area of the triangle is at most 20 is 5/9

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An equation which has one (1) solution include the following: D. |W| = 0.

In Mathematics, an absolute value function can be defined as a type of function that is composed of an algebraic expression, which is placed within absolute value symbols and measures the distance of a point on the x-coordinate to the x-origin (0) of a cartesian coordinate (graph).

Mathematically, an absolute value function can be represented by this mathematical expression:

|x| = x, x ≥ 0.

|x| = x, x < 0.

Generally speaking, an equation or absolute value function would have exactly one (1) solution when there is only one (1) value for the variable (W) that makes the equation to be true as shown below:

|W| = 0

W = ±0

W = 0

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Answer:

x = 6[tex]\sqrt{2}[/tex]

Step-by-step explanation:

using the cosine ratio in the right triangle and the exact value

cos45° = [tex]\frac{1}{\sqrt{2} }[/tex] , then

cos45° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{6}{x}[/tex] = [tex]\frac{1}{\sqrt{2} }[/tex] ( cross- multiply )

x = 6[tex]\sqrt{2}[/tex]

This is the exact value for x. It may be rounded if you wish

Answer:

[tex]x=6\sqrt{2}[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{9.4 cm}\underline{Trigonometric ratios} \\\\$\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}[/tex]

From inspection of the given right triangle:

Substitute the given values into the cosine trigonometric ratio and solve for x:

[tex]\implies \cos(45^{\circ})=\dfrac{6}{x}[/tex]

[tex]\implies \dfrac{\sqrt{2}}{2}=\dfrac{6}{x}[/tex]

[tex]\implies x\sqrt{2}=6 \cdot 2[/tex]

[tex]\implies x\sqrt{2}=12[/tex]

[tex]\implies x=\dfrac{12}{\sqrt{2}}[/tex]

[tex]\implies x=\dfrac{12}{\sqrt{2}}\cdot \dfrac{\sqrt{2}}{\sqrt{2}}[/tex]

[tex]\implies x=\dfrac{12\sqrt{2}}{2}[/tex]

[tex]\implies x=6\sqrt{2}[/tex]

Answer:

it is undefined

Step-by-step explanation:

Slope of the line x=-24 is undefined. We'll compare the line x = -24, with x = h. So this line is a vertical line that is parallel to the y-axis. We know that the slope of the y-axis is undefined. Since x=-24 and y-axis are parallel, so x=-24 will have the same slope, that is undefined.

Answer:

undefined slope

Step-by-step explanation:

When you have the line x=-24, you have a vertical line, where the x-value is constant, given in the equation, but the y-value varies between negative infinity and positive infinity. If we were to plug two points into the slope formula, we would get: [tex]\frac{y_2-y_1}{-24-(-24)}\to\frac{y_2-y_1}{0}[/tex], because there is no change in x, the x values are the same. Thus it is said that the slope is undefined.

Answer:

−12r+32−2r 2

Step-by-step explanation:

(−8−r)(2r−4)

Apply the distributive property by multiplying each term of −8−r by each term of 2r−4.

−16r+32−2r

2

+4r

Combine −16r and 4r to get −12r.

Answer:

R-12

Step-by-step explanation:

Open the parenthesis, then solve

-8-r + 2r-4

-r+2r-8-4

r-12

Your answer will be R-12

The coordinates of the vertices of polygon A'B'C'D' after the dilation are given as follows:

A'(-2, -2), B'(0, 2), C'(4,4), D'(4,-2).

A dilation happens when the coordinates of the vertices of an image are multiplied by the scale factor, changing the side lengths of a figure.

The vertices of the original polygon for this problem are given as follows:

A(-1,-1), B (0, 1), C (2, 2), and D (2, -1).

The scale factor for the dilation in this problem is given as follows:

k = 2.

Hence the coordinates of the vertices of polygon A'B'C'D' after the dilation are given as follows:

A'(-2, -2), B'(0, 2), C'(4,4), D'(4,-2).

(as each coordinate of each vertex was multiplied by the scale factor of 2).

The problem is incomplete, hence the coordinates of the vertices of the image after the dilation were obtained to show how the dilation works.

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Answer:

Step-by-step explanation:

the ratio of the circumference of any circle to the diameter of that circle. Regardless of the circle's size, this ratio will always equal pi. In decimal form, the value of pi is approximately 3.14.

Rewriting the sum in the form a(b+c) such that the integers b and c have a common factor. 35+42 is 7(5 + 6).

The process of factorization simply has to do with the division of arithmetic algebraic expressions into the sum of their factors. in this case, multiplying the variables will yield the original expression. It means the writing of a number into smaller or simpler numbers that give the original number.

The common factor to both 35 and 42 is 7. This will be:

35 + 42 = 7(5 + 6)

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Complete question

How do i rewrite the sum in the form a(b+c) such that the integers b and c have a common factor. 35+42

The distance the treat falls before Lola catches the treat is 3.5 feet.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

The distance of the treat from the ground = 5 feet.

The distance the dog jumps to catch the treat from the ground = 1.5 feet.

Now,

The distance the treat fall before Lola catches.

= 5 - 1.5

= 3.5 feet

Thus,

The treat falls for 3.5 feet.

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Answer:

-3/4

Step-by-step explanation:

y=mx+b is in slope-intercept form, in which m=-3/4 and b=7, describing the slope and y-intercept of a linear equation respectively.

The relative frequency table that summarizes the data is given by the image at the end of the answer.

The number of desired experiment results divided by the total number of experiment results is used to compute the relative frequency of an event in an experiment.

Given:

The percentage of people interested in waterskiing

= 90/250 x 100

= 36%.

Thus, the percentage of people that was not interested in waterskiing is

=100-36

= 64%

Now, the percentages related to paddle boarding are :

Yes: 72/250 = 28.8%.

No: 18/250 = 7.2%.

Of those not interested in waterskiing, the percentages related to paddle boarding are

Yes: 112/250 = 44.8%.

No: (120 - 72)/250 = 19.2%.

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Answer: 5. 2x+8  6. 5(x-9)   7. -3x+-21

Step-by-step explanation: Multiply the number outside the parenthesis by everything inside it

First, we assume that this conclusion is false. In other words, we assume that the contrary statement "none of the two angles has measure [tex]90^{\circ}[/tex] or greater" is true.

The assumption is equivalent to the following two statements:

(1) [tex]m\angle A\text{ } \boxed{ < 90^{\circ}}[/tex]

(2) [tex]m\angle B\text{ } \boxed{ < 90^{\circ}}[/tex]

Using (1) and (2) and the addition properties of inequalities, we conclude that [tex]m\angle A+m\angle B \text{ } \boxed{ < } \text{ } 180^{\circ}[/tex].

On the other hand, two adjacent angles form a linear pair. Thus, the last statement contradicts the Linear Pair Property, which states that for a linear pair of angles [tex]\angle A[/tex] and [tex]\angle B[/tex], [tex]m\angle A+m\angle B \text{ } \boxed{=} \text{ } 180^{\circ}[/tex].

Therefore, the assumption made is false, and the statement "at least one of the angles [tex]\angle A[/tex] and [tex]\angle B[/tex] has measure [tex]90^{\circ}[/tex] or greater" is true.

The minimum is the smallest value in the data set. The maximum is the largest value in the data set.

We will set the first derivative of the function to zero and solve for x to get the critical point. If we take the second derivative or f''(x), then we can find out whether this point will be a maximum or minimum. If the second derivative is positive, it will be a minimum value.

A minimum or a maximum is called an extreme point. A local extreme point is the smallest or largest value in its neighborhood. If it is also the smallest or largest at the entire domain of the function, it is called a global extreme point. The local minima and maxima can be found by solving f'(x) = 0.

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Complete question is: What is the difference between Minimum or maximum value?

Answer:

7.5 units

Step-by-step explanation:

5-(-2.5)=7.5

a. The area of the parallelogram ABCD in this problem is given as follows: 24 units squared.

b. The fraction of the area of the parallelogram that is shaded is given as follows: 1/4. (option C).

The area of a parallelogram is given by the multiplication of the length of the base by the height, as follows:

Area = base x height.

The base and the height for this problem are obtained counting the number of dots, hence:

Hence the area is given as follows:

Area = 4 x 6

Area = 24 units squared.

The shaded region is composed by a triangle with base 4 and height 3, hence:

Area shaded = 0.5 x 4 x 3 = 6 units squared.

(formula for the area of the triangle).

Meaning that the fraction is given as follows:

6/24 = 1/4.

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The end behavior of the function f(x) = 1/9 x¹² is

The end behavior of the function f(x) = -1/10 x¹⁸ is

The end behavior of function typically says the characteristics of the function at the ends

The given function is:

f(x) = 1/9 x¹²

The positive exponents will mean that x will always yield positive values hence f(x) is always positive

f(x) = -1/10 x¹⁸

The positive exponents will mean that x will always yield positive values however the negative constant -1/10 will make f(x) always negative hence f(x) is always negative

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Therefore , the solution of the given problem of expression comes out to be probably 4 slices.

In mathematics, it is possible can multiply, division, add, or remove. The construction of an expression is as follows: Expression, number, and mathematical operator Numbers, variables, and functions are the building blocks of a mathematical expression. Expressions and phrases can be contrasted.

Here,

you figure if a toaster takes about 1-2 minutes to toast a piece of bread  and a toaster usually can fit 2 slices at a time i would say 4.

Preheat oven broil to high. Move oven rack to highest position.

Place sliced bread on an ungreased baking sheet. 4 slices of bread.

Broil bread for 1 minute, or until golden brown, then flip and broil for another 20-30 seconds. ...

Top with butter, jam, or any other favorite topping!

The temperature needed for the hot ambient air in a toaster, which makes the bread turn brown, is around 310°F (146°C). The heating element inside a toaster is a nickel-chromium alloy. The electrical current that runs through it heats it to make it red hot, with a temperature of 1,100°F to 1,200°F (519°C to 566°C).

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Answer: The equation of a line in the form y = mx + b can be written as y - mx - b = 0. So we can rewrite the equation of the line as 2y - 3x + 5 = 0. This means that the slope of the line is -3/2.

The slope of a line perpendicular to this line would be the negative reciprocal of -3/2, which is 2/3. Let's call the point M (x, y). We know that the line passing through (2, 6) has a slope of 2/3. So we can write the equation of this line as:

y - (2/3)x - b = 0

Substituting the point (2, 6) into this equation, we get:

6 - (2/3)(2) - b = 0

b = 4

So the equation of the line passing through (2, 6) is:

y - (2/3)x - 4 = 0

To find the coordinates of point M, we need to find the point where these two lines intersect. Setting the two equations equal to each other and solving for x and y, we get:

2y - 3x + 5 = y - (2/3)x - 4

5 - 2y = y - (5/3)x + 4

(5/3)x = 3 - y

x = (3 - y) * (3/5)

Substituting this expression for x into one of the original equations, we can solve for y:

2y - 3((3 - y) * (3/5)) + 5 = 0

2y - (9 - 3y)(3/5) + 5 = 0

(10/5)y - (9/5) + 5 = 0

y = (9/5) + (5/5)

y = 2

Substituting this value for y back into the expression for x, we get:

x = (3 - 2) * (3/5)

x = 1

So the coordinates of point M are (1, 2).

Step-by-step explanation:

The expression A' represents the statement for all of the elements which are not in set A.

A set is a collection of well defined objects.

Given that A students wants to write an expression for all of the elements which are not in set A.

The elements within set A are denoted by A.

We have to find  all of the elements which are not in set A.

U represents the universal set and A is the given set.

A'=U-A

Hence, the expression A' represents the statement for all of the elements which are not in set A.

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The compound ratio of natural number ratios 2 : 3 and 5 : 4 is equal to 5 : 6.

Herein we must determine a compound ratio, that is, the product of two ratios, whose definition is shown below:

For a : b and c : d, where a, b, c, d are natural numbers, the compound ratio is equal to (a · c) / (b · d).

If we know that a : b = 2 : 3 and c : d = 5 : 4, then the compound ratio is equal to:

r = (2 · 5) : (3 · 4)

r = 10 : 12

Finally, we simplify the resulting expression:

r = 5 : 6

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The values of a , b and c from the equation is ( 3 , 0 , -1 )

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

( 6 × 10ᵃ ) + ( 6 × 10ᵇ ) + ( 6 × 10^c ) = 6006.6   be equation (1)

Now , the number 6006.6 is written as

6000 + 6 + 0.6 = 6006.6

On simplifying the equation , we get

( 6 × 10ᵃ ) = 6000

Divide by 6 on both sides of the equation , we get

10ᵃ = 1000

So , 10ᵃ = 10³

Therefore , the value of a = 3

Now , ( 6 × 10ᵇ ) = 6

Divide by 6 on both sides of the equation , we get

10ᵇ = 1

when b = 0

10⁰ = 1

Therefore , the value of b = 0

Now , ( 6 × 10^c ) = 0.6

Divide by 6 on both sides of the equation , we get

10^c = 0.1

when c = -1

10⁻¹ = 0.1

Therefore , the value of c = -1

Hence , the value of a , b and c is 3 , 0 and -1 respectively

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On solving the provided question, we can say that - here in the percentage obtained = 500 => so, 500/1000X100 = 50%

A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. It is frequently denoted using the percent symbol "%," though. The amount of percentages has no dimensions. With a denominator of 100, percentages are basically fractions. To show that a number is a percentage, place a percent symbol (%) next to it. For instance, if you correctly answer 75 out of 100 questions on a test (75/100), you receive a 75%. To compute percentages, divide the amount by the total and multiply the result by 100. The percentage is calculated using the formula (value/total) x 100%.

here,

total is = 1000

obtained = 500

so, 500/1000X100 = 50%

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Answer:

(a)  13.9 blocks (nearest tenth)

(b)  32.9 blocks (nearest tenth)

Step-by-step explanation:

The given scenario can be modeled as a right triangle.

If Amy walks south 7 blocks, one leg of the triangle is 7.

If Amy then walks west 12 blocks, the other leg of the triangle is 12.

To calculate the number of blocks Amy walks on her way home if she walks directly from school to her home, find the length of the hypotenuse of the right triangle.

[tex]\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}[/tex]

Substitute a = 7 and b = 12 into Pythagoras Theorem and solve for c (hypotenuse):

[tex]\implies 7^2+12^2=c^2[/tex]

[tex]\implies 49+144=c^2[/tex]

[tex]\implies 193=c^2[/tex]

[tex]\implies c=\sqrt{193}[/tex]

[tex]\implies c=13.8924439894...[/tex]

Therefore, Amy walks 13.9 blocks (nearest tenth) on her way home.

To calculate the number of blocks Amy walks in one day for her round trip to school and back home, sum the side lengths of the right triangle:

[tex]\implies 7 + 12 + 13.9 = 32.9[/tex]

Therefore, Amy walks 32.9 blocks (nearest tenth) in one day for her round trip to school and back home.

A number between 47 and 53 such that the prime factors are not repeated is:

3*17 = 51

Remember that any number can be written as a product of prime factors.

If we want to find a number between 47 and 53, such that there are no repeated factors, we just need to take different primes and multiply them.

For example:

2*3*5*7 = 210

There are no repeated factors, but the number is not in the desired range.

2*5*7 = 70

Still not in the range.

You can try some times until you get for example:

3*17 = 51

This a number in the desired range, such that their prime factors are not repeated.

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The solution to the product expression 4/3 * 5/3 is 20/9

From the question, we have the following parameters that can be used in our computation:

The product 4/3*5/3

To start with, we need to represent the statement as an expression

So, we have the following representation

4/3 * 5/3

Using a calculator, we multiply the numerator

So, we have the following representation

4/3 * 5/3 = 20/3 * 1/3

Using a calculator, we multiply the denominator

So, we have the following representation

4/3 * 5/3 = 20/9

Hence, the solution is 20/9

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