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Which set of angles can form a triangle?
2 acute and 1 right
1 acute and 2 right
1 acute, 1 right, and 1 obtuse
1 acute and 2 obtuse

The measure of the angle ∠5 in the parallel line is 98 degrees.

When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate interior angles, alternate exterior angles, vertically opposite angles, linear angles, same side interior angles etc.

Therefore, lets' find the angle 5 in the parallel lines as follows:

Hence,

∠5 = 180 - 82(same side interior angles)

∠5 = 98 degrees

Same side interior angles are supplementary.

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Answer:

x = 12.1

Step-by-step explanation:

Answer8000x-10000=14200+5000x

2000x=24200

24200/2000=13.1

Answer:

24

Step-by-step explanation:

i dont know if its correct

Answer:

y= -3x+1

Step-by-step explanation:

x1= -2 x2=2 y1=7 y2=-5

using the formula

(y-y1)/(x-x1)=(y2-y1)/(x2-x1)

(y-7)/(x-(-2))=(-5-7)/(2-(-2))

(y-7)/(x+2)=(-5-7)/(2+2)

(y-7)/(x+2)=(-12)/4

(y-7)/(x+2)=-3

cross multiply

y-7=-3(x+2)

y-7=-3x-6

y=-3x-6+7

y=-3x+1

Answer:

7

Step-by-step explanation:

f(-1) = -2(-1)+5

f = 2+5

f = 7

Answer:

The smallest perfect square that is exactly divisible by 10, 12, and 15 is 900.

Step-by-step explanation:

The explanation is:

A perfect square is a number that is the product of two equal integers. For example, 25 is a perfect square because it is 5 times 5.

A number that is exactly divisible by 10, 12, and 15 must have all the prime factors of these numbers in its prime factorization. The prime factors of 10 are 2 and 5, the prime factors of 12 are 2 and 3, and the prime factors of 15 are 3 and 5. Therefore, the number must have at least two 2s, one 3, and one 5 in its prime factorization.

To make the number a perfect square, each prime factor must appear an even number of times. Therefore, we need to add another 2, another 3, and another 5 to the prime factorization. The number becomes 2 x 2 x 2 x 2 x 3 x 3 x 5 x 5, which is equal to 900.

We can check that 900 is a perfect square by finding its square root. The square root of 900 is 30, which is an integer. We can also check that it is exactly divisible by 10, 12, and 15 by dividing it by these numbers. The quotients are all integers: 90, 75, and 60 respectively.

Solving a quadratic equation, it is found that the largest possible value of a is of a = 5.

A quadratic equation is modeled by the following rule:

y = ax + bx + c

The solutions of the equations are the values of x for which y = 0.

For this problem, the equation is:

a² - 6a - 9 = b.

b = -9 - a, hence we replace in the equation as follows;

a² - 6a - 9 = -9 - a

a² - 5a = 0.

Traditionally, the solutions are given using Bhaskara's formula, however, since the coefficient c is zero, we can solve the equation by elimination as follows:

a² - 5a = 0.a(a - 5) = 0

Then the solutions are:

a = 0.

a - 5 = 0 -> a = 5.

5 > 0, hence the largest possible value of a is of a = 5.

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Answer:1 16

Step-by-step explanation:

The answer is : sinL = 9/41, cosL = 40/41, and tanL = 9/40.

In a right triangle, the side opposite the right angle is called the hypotenuse, and the other two sides are called the legs. We have been given that the side lengths of the right triangle are 9, 40, and 41 as shown below.

To find the sine, cosine, and tangent ratios of the angle L, we first need to identify which side of the triangle corresponds to the hypotenuse and which sides correspond to the legs. In this case, the hypotenuse is the side with length 41, and the legs are the sides with lengths 9 and 40.

Using these values, we can find the sine, cosine, and tangent ratios using the following formulas:

- Sine (sinL) = opposite side / hypotenuse = 9 / 41

- Cosine (cosL) = adjacent side / hypotenuse = 40 / 41

- Tangent (tanL) = opposite side / adjacent side = 9 / 40

These trigonometric ratios represent the relationships between the side lengths in the right triangle and the angle L. They are often used in real-world applications such as engineering, physics, and navigation.

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When you deposit x dollars in Account B instead of Account A, you would earn an additional 0.045x dollars in interest per year.

We need to compare the interest earned from each account.

The interest earned for Account A with a 1.5% simple annual interest rate can be computed as follows:

Interest A = (Simple interest rate A / 100) * Principal A

The calculation of the interest earned for Account B with a simple yearly interest rate of 6% is as follows:

Interest B = (Simple interest rate B / 100) * Principal B

Subtracting the interest earned in Account A from the interest earned in Account B yields the difference in interest:

Difference in interest = Interest B - Interest A

Let's plug in the values and calculate the difference:

Difference in interest = ((6 / 100) * x) - ((1.5 / 100) * x)

= (0.06x) - (0.015x)

= 0.045x

Therefore, when you deposit x dollars in Account B instead of Account A, you would earn an additional 0.045x dollars in interest per year.

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Group B has lower range.

Group A shows variability.

Mean is the best to make concussion about age of Salsa students.

Upon visual examination, it appears that Group A is likely to have a lower average age of music students compared to Group B.

This inference is supported by the observation that the majority of data points in Group A are concentrated around younger ages such as 6, 8, 9, 11, and 13. In contrast, Group B exhibits a more dispersed distribution of data points across a wider range of ages, including higher ages like 19 and 21.

So, Group B has lower range.

and, Group A shows variability.

Lastly, Mean is the best to make concussion about age of Salsa students.

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Answer:

7((x-2)(3x+4))

Step-by-step explanation:

Common factor of 7 in this quadratic formula. [tex]7(3x^2-2x-8)[/tex]; -8 * 3x^2 = -24x^2, now find factors of this product that equal to -2x when added. The factors that fit this is -6x and 4x. So, if you make a generic rectangle you can find the product.  You get 7((x-2)(3x+4))

The graph of this equation will exhibit a symmetrical heart-shaped curve.

The equation r² = 64cos(2θ) represents a polar curve.

The given equation is in the form of a polar equation, where r represents the radial distance from the origin, and θ represents the angle measured from the positive x-axis.

The equation r²= 64cos(2θ) represents a cardioid, which is a type of curve. It has a characteristic heart-shaped pattern.

The equation implies that the distance from the origin squared, represented by r, is determined by the cosine function of twice the angle, 2θ, multiplied by 64.

When plotted, the graph of this equation will exhibit a symmetrical heart-shaped curve.

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The calculated perimeter of the triangle is 3/5

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

The side lengths: 1/5, 1/5 and 1/5

This means that the triangle is an equilateral triangle

The perimeter of an equilateral triangle is calculated as

Perimeter = 3 * side length

substitute the known values in the above equation, so, we have the following representation

Perimeter = 3 * 1/5

Evaluate

Perimeter = 3/5

Hence, the perimeter of the triangle is 3/5

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The answer is option (B) 3/8, the probability of getting the color purple is 3/8.

To calculate the probability of getting the color purple, we need to consider the total number of colors and the number of times purple appears.

Given:

Green = 90°

Orange = 90°

Red = 45°

Purple = 135°

There are a total of 360° in a circle, representing all possible outcomes.

To calculate the probability, we divide the number of degrees for purple by the total number of degrees:

Probability of getting purple = Degrees for purple / Total degrees

Degrees for purple = 135°

Total degrees = 360°

Probability of getting purple = 135° / 360°

Simplifying the fraction:

Probability of getting purple = 3/8

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[tex]\phi =\{u : u\neq u\}[/tex] means that the set is empty and has no element in it.

[tex]\phi =\{u : u\neq u\}[/tex] is a set notation that represents the empty set. In set theory, the empty set, denoted by the symbol [tex]\phi[/tex] or {}.

An empty set is defined as a set that does not contain any elements and it is just empty or null.

For this question,  [tex]\phi =\{u : u\neq u\}[/tex], the set is defined using a condition or property.

The condition given is u ≠ u, which is always false for any element. So we can say that it implies that there is no element that satisfies the condition u ≠ u, meaning there are no elements in the set. Hence, the set is empty.

Thus, the given symbol in set expression represents an empty set.

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The length of EF is  35. 4 yd

To determine the value of the side, we need to know the different trigonometric identities.

These identities are listed as;

From the information given, we have that;

The angle, theta = 40 degrees

Hypotenuse = 55yd

Opposite side = EF

Using the sine identity, we have that;

sin 40 = EF/55

cross multiply the values

EF = 0. 6427(55)

Multiply the values

EF = 35. 4 yd

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The central angle is approximately 2.357 radians.

To find the central angle, we can use the formula:

Central angle (θ) = arc length ÷ radius

Given:

Arc length (mXY) = 18 in

Radius (ZY) = 7.64 in

Plugging in the values:

Central angle (θ) = 18 in ÷ 7.64 in

Calculating the division:

θ ≈ 2.357 radians

Therefore, the central angle is approximately 2.357 radians.

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The sampling that would most likely introduce a sampling error is (a) Choosing the first 10 events for the sample

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

The list of options

Also, we have

Tosses = 20

From the list of options, we have

(a) Choosing the first 10 events for the sample

This techique will introduce a sampling error because the selection done by the sampling is not a random selection

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The correct option is not available among the choices provided (A. 49.4, B. 39.5, C. 55.2, D. 50.45).

To find the measure of angle A in triangle ABC using the Law of Sines, we can use the formula:

sin(A)/a = sin(B)/b = sin(C)/c

Given that a = 14, b = 17, and c = 22, we can substitute these values into the formula:

sin(A)/14 = sin(B)/17 = sin(C)/22

To find angle A, we need to solve for sin(A) and then take the inverse sine (arcsin) of that value.

First, let's find sin(B) using the given information:

sin(B)/17 = sin(A)/14

sin(B) = (17 * sin(A))/14

Next, let's find sin(C):

sin(C)/22 = sin(A)/14

sin(C) = (22 * sin(A))/14

Since the sum of angles in a triangle is 180 degrees, we can calculate angle C:

angle C = 180 - angle A - angle B

Now, we can substitute the expressions for sin(B) and sin(C) into the equation:

(22 * sin(A))/14 = (17 * sin(A))/14 + sin(B)

To solve for sin(A), we can multiply both sides of the equation by 14:

22 * sin(A) = 17 * sin(A) + 14 * sin(B)

22 * sin(A) - 17 * sin(A) = 14 * sin(B)

5 * sin(A) = 14 * sin(B)

sin(A) = (14/5) * sin(B)

Finally, we can take the inverse sine (arcsin) of sin(A) to find the measure of angle A:

A = arcsin((14/5) * sin(B))

Now, since the values of angles B and C are not provided, it is not possible to directly determine the measure of angle A using the given information.

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Answer:

¿Por qué borraste mi comentario? ¿Es porque hablo español? Lo lamento

Step-by-step explanation:

Answer:

-18$

Step-by-step explanation:

Pepe will have a loan of 18$ since they don't have 20 dollars but Billy took it away

peep have 18dollars.

20-2

=18

The measure is MN = 19. 05 ft

To determine the value of the variable, we have that;

The different trigonometric identities are expressed as;

From the information given, we have that;

The opposite side of the triangle is MN

The adjacent side is 11ft

Using the tangent identity;

tan θ = opposite/adjacent

substitute the values

tan 60 = MN/11

cross multiply the values, we have;

MN = 1.73(11)

MN = 19. 05 ft

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Answer: x = 15

Step-by-step explanation:

4x + 2x = 90 (the square in the corner indicates a 90deg angle)

6x = 90

x/6 = 90/6

x = 15

Additive inverse property of real numbers was used to transition from step 3 to step 4

The property of real numbers used to transition from Step 3 to Step 4 is the additive inverse property or the property of adding the opposite. The additive inverse property states that for any real number a, there exists an additive inverse -a, such that a + (-a) = 0. In other words, adding the opposite of a number results in the sum being zero.

In Step 3 of the given expression, we have "12 + (-12) + 6x." Notice that "-12" is the opposite of "12." To simplify this expression further, we can apply the additive inverse property by combining the positive and negative numbers.

Adding 12 and its additive inverse (-12) results in 0, according to the additive inverse property. So, in Step 4, we replace "12 + (-12)" with "0." By applying the additive inverse property, the expression simplifies to "0 + 6x," which can be further simplified to just "6x."

The use of the additive inverse property is crucial in algebraic simplifications as it allows us to eliminate terms that add up to zero. This property helps streamline calculations and reduce complex expressions to simpler forms.

Overall, the transition from Step 3 to Step 4 in the given expression utilizes the additive inverse property to eliminate the sum of opposite numbers and simplify the expression to its final form, which is "6x."

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A decrease in the term from 30 years to 20 years on any rate will give the greater reduction in total interest paid .

Given,

Circumstances on which interest will be lower .

Now,

Consider decrease in the term from 30 years to 20 years on any rate of interest .

Let us assume the principal to be $100.

Let us assume the rate of interest to be 1% .

Now for simple interest,

Firstly let time period be 30 years .

SI = P*R*T/100

SI = $100 *1*30/100

SI = $30

Secondly the time period will be 20 years

SI = P*R*T/100

SI = $100 *1*20/100

SI = $20

Hence,

The reduction in interest is 33. 33% which is highest among all the other given options .

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Answer:

A) Bicycle: Circumference: 188.4cm  

                   Distance of 100 Turns: 18840cm

                   Diameter: 60

B) In-line skate: Circumference: 25.12cm

                         Distance of 100 Turns: 2512cm

                          Diameter: 8

C) Skateboard: Circumference:  15.7cm

                         Distance of 100 Turns: 1570cm

                         Diameter: 5

Step-by-step explanation:

The circumference would be one turn. So, you simply multiply the circumferences by 100.

A) 188.4 x 100 = 18840

B) 25.12 x 100 = 2512

C) 15.7 x 100 = 1570