100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!

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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The HCF of 360, 456, and 696 using the division method is 24.

To find the highest common factor (HCF) of 360, 456, and 696 using the division method, we can follow these steps:

Step 1: Begin by dividing the largest number (696) by the smallest number (360). Record the quotient and the remainder.

696 ÷ 360 = 1 remainder 336

Step 2: Now, divide the divisor (360) by the remainder (336) obtained in the previous step.

360 ÷ 336 = 1 remainder 24

Step 3: Repeat step 2 by dividing the previous remainder (336) by the new remainder (24).

336 ÷ 24 = 14 remainder 0

Step 4: Since the remainder has become zero, the divisor at this point (24) is the HCF of the given numbers.

Therefore, the HCF of 360, 456, and 696 using the division method is 24.

The division method for finding the HCF involves repeated division of the given numbers until the remainder becomes zero. At each step, we divide the divisor by the remainder obtained in the previous step. The process continues until the remainder becomes zero.

The divisor at that point is the HCF. In this case, we divided 696 by 360, then 360 by 336, and finally 336 by 24 until the remainder became zero. The last divisor we obtained, which is 24, is the HCF of the given numbers.

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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 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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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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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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Answer:

  168 bedrooms

Step-by-step explanation:

You want the number of bedrooms Greg and his partner can paint in 24 hours if they can individually paint 4 and 3 bedrooms per hour, respectively.

The total work is the product of (work per time) and (time).

  total work = Greg's work + Partner's work

  total work = (4 bdrm/h)(24 h) +(3 bdrm/h)(24 h)

  total work = 96 bdrm + 72 bdrm = 168 bdrm

Greg and his partner can paint 168 bedrooms in 24 hours.

__

Additional comment

This is a little different than the usual "working together" problem. Often the individual rates are given as "time per work", 4 hours per bedroom, for example.

If the work rates were 4 hours and 3 hours per bedroom, respectively, then in 24 hours, they could paint 6 + 8 = 14 bedrooms.

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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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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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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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Answer:

7

Step-by-step explanation:

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

f = 2+5

f = 7

[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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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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The linear equation models this situation showing the relationship between her pay (p)and pairs of shoes (s) sold is p = 5s + 25.

It is an equation with one or more variables in which each variable has an exponent equal to one and there can be no multiplication or division between them. Thus, ax + by = 0 is a linear equation, because the variable is x and its exponent is equal to one (x¹) and the variable y also has an exponent equal to one (y¹).

Knowing that:

With this information we can write the equation as:

[tex]p = 5s + 25[/tex]

Therefore, the equation multiplies the number of pairs of shoes by 5 and adds the base salary of $25 to calculate her total pay.

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Answer:

x = 12.1

Step-by-step explanation:

Answer8000x-10000=14200+5000x

2000x=24200

24200/2000=13.1

we have

--------> inequality A

--------> inequality B

Using a graphing tool

the solution of the inequality A is the shaded area above the dashed line  

see the attached figure N        

the solution of the inequality B is the shaded area below the dashed line  

see the attached figure N

therefore

the solution of the compound system of inequalities is the shaded area between the two dashed lines

see the attached figure N

therefore

the answer in the attached figure N

Answer: 6 days 6 hours 50 minuets.

Step-by-step explanation:

Separate each unit of time and add them up:

5 days , 29 hours, 110 minuets.

since there are 24 hours in a day, you will add one to days and subtract 24 from hours.

6 days, 5 hours and 110 minuets.

60 minuets are in an hour, to simplify it, you subtract 60 from 110 mins and carry that 1 to hours.

6 days, 5 hours and 50 mins.

Hope this helps:D

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.

Answer:

  Part A:  (b) (7, 6)

  Part B:  (c) (-6, -4)

Step-by-step explanation:

You want the coordinates of points of rectangle PQRS that have been subject to rotation, reflection, and translation.

Rotation 90° CCW is accomplished by the transformation ...

  (x, y) ⇒ (-y, x)

Then point R gets rotated to ...

  R(6, -7) ⇒ R'(7, 6)

Reflection across the y-axis changes the sign of the x-coordinate:

  (x, y) ⇒ (-x, y) . . . . . . reflection in the y-axis

Translation adds the translation amount to the relevant coordinate:

  (x, y) ⇒ (x, y -2) . . . . translation down 2 units

Together, the effect on point Q is ...

  (x, y) ⇒ (-x, y -2)

  Q(6, -2) ⇒ Q''(-6, -4)

__

Additional comment

You can figure the transformation related to rotation by considering "where did it come from?"

If a point ends up on the x-axis after a rotation of 90° CCW, it had to come from the -y axis.

If a point ends up on the y-axis after a rotation of 90° CCW, it had to come from the +x axis.

These observations can be written as the transformation ...

  (x, y) ⇒ (from -y, from +x) = (-y, x) . . . . . . rotation 90° CCW

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Answer:

24

Step-by-step explanation:

i dont know if its correct

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

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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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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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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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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