Mathematics College

Set up an equation for x and solve to the nearest degree

Answers

Answer 1

In the right triangle, the value of x is approximately 64°

Trigonometry: Solving for the value of x

From the question, we are to set up an equation for x and then solve for the value of x.

To determine the value of x, we will use SOH CAH TOA

sin (angle) = Opposite / Hypotenuse

cos (angle) = Adjacent / Hypotenuse

tan (angle) = Opposite / Adjacent

In the given diagram,

x is the included angle

Adjacent = 12

Opposite = 25

Thus,

We can write that

tan (x) = 25/12

tan (x) = 2.0833

x = tan⁻¹ (2.0833)

x = 64.3586

x ≈ 64° (to the nearest degree)

Hence,

The value of x is approximately 64°

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Related Questions

What is the base of the following natural logarithm?
In(x)
O 1
O 10
O e

Answers

The base of the natural logarithm ln(x) expression is 10

What is the base of the natural logarithm?

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

ln(x)

The base of the above expression is not stated

The general rule of logarithm is that when the base of the expression is not stated, then the base is 10

If the base of the expression is stated, then the expression would take the form

lnₐ(x), where the base is represented with the variable a

This means that the base of the natural logarithm ln(x) expression is 10

Answers

In 58 seconds after starting its descent, the aircraft will touch down.

The plane will land when its altitude y is zero.

So we can set y = 0 in the equation:

0 = 464 - 8x

Solving for x:

8x = 464

x = 58

Therefore, the plane will land 58 seconds after it begins its descent.

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We often use the phrase "to the power of" when talking about exponents. For example, x¹3 is
referred to as x to the power of 13. Why do you think that they would name it like this? How does
increasing the exponent of a number increase its "power"?
Hint: Use a number as an example. (for instance 2) if you keep increasing the power, what happens
to the answer? (i.e. compare 2¹, 2^2, 2^3, 2^4,..., 2^13, 2^14,... until you see the answer you are looking
for!)

Answers

In mathematics, the expression "to the power of" pertains to the exponent, signifying how many times a key number is to be multiplied by itself.

What is the exponents about?

Expressing this idea in English can be done well by using the term "to the power of." To show this, 2 raised to the third power can be interpreted as 2 multiplied by itself three times, resulting in 8.

Therefore, the possible reason behind using the word "power" is probably due to the fact that when the exponent rises, the outcome number is wide, either being greater or smaller, made on the base being above or below 1. This implies that the figure holds more significant value.

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Becky worked part-time at a restaurant. The amount of money she earned for each of six weeks is shown.
$50, $82, $39, $50, $31, $70
Becky earned $23 for working a seventh week. Which statement for these seven weeks is true?
OA. The median decreases and the mean remains the same.
OB. The mean and the median both decrease.
OC. The median and the mean both remain the same.
OD. The mean decreases and the median remains the same.

Answers

Answer:

Step-by-step explanation:

To answer this question, we need to calculate the mean and median of the given data set and then see how the additional earnings affect them.

First, let's calculate the mean of the original data set:

Mean = (50 + 82 + 39 + 50 + 31 + 70) / 6 = 322 / 6 = 53.67

Next, let's calculate the median of the original data set. To do this, we need to arrange the data set in order:

31, 39, 50, 50, 70, 82

The median is the middle value, which is 50.

Now, let's add Becky's earnings of $23 to the data set:

31, 39, 50, 50, 70, 82, 23

The new data set has 7 values. Let's calculate the new mean:

Mean = (50 + 82 + 39 + 50 + 31 + 70 + 23) / 7 = 365 / 7 = 52.14

The new mean is less than the original mean, so we can eliminate options A and C.

Now let's calculate the new median. We need to arrange the data set in order:

23, 31, 39, 50, 50, 70, 82

The median is still 50.

Therefore, the answer is option D: The mean decreases and the median remains the same.

new car is purchased for 18700 dollars. The value of the car depreciates at
14.25% per year. To the nearest year, how long will it be until the value of the
car is 3000 dollars?

Answers

The minimum time required to depreciate the value of the car is 12 years.

Let us assumed the time to be t. Representing the formula for calculation of time-

Final value = Principal value × [tex] {(1 - rate of depreciation)}^{t} [/tex]

Keeping the values in formula to find the time period

3000 = 18700 × [tex] {(1 - 14.25%)}^{t} [/tex]

Solving the expression

[tex] {(0.8575)}^{t} [/tex] = 3000/18700

Cancelling zeroes common in numerator and denominator

3000/18700 = [tex] {(0.8575)}^{t} [/tex]

Taking log on both sides of the equation

t log 0.8575 = 30/187

Keep the value

t = log 0.8575 30/187

t = 12 years

Hence, it will take 12 years for value depreciation.

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graph the following linear inequalities: y < -2+7

Answers

The graph of the inequality is added as an attachment

How to determine the graph

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

y < -2 + 7

The above expression is an inequality that implies that

The value of y is less than the sum of -2 and 7

Next, we plot the graph

See attachment for the graph of the inequality

Answers

92 more students favor visiting Florida than Colorado

How many more students favor visiting Florida than Colorado?

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

Students = 400

Florida = 38%

Colorado = 15%

The percentage difference is

Difference = 38% - 15%

So, we have

Difference = 23%

This means that

Students = 23% * 400

Evaluate

Students = 92

Hence, the number of students is 92

Answers

The distance between the areas of the two states is A = 1.727 x 10⁵ km²

Given data ,

Let the area of Nebraska = 2 x 10⁵ km²

Let the area of Massachusetts = 2.73 x 10⁴ km²

The difference between the areas of Nebraska and Massachusetts A = the area of Nebraska - the area of Massachusetts

On simplifying the exponents , we get

A = 2 x 10⁵ km² - 2.73 x 10⁴ km²

Taking the common factor , we get

A = 10⁴ ( 20 - 2.73 )

A = 10⁴ ( 17.27 )

A = 1.727 x 10⁵ km²

Hence , the area is A = 1.727 x 10⁵ km²

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What is the style of William Holman Hunt's The Awakening Conscience (1853)?

Pre Raphaelite

Impressionism

Nabis

Realism

Answers

Answer:

The style of William Holman Hunt's The Awakening Conscience (1853) is Pre-Raphaelite.

Abe purchased a candle at the candle store. The candle is nine inches long and the packaging states the candle burns down at the rate of 1/2 an inch per hour. Write a function to determine the length of the candle, y, after burning for x number of hours.

Answers

The function to determine the length of the candle, y, after burning for x number of hours is y = 9-x/2

Given that, a candle is nine inches long and the packaging states the candle burns down at the rate of 1/2 an inch per hour.

We need find function to determine the length of the candle, y, after burning for x number of hours.

Since, the melting rate of the candle is 1/2 per hour,

So, the function will be =

y = 9-x/2

Hence, the function to determine the length of the candle, y, after burning for x number of hours is y = 9-x/2

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Explain how decimal place value is like place value with whole numbers. Use pictures or words to explain your thinking.

Answers

The tenths place is represented by the first digit following the decimal. The hundredths place is represented by the digit that follows the decimal.
Up until there are no more digits, the remaining ones keep the place values filled in.

mrs. watson is buying vintage records for a friend at a local records shop. Thre price of a record is based on its condition. The table shows the total cost of x number of records for each condition.

Answers

The equation for total cost of buying and shipping the records is

76.4x + 80

We have,

She buys 3 in good condition

So, the cost for 3 good condition

= 3 (10.5x)

= 31.5 x

and, She buys 1 in Fair condition

So, the for 1 fair condition

= 5x

and, She buy 2 new condition then the price is

= 39.9 x

So, the equation for total cost of buying and shipping the records is

= 31.5x + 5x + 39.9x + 8

= 76.4x + 8

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I need help with this please

Answers

Answer: a. d. f.

Step-by-step explanation:

A rectangular prism is 38 centimeters long, 18 centimeters wide, and 13 centimeters high. What is the surface area of the rectangular prism?'

Answers

Answer:

53,352 cm

Step-by-step explanation:

1. The first step is to draw the rectangle draw one rectangle over the other and start labeling the sides.

2. After labeling use the rectangle prism formula: L times W times H in this case it would be 38 times 18 times 13 this is equal to 8,892.

3. From there, we know that there are six sides so we can multiply this value by 6 so it would be 8,892 times 6 = 53,352 cm.

If I made a mistake or if have any questions feel free to tell me!

-Mathematics and Science Major for Middle School Students at Harvard University

I really need help please
Applying the Solution to a 3X3 System

At a family reunion, there only blood relatives, consisting of children, parents, and grandparents, in attendance. There were 400 people total. There were twice as many parents as grandparents, and 50 more children than parents. How many children, parents, and Grandparents were in attendance?

Show up all steps please

Answers

Using an equation, the number of children, parents, and grandparents in attendance were:

Children = 190Parents = 140Grandparents = 70.

What is an equation?

An equation is an algebraic statement showing the equality or equivalence of two or more mathematical expressions.

Mathematical expressions combine variables, numbers, values, and constants using mathematical operands.

The total number of people in attendance at the family reunion = 400

Let the number of grandparents = x

Let the number of parents = 2x

Let the number of children = 2x + 50

Equation:

x + 2x + 2x + 50 = 400

5x = 350

x = 70

Summary of Attendance:

Grandparents = 70

Parents = 140 (2 x 70)

Children = 190 (2 x 70 + 50)

Total = 400 (70 + 140 + 190)

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a) Use the triangle below to answer questions a) and b). B 10 cm A 14 cm Determine which interior angle of the triangle is the largest,

Answers

The largest interior angle of the triangle is the angle A

Determining the largest interior angle of the triangle

The side lengths of the triangles are given as

b = 10 cm

a = 14 cm

The other side length is not given

So, we solve the question using the two side lengths

Having said that:

The general rule is that; the higher the side length, the larger the angle

14 cm is greater than 10 cm

This means that the angle A is greater than the angle B

Answers

The total amount of FICA tax that was deducted from the executive's paychecks for the year 2018 is $10,860.80.

What is the total amount of FICA tax?

The FICA tax is imposed on both employees and employers to fund Social Security and Medicare which are federal programs that provide benefits for retirees, the disabled and children of deceased workers.

The Social Security tax will be calculated on the maximum taxable earnings of $128,400:

= $128,400 x 6.2%

= $7,961.20

The Medicare tax will be calculated on the entire earnings:

= $200,000 x 1.45%

= $2,900.

The total FICA tax will be:

= Social Security tax + Medicare tax

= $7,960.80 + $2,900

= $10,860.80.

Answers

A line that has a slope of 5/3 and a y-intercept of -4 is -5x+3y=-12
A line that contains the point (0,-8) with a slope of 3/2 is y= 3/2x-8
A line that contains the y intercept (0,-2) and a slope of -3/4 is y=-3/4x - 2
A line that contains the points (0,-2) and (4,0) is 2y-x=-4

Find the volume of a right circular cone that has a height of 11.9 ft and a base with a radius of 16.3 ft. Round your answer to the nearest tenth of a cubic foot.

Answers

The volume of a right circular cone which has a height of 11.9 ft and a base with a radius of 16.3 ft as required is;

What is the volume of the right circular cone?

As evident in the task content; the volume of a right circular cone a height of 11.9 ft and a base with a radius of 16.3 ft is to be determined.

Recall, the volume of the cone is;

V = (1/3) × πr²h

V = (1/3) × π × 16.3² × 11.9

V = 3310.9 ft³.

Ultimately, the volume of the right circular cone is; 3310.9 ft³.

Answers

Answer:79

Step-by-step explanation:

Eloise bought 30 pounds of sand to refill 4 sandboxes at a local park. She is going to put the
same amount of sand in each sandbox. Which statement about this situation is true?

Answers

The amount of sand Eloise will put in each sandbox is 7.5 pounds (30 divided by 4).

I need help on number 6

Answers

x=11. if you add all the given degrees up, you have 320, 360 is needed to be a full circle. 4 x 11= 44-4= 40

Describe los Tipos de ángulos que se forman cuando divides un círculo en 4 partes iguales

Answers

The angles that you get when a circle is divided into 4 equal parts, would be four 90 degree angles.

How to describe the angles ?

The reason these angles are called 'right angles' is because they create an exact 90-degree angle, signifying one fourth of a complete circle. Every specific angle is named as a 'quadrant,' as it covers a quarter or a quadrant of the circle.

These four perpendicular angles stand side by side - having in common not just one diameter of the circle but also a shared vertex, which is at the center of the circle. Together, they share uniformly the circle into four unique sections - each turning toward a distinct quadrant of the circle parallel to their placement.

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Express the area of the entire rectangle. Your answer should be a polynomial in standard form. An area model for a rectangle that has a height of x plus two and a width of x plus six. The rectangle is broken into four rectangles to isolate each term in the height and the width. The top left rectangle has a height of x and a width of x. The top right rectangle has a height of x and width of six. The bottom left rectangle has a height of two and a width of x. The bottom right rectangle has a height of two and a width of six.

Answers

The area of the entire rectangle as polynomial is x^2 + 8x + 12

Expressing the area of the entire rectangle as polynomial

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

Height = x + 2; Width = x + 6

Broken rectangles

Height = x; Width = xHeight = x; Width = 6Height = 2; Width = xHeight = 2; Width = 6

The area of the rectangle is the product of the dimensions

Adding the heights and the width of the individual rectangles, we have

Height = x + 2; Width = x + 6

So, the area is

Area = (x + 2)(x + 6)

Expand

Area = x^2 + 8x + 12

Hence, the area expression is x^2 + 8x + 12

Answers

The equations that can be used to solve for y, the length of the room are y * (y - 5) = 750, y^2 - 5y = 750 and (y + 25)(y – 30) = 0

Which equations can be used to solve for y, the length of the room?

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

Area = 750

Length = y

Width = y - 5

The area is the product of the length and the width

So, we have

y * (y - 5) = 750

When expanded. we have

y^2 - 5y = 750

Lastly, we have

(y + 25)(y – 30) = 0 -- when factored

Answers

Answer:

B. 122.88

Step-by-step explanation:

Since t is the number of years since 1910, we can find the t value we need for the equation by subtracting 1910 from 1980:

t = 1980 - 1910 = 70

Now, we can plug in 70 for t to find the amount of currency in 1980:

[tex]M(t)=2.08(1.06)^t\\M(70)=2.08(1.06)^7^0\\M(70)=122.8779348\\M(70)=122.88[/tex]

Thus, the amount of currency in 1980 according to the model was $122.88 billion

What is the square root of ab²?
O ab
Ob√a
Oa²b²
Ob²

Answers

Answer:

b[tex]\sqrt{a}[/tex]

Step-by-step explanation:

using the rule of radicals

[tex]\sqrt{ab}[/tex] = [tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] , then

[tex]\sqrt{ab^2}[/tex]

= [tex]\sqrt{a}[/tex] × [tex]\sqrt{b^2}[/tex]

= [tex]\sqrt{a}[/tex] × b

= b[tex]\sqrt{a}[/tex]

The radius of a circle is 12 cm. Find its area nearest whole number

Answers

Answer:

452 square centimeters.

Step-by-step explanation:

To find the area of a circle, we use the formula:

A = πr^2

Where A is the area of the circle, r is the radius, and π is a mathematical constant (approx. 3.14).

Given that the radius of the circle is 12 cm, we can substitute r = 12 in the formula:

A = π(12)^2

A = 3.14 x 144

A = 452.16

Therefore, the area of the circle is approximately 452.16 square centimeters. However, we need to round the answer to the nearest whole number.

Since the decimal part of the answer is less than 0.5, we round the answer down to the nearest whole number. Therefore, the area of the circle nearest the whole number is 452 square centimeters.

Look at the figure shown. Which angle is obtuse?
Angle CDA.
Angle BAD.
Angle CBA.
Angle DAB.
A
60
B
120
120
C
60
D

Answers

The angle that is an obtuse angle (that is, greater than 90° but less than 180°) is 120°. The correct option is B. 120°

What is an obtuse angle?

An obtuse angle is an angle that is greater than 90° but less than 180°. Thus, if x is an obtuse angle, the range of values for x are

90° < x < 180°

From the given question, we are to determine the angle which obtuse.

In the given figure, to determine the angle which is obtuse, we will determine the angle that is greater than 90° but less than 180°.

The angle that is greater than 90° but less than 180° is 120°.

Thus,

The obtuse angle is the angle that measures 120°

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The vertices of SRT are S (1, 4), R (2, 2) and T (1, 3). A reflection across the line _________ [ (A) x = 4, (B) x = 6, (C) y = –x + 5,(D) y = –x + 6] and then across the line _________ [ (A) y = 6, (B) y = 8, (C) y = –x + 10, (D) y = –x + 12] is the same as a translation of 4 units to the right and 4 units up because the lines are _________ [ (A) congruent, (B) parallel, (C) perpendicular, (D) similar].

Answers

The given reflection transformation is a rigid transformation, such that the dimensions are preserved

The statements that are true about the image of triangle ABC following a reflection Bout the the line y = 2·a are;

AB = RS

ΔABC ≅ ΔRST

m∠BAC ≅ m∠SRT

Reasons:

The given parameters are;

Triangle ΔABC is reflected across the line y = 2·x

Given that a reflection is a rigid transformation, we have;

The distance between two points on a preimage is the same as the distance between the corresponding points on the image;

Therefore;

ΔABC is congruent to ΔRST by Side-Side-Side SSS, rule of congruency, such that we have;

AB ≅ RS, BC ≅ ST, and AC ≅ RT

m∠BAC ≅ m∠SRT

m∠BCA ≅ m∠STR

m∠BAC ≅ m∠SRT

Therefore;

The true statements are;

AB = RS

ΔABC ≅ ΔRST

Therefore;

m∠BAC ≅ m∠SRT given that ΔABC ≅ ΔRST

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complete question:

Triangle ABC is reflected across the line y=2x to map onto triangle RST. Select all statements that are true.

Question 3 options:

AB=RS

AB=2RS

ΔABC~ΔRST

△ABC≅ΔRST

m∠BAC=m∠SRT

m∠BAC=2m∠SRT

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