The legs of a right triangle measure 14 and 25 what is the measure of the angle opposite to the shortest side

Answers

Answer 1
tan x = 14/25     (angle we want is opposite the side of length 14)

angle =  29.25 degrees
Answer 2

The measure of the angle opposite to the shortest side is, 29.25°

What is mean by Triangle?

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

The legs of a right triangle measure 14 and 25.

Now, We know that;

⇒ tan θ = Perpendicular / Base

⇒ tan θ = 14 / 25

⇒ θ = tan ⁻¹ (14/25)

⇒ θ = 29.25°

Thus, The measure of the angle opposite to the shortest side is, 29.25°

Learn more about the triangle visit;

brainly.com/question/1058720

#SPJ6


Related Questions

How many different selections of 4 books can be made from a bookcase displaying 12 books?

Answers

(12 x 11 x10 x9) / (4 x3 x 2 x 1) = 495

there are 495 different ways to select 4 books

Find two positive numbers such that their product is 192 and their sum is a minimum pre-calc

Answers

This problem is a combination of algebra and calculus. First, we formulate an equation for the product. Let x be the first positive number and y be the other positive number. So, the equation would be

xy = 192

Let's rearrange this to make the equation explicit: y = 192/x
Then, the other equation is for the sum. Let S be the sum of the two positive numbers.

S = x + y

Now, substitute the other equation into this one:

S = x + 192/x

Here's where we apply calculus. We can determine the minimum S by getting the first derivative of S with respect to y and equating to zero. Thus,

dS/dx = 1 - 192x⁻² = 0
1 = 192x⁻²
x² = 192
x = +/- √192

But since we are finding the positive number,  x = + √192
Then, we use this to the first equation:

y = 192/√192 = √192

Therefore, the two positive numbers are equal which is √192 or 13.86. 

The two numbers with a product equal to 192 such that their sum is minimized are:

A = √192 and B = √192

How to find the two numbers?

Let's define A and B as our two numbers, we know that their product must be equal to 192, then we have:

A*B = 192.

Now, the sum of these two numbers is:

A + B.

And we want to minimize this, to do it, we need to use the first equation to rewrite one variable in terms of the other. For example, if we isolate A, we get:

A = 192/B

Replacing this in the sum, we get:

192/B + B

To minimize this, we need to find the values of B that make 0 the differentiation of the above expression.

The differentiation is:

-192/B^2 + 1

Then we need to solve:

-192/B^2 + 1 = 0

192/B^2 = 1

192 = B^2

√192 = B

To get the value of A, we use:

A = 192/B = 192/√192  = √192

Then we can conclude that the two positive numbers such that their product is 192, and their sum is minimized, is:

A = √192 and B = √192.

If you want to learn more about minimization, you can read:

https://brainly.com/question/18585083

The following two-way table shows the number of students of a school who have a video game and/or have a laptop:


Have Video Game Do Not Have Video Game Total
Have Laptop
15
50
65
Do Not Have Laptop
50
15
65
Total
65
65
130


Based on the table, how many students have both a laptop and a video game?
15
50
65
130

Answers

                                have game               dont have it               total
have laptop                   15                              50                         65
dont have                       50                             15                         65
total                                65                              65                       130

have both a laptop and a game : 15

Based on the table given, the number of students who have both a laptop and a video game is 15 students.

Which students have both laptops and video games?

In order to solve this question, look at the part of the table where the row on students who have laptops intersects with the column on those who have video games.

That part of the table has 15 in the cell. This means that 15 students have both video games and laptops.

Find out more on using two-way tables at https://brainly.com/question/27448159.

#SPJ5

Triangle XYZ is a right triangle. Angle Z is a right angle and m∠X = 68°. What is m∠Y?

Answers

interior angles of a triangle add up to 180

< X + < Y + < Z = 180
68 + Y + 90 = 180
158 + Y = 180
Y = 180 - 158
Y = 22 <==

m∠Y is 22°

What is right triangle?

Right triangle is defined as a triangle which one angle is a right angle or two sides are perpendicular.

Given,

ΔXYZ is a right triangle

m ∠Z = 90°

m∠X = 68°

Let  m∠Y = x,

Addition of interior angles of a triangle is 180°

So, m∠X + m∠Y +m ∠Z = 180°

Subsitute the values,

68° + x + 90° = 180°

x = 180 - 158

x = 22

Hence, m∠Y = 22°

Learn more about right triangle here

brainly.com/question/6322314

#SPJ2

Which sample fairly represents the population? CHECK ALL THAT APPLY.

--measuring the heights of every fiftieth person on the school roster to determine the average heights of the boys in the school

--calling every third person on the soccer team’s roster to determine how many of the team members have completed their fundraising assignment

--observing every person walking down Main Street at 5 p.m. one evening to determine the percentage of people who wear glasses

--sending a confidential e-mail survey to every one-hundredth parent in the school district to determine the overall satisfaction of the residents of the town

--taking a poll in the lunch room (where all students currently have to eat lunch) to determine the number of students who want to be able to leave campus during lunch

Answers

taking a poll in the lunch room (where all students currently have to eat lunch) to determine the number of students who want to be able to leave campus during lunch

Answer:

The population is defined by: The set of all possible individuals who are likely to be selected for a study and who also share some observable characteristic. In this way, the correct answer is:

Taking a poll in the lunch room (where all students currently have to eat lunch) to determine the number of students who want to be able to leave campus during lunch

Step-by-step explanation:

(30 Points) Paysly is studying a mosquito with a mass of 2.5×10^-6 kilograms and a housefly with a mass of 2×10^-5 kilograms. Which statement is true?

Answers

Housefly with a mass of 2x10^-5 kiligrams
[tex] \cfrac{2*10^{-5}}{2.5*10^{-6}} =0.8*10^1=8[/tex]

B.The housefly is 8 times the mass of the mosquito. 

Start with a square piece of cardboard to produce a box that is 8 cm deep and whose capacity is exactly 1 liter. how large must the original square be

Answers

 

The formula for the volume of a square prism or box is calculated using the formula:

V = s^2 * h

where,

s is the measure of the sides of a square

h is the height of the prism or box = 8 cm

 

We are given that the volume capacity of the box must be 1 Liter. We know that 1 Liter is equivalent to 1000 cm^3. Therefore calculating for s:

1000 cm^3 = s^2 * (8 cm)

s^2 = 125 cm^2

s = 11.18 cm

 

Therefore the measure of the sides of the square must be about 11.18 cm. If the problem ask for the area of the square, A = s^2 = 125 cm^2.

How do I simplify this problem?

Answers

Expanding (x+h)^3, we get (5x^3+15x^2h+15xh^2+5h^3-5x^3)/h=
(15x^2h+15xh^2+5h^3)/h= 15x^2+15xh+h^2

18 divided by 5593 equals 31-5400 = 193 what number should be placed in the box to help complete the division calculation?

Answers

The number that should be placed in the box to complete the division calculation is -7.

To find the number that should be placed in the box to complete the division calculation, let's analyze the given information:

- Dividend: 5593

- Divisor: 18

- Quotient: 31 (hundreds place is 3 and tens place is 1)

- When 5400 is subtracted from 5593, the result is 193.

- The box represents an unknown number in the ones place of the quotient.

To find the value in the box, we need to consider the units place. Since 5400 is subtracted from 5593 to give 193, the difference between the units places should be the value in the box.

193 - 5400 = -5207

So, the number that should be placed in the box to complete the division calculation is -7.

Correct question is:  

What number should be placed in the box to help complete the division calculation?

Long division setup showing an incomplete calculation. 18 is in the divisor, 5593 is in the dividend, and 3 hundreds and 1 tens is written in the quotient.

5400 is subtracted from 5593 to give 193.

An unknown value represented by a box is being subtracted from 193.

The tip of an 11-inch wiper blade wipes a path that is 31 inches long. What is the angle of rotation of the blade in radians to the nearest tenth?

Answers

length of arc = Cr    where C = angle of rotation and r = radius

31 = C*11

C =  31/11 =  2.8 radians to nearest tenth

2.8 radians is the answer.

find the solution to the two equations shown below y=16x-9 y=-4x+21

Answers

Answer: (1.5, 15)

Step-by-step explanation:

The given system of equations :-

[tex]y=16x-9...................(1)\\\\y=-4x+21..................(2)[/tex]

Substituting the value of y from equation (1) in equation (2), we get

[tex]16x-9=-4x+21[/tex]

Now, Adding 4x and 9 on both the sides , we get

[tex]16x+4x=21+9\\\\\Rightarrow\ 20x=30\\\\\Rightarrow\ x=\dfrac{3}{2}=1.5[/tex]

Substitute the value of x in equation (1), we get

[tex]y=16(1.5)-9=15[/tex]

Hence, the solution to the given system of equations : (1.5, 15)

The solution to the given system of equation is (1.5, 15).

The given system of equations are

y=16x-9 ---------(i)

y=-4x+21 ---------(ii)

From equation (i) and (ii), we get

16x-9=-4x+21

16x+4x=21+9

20x=30

x=30/20

x=1.5

Substitute x=1.5 in equation (i), we get

y=16×1.5-9

y=24-9

y=15

Therefore, the solution to the given system of equation is (1.5, 15).

To learn more about the linear system of an equations visit:

https://brainly.com/question/27664510.

#SPJ6

PLEASE HELP!!!!!!!

f(x)=x^2−3x+9
g(x)=3x^3+2x^2−4x−9

Find (f−g)(x)

Select one:
a. −3x^3−x^2+x+18

b. 3x^3+3x^2−7x

c. 3x^3+x^2−x−18

d. 3x^3−x^2−x

Answers

Answer: Choice A) -3x^3-x^2+x+18

-----------------------------

Work Shown:

(f-g)(x) = f(x) - g(x)
(f-g)(x) = [ f(x) ] - [ g(x) ]
(f-g)(x) = [ x^2-3x+9 ] - [ 3x^3+2x^2-4x-9 ]
(f-g)(x) = x^2-3x+9 -3x^3-2x^2+4x+9
(f-g)(x) = -3x^3+(x^2-2x^2)+(-3x+4x)+(9+9)
(f-g)(x) = -3x^3-x^2+x+18

Planes Q and R are parallel. Explain how you know lines a and b are skew.



Sample Response: Skew lines are noncoplanar and do not intersect. Line a lies in plane Q and line b lies in plane R, so the lines are not coplanar. No other plane can be drawn through the lines, so they are not parallel. So, a and b are skew

Answers

By definition, skew lines are a pair of lines that are not parallel but do not intersect each other either. Hence, the conclusion would be, the lines are non-coplanar. An example would two random lines drawn in the x and y axes in a cartesian plane, respectively.

Sample Response:

Skew lines are noncoplanar and do not intersect. Line a lies in plane Q and line b lies in plane R, so the lines are not coplanar. No other plane can be drawn through the lines, so they are not parallel. So, a and b are skew.

The function P(t) = 5,000 (0.93)t is the value of a motor scooter t years after it is purchased. Which of the following values show the annual depreciation of the value of the motor scooter?
93
-7
50
7

Answers

P(t) = 5,000 (1-r)t
P(t) = 5,000 (1-7%)t
P(t) = 5,000 (0.93)t

The annual depreciation rate is 7%

Answer:

Option 4 - 7%

Step-by-step explanation:

Given : The function [tex]P(t) = 5000 (0.93)^t[/tex] is the value of a motor scooter t years after it is purchased.

To find : Which of the following values show the annual depreciation of the value of the motor scooter?

Solution :

We are given a function p(t) which is represented as:

[tex]P(t) = 5000 (0.93)^t[/tex]

Where, p(t) is the value of a motor scooter t years after it is purchased.

Depreciation is the amount that has been deducted from the cost of an item.

The rate of change is 1-0.93=0.07 i.e. 7%.

So, The function P(t) has 7% of the amount has been deducted each year and the value of the motor scooter is 93% of the amount of the previous year.

Therefore, The annual rate of depreciation is 7%.

So, option 4 is correct.

If n is a positive integer and the product all the integeres from 1 to n inclusive is a multiple of 990 what is the least possible value of n

Answers

Hello,

Since 990=2*3²*5*11 ==>n=11

cot^2x-csc^2x=-1 for all values of x true or falsse

Answers

Our basis for this equality is the pythagorean theorems of trigonometry. There are three equations for the pythagorean theorems. These are:

sin²x + cos²x =1
1 + tan²x = sec² x
1 + cot² x = csc² x

These are all derived from circle geometry on the cartesian plane. Now, the useful trigonometric property to be used is the third one. Rearranging this, we come up with

cot²x - csc²x = -1

This coincided with the given equation. Therefore, this is true. This is because it is already established from the pythagorean theorems.

The original equation cot^2x - csc^2x = -1 is true for all values of x.

How to determine if cot^2x-csc^2x=-1 for all values of x

The equation cot^2x - csc^2x = -1 is true for certain values of x, but not for all values of x.

To see why, let's break down the equation using trigonometric identities:

cot^2x - csc^2x = -1

Using the reciprocal identities, we can rewrite cot^2x and csc^2x in terms of sine and cosine:

(cos^2x / sin^2x) - (1 / sin^2x) = -1

Now, let's simplify:

(cos^2x - 1) / sin^2x = -1

Using the Pythagorean identity cos^2x + sin^2x = 1, we can substitute cos^2x with (1 - sin^2x):

(1 - sin^2x - 1) / sin^2x = -1

-sin^2x / sin^2x = -1

Now, we can cancel out the sin^2x terms:

-1 = -1

This equation holds true for all values of x. Therefore, the original equation cot^2x - csc^2x = -1 is true for all values of x.

Learn more about equation at https://brainly.com/question/29174899

#SPJ6

juanita and lauren are painting a circular mural on one wall of the community center. the area of the mural is 66 square meters. what is the radius

Answers

Final answer:

The radius of Juanita and Lauren's circular mural with an area of 66 square meters is approximately 4.58 meters.

Explanation:

Juanita and Lauren's mural has an area of 66 square meters, and we need to find the radius of the circular mural. To find the radius, we can use the formula for the area of a circle, which is A = πr², where A is the area and r is the radius. Since the area of the mural is 66 square meters, we have:

66 = πr²

To solve for the radius (r), we divide both sides of the equation by π:

r² = 66 / π

Then, take the square root of both sides to get:

r = √(66 / π)

Using a calculator to compute this, we find:

r ≈ 4.58 meters (rounded to two decimal places)

Therefore, the radius of the circular mural is approximately 4.58 meters.

Please show work on how you got the answer

Answers

(See attached diagram.)  The positions of the vaulter's left and right hands are marked. The length of the entire pole is 15 feet. The segment below her left hand is twice as long as the segment above, so label those two parts with x and 2x. Those two segments add up to 15 feet:

[tex]x+2x=15[/tex]
[tex]3x=15 \newline x=5[/tex]

The lower segment is 10 feet long. The vaulter's right hand is 1.5 feet above her left, so it is 10 + 1.5 = 11.5 from the bottom of the pole.

The coordinates of a point are (4, –1). which matrix expression represents translating the point 3 units to the left and 7 units up?

Answers

The point (4, -1) is represented as:

| 4 |
|    |
|-1 |

Please, understand that the three vertical | represent a continuous line, which is the matrix representation.

The traslataion of 3 units to the left and 7 units up means that you have to add the matrix:

|- 3|
|    |
|7  |

So the representation is:

|4  |          |-3 |       |1  |
|    |    +    |    | =    |    |
|-1 |          |7  |       |6  |

The masses, in kg, of some bags on an airplane are shown below: 7, 6.2, 6.1, 6.8, 6.1, 6.2, 6.8, 5.8, 6.2, 6.3 Jack made the following box plot to represent the masses: box plot shows minimum at 5.8, first quartile at 6.1, median at 6.3, third quartile at 6.8 and maximum at 7 Which of the following did Jack show incorrectly on his box plot?

Answers

the correct answer would the median it should be 6.2 not 6.3

Answer:

The value that Jack show incorrectly on his box plot is:

Median ( As he showed median is 6.3 but median is 6.2)

Step-by-step explanation:

We are given the mass of the bags as:

7, 6.2, 6.1, 6.8, 6.1, 6.2, 6.8, 5.8, 6.2, 6.3

On arranging the data in the increasing order we have:

5.8   6.1    6.1    6.2    6.2    6.2    6.3    6.8    6.8    7

There are a total of 10 data points.

Also, the minimum value is: 5.8

Maximum value is: 7

The median is the central tendency of the data and lie in the middle of the data.

Hence, Median lie between 6.2 and 6.2

Hence, Median=6.2

Also, the lower set of data is: 5.8   6.1    6.1    6.2  

The lower quartile or first quartile is the median of lower set of data is: 6.1

Also, the upper set of data is: 6.3    6.8    6.8    7

The upper quartile or Third quartile is the median of lower set of data is: 6.8

        Hence, he showed median incorrectly in the box plot.

:)

What are the phase shift and period for the function y = 3cos[4(θ + 60°)] − 2?

 Phase shift = right 60°, period = 90°

 Phase shift = right 60°, period = −90°

 Phase shift = left 60°, period = 90°

 Phase shift = left 60°, period = −90°

Answers

The plus sign inside the parenthesis indicates that the shift is to the left, And the formula for the period is 2pi/B and our B is 4, so 2pi/4 = pi/2 which is 90. So your answer is the third one down, left 60 period 90

Please help with this question! thanks :)

Answers

the tallest line in the graph is 3

 so 3 would be the answer


The French club is sponsoring a bake sale. If their goal is to raise at least $135, how many pastries must they sell at $2.50 each in order to meet that goal? Write and solve an inequality.

Answers

Let x be the amount they must sell

X * 2.5 ≥ 135
X ≥ 54
The answer should be 135/2.50 = 1350/25 = (4*1350)/(4*25) = 5400/100 = 54

So answer will be 54 pastries

Solve log2(6-2x)-log2x=3

Answers

Assuming you have log in base 2.

Join logarithms (always):

log2(6-2x)-log2(x) = log2( (6-2x/x) )

Then get rid of it! :)

(6-2x)/x = 2^3=8,

Solve the equation:

6-2x=8x ---> 10x=6 ---> x = 3/5.

The length of a rectangular lawn is measured to twice its width. the perimeter of the lawn is given as 30 m. find the length and width of the lawn.

Answers

The length is 15m and the width is 5.25m

The line y = x − 6 y=x−6 has exactly one point in common with the circle x 2 + y 2 = r 2 x2+y2=r2. what is the value of r 2 r2?

Answers

Given:
y = x - 6         (1)
 for the line
x² + y² = r²     (2)
 for the circle

When the line intercepts the circle, the x and y values will be equal.
Equate the values of y by substituting (1) into (2).
x² + (x - 6)² = r²
x² + x² - 12x + 36 = r²
2x² - 12x + 36 = r²

Answer:  r² = 2x² - 12x + 36

Solve x3 = 64 over 27.

±8 over 3
8 over 3
±4 over 3

Answers

x³=64/27
Cube root the answer
³√x³=³√64/27
x=4/3.
Check:
x=4/3
x³=(4/3)³
x³=64/27. As a result, the correct answer is 4/3 or 4 over 3. If you wonder why don't I choose the answer as ±4 over 3 because of this
±4/3
Choose positive first
(4/3)²=64/27 Correct. However, then choose negative signs
(-4/3)³=-64/27 Incorrect. Hope it help!

The solution of the given equation is ±8/3.

What is an equation?

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.

The given equation is x³= 64/27

x=±∛(64/27)

x=±∛(8³/3³)

x=±8/3

Therefore, the solution of the given equation is ±8/3.

To learn more about an equation visit:

https://brainly.com/question/14686792.

#SPJ3

Bicycle city makes custom bicycles. They charge $160 plus $80 for each day that it takes to build the bicycle. If you have $480 to spend on your new bicycle, how many days can it take Bicycle City to build the bike?

Answers

It would take Bicycle City 4 days to build the bike 
160+80d≤480 subtract 160 from both sides

80d≤320  divide both sides by 80

d≤4

So the maximum number of days it can take them to build the bicycle so that $480 will cover the cost.

The sum of four consecutive even integer numbers is 84. find the four numbers.

Answers

84/4=21

 now take the 2 even numbers below 21 and the 2 even numbers above 21

18 +20 + 22 +24 = 84

 the numbers are 18, 20, 22 & 24

A sum of money amounting to $4.25 consists of dimes and quarters if there are 26 coins in all how many are quarters

Answers

d= dimes

q = quarters

d+q=26 coins

 rewrite as d=26-q

0.25q +0.10d=4.25

0.25q+0.10(26-q)=4.25

0.25q+2.6-0.10q=4.25

0.15q=1.65

q=11

d=26-11=15

11*0.25 = 2.75, 15*0.10=1.50, 2.75+1.50=4.25

 there are 11 quarters

Other Questions
You buy a commemorative coin for $110. Each year, t, the value V of the coin increases by 4%Part a: Write a function that can be used to find the coins value after t years.Part b: If the coins value continues to grow 4% per year, what will the approximate value be in 8 years? Round to two decimal places. Sam is 5 years old. His older brother, Tom, is three times as old as Sam. When Sam is 20, how old will Tom be? Which term refers to the unique sound quality that allows us to distinguish between instruments and voices? To communicate with the operating system running on the computer, each device also requires a software element known as what? What is the value of y in the parallelogram shown below? Which of the following regions did not become part of the Byzantine Empire? ThraceItalyEgyptBritain A certain solution has a hydrogen ion concentration of 3.54 x 105 moles per liter. Write this number in standard notation. What can you conclude about the slope of the values in the table? Check all that apply.The slope is 3.The slope is 0.The slope is undefined.The graph will be a horizontal line.The graph will be a vertical line.The graph will have a line with a positive slope. The layer of nearly molten rock right under the earth's crust is called its ______. why is it important for an organisation to know who its stakeholders are? The longest side of an acute triangle measures 30 inches. The two remaining sides are congruent, but their length is unknown.What is the smallest possible perimeter of the triangle, rounded to the nearest hundredth? imagine you live only one mile from work and you decide to walk if you walk 4 miles per hour how long will it take you to walk one mile Which statement best describes a country with a diversified economy? Country C has ten percent farmable land and uses all of it to produce corn. Country D has crude oil reserves and also exports gold and grain. Country B has wheat crops that make up 90 percent of its trade exports. Country A imports more goods and services than it exports. PLEASE HELP NOW!! Which of the following must be the same for two isotopes of an element? A.The number of neutrons B.The atomic number C.The mass D.The charge The American Dietetic Association and American College of Sport nutrition recommends Two benefits of the initiative and referendum process are that they allow citizens to A passenger plane travels at about 7.62 x 10^2 feet per second. The plane takes 1.23 x 10^4 seconds to reach its destination. About how far must a plane travel to reach its destination? Write your answer in scientific notation. The founding fathers created a separation of powers system in the u.s. constitution because they wanted to __________. What are the prime factorization of 36 According to MLA style, titles of sources contained in larger works, such as short stories or magazine articles, are usually _____.boldenclosed in quotation marksitalicizedunderlined Steam Workshop Downloader