Answers
Answer:
x=5.11
Step-by-step explanation:
Hi there!
We are given a right triangle (notice the right angle), with one of the angles being equal to 64 degrees
We also know one of the sides is 42, another is x, and the other one is not marked
We want to find the value of x, which we can do using trigonometry
The 3 main trigonometric functions are:
Sine, which is opposite/hypotenuse
Cosine, which is adjacent/hypotenuse
Tangent, which is opposite/adjacent
First, let's find which side is which
The side opposite the 64 degree angle is the opposite; this side is the side marked as 42
The adjacent side would be the other leg (one of the sides creating the right angle); in this case, that would be the side marked as x
The hypotenuse in this case would be the side that hasn't been marked yet
Since we are given values for both the opposite and the adjacent, let's use tangent to find x
Since 64° was the angle we referenced to determine which side was which, we will also make the ratio with this angle.
Therefore, the ratio will be:
[tex]tan(64)=\frac{42}{x}[/tex]
Now we need to solve for x; start by multiplying both sides by x
x * tan(64) = 12
Now divide both sides by tan(64)
x = [tex]\frac{12}{tan(64)}[/tex]
Plug [tex]\frac{12}{tan(64)}[/tex] into your calculator; make sure the calculator is on degree, not radian mode
[tex]\frac{12}{tan(64)}[/tex] ≈ 5.11 (rounded to the nearest hundreth)
So x is about 5.11
Hope this helps!
Topic: trigonometry in right triangles
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Related Questions
Simplify: (5 + i)(5 − i)
A) −12
B) 24i
C) 26
D) 8i
Answers
Answer:
C) 26
Simplify using the FOIL method--used to multiply binomials--and then combine real and imaginary parts of the problem.
5 × 5 = 25 + positive 1(i) = 26
Answer:
option c, 26
Step-by-step explanation:
(5 + i)(5 - i)
Apply complex arithmetic rule: (a + bi)(a - bi) = a^2 + b^2
a = 5, b =1
(5)^2 + (1)^2
(5)^2 = 25
(1)^2 = 1
25 + 1
In triangle ABC, mZA = 47° and mZB= 70°
B
70
47
A
С
What is the measure of angle C?
Enter your answer as the correct value. like this: 42
Answers
180-(70+47)=63
Because in triangle sum of all angles is 180 degree.
3(x+1)=5(x−2)+7
solve for x
Answers
3(3+1)=12
5(3-2)+7=12
A rectangular fence is to a total perimeter of 200 feet. If the length is twice the width, find the measurements of the length and width of the rectangular fence.
Answers
A rectangular fence is to a total perimeter of 200 feet. If the length is twice the width, find the measurements of the length and width of the rectangular fence.
✪ Explanation -:In this question we are provided with the perimeter of a rectangle fence that is 200 feet. It is also given that the length of the fence is twice its breadth. We are asked to calculate it's dimensions.
First we will form an equation.
Let us assume the breadth as x
Then, length = 2x
It is given that the perimeter is 200 feet.
We know,
[tex] \bull \: \small\boxed{ \rm{ Perimeter_{(rectangle)} = 2(length + breadth)}}[/tex]
Substituting the values we get
[tex] \small\sf{ 200 = 2(2x + x)}[/tex]
Now we will solve this equation and find out the value of x.
[tex] \small\sf{ 200 = 2(2x + x)}[/tex]
[tex] \longmapsto \small\rm{ 200 = 2(3x )}[/tex]
[tex] \longmapsto \small\rm{200 = 6x} [/tex]
[tex] \longmapsto \small\rm{ \dfrac{ \cancel{200} \: \: 33.33}{ \cancel{6}} = x } [/tex]
[tex] \small\sf{x = 33.33} [/tex]
We will substitute the value of x = 33.33.
Length = 2x = 2 × 33.33 = 66.66 feet
Breadth = x = 33.33 feet
Hence the length of the rectangular fence is 66.66 feet and the breadth is 33.33 feet.It is found that children’s shoe size is correlated with scores on an achievement test. Explain, in words, if this is evidence that correlation implies causation.
Answers
Step-by-step explanation:
If you agree that increasing age (for elementary school children) causes increasing foot size, and therefore increasing shoe size, then you expect a correlation between age and shoe size. Correlation is symmetric, so shoe size and age are correlated.
a Sam purchases a home for $1, 240, 500. Each year the value of the home appreciates by 3%. What is the value of the home after 6 years?
Answers
Answer:
lol
Step-by-step explanation:
Other question! 5th grade! help asap
Answers
The names of this polygon include:
Acute triangle. Scalene triangle. Which polygon is described?The polygon given has three sides which means that it is a triangle. It is an acute triangle because the angles are all less than 90°.
It is also a scalene triangle because all the sides have different lengths from each other.
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Answer:
Step-by-step explanation:
I: acute triangle
L: Isosceles triange
(sorry if im wrong i have not done this in a good few years lol)
The legs of a right triangle are 8 and 9 units long. What is the area of the triangle in square units?
Answers
Answer:
Step-by-step explanation:
Area of a triangle is a*b divided by 2
Lets assume a = 8 and b= 9
8 *
9=72
72/2=36
Challenge. The mean of two numbers is
28. Find the numbers if 3 times one of the
numbers equals half the other number.
Hint. The mean of x and y is (x + y)/2 =
1/2(x + y).
Answers
Answer:
8 and 48
Step-by-step explanation:
Here is how to find it mathematically
x = one number 6x = other number ( because 3x is 1/2 of x)
(x + 6x) /2 = 28
7x = 56
x = 8 then 6x = 48
Solve ABC given A= 74 , a= 126, b=84
Answers
Please leave comments if you can’t read something. I’ll get back to you as soon as possible!
How is the step by step of this problem
Answers
Answer:
I would edit this answer and tell you what I hope would be the correct answer if you give me the problem you are confused with
Step-by-step explanation:
I can't help you otherwise
Sorry
For the graph, what is a reasonable constraint so that the function is at least 600?
I took the test and got this question wrong, as you can see from the image below. Anyone else want to try?
Answers
Answer:
[tex]0 \leqslant x \leqslant 20[/tex]
help me pleaseeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answers
Since the variable x is the numerator of the fraction, we first need to multiply each side by 6, since the denominator is 6. After doing this, the equation should now look like this: [tex]18 = x + 31[/tex]. Next, we subtract 31 from 18 following the rule. 18 - 31 = -13. x is equal to -13.
For shown work in order:
[tex](6) 3 = x +31[/tex]
[tex]18 = x + 31[/tex]
[tex]18 - 31 = x[/tex]
[tex]x = -13[/tex]
Suppose the heights of the members of a population follow a normal
distribution. If the mean height of the population is 72 inches and the
standard deviation is 3 inches, 99.7% of the population will have a height
within which range?
A. 63 inches to 81 inches
B. 66 inches to 78 inches
C. 60 inches to 84 inches
D. 69 inches to 75 inches
Answers
The option (A) 63 inches to 81 inches is correct after using the empirical Rule.
What is the standard deviation?It is defined as the measure of data disbursement, It gives an idea about how much is the data spread out.
We have:
The mean height of the population is 72 inches and the standard deviation is 3 inches, 99.7% of the population will have a height
99.7% of data observed following a normal distribution lies within 3 standard deviations of the mean.
The lower range = 72 – 3(3) = 63 inches
The upper range = 72 + 3(3) = 81 inches
Thus, the option (A) 63 inches to 81 inches is correct after using the empirical Rule.
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please help me!!!
4) There are five nickels and seven dimes in
your pocket. You randomly pick a coin
out of your pocket and then return it to
your pocket. Then you randomly pick
another coin. The first coin is a nickel and
the second coin is a dime.
2
A) //1²
≈ 0.182
B) None of these
11
25
C)
≈ 0.29
D)
≈ 0.148
169
E)
49
169
1
4
= 0.25
5)
E
Answers
Answer:
B. None of these
Step-by-step explanation:
There are a total of 12 coins in your pocket.
The probability of drawing a nickel first is 5/12
Since you return the coin, the total number of coins in your pocket doesn't change.
The probability of drawing a dime second is 7/12
Since this is a compound probability problem, multiply the two probabilities together.
5/12 x 7/12 = 35/144
35/144 = 0.243
help please i need help
Answers
a) Line AE, and Line BC are parallel
b) Line ED, and Line CD
c) 3
Step-by-step explanation:
Henry deposits $750 into a college savings account that is compounded annually when is his parents received as a stimulus package . If Henry let’s the money sit in the account without adding or removing any and receives a 8.5% interest rate , How much more money will he have total after 5 years ?
Answers
Answer:
The answer should be $1127.74
The diameter of a circle is 8 in. Find the circumference \textit{to the nearest tenth}to the nearest tenth.
Answers
Answer: C ≈ 25.1
Step-by-step explanation:
The circumference of a circle can be found with the following formula. We will plug in the diameter given, and solve.
C = dπ
C = (8)π
C ≈ 25.1
hi! how do i do this? the answer is 2k
Answers
[tex]\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}[/tex]
[tex] log_{4}x = k \\ \\ \longrightarrow \: log_{4}x = log_{2 {}^{2} }x \\ \\ \longrightarrow \: 2 log_{2}x \\ \\ now , \\ \\ log_{2}x = k \\ \\ \therefore \: 2( log_{2}x) = 2(k) \\ \\ \longrightarrow \: 2k[/tex]
hope helpful ~
Need this answered ASAP can’t find it anywhere online
Answers
Answer:
The value of the rational expression when x = -3 is undefined.
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to RightAlgebra II
Rational Functions
Asymptotes, HolesStep-by-step explanation:
Step 1: Define
Identify given.
[tex]\displaystyle \frac{x}{x^2 - 9} ,\ x = -3[/tex]
Step 2: Find Value
[Rational Expression] Substitute in x:[tex]\displaystyle\begin{aligned}\frac{x}{x^2 - 9} ,\ x = -3 & \rightarrow \frac{-3}{(-3)^2 - 9} \\\end{aligned}[/tex][Order of Operations] Evaluate:
[tex]\displaystyle\begin{aligned}\frac{x}{x^2 - 9} ,\ x = -3 & \rightarrow \frac{-3}{(-3)^2 - 9} \\& \rightarrow \frac{-3}{0}\end{aligned}[/tex]
∴ since we can't divide by 0, our rational expression when x = -3 will have to be undefined.
___
Topic: Algebra II
Ammaar put 4/7 of the money he earned raking leaves in the bank. He spent 1/3 of the money on a book.
Create an expression with common denominators that can be used to find the difference between the fraction of money Ammaar put in the bank and the fraction he spent on the book
Answer for grade 6 pls
Answers
The expression that can be use to find the difference between the fraction of money Amar put in the bank and the fraction he spent on the book is 4 / 7 x - 1 / 3 x
How to create an expression?Amar put 4/7 of the money he earned raking leaves in the bank. Therefore,
let the money she earned = x
Hence,
amount put in bank = 4 / 7 x
She spent 1 / 3 of the money on books. Therefore,
money spent on books = 1 / 3 x
Therefore, the expression that can be use to find the difference between the fraction of money Amar put in the bank and the fraction he spent on the book is as follow:
4 / 7 x - 1 / 3 x
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solving system of equations by graphing.
Answers
Answer:
see attached image
Step-by-step explanation:
plssssss helppppp i give 98 points
Answers
To write 28 + 24 as a product of two factors, we need to determine the HCF of the addends (28 and 24). This can be done by listing the factors of the addends. The greatest factor that is common in 28 and 24 is the HCF.
If the number is in bolded text, the number is a common factor.
Factors of 28: 1, 2, 4, 7, 14, 28Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24Since 4 > 2 > 1, the HCF is 4.
2) Writing 28 and 24 as a product of two factorsNow, let us put the provided expression between parentheses.
⇒ (28 + 24)Finally, factor four out of the expression, as it is the GCF of 28 and 24.
⇒ (28 + 24)⇒ [(4 × 7) + (4 × 6)]⇒ 4(7 + 6)Therefore, 28 + 24 as a product of two factors is 4(7 + 6).
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The formula for the area of a triangle is, where b is the length of the base and h is the height.
Find the height of a triangle that has an area of 30 square units and a base measuring 12 units.
Answers
Answer: The formula for area of a triangle is area equals base times height divided by 2. the height is 5 units.
Step-by-step explanation:
Which is the graph of -2x + y < 5?
Answers
Answer:
Graph D
Step-by-step explanation:
Graph D is the graph of -2x + y < 5
9. The longitude of a geographic location is measured in degrees east (E) or west (W) from the
prime meridian (0°) to the international date line (180°). Quito, Ecuador, on the west coast of
South America, has a longitude of 78.5º W. Singapore, on the Malay Peninsula in Asia, has a
longitude of 104° E. Both cities are very close to the equator. The diameter of Earth at the
equator is 7928 miles. What is the shortest distance from Quito to Singapore? Explain how you
found your answer.
Answers
Based on the longitudes of Quito and Singapore, the shortest distance between the two areas is 19,702.5 km .
How far is Quito from Singapore?Because both cities are close to the equator, you use the longitudinal difference method to find the shortest distance.
First find the difference in longitudes:
= Singapore - Quito
= 104 - (-78.5) because Quito is west
= 104 + 78.5
= 182.5°
Then subtract this from 360°:
= 360 - 182.5
= 177.5°
Every 1° longitude along the Equator is 111 km so the shortest distance is:
= 177.5 x 111
= 19,702.5 km
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The price of a jacket was increased from $110 to $126.5. What was the percent increase in the price of the jacket?
Answers
Answer:
15%
Step-by-step explanation:
percent increase is actual increase divided by starting value16.5/110 = 0.1515%Percent increase in the original price of jacket = 15%
What is percentage?Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
Given,
Original price of jacket = $110
Increased price of jacket = $126.5
Increased amount = $126.5 - $110
= $16.5
Increased amount in percentage = ($16.5/$110) × 100
= 0.15 × 100
= 15%
Hence, 15% is increase in the original price of jacket.
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What is the equation of the that contains the point (3,-2) and has a slope of 5?
Answers
Answer:
y = 5x-17
Step-by-step explanation:
point slope form would be
y- -2 = 5(x-3) or re-arrange to: y = 5x -17
On a place-value chart, you use exactly 12 counters to represent one decimal number and exactly 15 counters to represent another decimal number.
When you add the two numbers, you get a number you can represent with only 9 counters.
When you subtract the two numbers, you need more than 9 counters for the result.
• What could your numbers be For adding it be
• Explain how you came up with your numbers and why they work.
Answers
The possible number represented by the 9 counter is 27
How to determine the possible number?The counters are given as:
12 counters and 15 counters
When added, we get a number that can be represented by 9 counters.
This means that:
12 + 15 = 9x
Evaluate the sum
27 = 9x
Divide by 9
x = 3
When subtracted, you need more than 9 counters.
This means that:
x = 15 - 12 = 3
So, we conclude that the number is a multiple of 3 and 9
In other words, the decimal number is a multiple of 9 (i.e. 27)
Hence, the possible number is 27
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simplify (-1 1/2) ÷ 3/4 x -2/3
Answers
Answer:
Step-by-step explanation:
1[tex]\frac{1}{2}[/tex]=1×[tex]\frac{2}{2}[/tex], +[tex]\frac{1}{2}[/tex]
(-[tex]\frac{3}{2}[/tex])÷[tex]\frac{3}{4}[/tex]×(-[tex]\frac{2}{3}[/tex])
[tex]\frac{3}{2}[/tex]×[tex]\frac{4}{3}[/tex]×[tex]\frac{2}{3}[/tex]
[tex]\frac{1}{2}[/tex]×4×[tex]\frac{1}{3}[/tex]
4×[tex]\frac{1}{3}[/tex]=[tex]\frac{1}{3}[/tex]+[tex]\frac{1}{3}[/tex]+[tex]\frac{1}{3}[/tex]+[tex]\frac{1}{3}[/tex]
=[tex]\frac{4}{3}[/tex]