Find the missing side lengths. Leave your answers as radicals in simplest form.
Answers
Answer:
B x = 3, y= 3
Step-by-step explanation:
Trigonometric ratios
[tex]\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}[/tex]
where:
[tex]\theta[/tex] is the angleO is the side opposite the angleA is the side adjacent the angleH is the hypotenuse (the side opposite the right angle)Given:
[tex]\theta[/tex] = 45°O = [tex]x[/tex]A = [tex]y[/tex]H = [tex]3\sqrt{2}[/tex][tex]\implies \sin(45^{\circ})=\dfrac{x}{3\sqrt{2}}[/tex]
[tex]\implies x=3\sqrt{2}\sin(45^{\circ})[/tex]
[tex]\implies x=3\sqrt{2} \cdot \dfrac{\sqrt{2}}{2}[/tex]
[tex]\implies x=\dfrac{3\sqrt{2} \sqrt{2}}{2}[/tex]
[tex]\implies x=\dfrac{3 \cdot 2}{2}=3[/tex]
[tex]\implies \cos(45^{\circ})=\dfrac{y}{3\sqrt{2}}[/tex]
[tex]\implies y=3\sqrt{2}\cos(45^{\circ})[/tex]
[tex]\implies y=3\sqrt{2} \cdot \dfrac{\sqrt{2}}{2}[/tex]
[tex]\implies y=\dfrac{3\sqrt{2} \sqrt{2}}{2}[/tex]
[tex]\implies y=\dfrac{3 \cdot 2}{2}=3[/tex]
Related Questions
What is the formula for finding the midpoint of a segment? Circle your choice.
Answers
Answer:
Choice D is the correct answer. (I assure you)
{Answer choice B is incorrect.}
The formula for finding the midpoint of a segment is :
( (x₁ + x₂)/2, (y₁ + y₂)/2). Hence, Option D is correct.
Use the concept of coordinates defined as:
A pair of numbers that describe the exact position of a point on a cartesian plane by using horizontal and vertical lines are called the coordinates.
Consider two opposite points of a segment (x₁, y₁) and (x₂, y₂).
Then x coordinate of the midpoint of the line joining this point is :
(x₁ + x₂)/2
And y coordinate of the midpoint of the line joining this point is :
(y₁ + y₂)/2
Therefore,
The coordinate of the midpoint of this segment is ( (x₁ + x₂)/2, (y₁ + y₂)/2)
Hence, Option D is the correct coordinate to find the midpoint.
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34. The number of songs that an MP3 player can
store varies inversely with the average size of the
song. A certain MP3 player can store 800 songs
with an average size of 4 megabytes. If the
average size of a song is 5 megabytes, how many
songs can the player store?
Answers
Answer:
Step-by-step explanation:
640
Determine whether each of the following sequences are arithmetic, geometric or neither. If arithmetic, state the common difference. If geometric, state the common ratio. 4, 13/3, 14/3, 5, 16/3, …
Answers
Answer:
sequence is arithmetic
Step-by-step explanation:
An arithmetic sequence has a common difference between consecutive terms.
A geometric sequence has a common ratio between consecutive terms.
given
4 , [tex]\frac{13}{3}[/tex] , [tex]\frac{14}{3}[/tex] , 5 , that is
[tex]\frac{12}{3}[/tex] , [tex]\frac{13}{3}[/tex] , [tex]\frac{14}{3}[/tex] , [tex]\frac{15}{3}[/tex] , then
[tex]\frac{13}{3}[/tex] - [tex]\frac{12}{3}[/tex] = [tex]\frac{14}{3}[/tex] - [tex]\frac{13}{3}[/tex] = [tex]\frac{15}{3}[/tex] - [tex]\frac{14}{3}[/tex] = [tex]\frac{1}{3}[/tex]
there is a common difference d = [tex]\frac{1}{3}[/tex] between consecutive terms
thus the sequence is arithmetic
Brian cut a piece of wood 10 1/2 m long into three equal pieces. What is the length of one of the pieces of wood?
Answers
Answer:
3.5 or 3 1/2 m
Step-by-step explanation:
If you divide 10 1/2 by 3 you get 3.5 or 3 1/2. That means if you were to add 3.5 + 3.5 + 3.5 you would get the original length of wood.
Jane has a piece of wood in the shape of a right rectangular prism. She cuts out 44 identical square holes in the wood. What is the surface area of the piece of wood after she cuts it?.
Answers
I really need help, Giving 100 points!!!!!!
1. Mrs. Galicia is creating a bunny farm. The farm starts with 820 bunnies and is growing at a rate of 20.75% per month. How many months will it take for the farm to triple in size? **Must solve using log/ln method**
2. Convert the following functions.
(a) Convert the exponential function, 12x^4y^3z^6 , to its corresponding logarithmic function.
(b) Write the log form from Part A into the expanded log form. **expression must be fully expanded for
Answers
Answer:
Step-by-step explanation:
1) 3 = (1.2075)^n where n = number of months take log of both sides
log 3 = n log 1.2075
log3 / log1.2075 = n = 5.82 months
please help its USA Test Prep and i need an answer please and thank you
Answers
Answer:
C. 8
Step-by-step explanation:
Answer:
C 8
Step-by-step explanation:
320/40 = 8
it can also work as:
320:40 divided by 40 =
8:1
15. What is the value of the expression below?
Answers
Answer:
-4 3/8 thus A. is the answer
Step-by-step explanation:
Simplify the following:
-7/2 - (5/8 + 1/4)
Put 5/8 + 1/4 over the common denominator 8. 5/8 + 1/4 = 5/8 + 2/8:
-7/2 - (5/8 + 2/8)
5/8 + 2/8 = (5 + 2)/8:
-7/2 - ((5 + 2)/8)
5 + 2 = 7:
-7/2 - 7/8
Put -7/2 - 7/8 over the common denominator 8. -7/2 - 7/8 = (4 (-7))/8 - 7/8:
(4 (-7))/8 - 7/8
4 (-7) = -28:
(-28)/8 - 7/8
-28/8 - 7/8 = (-28 - 7)/8:
(-28 - 7)/8
-28 - 7 = -(28 + 7):
(-(28 + 7))/8
| 1 |
| 2 | 8
+ | | 7
| 3 | 5:
Answer: (-35)/8 now converto to a mixed number:
Convert to a mixed number:
-35/8
Divide 35 by 8:
8 | 3 | 5
8 goes into 35 four times. Multiply and subtract:
| | 4 |
8 | 3 | 5 |
- | 3 | 2 |
| | 3 |
The quotient is 4 (the number on top of the bracket) and the remainder is 3 (the number at the bottom of the grid):
| | 4 | (quotient)
8 | 3 | 5 |
- | 3 | 2 |
| | 3 | (remainder) invisible comma
35 = 4×8 + 3
The quotient of 35/8 is 4 with remainder 3, so:
4 3/8
Replace the negative sign:
Answer: -4 3/8
Refer to the article "The Future of Money" in your Money, Money, Money magazine for a complete version of this text.
What is the overall structure of the "Pros and Cons of Cryptocurrency" section of "The Future of Money"?
It contrasts positive aspects of cryptocurrency with negative aspects of cryptocurrency.
It uses comparison to show differences between digital currency and traditional currency.
It explains how advances in computer and phone technologies created a need for cryptocurrency.
It uses reasons and evidence to support opinions about the future of cryptocurrency
Answers
The general structure of this section of the text is to describe both positive and negative aspects of cryptocurrency.
What is "The Future of Money about"?This is a text that describes the recent evolution of money into more modern forms as well as possible ways money might evolve.
What is the section "Pros and Cons of Cryptocurrency" about?This section focuses on the pros (advantages) and cons (disadvantages) of cryptoccurency. Due to this, the section follows a contrasting structure to show negative and positive aspects.
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Answer:
It contrasts positive aspects of cryptocurrency with negative aspects of cryptocurrency.
Step-by-step explanation:
i hope this help anyone that see this :D
help pls due in 5 minutes
Answers
Answer:
D
Step-by-step explanation:
[tex]2(\frac{7\times 6}{2})+3(13.1\times 7)[/tex]
ANSWER IS D
What is the slope of the line 3x – 9y = 4? -3, -1/3. 1/3, or 3
Answers
Answer:1/3
Step-by-step explanation:
Triangle ABC is a right triangle and cos(22.6o)=StartFraction b Over 13 EndFraction. Solve for b and round to the nearest whole number.
Triangle A B C is shown. Angle A C B is 90 degrees and angle C A B is 22.6 degrees. The length of hypotenuse A B is 13 centimeters, the length of A C is b, and the length of C B is a.
Which equation correctly uses the value of b to solve for a?
tan(22.6o) = StartFraction a Over 13 EndFraction
tan(22.6o) = StartFraction 13 Over a EndFraction
tan(22.6o) = StartFraction a Over 12 EndFraction
tan(22.6o) = StartFraction 12 Over a EndFraction
Answers
Answer:
C just took the test
Step-by-step explanation:
have a good rest of your day
Answer:
c. tan(22.6o) = StartFraction a Over 12 EndFraction
Ally and Christian bought 4 pounds of butter and 2 pounds of chocolate chips for cookies. How many ounces of products did they purchase?
Answers
Together, Ally and Christian bought 6 pounds of chocolate chips (because 4 + 2 = 6).
6 times 16 ounces equals 96.
So, Ally and Christian bought 96 ounces of products.
(HELP PLS) Monica is building her dream home. It will have a total floor area of 2.150 sq. ft.
a. If Monica wants the living room to be 30% of the total area, what would the living room's area be?
b. The house Monica currently lives in has only 65% of the floor area of her dream home. What is the floor area of her current home?
Answers
The living room area of Monica's home is 0.645 ft².
The floor area of her current home is 1.3975 ft²
How to find percentage of an area?
The total floor area of Monica's dream home should be 2.150 ft².
Monica wants the living room to be 30% of the total area. Therefore, the living room area will be as follows:
living room area = 30 / 100 × 2.150 = 64.5 / 100 = 0.645 ft²
Her current house has only 65% of the floor area of her dream house. Therefore, the floor area of her current home is as follows:
Floor area of her current home = 65 / 100 × 2.150
Floor area of her current home = 139.75 / 100
Floor area of her current home = 1.3975 ft²
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Show your work to earn full credit.
Jenae goes to the mall to buy a jacket. A store is having a sale for 30% off the original price of the jacket. Jenae also has a $10 off coupon she will use to make the purchase. The expression below can be used to find her final price for a jacket with an original price of p dollars.
0.7p - 10
The jacket she decides to purchase has an original price of p=$87.99. What is the final price of the jacket Jenae is buying?
Answers
Answer:
$51.60
Step-by-step explanation:
This is essentially substitutionI have found that shops tend to round up the .99, so I will work with $880.7 × 88 - 10 = $61.60 - 10 = $51.60need help 20 points and brainliest
Answers
Answer:
The smallest Number of ppl who bought banana's, number of kids at the park, number of ppl who landed at airport and the biggest is the number of residence in the usa
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
a tuba creates a 4th harmonic of frequency 116.5 hz what is the length of the pipe in the tuba
Answers
Since the tuba creates a 4th harmonic of frequency 116.5 hz, the length of pipe in tuba is 6.57 m
Since the tuba is an closed-pipe instrument, we need to find the frequency of a closed pipe
What is the frequency of an closed pipe?The frequency of a closed pipe f = nV/4L where
n = harmonic V = speed of sound and L = length of pipe in tubaLength of pipe in tubaMaking L subject of the formula, we have
L = nV/4f
Since the tuba creates the 4th harmonic with frequency 116.5 Hz.
n = 9 and f = 116.5 HzSubstituting the values of the variables into the equation, we have
L = nV/4f
L = 9 × 340 m/s/4 × 116.5 Hz
L = 3060 m/s ÷ 466 Hz
L = 6.57 m
So, the length of pipe in tuba is 6.57 m
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Answer:
5.88
Step-by-step explanation:
correct on acellus
(D) How do you write 172% as a fraction
Answers
Answer:
118/25 as a fraction hope it helps
Answer:
1 72/100 or 1 18/25 as simplified.
Step-by-step explanation:
100% is 100/100. 172/100 would be the fraction for this, but it is an improper fraction.
x^2+11x+28/x^2+5x+4 simplify expression
Answers
Answer:
(x + 7)/(x + 1)
Step-by-step explanation:
Simplify the following:
(x^2 + 11 x + 28)/(x^2 + 5 x + 4)
The factors of 4 that sum to 5 are 4 and 1. So, x^2 + 5 x + 4 = (x + 4) (x + 1):
(x^2 + 11 x + 28)/((x + 1) (x + 4))
The factors of 28 that sum to 11 are 7 and 4. So, x^2 + 11 x + 28 = (x + 7) (x + 4):
((x + 4) (x + 7))/((x + 4) (x + 1))
((x + 7) (x + 4))/((x + 4) (x + 1)) = (x + 4)/(x + 4)×(x + 7)/(x + 1) = (x + 7)/(x + 1):
Answer: (x + 7)/(x + 1)
Next time write the expression how it needs to be, the way you wrote it woould have given a toally different result.
x^2 + 11 x + 28/x^2 + 5 x + 4
Answer:
solving this as you would in algebra 2:
x2+11x+28 / x2+5x+4 = x+7 / x+1
Step-by-step explanation:
solving this as you would in algebra 2:
x2+11x+28 / x2+5x+4
1. on both the top and the bottom you have to find a factor of the last number (in this case 28 and 4) that multiplys to be the number but adds to be the 2nd term (11x and 5x)
2. for the top the two terms would be (x+7) and (x+4). on thebottom half it would be (x+4) and (x+1)
** 7 times 4 equals 28, 7 plus 4 equals 11; 4 times 1 equals 4, 4 plus 1 equals
3. x+4 is common term on both the top side and the bottom half so you cross it out. this leaves us with our answer of: x+7 over x+1
hope this helps:)
The surface area of this cylinder is 1,582.56 square feet. What is the height?
Answers
There are five basic equations which completely describe the cylinder with given radius r and height h:
Volume of a cylinder: V = π * r² * h,Base surface area of a cylinder: A_b = 2 * π * r²,Lateral surface area of a cylinder: A_l = 2 * π * r * h,Total surface area of a cylinder: A = A_b + A_l,Longest diagonal of a cylinder: d² = 4 * r² + h².Sometimes, however, we have a different set of parameters. With this height of a cylinder calculator you can now quickly use ten various height of a cylinder formulas which can be derived directly from the above equations:
Given radius and volume: h = V / (π * r²),Given radius and lateral area: h = A_l / (2 * π * r),Given radius and total area: h = (A - 2 * π * r²) / (2 * π * r),Given radius and longest diagonal: h = √(d² - 4 * r²),Given volume and base area: h = 2 * V / A_b,Given volume and lateral area: h = A_l² / (4 * π * V),Given base area and lateral area: h = √(A_l² / (2 * π * A_b)),Given base area and total area: h = (A - A_b) / √(2 * A_b * π),Given base area and diagonal: h = √(d² - 2 * A_b / π),Given lateral area and total area: h = A_l / √(2 * π * (A - A_l)).find the value of x
Answers
Answer:
x = 60°
Step-by-step explanation:
x + 2x + x + 2x = 360
Angles in a parallelogram add up to 360°
6x = 360
x = 60°
Answer: 60
Step-by-step explanation: The angles of a parallelogram alway add up to 360 degrees. We can use this and set the 4 angles (2x,2x,x,x) equal to 360.
2x+2x+x+x=360
6x=360
x=60
An exam will have 20 questions worth a total of 100 points. There will be true-false questions worth 3 points each and short answer worth 11 points each. The students want to know how many of each type there will be on the test. The teacher won't tell. How many short answer questions are there?
Answers
Answer:
4 true false and 8 short answer
Or 15 true false and 5 short answer
Or 26 true false and 2 short answer
Step-by-step explanation:
let x be the number of true-false questions
y be the number of short-answer questions
Then we have to solve the equation 3x + 11y = 100
Important: x and y are natural numbers
3x + 11y = 100 ⇔ 100 - 11y = 3x
If y=10 ⇒ 100 - 11×10 = −10 = 3x impossible because x ≥ 0
If y=9 ⇒ 100 - 11×9 = 1 = 3x impossible because x is a natural number
If y=8 ⇒ 100 - 11×8 = 12 = 3x ⇒ x = 12/3 = 4
Then (x,y) = (4,8) is a solution to the equation
If y=7 ⇒ 100 - 11×7 = 23 = 3x impossible because x is a natural number
If y=6 ⇒ 100 - 11×6 = 34 = 3x impossible because x is a natural number
If y=5 ⇒ 100 - 11×5 = 45 = 3x ⇒ x = 45/3 = 15
Then (x,y) = (15,5) is a solution to the equation
If y=4 ⇒ 100 - 11×4 = 56 = 3x impossible because x is a natural number
If y=3 ⇒ 100 - 11×3 = 67 = 3x impossible because x is a natural number
If y=2 ⇒ 100 - 11×2 = 78 = 3x ⇒ x = 78/3 = 26
Then (x,y) = (26,2) is a solution to the equation
If y=1 ⇒ 100 - 11×1 = 89 = 3x impossible because x is a natural number
If y=0 ⇒ 100 - 11×0 = 100 = 3x impossible because x is a natural number
What did Alexander Fleming discover during his research?
options:
The nucleus of an atom
X-Rays
Penicillium
Germs
Answers
Answer:
Penicillium
Step-by-step explanation:
Your answer is option c
Scottish bacteriologist Alexander Fleming is best known for his discovery of penicillin in 1928, which started the antibiotic revolution. For his discovery of penicillin, he was awarded a share of the 1945 Nobel Prize for Physiology or Medicine
if a turtle can move 1/7 of a mile every hour, then how many hours would it take for a turtle to go 5 miles?
Answers
Answer:
35 hours
Step-by-step explanation:
1 mile would be 7 hours- 7x5=35
*HEEEEEEEELP MEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE* I WILL GIVE ALOT OF POINTS AND BRAINLIEST, BUT THIS BETTER BE A TREE DIAGRAM.*Many games involve chance, and they usually involve either dice or cards. For this activity, we will look at a common game called 7‐11 where two dice are rolled. If the roll adds up to 7 or 11, the player wins. If the roll adds up to 2, 3, or 12, the player loses. If there is any other sum, it is a draw (no winner or loser). Use this two‐dice roll scenario to complete the problems below.
1. Create a tree diagram to determine all the possible outcomes of rolling two dice.
Answers
Answer: If dice is rolled then the possible outcomes are 1,2,3,4,5,6,???
Step-by-step explanation:
if that makes sense
A surgery shows that 85 percent of students carry a backpack to school. Is there are 230 students in the school,how many students carry a backpack
Answers
Will award brainliest for the correct answer!
Answers
how do i find these in surface area with work??
Answers
Answer:
Just multiply. the numbers that they r showing u is for the surface.
Step-by-step explanation:
I do it all the time and get it right.
PLS GIVE ME BRAINILIEST IT WOULD REALLY HELP ME!
LeAnn is playing a math game. She chooses three cards. The value of each of her cards is shown.
First card: -12
Second card: 3
Third card: -5
What is the sum of the values of LeAnn’s three cards?
Answers
Answer:
-14
Step-by-step explanation:
The sum (addition) of the three numbers would be -14 because -12+-5 is -17. Then, -17+3 would be -14.
Worth a lot of points! Mark brainliest if u show ur work and get the right answer.
Answers
Answers:
AC = 221.37 feet
BC = 181.34 feet
The values are approximate.
=========================================================
Explanation:
Focus on triangle ACD for now.
The 67 degree angle adjacent to angle D helps us find that angle D = 180-67 = 113 degrees.
Let's find the missing angle C.
A+C+D = 180
55+C+113 = 180
C+168 = 180
C = 180-168
C = 12
Now we can use the Law of Sines to find side d, which is opposite angle D. This is the segment AC.
[tex]\frac{\sin(C)}{c} = \frac{\sin(D)}{d}\\\\\frac{\sin(12)}{50} = \frac{\sin(113)}{d}\\\\d\sin(12) = 50\sin(113)\\\\d = \frac{50\sin(113)}{\sin(12)}\\\\d \approx 221.369 190\\\\d \approx 221.37\\\\[/tex]
Segment AC is roughly 221.37 feet long.
Keeping our attention on triangle ACD, let's find side 'a'. This is the segment CD.
[tex]\frac{\sin(C)}{c} = \frac{\sin(A)}{a}\\\\\frac{\sin(12)}{50} = \frac{\sin(55)}{d}\\\\a\sin(12) = 50\sin(55)\\\\a = \frac{50\sin(55)}{\sin(12)}\\\\a \approx 196.995 186\\\\[/tex]
Segment CD is roughly 196.995186 feet long.
----------------------------------------------
Now move onto triangle BCD.
Use the sine ratio to determine side BC.
[tex]\sin(\text{angle}) = \frac{\text{opposite}}{\text{hypotenuse}}\\\\\sin(\text{D}) = \frac{\text{BC}}{\text{CD}}\\\\\sin(67) \approx \frac{\text{BC}}{196.995186}\\\\\text{BC} \approx 196.995186*\sin(67)\\\\\text{BC} \approx 181.335025\\\\\text{BC} \approx 181.34\\\\[/tex]
Segment BC is roughly 181.34 feet long.