Determine the unknown length or angle measurement. Round each answer to the nearest whole number
Answers
Answer:
Θ ≈ 37° , x ≈ 13 cm
Step-by-step explanation:
(a)
using the cosine ratio in the right triangle
cosΘ = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{8}{10}[/tex] , then
Θ = [tex]cos^{-1}[/tex] ([tex]\frac{8}{10}[/tex] ) ≈ 37° ( to the nearest whole number )
(b)
using the sine ratio in the right triangle and the exact value
sin60° = [tex]\frac{\sqrt{3} }{2}[/tex] , then
sin60° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{x}{15}[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] ( cross- multiply )
2x = 15[tex]\sqrt{3}[/tex] ( divide both sides by 2 )
x = 7.5[tex]\sqrt{3}[/tex] ≈ 13 cm ( to the nearest whole number )
Related Questions
what is the classification of the triangle by its angles and by its sides??
ANSWER ASAP!!! PLS
Answers
Answer:
right triangle
Step-by-step explanation:
whenever there is a box in the corner it means its 90° and 90° is a right angle.
A square has an area of 64 square units. If its sides were only half as long, what would its area be?
Answers
Answer:
16
Step-by-step explanation:
the sides now are 8x8
1/2 of that is 4x4 and 4x4=16
The length of a driveway is 18 yards what is it in feet?
Answers
Answer:
Step-by-step explanation:
18yd(3ft/yd)=54ft
Answer:
Hello! :) have a good day!
54 feet
Adam made note of all the bicycles and cars he could see parked or locked on a
certain city block. All the cars had exactly four wheels, and all the bicycles had exactly
two wheels. How many wheels were on the block if there were 15 bicycles and 7 cars?
How many wheels were on the block if there were x bicycles and y cars?
Answers
Answer
68 bicycles.
Let there be x bicycles, then there are (93 - x) tricycles.
From the given values:
2x + 3(93 - x) = 211
2x + 279 - 3x = 211
-x = 211 - 279 = -68
x = -68/-1 = 68.
Hence, the wheels were on the block if there were [tex]x[/tex] bicycles and [tex]y[/tex] cars are [tex]x=68[/tex] bicycles.
What is the simplification?
Simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving. '
Here given that,
Adam made note of all the bicycles and cars he could see parked or locked on a certain city block. All the cars had exactly four wheels, and all the bicycles had exactly two wheels.
Suppose that there are [tex]x[/tex] bicycles, then there are [tex](93 - x)[/tex] bicycles.
So,
[tex]2x + 3(93 - x) = 211\\2x + 279 - 3x = 211\\-x = 211 - 279 = -68\\x = \frac{-68}{-1}\\x= 68.[/tex]
Hence, the wheels were on the block if there were [tex]x[/tex] bicycles and [tex]y[/tex] cars are [tex]x=68[/tex] bicycles.
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cos4A+sin4A-2cos2Asin2A=(2cos2A-1)2 prove it.
Answers
cos4A-sin4A=2cos2A-1
proved below.
Step-by-step explanation:
Given:
cos^4A-sin^4A=2cos^2A-1
LHS=cos^4A-sin^4A
=[cos^2A]^2-[sin^2A]^2
=[cos^2A+sin^2A][cos^2A-sin^2A]
=[1][cos^2A-(1-cos^2A)] [ cos^2A+sin^2A=1]
=[cos^2A-1+cos^2A]
=2cos^2A-1
=RHS.
(3/8)^-2(1/3x3/8)^3(1/3)^4
Answers
1/157464 x^9 is the answer
(100 POINTS!!!) PLEASE HELP ME!!! FIRST TO ANSWER WILL GET BRAINLIEST! 14:40 LEFT!
Answers
Answer:
the third one
Step-by-step explanation:
Answer:
that would be c
Step-by-step explanation:
Horse kg of grass in 12 days how much how much does he eat in 9 days
Answers
Step-by-step explanation:
The horse eats 9/12 in 9 days.
A recipe uses 2 cups of milk to make 4 servings. If the same amount of milk is used for each serving, how many servings can be made from three pints?
Answers
Answer:
12 servings
Step-by-step explanation:
Please let me know if you want me to write an explanation for my answer :)
kayden mixed two solutions together which causes a chemical reaction and the solution becomes warm. which statement best describes what has happened
A. energy has been transformed from one form to another
B. energy has been created, where it did not exist before
C. the chemicals energy of the solution had been described
D. more energy has been created than has been destroyed
Answers
According to law of conservation of energy, the statement which best describes what has happened is that energy has been transformed from one form to another.
What is law of conservation of energy?According to law of conservation of energy, it is evident that energy is neither created nor destroyed rather it is restored at the end of a chemical reaction .
Law of conservation of mass and energy are related as mass and energy are directly proportional which is indicated by the equation E=mc².Concept of conservation of mass is widely used in field of chemistry, fluid dynamics.
Law needs to be modified in accordance with laws of quantum mechanics under the principle of mass and energy equivalence.This law was proposed by Julius Robert Mayer in the year 1812.
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plz help just look at the picture
Answers
Answer:
120
Step-by-step explanation:
Answer:
the answer is C) 120
Step-by-step explanation:
2.5 pounds of grapes cost $2.25 what is the cost per pound
Answers
Answer:
$0.9 per pound
Step-by-step explanation:
$2.25 divided by 2.5
Answer:
$0.9 per pound
Step-by-step explanation:
$2.25 divided by 2.5
divide the cost of the item by its weight in pounds
*WILL GIVE BRAINLIEST 15 POINTS*
Find the volume of the triangular prism:
formula: V=12x base x height x length
Question 4 options:
A: 39 units3
B: 90 units3
C: 1,944 units3
D: 972 units3
Answers
helppp pleaasssseeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answers
Answer:
54.3701 feet or 16.57200648 meters
Step-by-step explanation:
50 PTSSSSSSSSSSSSSSSSSS
The expression 500(1.03)t models the population of a city in thousands of people t years since 2010. Based on this model, answer the following question: What is the expected population in the year 2025?
Answers
Answer:
515
Step-by-step explanation:
The express elevator in the Empire State Building in New York City travels nonstop from
the ground floor to the top floor at a rate of 1,400 feet per minute.
The express elevator in the John Hancock Center in Chicago travels nonstop from the
ground floor to the observatory on the top floor at a rate represented by the equation
y = 30x, where y is the height, in feet, and is the number of seconds
Graph the two relationships on the grid below to compare the rates of the
two elevators,
ELEVATOR RATES
I
Height (feet)
1,000
900
800
700
600
500
400
300
200
100
0
10
40
50
20 30
Time (seconds)
Which elevator travels at a faster rate?
Using the information from the graph, explain how you got your answer.
Answers
The elevator of John Hancock Center in Chicago travels at a faster rate.
The standard equation of a line is y = m + bm is the slope or rate of changeb is the y-intercept.For the equation represented by the height of the elevator of John Hancock Center in Chicago given as y = 30x, the rate of change is 30 ft/s which is equivalent to 1800 per minute.
Since the express elevator in the Empire State Building in New York City travels nonstop from the ground floor to the top floor at a rate of 1,400 feet per minute, hence the elevator of John Hancock Center in Chicago travels at a faster rate.
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how many cubes with a .25 inch side length will fit in a rectangular prism with a volume of 35.62
Answers
Answer:
142.48
Step-by-step explanation:
this i think is the answer
What is the circumference of a circle with a diameter of 9 inches.
Answers
Answer:
28.26 inches
Step-by-step explanation:
Given
diameter (d) = 9 inches
circumference (c)
= π d
= 3.14 * 9
= 28.26 inches
You have 0.2 liter of an acid solution whose acid concentration is 16 moles per liter. You want to dilute the solution with water so that its acid concentration is only 12 moles per liter. Use the given model todetermine howmany liters of water you should add to the solution.
Answers
Answer: 0.067 litres of water
Step-by-step explanation:
The mode is:
Concentration of new solution = Moles of acid in original solution / (Volume of original solution + Volume of water added)
Assume volume of water added is w.
12 = 16 (0.2) / (0.2 + w)
(0.2 + w) * 12 = 3.2
0.2 + w = 3.2 / 12
w = (3.2 / 12) - 0.2
w = 0.067 litres of water
The amount of water you should add to the solution is 0.067 liters.
Given
You have 0.2 liters of an acid solution whose acid concentration is 16 moles per liter.
You want to dilute the solution with water so that its acid concentration is only 12 moles per liter.
The concentration of new solution;You can also use the solution dilution calculator in order to calculate the concentration of ions in a diluted solution.
The amount of water you should add to the solution is given;
[tex]\rm Concentration \ of \ new \ solution =\dfrac{\text{Moles of acid in original solution } }{\text{Volume of original solution + Volume of water added}}\\\\12=\dfrac{16(0.2)}{0.2+w}\\\\12 (0.2+w)=16(0.2)\\\\2.4 +12w=3.2\\\\12w=3.2-2.4\\\\12w=0.8\\\\w=\dfrac{0.8}{12}\\\\w=0.067[/tex]
Hence, the amount of water you should add to the solution is 0.067 liters.
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1. Use the number line to help you decide which statement is true.
Answers
Answer:
2/5 < 1/2
Step-by-step explanation:
First, find the LCM for both denominators because you can't multiply 2 to get to 5. The LCM of 5 and 2 are 10, so you put that as their denominator. Then you have to think what you multiplied by 5 or 2 to get 10. For 2/5, you multiplied 5 by 2 to get 10, so multiply the numerator by 2 too. For 1/2, you multiplied 2 by 5 to get 10, so multiply the numerator by 5. Now, you will have 4/10 and 5/10. It's pretty obvious that 5/10 is bigger than 4/10, so the correct answer is 2/5 < 1/2
ASAP please help me correct this if it is wrong
Answers
Answer:
I believe the answer for the first one is -3, 3, number 3 would be 12
Step-by-step explanation:
Because if you are dilating by 1/3 then you will be dividing by 3, so if your point A coordinates are -9,9 then that divided by 3 is -3,3
Number 3 is 12 because your total of units from point D to C is 18 and it says to dilate by scale factor of 2/3 which again means to divide by 2/3 making your new length 12 units.
someone help me pls 10 points
Answers
Answer:
x=-5
Step-by-step explanation:
is there anyone who can help with this????
Answers
Answer:
C equals 48
Step-by-step explanation:
You add the two angles you have and take that answer and subtract it from 180 and that is the missing angle measure
Antwan drew the circle graph below
describing his time spent at school in 1
day. His teacher said that the number of
hours listed were correct, but that the
central angle measures for the sectors
were not correct. What should be the
central angle measure for the Core
subject sector?
A. 72°
B. 80°
C. 160°
D. 200°
E. 288°
Answers
A high school sponsored a badminton tournament. After each round, one-half of the players were eliminated. If there were 64 players at the start of the tournament, which equation models the number of players left after round 3?
(1) y=64(1-.5)^3
(2) y=64(1+.5)^3
(3) y=64(1-.3)^.5
(4) y=64(1+.3)^.5
Answers
Answer:
(1) y = 64(1 - .5)^3
Step-by-step explanation:
(1) y = 64(1 - .5)^3
If you are eliminated half, then you are removing 50% or .5 of the teams. The number of teams is getting smaller, so eliminate the choices with "+". The exponent refers to the number of rounds.
This is an easy one to check: 64, 32, 16, 8. There are 8 teams after three rounds.
y=64(1 - .5)^3
y= 64(.5)^3
y= 64(.125)
y= 8
What is the area of a parallelogram with a base of 14 feet and a height of 6 feet? Make sure you label your answer correctly too.
Answers
Answer:
84 Square Feet.
Step-by-step explanation:
In order to calculate the area of a parallelogram, just multiply base by height. So the area of this parallelogram is 14 x 6 = 84 Square Feet.
Factor ab + bc+ b² + ac.
A. (a + b)(b + c)
B. (a + c)(b + c)
C. b(a + b)(b + c)
Answers
Answer:
A. (a + b)(b + c)
Step-by-step explanation:
b( a + b ) + bc + ac
b( a + b ) + c ( b + a )
= (a + b)(b + c)
hope it helps!
Answer:
A
Step-by-step explanation:
a(b+c)+bc+bb
a(b+c)+b(c+b)
(b+c)(a+b)
Please help me I am struggling I’m only in 6th grade doing harder math
Answers
Answer:
-7a+11
Step-by-step explanation:
I NEED HELP ASAP PLEASE
Answers
Answer:
1679616
Step-by-step explanation:
6*6
36*36*36*36
Answer:
[tex]6^{8}[/tex]
Step-by-step explanation:
[tex](6^{2})^{4} = 6^{2*4} = 6^{8}[/tex]
I NEED HELP ASAP!!!!!!!!
Answers
Step-by-step explanation:
[tex]slope = \frac{rise}{run} = \frac{y2 - y1}{x2 - x1} \\ = \frac{ - 7 - 13}{5 - ( - 3)} \\ = \frac{ - 20}{8} \\ = \frac{ - 2 \times 10}{2 \times 4} \\ = \frac{ - 10}{4} \\ = \frac{ - 2 \times 5}{ 2 \times 2} = \frac{5}{2} [/tex]