7. What is the value of x?
6
6√3
12
12√3
8. What is the value of x?
7
7√2
14
14√2
9.What is the area of this triangle?
Enter your answer as a decimal in the box. Round only your final answer to the nearest tenth.
cm²
10. In △ABC, AC=12 in., BC=1.5 in., and m∠C=63°.
What is the area of △ABC?
Enter your answer as a decimal in the box. Round only your final answer to the nearest hundredth.
11. The relative locations of Pedro's house, the grocery store, and the bank are shown in the diagram.
What is the distance between the grocery store and the bank?
Enter your answer in the box. Round your final answer to the nearest mile.
mi
12. Marco, Garret, and Dino are hiding during a game of hide-and-seek. Their relative locations are shown in the diagram.
What is the distance between Garret and Dino?
Enter your answer in the box. Round your final answer to the nearest yard.
Answers
This is a 30-60-90 triangle. The short leg is half of the hypotenuse so 12/2 = 6 units long
The long leg, x, is equal to sqrt(3) times the short leg
long leg = (short leg)*sqrt(3)
long leg = (6)*sqrt(3)
long leg = 6*sqrt(3)
Answer: Choice B
=====================================================
Problem 8
This is a 45-45-90 triangle. The two legs are congruent. In this case, they are both 7*sqrt(2) units long.
Hypotenuse = (leg)*sqrt(2)
Hypotenuse = (7*sqrt(2))*sqrt(2)
Hypotenuse = 7*(sqrt(2)*sqrt(2))
Hypotenuse = 7*sqrt(2*2)
Hypotenuse = 7*sqrt(4)
Hypotenuse = 7*2
Hypotenuse = 14
So the value of x is 14
=====================================================
Problem 9
Use the SAS area of a triangle rule
Area of triangle = 0.5*(side1)*(side2)*sin(included angle)
A = 0.5*(8)*(12)*sin(65)
A = 48*sin(65)
A = 43.5027737777591
A = 43.5
Answer: 43.5
=====================================================
Problem 10
Angle C is the included angle (aka the angle between the given sides). Like with problem 9, we use the SAS area rule
Area = 0.5*(side1)*(side2)*sin(included angle)
Area = 0.5*12*1.5*sin(63)
Area = 9*sin(63)
Area = 8.01905871769531
Area = 8.02
Answer: 8.02
=====================================================
Problem 11
G = Grocery Store
B = Bank
P = Pedro's house
Given: GP = 11
What we want to find: Distance from G to B (ie find the length of GB). Call this distance x for now
a
Law of Sines:
sin(B)/GP = sin(P)/GB
sin(75)/11 = sin(54)/x
x*sin(75) = 11*sin(54)
x = 11*sin(54)/sin(75)
x = 9.21311626205676
Rounding to the nearest mile, x is roughly 9 miles
Answer: 9 miles
=====================================================
Problem 12
D = Dino
G = Garret
M = Marco
Given Info:
DM = 17 yards
GM = 15 yards
angle M = 81 degrees
What we want to find:
distance from D to G, aka the length of DG
Call this value x for now
Use the law of cosines to find x
(DG)^2 = (DM)^2 + (GM)^2 - 2*(DM)*(GM)*cos(M)
x^2 = 17^2 + 15^2 - 2*17*15*cos(81)
x^2 = 289 + 225 - 510*cos(81)
x^2 = 514 - 510*cos(81)
x^2 = 514 - 79.7815771705178
x^2 = 434.218422829482
sqrt(x^2) = sqrt(434.218422829482)
x = 20.8379083122439
Rounded to the nearest yard, the distance from Garret to Dino is roughly 21 yards.
The solution to the parts is given below.
What is Trigonometry?Trigonometry is a discipline of mathematics that studies the relationship between the sides of a triangle (right triangle) and their angles. There are six trigonometric functions that define the relationship between sides and angles.
1. Using Trigonometry
sin 60 = P/H
√3/2 = x/ 12
x = 12√3 / 2
x= 6√3
2. Using Trigonometry
sin 60 = P/H
1/√2 = 7√2 / x
x/√2 = 7√2
x = 14 unit
3. Using sine law
sin 75 /11 = sin 54 / x
0.965 / 11 = 0.809 / x
0.0877 = 0.809 / x
x = 9.224 miles
Learn more about Trigonometry here:
https://brainly.com/question/29002217
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Related Questions
PLEASE HELP ME ANSWER THIS
Answers
Answer:
25
Step-by-step explanation:
It is the product of the 3rd row of the first matrix with the second column of the second matrix:
(5)(8) +(-2)(6) +(1)(-3) = 40 -12 -3 = 25
Fourteen students are surveyed about the books they read. Four students read only science fiction books. Three students read only fantasy books. Five students do not read science fiction or fantasy. How many students read both science fiction and fantasy?
Answers
14 - 4 = 10
10 - 5 = 5
5 - 3 = 2
2 students read both science fiction and fantasy books
A sample of water is heated from 10.0 (degrees Celsius) to 15.0 (degrees Celsius) by the addition of 125 J of heat. What is the mass of the water?
(I understand what the question is asking me and I know that I have to use the formula q=m•c•DT but I don’t understand how to plug in a specific heat capacity if they don’t give it to me. Please help!!)
Answers
The family is going on a vacation they will drive 4,180 miles over two weeks about how many miles will they drive on average each day
Answers
Answer:
About 298 miles a day for two weeks because 4180/14=298.571428571
Step-by-step explanation:
Have a great day
In one day, the family will cover 298.57 miles
What is unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying it with the value of a single unit.
Given is a family which is going on a vacation they will drive 4,180 miles over two weeks
Now, in two weeks the family will drive = 4180 miles
This means that -
In 14 days, the family will cover 4180 miles.
Then, in one day, the family will cover (4180/14) or 298.57 miles
Therefore, in one day, the family will cover 298.57 miles
To solve more questions on unitary method, visit the link below-
brainly.com/question/18174151
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Suppose a college student pays $500 for tuition fees. However, she also has to pay $350 for her textbooks (ouch!). What percent of her total education costs does she pay for her books?
Answer: Her books represent
percent (as a decimal) of her total costs.
Write your answer to the nearest tenth of a percent, but in decimal form. For example, if you saved 34.67%, you would round to 34.7% and enter .347 as your answer.
Answers
Textbook costs = $350
Total cost = 500 + 350 = $850
Percent of costs due to textbooks = 100*(350/850) = 41.1765%
Her books represent 41.2% of her total costs.
Answer: 0.412
Can a 3 foot-by-9 foot rectangle be a scaled copy of a 3 foot-by-1 foot rectangle? Explain
Answers
Find the distance between the given points . find the midpoint of the segment with the given endpoints. round to the nearest tenth, if necessary
Answers
BD =4x + 5 and BF =9x
How to slove this problem
Answers
The centroid theorem, the value of x is: 2.5.
According to the centroid theorem, the centroid of a triangle is two-thirds of the distance from each midpoint to each vertex.
Given:
BD = 4x + 5
BF = 9x
Thus:
BD = 2/3(BF)
Replace 4x + 5 = 2/3(9x) with
4x + 5 = 6x
4x - 6x = -5
-2x = -5
x = 5/2
x = 2.5
As a result of the centroid theorem, the value of x is: 2.5.
Complete question:
Point D is the centroid of △ABC. Use the given information to find the value of x.
BD=4x+5 and BF=9x
x=
what is 10 times as much as 1.0
Answers
Hope this helps!!
6x^2-5x+1
Factor polynomial
Answers
=6x²-3x-2x+1
=3x(2x-1)-1(2x-1)
=(3x-1)(2x-1)
Write y-6x-9=0 in function notation
Answers
y - 6x - 9 = 0
y = 6x + 9
now, to put it in function notation, sub in f(x) for y
f(x) = 6x + 9 <== function notation
hope this helps:D
plz give brainiest
Urgent PLEASE!!!!!!!!!!!!!!!!!!
A bicycle manufacturing company makes a particular type of bike. Each child bike requires 4 hours to build and 4 hours to test. Each adult bike requires 6 hours to build and 4 hours to test. With the number of workers, the company is able to have up to 120 hours of building time and 100 hours of testing time for a week. If c represents child bikes and a represents adult bikes, determine which system of inequality best explains whether the company can build 20 child bikes and 6 adult bikes in the week.
No, because the bike order does not meet the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100
No, because the bike order does not meet the restrictions of 4c + 4a ≤ 120 and 6c + 4a ≤ 100
Yes, because the bike order meets the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100
Yes, because the bike order meets the restrictions of 4c + 4a ≤ 120 and 6c + 4a ≤ 100
Answers
20(4) +6(6) = 80 +36 = 116 total building time
20(4) +6(4) = 80 +24 = 104 total testing time ( this is greater than the allowed 100 hours)
Answer is: No, because the bike order does not meet the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100
Answer:
?
Step-by-step explanation: got 2 ur my streaks back up my n1g but i agree with the other person feel me.
Complete the pattern 5, 10, 30, 60, 180
Answers
5*2=10
10*3=30
30*2=60
60*3=180
180*2=360
360*3=1,080
Which of the following terms are like 3x^2y? Select all that apply.
3xy
3x^2y^2
-10x^2y
12xy^2
12x^2y
Answers
-10x^2y
12xy^2
12x^2y
all have Roots of x=0 and y=0
for a school field trip, there must be 1 adult to accompany 12 students, 3 adults to accompany 36 students, and 5 adults to accompany 60 students. Show that the relationship between the number of adults and the number of students is a proportional relationship. then write an equation for the relationship?
Answers
x is amount of adult
y is the student
-i hope this helps and have a wonderful day!!
Find the domain and range of the following function ƒ(x) = 3|x + 7| - 2?
A.Domain: [-2,∞) Range: (-∞,∞)
B.Domain: (-2,∞) Range: (-8∞,∞)
C.Domain: (-∞,∞) Range: [-2,∞)
D.Domain: (-∞,∞) Range: (-2,∞)
Answers
Answer:
D.Domain: (-∞,∞) Range: (-2,∞)
is the right answer.
Step-by-step explanation:
Given is a function as
[tex]f(x) = 3|x+7|-2[/tex]
This is an absolute value function hence the minimum value of
|x+2|=0
Hence the range cannot be below -2
For maximum no limit
[tex]Range = [-2,\infty)[/tex]
Domain can be any real value
Hence option d is correct answer.
Answer:
A) domain: (-∞, ∞) range: (-∞, ∞)
Step-by-step explanation:
A rectangle with an area of 120 in 2 has a length 8 inches longer than two times its width. What is the width of the rectangle?
Answers
width = x
length = 2x+8
area = l x w
x(2x+8)=120
2x^2+8x−120=0
x^2+4−60=0
(x+10)(x−6)=0
x=−10 and x=6
width has to be a positive number
Width = 6
inches.
Which of the following expressions is equal to 5 - 2m?
7 - 2(m + 1)
7 - (2m - 5)
7 - 2(m - 2)
Answers
Which of the following sets is a function?
{(0, 1), (-2, 8), (5, 19), (2, 8)}
{(1, 0), (11, 0), (-5, 7), (1, 9)}
{(17, -8), (1, 16), (53, 9), (1, 23)}
Answers
{(0,1), (-2,8), (5,19), (2,8)}....this has no repeating x values and is therefore, a function
What is the value of x? x+13=9
Enter your answer in the box in simplest form.
x =
Answers
x=6
that answer is 6
Find area of a rectangle
Answers
Area = l*w = 72
L = 72/w
Perimeter = 2l+ 2w
44 = 2(72/w) +2w
22 = 72/w +w
W^2-22w +72 =0
(w-18) (w-4) = 0
W = 18
L = 4
One inlet pipe can fill an empty pool in 4 hours, and a drain can empty the pool in 8 hours. how long will it take the pipe to fill the pool if the drain is left open?
Answers
Given that one inlet pipe can fill an empty pool in 4 hours. The outlet pipe can empty the pool in 8 hours. We know that rate x time = work done.
Rate = work done / time
Rate of inlet pipe = ¼ hours.
Rate of outlet pipe = 1/8 hours
Here 1 represent the work completed.
Let x be the time taken to fill the pool by the inlet pipe if the drain is left.
Work done by inlet pipe – work done by outlet pipe = 1 work completed.
x/4 – x/8 = 1.
To solve the rational equation, first we clear the fractions by multiplying it with LCD (4,8)=8 to each item.
8(x/4) – 8(x/8) = 8(1)
2x – x = 8
X = 8
Time taken for the pipe to fill the pool if the drain is left open = 8 hours
What events forced the passengers on the mayflower to write and sign the mayflower compact? -?
Answers
The line graphed by the original function f(x)=13x+1 is translated to g(x)=13x−17 using the mapping statement f(x)↦f(x)+k. What is the value of k?
Answers
k = g(x) - f(x)
k = 13x - 17 -(13x +1)
k = 13x -17 - 13x -1
k = -18
Question 2 says: With out multiplying, determine the sign of the product
(19)(-2)(37)(-0.8)(122)
A.Positive
B.Negative
C.The product is zero
Answers
in this case, there are two negatives, the the product is a positive number
A population consists of 200 elements. we want to draw a simple random sample of 40 elements from this population. on the first selection, the probability of an element being selected is
Answers
The probability of an element being selected on the first selection of a simple random sample is 0.2.
Explanation:The probability of an element being selected on the first selection of a simple random sample can be calculated by dividing the size of the sample (40) by the size of the population (200).
In this case, the probability is 40/200 = 0.2.
how to solve log base 5 of x + log base 5 of (4x-1)
Answers
As the bases are the same the number doesn't matter
Log (a) + log(b) =log (ab)
Log(4x^2-x)
(x )(4x-1)
x=0.25 or x=0
Log(4×0.25^2-0.25) = log(0) = Infinity
Same with 0. So no answer
To solve for log base 5 of x + log base 5 of (4x-1), combine the two logarithms using the property that the sum of logarithms is equal to the logarithm of the product: log base 5 of x + log base 5 of (4x-1) = log base 5 of (x(4x-1)).
To solve the logarithmic expression log5(x) + log5(4x-1), we can combine the two logarithms using the property that the sum of logarithms is equal to the logarithm of the product. This gives us:
log5(x) + log5(4x-1) = log5(x(4x-1))
So the solution to the expression is log5(x(4x-1)).
Tracey paid $170 for an item that was originally priced at $580. What percent of the original price did Tracey pay? Round your answer to two decimal places.
Answers
Just divide the new price by the original price and multiply that by 100 :)
You get 0.2931.....
So round it to 0.29
Then that’s equal to 29%.
Explain the difference between a population and a sample. choose the correct answer below.
Answers
△RST is mapped to △R′S′T′ using the rule (x, y)→(x, −y) followed by (x, y)→(3x, 3y) .
Which statement correctly describes the relationship between △RST and △R′S′T′ ?
△RST is not congruent to △R′S′T′ because the rules do not represent a sequence of rigid motions.
△RST is congruent to △R′S′T′ because the rules represent a reflection followed by a rotation, which is a sequence of rigid motions.
△RST is congruent to △R′S′T′ because the rules represent a reflection followed by a translation, which is a sequence of rigid motions.
△RST is congruent to △R′S′T′ because the rules represent a rotation followed by a translation, which is a sequence of rigid motions.
Answers
(y->-y) followed by a dilation (x->3x, y->3y). Reflections and rotations ARE congruent because rigid motions, but dilations/contractions change size, are NOT rigid, and therefore NOT congruent.