The accompanying diagram shows a flagpole that stands on level ground. Two cables, r and s,
are attached to a pole at a point 20 feet above the ground. The combine length of the two cables
is 70 feet. If cable r is attached to the ground 8 feet from the base of the pole, what is the
measure of the angle, x, to the nearest degree, that cable s makes with the ground?
Answers
Answer:
x = [tex]24^{o}[/tex]
Step-by-step explanation:
r + s = 70 feet
Applying Pythagoras theorem to the triangle formed by cable r;
[tex]/hyp/^{2}[/tex] = [tex]/adj1/^{2}[/tex] + [tex]/adj2/^{2}[/tex]
[tex]/r/^{2}[/tex] = [tex]/20/^{2}[/tex] + [tex]/8/^{2}[/tex]
[tex]r^{2}[/tex] = 400 + 64
= 464
r = [tex]\sqrt{464}[/tex]
= 21.541
Length of cable r is 21.54 feet.
So that,
r + s = 70 feet
21.54 feet + s = 70 feet
s = 70 feet - 21.54 feet
= 48.46 feet
Length of cable s is 48.46 feet.
Applying trigonometric function to the triangle formed by cable s, we have;
Sin θ = [tex]\frac{opposite}{hypotenuse}[/tex]
Sin x = [tex]\frac{20}{48.46}[/tex]
= 0.4127
x = [tex]Sin^{-1}[/tex] 0.4127
= 24.3746
x = [tex]24^{o}[/tex]
The measure of angle that s makes with the ground is approximately [tex]24^{o}[/tex].
Related Questions
Her teacher asked her to write the correct equation or inequality that matches the graph. Laurie wrote the following:y>2x-4 . Her teacher marked her answer incorrect. Explain the error that Laurie made and then write the correct solution.
Answers
The correct solution of Laurie's inequality expression is y ≥ 2x - 4
How to explain the error that Laurie made and then write the correct solution?Laurie's inequality expression is given as
y > 2x - 4
The graph of the inequality expression that completes this question is added as an attachment
From the attached graph, we can see that the line of the inequality is a thick or closed line
Thick and closed line are represented by the inequality signs ≤ and ≥
Since the upper region is shaded, we make use of ≥ inequality sign
Hence, the correct solution of Laurie's inequality expression is y ≥ 2x - 4
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maria walks 22 feet, then goes another 40 feet on a path that makes a 70 degree angle with the path she was on. how far is she, in feet, from her starting location?
Answers
Answer:
132 feet
Step-by-step explanation:
22+60+70
The distance of the Maria from her starting location is 109.9 feet.
What is trigonometry?Right angle triangles are the focus of the mathematical field of trigonometry. Calculations involving specific functions of angles are the focus of trigonometry.
In trigonometry, the following six functions are frequently used: sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (cosec)
Let's call the distance Maria is from her starting location "x".
The 70 degree angle forms a right triangle with the distance Maria walked initially (22 feet) and the distance she is from her starting location (x). We can use the trigonometric function tangent to find x:
tan(70°) = x/40
Multiplying both sides by 40, we get:
x = 40 tan(70°)
Using a calculator, we find that tan(70°) is approximately 2.7475. Multiplying by 40, we get:
x = 109.9
So Maria is approximately 109.9 feet from her starting location.
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What is an equation of the line that passes through the points
(-3,-1) and(-6, 3)? Put your answer in fully reduced form.
Answers
Use synthetic division to divide x³ + 3x² - 4x - 10 by x - 2
2
1
1
The quotient is:
The remainder is: 2
2
5
3
10
6
-4
>
>
Note: Enter only a number for the remainder, no fraction.
12
2
-10
Answers
The Quotient and remainder of the polynomial is x² + x -6 and 2 respectively
Synthetic division method is one of the method used to divide the polynomial equations.
The polynomial equation given here is
x³ + 3x² - 4x - 10
We need to divide this polynomial equation with x - 2
Thus by dividing the polynomial x³ + 3x² - 4x - 10 with x - 2, we get
the quotient as x² + x -6 and
Remainder as 2
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how do you solve this equation step-by-step? (below)
4a + 8 - 2a - 3 = 45
Answers
Answer:
a=20
Step-by-step explanation:
Answer:
Step-by-step explanation:
4a-2a+8-3=45
2a+5=45
2a+5-5=45-5
2a/2=40/2
a=20
Write an equation in slope-intercept form for the line that passes through (1,9), and (3,5).
Answers
To write the equation of the line, we will use the point-slope formula.
To do this, we need a point and a slope.
We can find out slope by using the slope formula.
m = y₂ - y₁ / x₂ - x₁
So we have 5 - 9 / 3 - 1 or -4/2 which is -2.
Now let's use the point-slope formula.
y - y₁ = m(x - x₁)
Now substitute one of our points (x₁, y₁) into our formula.
So we have y - 5 = -2(x - 3).
Distributing the -2 gives us y - 5 = -2x + 6.
Moving the -5 to the right, we have y = -2x + 11.
So y = -2x + 11 is our equation.
Use a formula: y2-y1/x2-x1 aka rise/run
So that makes it 5-9/3-1 = -4/2 = -2
Then you can plug in one of the given points and the slope you just found into the slope-intercept form equation.
Slope intercept form: y=mx + b
Plug in the points: (3,5) and slope - 2
5=-2(3) + b
5=-6+b
11=b
Now that we have our y intercept and our slope who can write the equation in slope-intercept form
Y = -2x + 11
This is the equation of the line. You can check it by plugging in the points given and seeing If it works
Good luck! :)
A line segment has end points at (3, -5) and (4, 1) What is its length?
a. 9 units
b. 6.9 units
c. 9.2 units
d. 5 units
need an explanation if possible please.
Answers
Answer:
6.08units
Step-by-step explanation:
The distance between two points of a line is expressed as;
D = √(y2-y1)²+(x2-x1)²
Given the coordinates (3, -5) and (4, 1);
D = √(1+5)²+(4-3)²
D = √(6)²+(1)²
D = √36+1
D = √37
D = 6.08 units
Hence its length is 6.08units
A group of adults and students buy tickets for a dance performance.
*Each ticket costs $5.35
*The total cost of the tickets for the group is $69.55
*There are exactly 3 adults in the group.
What is the number of students in the group?
Explain your steps on how you solved this problem.
Answers
Answer:
There are 10 students
Step-by-step explanation:
69.55-(5.35*3)= 53.5
53.5/10=5.35 which is what each ticket costed
So the answer is 10 students
[tex] \sqrt{122} + \sqrt{160} [/tex]
plz answer in root
Answers
Please help I will give anyone brainliest
Answers
Answer:
Equation: 190 = 6 + 23p
Answer: p = 8
Step-by-step explanation:
So first we have a total of $190 and regardless of how many people go, parking is going to cost $6 so that amount will be reduced from the total money they have for the amusement park. The rest left will go towards the tickets. That means the amount they have is $190-$6 = $184. 23 x the number of tickets = $184. You need to divide the 184 by 23 to get the number of tickets. Which is p in this situation. Therefore the answer for p would be 8. For the equation, you have 190 = 6 + 23p. Therefore those two is our answers.
2. Mrs. Cianciaruso and Mrs. Braithwaite were folding report cards to send home to parents. The ratio of report cards Mrs. Cianciaruso folded to the number of report cards Mrs. Braithwaite folded is 2:3) At the end of the day, Mrs. Braithwaite folded a total 12 more report cards than Mrs. Cianciaruso. How many did they fold together?
Answers
Mrs Cianciaruso folded 24 report cards and Mrs Braitwaite folded 36 report cards
The ratio of report cards folded by Mrs Cianciaruso and Mrs Braithwaite is 2:3
Let x be the number of report cards folded by Mrs Cianciaruso, therefore:
No. of report cards folded by Mrs Cianciaruso = x
It is given that Mrs Braithwaite folded 12 more report cards than Mrs Cianciaruso therefore, No. of report cards folded by Mrs Braithwaite = x +12
The equation will be:
x/x+12 = 2/3
3x = 2x + 24
x = 24
Hence, Mrs Cianciaruso folded 24 report cards and Mrs Braitwaite folded 36 report cards
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Does anyone know how to do this
Answers
35 hours worked at $7.75 per hour.
Hourly Rate
$7.75
X
Hours Worked
35
Straight-Time Pay
$271.25
Example 2
367 hours worked at $8.775 per hour.
Calculator:
Hourly Rate
$8.775
$8.775
Hours Worked
36.75
36.75
Straight-Time Pay
$322.481
$322.48125
given the equation y= -1/3x - 10, find the value of y when x is -9
Answers
Answer:
-13
Step-by-step explanation:
Because
Fred and Winnie O'Callahan have put themselveson a very strict budget. Their goal at the end of the year is to buy a car for $14,200 in
cash. Their budget includes the following per dollar:
0.50 Food and lodging
0.30 entertainment
0.15 educational
Fred earns $2,170 per month and Winnie earns $2,570 per month. After 1 year will Fred and Winnie have enough cash to buy the car?
Yes or no
Answers
Answer:
No
Step-by-step explanation:
I'm not 100% sure that this was the question but I hope so
2170+2570=$4740 per month
4740*12=$56880 per year
Food: 56880*0.5=$28440
Entertainment: 56880*0.3=$17064
Educational: 56880*0.15=$8532
28440+17064+8532=$54036
56880-54036=$2844
Or a quicker method: 1-0.5-0.3-0.15=0.05
0.05*56880=$2844
Does anybody know what the answer to this question is?
If you know, please tell me. I'm really in a hurry.
Answers
Answer:
1.25
Step-by-step explanation:
45 over 36 is 1.25
.o. >_< ._. .-. .>. .,. .O. .0. :o :O ;o ;O .
PLEASE HELP ILL MARK BRAINLIEST
Answers
Answer:
top is 13 gallons left
bottom is 7.8 gallons left
Step-by-step explanation:
30=1 gallon
90= 3 gallons
246/30= 8.2
8.2*1=8.2
16-8.2=7.8
The radar system in an airport determines the location of inbound and outbound planes once they are within range. The range, based on the signal from the tower, is represented by the polar equation r = 10cos(θ). Which graph represents the signal range of the airport’s radar system?
Answers
Answer:The one with the circle on the right.
Step-by-step explanation:
It was A for me but its D for you that's why I'm saying the one with the circle on the Right
Answer: A
Step-by-step explanation:
Write in decimal form:
7 x 100 +
6 x 10 +
5x 1 +
0 (1/10) +
3* (1/100) +
7 x (1/1000)
Answers
Answer:
765 37/100
Step-by-step explanation:
The decimal form of the expression is 765.037
What is the decimal form?The decimal form is a way of expressing fractions and numbers as decimals.
In mathematical expressions, decimals are positioned in such a way as to differentiate between the whole number part and the fractional number part.
From the given information, we have:
[tex]\mathbf{=7 \times 100 + 6 \times 10 + 5\times 1 + 0 (\dfrac{1}{10}) + 3\times (\dfrac{1}{100}) + 7 \times (\dfrac{1}{1000})}[/tex]
[tex]\mathbf{=700+60 + 5+ 0 + \dfrac{3}{100} +\dfrac{7}{1000}}[/tex]
= 765.037
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Masha bought red, green, and yellow balloons for a party. She bought 40 red balloons. The number of green balloons Masha 3 bought is of the number of red balloons. The number of green 5
balloons is also 2 3 of the number of yellow balloons.
How many balloons did Masha buy for the party?
Answers
Using mathematical operations, the number of balloons that Masha bought for the party was 100, made up of red, green, and yellow balloons.
What is the mathematical operation?Mathematical operation includes the use of basic math operators, including addition, subtraction, division, and multiplication to determine and express mathematical values.
Data and Calculations:Red balloons = 40 balloons
Green balloons = 3/5 (40) = 24 balloons
Green balloons = 24 = 2/3 of yellow balloons
Yellow balloons = 24÷ 2/3 = 24 x 3/2 = 36 balloons
Total ballons bought:
Red = 40
Green = 24
Yellow = 36
Total = 100 (40 + 24 + 36)
Thus, using mathematical operations, the total number of balloons that Masha bought for the party was 100 balloons.
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Complete Question:Masha bought red, green, and yellow balloons for a party. She bought 40 red balloons. The number of green balloons Masha bought is 3/5 of the number of red balloons. The number of green balloons is also 2/3 of the number of yellow balloons. How many balloons did Masha buy for the party?
Solve the system by any method
3x - 7y + 7z = -11
-3x + 7y - 7z = 14
9x - 21y + 21z = -34
Answers
joey mows the back of his neighbors lawn. if he is rewarded 31.50 in 7 hours. how much does he make in 17 hours?
help!
Answers
Answer:
315.0
Step-by-step explanation:
31.50x10 is just moving the digits up one place
Answer:
$76.50
Step-by-step explanation:
To find out how much he makes each hour, we do
31.5/7
resulting in 4.5
if he works for 17 hours
17 * 4.5
He would earn $76.50
A: y=3/5x
B: y=5/3x
C: xy= 3/5
D: xy: 5/3
help pleaseee
Answers
What is the volume of a cylinder, in cubic ft, with a height of 9ft and a base diameter
of 16ft? Round to the nearest tenths place
Answers
Answer:
1809.6 cubic feet
Step-by-step explanation:
Use the formula for the volume of a cylinder, V = [tex]\pi[/tex]r²h
Plug in the height and radius:
V = [tex]\pi[/tex]r²h
V = [tex]\pi[/tex](8²)(9)
V = 1809.6
So, the volume of the cylinder is 1809.6 cubic feet
PLEASE HELP MEEEEEEEEEEEEEEEEEEEEEE
There are 360 people in a movie theater. Of these people, 35% bought student tickets, and 45% bought adult tickets. The rest bought senior-citizen tickets. how many people bought senior tickets?
Answers
45+35=80
100-80=20
360×20/100
72 so the answer is this and the formula E=T×%/100
guys, please hels asap imma mark as brainless
Answers
Step-by-step explanation:
Now it doesn't let me answer in the right question and it does let me answer here.
i will give brainlest
Answers
Answer:
b
Step-by-step explanation:
How you express the average of five quizzes is 85 in mathematical expression
Answers
y = (x1 + x2 + x3 + x4 + x5) / 5
since y = 85:
(x1 + x2 + x3 + x4 + x5) / 5 = 85
which is the correct answer?
Answers
Answer:
The answer is C.
Step-by-step explanation:
Square root of a negative number is non real.
(02.06 LC)
If one foot is the same length as 12 inches, how many inches equal 3.5 feet? (Only input whole numbers.)
Answer for Blank 1
Answers
At the grocery store, Mr. Arnett allowed each of his
children to fill their own bag with trail mix for their hike.
The table shows the amount of trail mix for each child.
Child
Ava
Grayson
Mason
Tyler
Amount of
Trail Mix (oz)
15
14
10
17
The trail mix costs $4.50 per pound. How much will Mr.
Arnett pay for all the trail mix?
Answers
Mr. Arnett will pay $207 for all the trail mix bought by his children.
Here, we are given that Mr. Arnett allowed each of his children to fill their own bag as follows-
Child Ava Grayson Mason Tyler
Amount of
Trail Mix (oz) 15 14 10 7
Further, cost of trail mix = $4.50 per pound
The total amount of trail mix collected by all 4 children will be-
15 + 14 + 10 + 7
= 46
Thus, in total the children put 46 pounds of trail mix in their bags.
Hence, the total cost will be-
46 × 4.5
= 207
Thus, Mr. Arnett will pay $207 for all the trail mix.
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