A 51-foot wire running from the top of a tent pole to the ground makes an angle of 58° with the ground. If the length of the tent pole is 44 feet, how far is it from the bottom of the tent pole to the point where the wire is fastened to the ground? (The tent pole is not necessarily perpendicular to the ground.)
Answers
Answer:
35.11 ft
Step-by-step explanation:
This given situation can be thought of as triangle [tex]\triangle PQR[/tex] where PQ is the length of pole.
PR is the length of rope.
and QR is the distance of bottom of pole to the point of fastening of rope to the ground.
And [tex]\angle Q \neq 90^\circ[/tex]
Given that:
PQ = 44 ft
PR = 51 ft
[tex]\angle R = 58^\circ[/tex]
To find:
Side QR = ?
Solution:
We can apply Sine Rule here to find the unknown side.
Sine Rule:
[tex]\dfrac{a}{sinA} = \dfrac{b}{sinB} = \dfrac{c}{sinC}[/tex]
Where
a is the side opposite to [tex]\angle A[/tex]
b is the side opposite to [tex]\angle B[/tex]
c is the side opposite to [tex]\angle C[/tex]
[tex]\dfrac{PR}{sinQ}=\dfrac{PQ}{sinR}\\\Rightarrow sin Q =\dfrac{PR}{PQ}\times sinR\\\Rightarrow sin Q =\dfrac{51}{44}\times sin58^\circ\\\Rightarrow \angle Q =79.41^\circ[/tex]
Now,
[tex]\angle P +\angle Q +\angle R =180^\circ\\\Rightarrow \angle P +58^\circ+79.41^\circ=180^\circ\\\Rightarrow \angle P = 42.59^\circ[/tex]
Let us use the Sine rule again:
[tex]\dfrac{QR}{sinP}=\dfrac{PQ}{sinR}\\\Rightarrow QR =\dfrac{sinP}{sinR}\times PQ\\\Rightarrow QR =\dfrac{sin42.59}{sin58}\times 44\\\Rightarrow QR = 35.11\ ft[/tex]
So, the answer is 35.11 ft.
Related Questions
Eddies saving account has a balance of $140. He deposits $17 for each of the next five weeks. He withdraws $11 in the final week. He wants to use his savings to buy a game system for $210. Do he have enough money to buy the game system?
Answers
Answer:
No. he need 64 more
Step-by-step explanation:
140+85=225-11=214
17x5=85
Find x. A. 22 B. 113–√ C. 222–√ D. 113√3
Answers
Answer:
x = 31.12
Step-by-step explanation:
First find the base (hypotenuse) of the smaller triangle (the isosceles triangle): Its three sides are 11, 11 and b. b can be found using the Pythagorean Theorem: b^2 = 11^2 + 11^2 = 242. Then b = √242, or b = approximately 15.56.
b (which is approximately 15.56) is the shorter leg of the large (right) triangle. The trig function needed to solve for x is the cosine:
adjacent side
cos 60 degrees = ----------------------
hypotenuse,
15.56
which becomes (1/2) = ------------
x
Solving this for x, we get: x = 2(15.56) = 31.12
1. At the end of one school day a teacher had 17 crayons left. The teacher remembered
giving out 14 crayons in the morning, getting 12 crayons back at recess, and giving out
11 crayons after lunch. How many crayons did the teacher have at the start of the
day?
Answers
Answer:
30 crayons
Step-by-step explanation:
Let x be the number of crayons he started with
gave out 14 crayons
x-14
Got 12 back
x-14+12
Gave out 11 after lunch
x-14+12 -11
This equals 17
x-14+12 -11 =17
Combine like terms
x-13 = 17
Add 13 to each side
x -13+13 =17+13
x = 30
Answer: 30
Step-by-step explanation:
For this problem work backwards. Start from 17 and add 14. You should get 31. Then subtract 12, which equals 19. Finally add 11 to 19, which equals 30. Basically you are doing the inverse operation to get your answer. Hope this helps!
The mean number of people per day visiting an art show in July was 110. If
20 more people each day visited the museum in August, what was the mean
number of people per day visiting in August?
A. 130
B. 620
C. 640
D. 110
Answers
Answer:
I believe the answer is A. 130
Answer:
A 130
Step-by-step explanation:
You and your best friend are both on the swim team. You want to beat your friend at the next swim meet so you decide to swim 151515 minutes longer than she does one day at practice. Write an equation for the number of minutes you swim, yyy, when your friend swims xxx number of minutes.
Answers
Answer:
y = x + 15
Step-by-step explanation:
My friend swims x minutes.
I swim 15 minutes more than my friends, so I swim x + 15 minutes.
I swim y minutes, so y equals x + 15
Answer: y = x + 15
Evaluate -3(8).
I know the answer is -24 but I don’t know who to work it out, can someone please help me
Answers
Answer:
-24
Step-by-step explanation:
-3 multiply 8 = -24
Because when ever you multiply a negative number with a positive number result will always be negative and 3 multiply 8 is 24.
Answer: -24
Step-by-step explanation: When you're asked to multiply
positives and negatives together, the rules are simple.
positive times a positive is a positive
positive times a negative is a negative
negative times a positive is a negative
negative times a negative is a positive
One way that I think will help you is to think
about the problem in terms of the signs.
If the signs are the same, the product will always be positive.
For example, (+3) · (+6) = +18 and (-6) · (-2) = +12.
If the signs are different, the product is negative.
So (+6) · (-4) is -24 and (-10) · (+5) is -50.
So don't get caught up on the signs.
Do the problem first, then determine if the
signs are the same or if they are different.
Zula has a conical bird feeder with a volume of 64.3 cubic centimeters and a height of 7 centimeters. Which equation can be used to find the area of the circular lid needed to cover the bird feeder?
Answers
Answer: [tex]64.3=\frac{1}{3}(B)(7)[/tex]
Step-by-step explanation:
[tex]V=\frac{1}{3} Bh[/tex]
B is the area of the base
h is the height of the cone
[tex]V=64.3 cm^3[/tex]
[tex]h=7cm[/tex]
[tex]64.3=\frac{1}{3}(B)(7)[/tex]
[tex]192.9=(B)(7)[/tex]
[tex]B=192.9/(7)[/tex]
[tex]=27.56cm^2[/tex]
For what real numbers x is x 2 − 10 x + 25 negative?
Answers
Answer:
no real numbers
Step-by-step explanation:
x^2 − 10 x + 25
Factor
What 2 numbers multiply to 25 and add to -10
-5*-5 = 25
-5+-5 = -10
( x-5) (x-5)
This touches the graph at x =5
The parabola is positive so there are no values where the graph is negative
Answer:
No real solutions
Step-by-step explanation:
Part 1: Factoring the quadratic
The equation is in quadratic form - ax² + bx + c = 0.
Therefore, we can use a factoring technique to solve for x. I will use the quadratic formula - [tex]x=\frac{-b \pm \sqrt{b^{2}-4ac} }{2a}[/tex].
[tex]x=\frac{-(-10)\pm \sqrt{(-10)^{2}-4(1)(25)} }{2(1)}\\\\x=\frac{10\pm\sqrt{100-4(25)} }{2}\\\\x=\frac{10\pm\sqrt{100-100}}{2}\\\\x=\frac{10\pm\sqrt{0}}{2}\\\\x=\frac{10\pm0}{2}\\\\x=\frac{10}{2}\\\\\boxed{x=5}[/tex]
Part 2: Using discriminant to determine roots
Because the discriminant (square root portion of formula) was equivalent to zero, this is the only solution that proves the equation correctly. Therefore, there is no possible negative value that can be substituted for x without altering the final value that the equation is equal to.
What is the 8th term of the sequence? −16, 24, −36, 54, ... −729/8 2187/8 −2187/8 729/8
Answers
Answer:
The answer is
[tex] \frac{2187}{8} [/tex]Step-by-step explanation:
The sequence above is a geometric sequence
For an nth term in a geometric sequence
[tex]A(n) = a ({r})^{n - 1} [/tex]
where n is the number of terms
r is the common ratio
a is the first term
From the question
a = - 16
To find the common ratio divide the previous term by the next term
That's
r = 24/-16 = -3/2 or -36/24 = - 3/2
Since we are finding the 8th term
n = 8
Substitute the values into the above formula
That's
[tex]A(8) = - 16 ({ - \frac{3}{2} })^{8 - 1} [/tex][tex]A(8) = - 16 ({ - \frac{3}{2} })^{7} [/tex][tex]A(8) = - 16( - \frac{2187}{128} )[/tex]We have the final answer as
[tex]A(8) = \frac{2187}{8} [/tex]Hope this helps you
A debt of $12,000 with interest at 5% compounded monthly is to be repaid by equal payments at the end of each year for three years and nine months. What is the term of repayment? None 12 months 3.9 years 3.75 years
Answers
Answer:
3.75 years
Step-by-step explanation:
If the debt is to be paid in 3 years, 9 months, then the term of the loan is ...
3 9/12 = 3 3/4 = 3.75 . . . years
It says to find the area of the shaded square, but I not sure how to get the answer.
Answers
Answer:
68 square cm
Step-by-step explanation:
Interior square WXYZ is making four right triangles of equal bases (8 cm) and heights (2 cm) inside the square ABCD. Therefore,
Area of shaded Square = Area of square ABCD - 4 times area of one right triangle.
[tex] = {10}^{2} - 4 \times \frac{1}{2} \times 8 \times 2 \\ = 100 - 32 \\ = 68 \: {cm}^{2} [/tex]
for 0°<θ<-180° which of the primary trigonometric functions may have positive values?
Answers
sine and cosecant.
you can see the graph or on unit circle, as the for these ratios, (which depend on y coordinate) 1st and 2nd quadrant have positive y coordinate
anyone know how to solve a functions equation such as x^2-x-x <0
Answers
Answer:
Step-by-step explanation:
[tex]x^{2} -x-x<[/tex] 0
[tex]x^{2} -2x[/tex] < 0
x^2-2x+1<1
(x-1）^2<1
-1<x-1<1
0<x<2
[tex](x-1)^{2}[/tex][tex](x-1)^{2}[/tex]
Given: -1/2x > 6. Choose the solution set. A {x | x R, x > -12} B{x | x R, x > -3} C{x | x R, x < -3}D {x | x R, x < -12}
Answers
Answer:
D
Step-by-step explanation:
-1/2x > 6 (you have to flip the sign when you multiply or divide by negative
x < -12
Se repartió una suma de dinero entre tres personas; la segunda recibió x pesos mas que la primera, la tercera b pesos más que la segunda. Expresa la suma repartida, siendo t la parte de la primera.
Answers
Answer:
3t + 2x + b
Step-by-step explanation:
primera: t
segunda: t + x
tercera: t + x + b
suma: t + t + x + t + x + b = 3t + 2x + b
E
What is the value of x in the equation 3x.. by y 18, when y27
Answers
Answer:
x = 15
Step-by-step explanation:
We need to find the value of x in the equation 3x – y = 18 when y = 27.
To find the value of x, put y = 27 in the above equation.
So,
3x - 27 = 18
3x = 45
x = 15
So, the value of x is 15.
Match each statement with its corresponding value for the system below:
y = -2(3)x and y = 9x - 2
1. The number of points of intersection.
2. The x-coordinate of the solution.
3. The y-coordinate of the solution.
Answers
Answer:
1. 1 point
2. The x-coordinate of the solution = 2/17
3. The y-coordinate of the solution = -16/17
Step-by-step explanation:
Given that the equation is of the form;
y = -2³×x and y = 9·x - 2, we have;
y = -8·x and y = 9·x - 2
1. Given that the two lines are straight lines, the number of points of intersection is one.
2. The x-coordinate of the solution
To find a solution to the system of equations, we equate both expression of the functions and solve for the independent variable x as follows;
-8·x = 9·x - 2
-8·x - 9·x= - 2
-17·x = -2
x = 2/17
The x-coordinate of the solution = 2/17
3. The y-coordinate of the solution
y = 9·x - 2 = 9×2/17 - 2 = -16/17
y = -16/17
The y-coordinate of the solution = -16/17.
The triangle is a right triangle with the right angle marked. Which equation correctly expresses The Pythagorean Theorem for this triangle?
Answers
r^2 + s^2 = t^2
The legs are length r and s. Square them and add the squares to get the square of the hypotenuse t. The hypotenuse is always opposite the 90 degree angle.
Answer:
Hey there!
The pythagorean theorem states that the square of one leg plus the square of another leg is equal to the square of the hypotenuse.
Thus, r^2+s^2=t^2.
This can be a challenging topic, and if you need a further explanation, let me know. Hope this helps :)
A driver of a car stopped at a gas station to fill up his gas tank. He looked at his watch, and the time read exactly 3:40 p.m. At this time, he started pumping gas into the tank. At exactly 3:44, the tank was full and he noticed that he had pumped 6 gallons.
Answers
Answer:
3.625 gpm
Step-by-step explanation:
Which expression is equivalent to the product of p+7/3 and6/p , where p0? PLZZZZ HELPPPPPPP
Answers
Answer: [tex]6+\dfrac{14}{p}[/tex] .
Step-by-step explanation:
To find : The expression is equivalent to the product of [tex]p+\dfrac73\text{ and }\dfrac6p[/tex], where p ≠0.
Product of [tex]p+\dfrac73\text{ and }\dfrac6p[/tex] = [tex](p+\dfrac73)\times\dfrac6p[/tex]
Using distributive property: [tex](b+c)a= ba+ca[/tex]
[tex](p+\dfrac73)\times\dfrac6p=p\times\dfrac6p+\dfrac73\times\dfrac6p\\\\= 6+\dfrac{7}{1}\times\dfrac2p\\\\=6+\dfrac{14}{p}[/tex]
Hence, the required expression is [tex]6+\dfrac{14}{p}[/tex] .
Answer:
B!!!
Step-by-step explanation:
Multiply then divide every number by 2 to simplify.
Answer ASAP, Will give brainliest!!
Answers
Answer:
First. 115°
Second. 65°
Third. 65°
Fourth. 7
Fifth. 425.25
First
angle DAB = angle ADC (since this is an isosceles trapezoid)
Second
In a trapezoid adjacent angle are supplmentary (that is their sum is 180°)
180-115 is 65°
Third
(Same reason as second)
Fourth
The side 3x+4 is same as the opposite side
So 3x + 4 = 25
on solving you get x = 7 in
Fifth
[tex]area \: = \frac{1}{2} \times length \: of \: the \: perpendicular \: (b1 + b2)[/tex]
area = 1/2 × 13.5 (20+43)
area = 1/2 × 13.5 × 63
Thus area is 425.25
Answer:
Step-by-step explanation:
1)As ABCD is isosceles trapezium,
∠ADC= ∠DAB
∠ADC = 115°
2) AD //BC
∠ADC + ∠DCB = 180° {co interior angles}
115 + ∠DCB = 180
∠DCB = 180 - 115
∠DCB = 65°
3) As ABCD is isosceles trapezium,
∠CBA = ∠DCB
∠CBA = 65°
4) As ABCD is isosceles trapezium, non parallel sides are congruent.
AB = DC
3x + 4 = 25 in
3x = 25 - 4
3x = 21
x = 21/3
x = 7 in
5) height = 13.5 in
a= 43 in
b= 20 in
Area of trapezium = [tex]\frac{(a+b)*h}{2}\\[/tex]
[tex]= \frac{(43 +20)*13.5}{2}\\\\=\frac{63*13.5}{2}\\\\\\= 425.25 in^{2}[/tex]
Plz Help I Will Mark Brainliest If Right!!!!!!!!!!!!!!!!!!!!!!!
Determine the domain of the function.
f as a function of x is equal to the square root of one minus x.
A). All real numbers
B). x > 1
C). x ≤ 1
D). All real numbers except 1
Answers
Hey There!!~
Your best answer choice is B). x > 1.
Good Luck!!
Based on the graph what are the solutions to ax^2 + bx+c=0 Select all that apply
A. X=-2
B. X=10
C. X=5
D. X=8
Answers
Answer:
x=-2 and x = 5
Step-by-step explanation:
The solutions to the equation are where the graph crosses the x axis
We can see that the graph crosses at x=-2 and x = 5
Answer:
x = -2
x = 5
Step-by-step explanation:
The answer is found when the graph crosses the x-axis
Hope this helps :D
The growth of a population of mountain lions can be described by the function f(x) = 500(1.015)^x, where x is the number of years after the first census. How do the mathematical domain and range compare to the reasonable domain and range? Check all that apply. Thank you!
Answers
Answer:
B E
Step-by-step explanation:
Answer:
B. The mathematical domain is the set of real numbers, while the reasonable domain only includes real numbers greater than or equal to 0.
E. The mathematical range has a minimum value greater than 0, while the reasonable range is limited to whole numbers and has a minimum value greater than or equal to 500.
Step-by-step explanation:
Edge 2021
Please give me the correct answer
Answers
Answer:
Height = 15Step-by-step explanation:
[tex]Volume = 392.5\\r = 5\\h =?\\\\V= \frac{1}{3} \pi r^2 h\\\\392.5 = \frac{1}{3} \times 3.14 \times 5^2 \times h\\\\392.5 = \frac{78.5h}{3} \\\\392.5 = 26.16h\\\\\frac{392.5}{26.16} =\frac{26.16h}{26.16} \\\\h = 15.00[/tex]
Answer:
h=15 in
Step-by-step explanation:
V=πr²(h/3)
h=3v/πr²
h=[3(392.5)]/[3.14(5)²]
h= 15 in
The minimal passing score for a test is 80%. There are 12 exercises on the test. What is the minimum number of correct exercises needed to earn a passing score?
Answers
Getting each exercise correct gets you 8.3(recurring)%. Therefore if you answer 10 exercises correctly you get 83.3%, and if you answer 9 exercises correctly you get 75%, this means that the minimal exercises you need to get correct is 10.
one day shahed was playing with numbers.He wrote 15 fractions using all natural numbers from 1 to 30 exactly once-either as numerator or as denominator.How many of these fractions are most is integers.
Answers
Answer:
15
Step-by-step explanation:
half of 30 is 15
he used all the numbers upto 30 once
all the numbers in between arent integers but decimals
Please help! Algebra 1.
Answers
Answer:
The correct answer is B.
Step-by-step explanation:The entrance fee ($18) and the cost per ball ($0.08B) added together should equal greater or equal to $75 in order to receive $10 off.
6=m/8 whats does m equal?
Answers
Answer:
m=48
Step-by-step explanation:
━━━━━━━☆☆━━━━━━━
▹ Answer
m = 48
▹ Step-by-Step Explanation
Rewrite:
m/8 = 6
Use the inverse operation:
8 * 6 = 48
m = 48
Hope this helps!
CloutAnswers ❁
━━━━━━━☆☆━━━━━━━
A man bought a car for 15000GH cedis . He later sold it at a profit of 25% .What was his selling price.
Answers
Answer:
3750 GH cedis
Step-by-step explanation:
Step-by-step explanation:
100%=15000GH cedis
125%=?
125×15000/100
18750GH cedis
