Using relations in a right triangle, it is found that the length of the zip line is of about 63.9 ft.
What are the relations in a right triangle?The relations in a right triangle are given as follows:
The sine of an angle is given by the length of the opposite side to the angle divided by the length of the hypotenuse.The cosine of an angle is given by the length of the adjacent side to the angle divided by the length of the hypotenuse.The tangent of an angle is given by the length of the opposite side to the angle divided by the length of the adjacent side to the angle.In this problem, the hypotenuse is the length of the line, considering that the base of 60 ft is adjacent to the angle of 20º, hence:
[tex]\cos{20^\circ} = \frac{60}{l}[/tex]
[tex]l = \frac{60}{\cos{20^\circ}}[/tex]
[tex]l = 63.9[/tex]
The length of the zip line is of about 63.9 ft.
More can be learned about the relations in a right triangle at https://brainly.com/question/18090623
Mr. Smith is 81 years older than his grandson, Victor. In 3 years, Mr. Smith will be four times as old as Victor. How old is Victor now?
♧ So, after 3 years = x+81 +3
81 + 3 + x = 4 ( x + 3 ) 84 + x = 4x + 12♧ now grouping the variables and constants together we get,
4x-x=84-12 3x = 72x = 72/3x = 24♧ Thus, Victor's present age is 24 yrs.
Hope it helps ya ~
Answer:
Victor's age = 24 years old
Step-by-step explanation:
Let age of Mr. Smith = x and age of Victor = y.
According to the question, we can find two equations.
=> 1) x = y + 81
=> 2) x + 3 = 4(y + 3)
Substituting value of x in (1) to (2)
y + 81 + 3 = 4y + 12
3y = 72
y = 24
Victor's age = 24 years old
Find the slope of the line through the points (-3, 1) and (-1,5).
Answer:
See below.
Step-by-step explanation:
(-3,1) and (-1,5)
The formula for finding slope is (y²- y¹)/(x²- x¹).
(5-1)/(-1-(-3))
(4)/(2)
2
The slope would be 2.
-hope it helps
Hi! I hope you're enjoying your day!
Use the Slope formula:
[tex]\bold{\displaystyle\frac{y2-y1}{x2-x1}}[/tex]
[tex]\bold{\displaystyle\frac{5-1}{-1-(-3)}}[/tex]
[tex]\bold{\displaystyle\frac{4}{-1+3} =\frac{4}{2} =2}[/tex]
Hence, the slope is
[tex]\boxed{\boxed{\bold{2}}}[/tex]
Hope everything is clear.
If you have any questions, please comment.
#LearningIsFun
[tex]\rule{250}{2}[/tex]
10. If mACD = (7x - 12) and
mBDC = (10x + 5), find x
Since both angles will be a part of triangle, and the third angle would be 90° as, the vertices meet at an centre of diagonal, hence they bisect each other.
7x-12 +(10x+5) = 90°
==> 17x -7= 90°
==> 17x = 97°
==> x = 97°/17
==> x = 5.70° (approx)
How would the expression x^3 - 64 be rewritten using difference of cubes? A. (x + 4)(x^2 - 4x + 16) B. (x-4)(x^2 + 4x + 16) C. (x+4)(x^2 - 4x - 16) D. (x-4)(x^2 + 16x+4)
Answer:
D)
Step-by-step explanation:
4 is an evident zero of the equation x^3 - 64.
x^3 - 64 can only be factorized with (x-4) and not with (x+4)
because x - 4 = 0 <==> x = 4 and 4^3 -64 = 0
Developing B) would be:
x^3 + 4x^3 + 16x - 4x^2 - 16x - 64 = 5x^3 - 4x^2 -64
So it doesn't match so it's D)
BRAINLIEST HURRYYY
The equation of a linear function is y = –2x + 3. Which table contains a set of points that lie in the graph of this function?
Answer:
The answer is A)
Step-by-step explanation:
To find out table contains a set of points that lie in the graph of this function , we have to hit and trial method ,
when we put the value of x in y = –2x + 3 this equation so ,
taking x = 1 , then the value of y is
=> y = -2(1)+3
=> y = -2+3
=> y = 1
taking x = 0 , then the value of y is
=> y = -2(0)+3
=> y = 3
now talking x = -3 , then the value of y is
=> y = -2(-3) +3
=> y = 6+3
=> y = 9
so , the option A is the right answer
Answer:
A)
Step-by-step explanation:
Given linear function: y = -2x + 3
Therefore, the slope is -2 and the y-intercept is (0, 3)
Therefore, we are looking for a set of ordered pairs that has a rate of change of -2
⇒ as the x-value increases by 1 unit, the y-value decreases by 2 units
i.e. as the x-value decreases by 1 unit, the y-value increases by 2 units.
The only set of ordered pairs that follows this rule is A)
Let's check by substituting the values of x = 1, x = 0 and x = -3 into the function:
when x = 1 → -2(1) + 3 = 1
when x = 0 → -2(0) + 3 = 3
when x = -3 → -2(-3) + 3 = 9
Confirming that the set of ordered pairs in A) lie on the graph of the given function.
Amount
Rate
Cost per ounce (Unit cost)
Total Cost
$1.28
16 Oz
Answer:
$20.48
Step-by-step explanation:
$1.28 multiplied by 16
David bought a poster for an art project. The poster is 2. 7 feet wide and 3. 9 feet tall. What is the area of the poster? Enter your answer as a decimal in the box. Ft2.
Answer:
10.53 ft.²
Step-by-step explanation:
Area of a rectangle: length x width
length: 3.9
width: 2.7
3.9 x 2.7 = 10.53
(4 7/8) (8 1/10) ( 3) HELP ASAP!!!!!!
Answer:
8.4
Step-by-step explanation:
(7/8) (4) = 3.5
(1/10) (8) = 0.8
3.5 × 0.8 × 3 = 8.4
Hope this helps.
Describe the term to term rule in this sequence:
10.8.6.4.2...
A tennis racket and a tennis ball cost $2.10. The tennis racket costs two dollars more than the tennis ball.
How much does the tennis ball cost?
Sn: I think it’s .10 but I wanna double check.
Answer:
4 dollars
Step-by-step explanation:
Answer:
4.10$
Step-by-step explanation:
Two less than the product of
5 and the cube of a number.
Answer:
5x^3-2
Step-by-step explanation:
Two less than the product of 5 and the cube of a number.
The product of 5 and the cube of a number can be translated to look like 5x^3.
You then take 5x^3 and subtract 2 to get 5x^3-2.
Fathi has $1.10 in his printing account. Each sheet of paper he uses reduces his printing account balance by $0.25. Fathi wants to print out a PDF document that is 47 pages long. To save paper, he decides to print on both sides of each sheet and to print two pages on each side of the sheet.
After Fathi prints, what will be the balance in his printing account?
Answer: Faith's printing account balance will become $-1.90, or $1.90 below 0.
Step-by-step explanation:
Each sheet of paper can print 4 pages. Since it is 47 pages long, she will need 12 pages. That will cost 3 dollars, since 0.25x12=3. 1.10-3=-1.90 dollars, which means that she is $1.90 in debt.
ben and winston are both selling cookie dough for a fundraiser. Although ben has already sold 10 tubs, Winston hasnt sold any yet. If ben starts selling 8 tubs per day and Winston begins selling 9 tubs per day, they will eventually sell the same amount of cookie dough. how many days will that take
?
Answer:
Step-by-step explanation:
On the first day, Ben (B) starts with 10 tubs and Winston (W) starts with 0 tubs.
After the first day, Ben sells 8 tubs per day while Winston sells 9 tubs per day.
Therefore we can write the following equation: (Where d = number of days)
B = 10 + 8d
W = 0 + 9d = 9d
We are told that eventually they will sell the same amount which means
B = W
This means we can say,
10 + 8d = 9d
If we subtract 8d from both sides we get
10 = d
Therefore it will take 10 days for them to sell the same amount of cookie dough.
Answer: 10 days
10 + 8 x 10 = 90
9 x 10 = 90.
It will take 10 days for Ben and Winston to sell the same amount of cookie dough.
Midpoint problem. Given two endpoints P1 (8, -4) and P2 (-3, 9), find the midpoint. Enter just the x-coordinate in this problem.
Given parameters:
The coordinates are:
P1 (8, -4) and P2 (-3, 9)
Unknown:
The midpoint of the endpoints = ?
Solution:
x₁ = 8
y₁ = -4
x₂ = -3
y₂ = 9
midpoints; x[tex]_{m}[/tex] , y[tex]_{m}[/tex] = [tex]\frac{x_{1} + x_{2} }{2} ,[/tex] [tex]\frac{y_{1} + y_{2} }{2}[/tex]
= [tex]\frac{8 +(-3)}{2}[/tex] , [tex]\frac{-4 + 9}{2}[/tex]
= [tex]\frac{5}{2}[/tex] , [tex]\frac{5}{2}[/tex]
The coordinate of the x-axis is [tex]\frac{5}{2}[/tex]
13. Is the following the graph of a function? Why or why not?
Rena is building a 1 : 180 scale model of a real castle. Her model has a rectangular base that is 3 feet wide and 4 feet long.
The width of the actual castle is ___feet.
Pleeeeassseee someone help me with this. I'm really struggling, and I'm in the middle of a test. Not to mention I'm being homeschooled, so that doesn't help at all. Any please if you can help, do it.
a banana costed 1 dollar how much does 3 bananas cost
please answer fast it will be very helpfull please it is a humble requst A samosa costs Rs 5 and a cold drink costs Rs 10. You take a samosa and cold drink every day for 6 days. The total money spent in 6 days is Rs
6x5+10
6x10+5
10x5+6
6x(5+10)
Evaluate the following logarithms. log12144 = log151 = log3 ( 1 81 ) = log 0.00001 =
Answer:
Answer(s): (2,0,-4,-5)
log12 144 = 2
log15 1 = 0
log3 ( 1/ 81 ) = -4
log 0.00001 = -5
The values of the expression are,
1. 2
2. 0
3. -4
4. -5
What is Logarithm?How many times must one "base" number be multiplied by itself in order to generate another specific number? The answer is found using a logarithm (or log).
For instance, how many times must a base of 10 be multiplied by itself to get 1,000? The answer is 3 (1,000 = 10 × 10 × 10).
Given that;
We have to use the property as;
aᵇ = x then
b = logₐx
So, we get;
log₁₂ 144 = a
12ᵃ = 144
12ᵃ = 12²
On comparing the base
= 2
Now, second is,
log₁₅ 1 = a
15ᵃ = 1
a = 0
Now, log₃ (1/81)
3ᵃ = 1/81
3ᵃ = 3⁻⁴
a = - 4
And, log 0.00001
= log (10)⁻⁵
= -5 log 10
= -5
Learn more about Logarithm here:
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The gas tank in Enrique's car has 15 gallons of gas. Enrique was able to determine that he can travel 35 miles and only use 2 gallons of gas. At this constant rate, he predicts that he can drive 240 more miles before he runs out of gas. Is he correct? Explain.
Answer:
Yes, he is correct, 240 miles will require a gas volume of 13.71 gallons which is less than 15 gallons in Enrique's car.
Step-by-step explanation:
Given;
total volume of gas in Enrique's car, V = 15 gallons
The rate of gas consumption [tex]= \frac{35 \ miles}{2 \ gallons} = 17.5 \ miles/gallon[/tex]
To drive 240 miles, he would need the following volume of gas;
[tex]V = 240 \ miles* \frac{1}{\frac{17.5 \ miles}{gallon} }\\\\ V = 240 \ miles*\frac{1*gallon}{17.5 \ miles}\\\\ V = (\frac{240 \ miles}{17.5 \ miles} )gallon\\\\V = 13.71 \ gallons[/tex]
The volume of gas needed to drive 240 miles is less than the total volume of gas in Enrique's car.
Thus, he is correct
If 14x + 5 = 12, what is the value of x?
Step-by-step explanation:
14x + 5 = 12
14x = 12 - 5
14x = 7
x = 7/14
x = 1/2
Hope it helps you!!Given: a and b are first-quadrant angles, sin a = 5/13 , and cos b = 3/5 , evaluate cos(a + b).
16/65
33/65
56/65
Step-by-step explanation:
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Belvedere has a swimming pool that needs to be drained. His pool holds 10,567.2 gallons of water and will need to drain completely in 11.8 hours. What is the change in the water level per hour for Belvedere's swimming pool? Round your answer to the nearest hundredth TIE
Answer:
895.53 gallons per hour
Step-by-step explanation:
rate of change in water level (r) = totals gallons divided by number of hours to drain
r = 10567.2/11.8
r = 895.53 gallons per hour
help me rn pleasee i dont understand
Answer:
Step-by-step explanation:
if 1l = 100cl
1l×1/100cl×4=1l /400cl
Lena runs 4 miles in 30 minutes. At the same rate, how many miles would she run in 48 minutes?
Answer:
6.4
Step-by-step explanation:
divide 4 by 30 in order to find out how many miles she can run in a minute. I got 0.13333333 and multiplied that by 48, which got me 6.4 as the answer but I'd double check.
Answer:
6.4 millas.
Step-by-step explanation:
es una simple regla de tres:
4 es a 30
x es a 48
x es igual a 48*4/30
x es igual a 6.4
£810 is divided between Paul, Brian & Colin so that Paul gets twice as much as Brian, and Brian gets three times as much as Colin. How much does Brian get.
Answer:
$486 (Paul)
$243(Brian)
$81(Colin)
Solving steps:
let Paul Be x, Brian be x,Colin be x
since Paul got twice as much as Brian which shows that brian and got three times
So Paul,= 3×2 so he got six times as much as the two others
while Brian got three times
and colins got once
so let's make an equation for this problem
=> 6x + 3x + x = $810
add 6 x + 3 x + x which give you 10 x
=> 10x = $810
divide both side by the coefficient of x
=> [tex] \frac{10x}{10} = \frac{810}{10} [/tex]
=> [tex]x = \frac{810}{10} [/tex]
=> x = 81
since you we have find what the value of x
insert into the previous equation which is
=> 6x + 3x + x
=> 6(81) = $486-----(for Paul)
3(81) = $243-------(for Brian)
(81) = $81 ---------(for Collin)
Write each number in scientific notation. Show your work/explain.
A. 14,700
B. 0.00083
C. 760,000,000
D. 0.038
E. 0.38
F. 3.8
G. 3,800,000,000,000
H. 0.0000000009
Answer: [tex]1.47*10^4[/tex]
[tex]8.3*10^{-4}[/tex]
[tex]7.6*10^8[/tex]
[tex]3.8*10^{-2}[/tex]
[tex]3.8*10^{-1}[/tex]
[tex]3.8*10^0[/tex]
[tex]3.8*10^{12}[/tex]
[tex]9.0*10^{-10}[/tex]
Step-by-step explanation:
Scientific notation is a way of expressing numbers that are too large or too small.
To figure out the power of 10, think "how many places do I move the decimal point?"
1. When the number is 10 or greater, the decimal point has to move to the left, and the power of 10 is positive.
2. When the number is smaller than 1, the decimal point has to move to the right, so the power of 10 is negative.
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match each linear equation with the correct description.
This is the Answer to this question
What tool could you use to measure the angle of a hexagon? Explain how to use the tool you chose. What is the measure?
Pls help me
Answer: A protractor The measure is 120
Explanation: Line up the vertex of the angle with the dot at the center of the protractor. Line up one side of the angle with 0 degrees on the protractor. Read the protractor to see where the other side of the angle crosses the number scale. (Hopes this helps!)
In the triangle below, suppose that mZc-(4-9). ZD=(31-3), and mLE=x° Find the degree measure of each angle in the triangle.
Answer:
Step-by-step explanation: