Using trigonometry and the tangent function, the height of the taller building, with a 42˚ angle of elevation from the smaller 32-foot building 35 feet away, is calculated to be approximately 63.514 feet. The formula tan(42˚) = (h₂ - 32) / 35 is utilized where tan(42˚) ≈ 0.9004. Solving this equation gives the height of the taller building.
The question asks: Two buildings are 35 feet apart. The elevation angle from the top of the smaller building to the top of the taller building is 42˚. The smaller building is 32 feet high. Find the height of the taller building.
To solve this problem, we will use trigonometry, specifically the tangent function, which relates an angle of a right triangle to the ratio of the opposite side to the adjacent side.
Let's denote the height of the smaller building as h₁ = 32 feet, the height of the taller building as h₂, and the horizontal distance between the buildings as 35 feet. The elevation angle from the top of the smaller building to the top of the taller building is 42˚.
First, we determine the difference in height (Δh) between the two buildings:
→ tan(θ) = opposite/adjacent
In this case:
→ tan(42˚) = (h₂ - h₁) / 35
We solve for the height difference:
→ (h₂- 32) = tan(42˚) * 35
Using a calculator to find tan(42˚):
→ tan(42˚) ≈ 0.9004
Substituting the value:
→ (h₂ - 32) = 0.9004 * 35
→ h₂ - 32 ≈ 31.514
Adding 32 to both sides:
→ h₂ ≈ 31.514 + 32
→ h₂ ≈ 63.514
Therefore, the height of the taller building is approximately 63.514 feet.
Find the volume of the sphere.
Either enter an exact answer in terms of \piπpi or use 3.143.143, point, 14 for \piπpi and round your final answer to the nearest hundredth.
the radius is 10
Answer:
Step-by-step explanation:
volume of sphere=4/3 πr³
=4/3 π×10³=4000/3 π
=4000×3.14÷3=12560/3
=4186.67
What is the domain of the function y= 3Vx
Based on the graph, the domain of the function [tex]y=3\sqrt{x}[/tex] is [0, ∞].
In Mathematics and Euclidean Geometry, a domain is the set of all real numbers (x-values) for which a particular relation or function is defined.
The horizontal section of any graph is typically used for the representation of all domain values. Additionally, all domain values are both read and written by starting from smaller numerical values to larger numerical values, which means from the left of a graph to the right of the coordinate axis.
By critically observing the graph shown in the image attached below, we can logically deduce the following domain:
Domain = [0, ∞], {x|x ≥ 0}.
Complete Question:
What is the domain of the function [tex]y=3\sqrt{x}[/tex]?
What is the answer to this equation -156-(-45)=
Answer:
-111
Step-by-step explanation:
-156 + 45 = -111
double negative becomes positive
Answer:
-201
Step-by-step explanation:
-156-(-45)= 156+45
156+45=201 add the - sign
A relative frequency histogram is given with four classes. The first three bars have a height of 0.25, 0.35, and 0.1 respectively. What is the helght of
the fourth bar?
Answer:
answer is 0.3
Step-by-step explanation:
To find the height of the fourth bar in a relative frequency histogram, calculate the total frequency, subtract the sum of the first three frequencies, and divide the remaining frequency by the total frequency.
Explanation:The relative frequency histogram given has four classes. The heights of the first three bars are 0.25, 0.35, and 0.1 respectively. To find the height of the fourth bar, we need to calculate the total frequency first. Then, subtract the sum of the first three frequencies from the total frequency. Finally, divide the remaining frequency by the total frequency to get the height of the fourth bar.
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Where on a check should you write the name of the payee? A. part A B. part B C. part C
Answer:
Part a - on the line where it says pay to the order of
Step-by-step explanation:
Answer:
Part A
Step-by-step explanation:
The number 47 is decreased to 44. What is the percentage by which the number was decreased, to the nearest tenth of a percent?
Answer:
6.38298% or 6.4%
hope this helps
To calculate the percentage decrease from 47 to 44, the difference is divided by the original number and then multiplied by 100. The result is approximately a 6.4% decrease.
Explanation:To calculate the percentage decrease of the number from 47 to 44, we use the following formula for percentage decrease:
Percentage decrease = ((Original Value - New Value) / Original Value) × 100%
In this case, the original value is 47 and the new value is 44. So the calculation would be:
Percentage decrease = ((47 - 44) / 47) × 100%
Percentage decrease = (3 / 47) × 100%
Percentage decrease = 0.0638 × 100%
Percentage decrease = 6.38%
To give the answer to the nearest tenth of a percent, we round 6.38% to 6.4%. So, the number 47 is decreased by about 6.4% to become 44.
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To solve 2x + 9 = 21, what is the first step?
A.Dividing each side by 2
B.Dividing each side by x
C.Subtracting 21 from each side
D.Subtracting 9 from each side
WILL GIVE BRAINLIEST ANSWER TO WHOEVER ANSWERS FIRST AND CORRECTLY EXPLAIN WHY YOURE CORRECT
Answer:
I believe its A
Step-by-step explanation:
You have to count the units to the subway to the house
You start by counting the squares from the subway to the right till you meet the same line as the house is located than you count up from there to the house
I got 13
Sorry if its wrong
Kiran, Mai, Jada, and Tyler went to their school carnival. They all won chips that they could exchange for prizes. Kiran won as many chips as Jada. Mai won 4 times as many chips as Kiran. Tyler won half as many chips as Mai.
Write an expression for the number of chips Tyler won. You should only use one variable: , which stands for the number of chips Jada won.
Answer:
Mai, Tyler Kiran,Jada ratio = 4,2,1,1Tyler is double that of Jada
So expression could be f(t) 2 x 1t x 5 = 10
Step-by-step explanation:
The expression for the number of chips Tyler won, based on the number of chips Jada won, is 2j.
Explanation:In this problem, we are asked to develop an expression for the number of chips Tyler won based on the amount Jada won. The relationships between the chips won are as follows: Kiran won as many chips as Jada (so if Jada won j chips, Kiran also won j chips), Mai won 4 times as many chips as Kiran (so Mai won 4j chips), and Tyler won half as many chips as Mai (so Tyler won 1/2 * 4j = 2j chips).
So, using j to represent the number of chips Jada won, the expression for the number of chips Tyler won would be 2j.
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if Nicole saves $0.05 every day how much money will she have in 3 years
Answer:
$54.75
Step-by-step explanation:
0.05 x 365 = 18.35
18.25 x 3 = 54.75
Answer:
54.75
Step-by-step explanation:
To find this answer we will first take our 3 years and turn them into days instead.
There are 365 days in a year, so, 365 x 3 = 1095 days
Next, take the 1095 days and multiply it by the number she is saving everyday
1095 x .05 = 54.75
Nicole will have saved 54.75 in three years.
Hope this helps! :)
Write -9.31 as a mixed number.
Answer:
[tex] - 9 \frac{31}{100} [/tex]
Step-by-step explanation:
[tex] - 9.31 \times 100 = - 931[/tex]
[tex] - 9 .31 = - \frac{931}{100} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = - 9 \frac{31}{100} [/tex]
This net can be folded to make a square pyramid. What is the surface area of the pyramid?
Answer:
[tex]85in^2[/tex]
Step-by-step explanation:
to find the surface area we need to find the followng areas:
area of the square area of a triangle and multiply it by 4 (because there are 4 triangles)And once we have those areas, we add them to find the surface area.
Area of the square:
the formula to find the area of a square is:
[tex]a_{square}=l^2[/tex]
where [tex]l[/tex] is the length of the side: [tex]l=5in[/tex]
thus the area of the square is:
[tex]a_{square}=(5in)^2\\a_{square}=25in^2[/tex]
Area of the triangles:
the are of 1 triangle is given by
[tex]a_{triangle}=\frac{b*h}{2}[/tex]
where [tex]b[/tex] is the base of the triangle: [tex]b=5in[/tex] (the base of the triangle is the side of the square)
and [tex]h[/tex] is the height of the triangle: [tex]h=6in[/tex]
thus, the area of 1 triangle is:
[tex]a_{triangle}=\frac{(5in)*(6in)}{2}\\ a_{triangle}=\frac{30in^2}{2}\\ a_{triangle}=15in^2[/tex]
the area of the 4 triangles is (we multiply by 4):
[tex]a_{4-triangles}=4(15in^2)\\a_{4-triangles}=60in^2[/tex]
finally we add the area of the square and the area of the 4 triangles to find the total surface area:
[tex]Surface=25in^2+60in^2\\Surface=85in^2[/tex]
Answer:
85 square inches
Step-by-step explanation:
The key to solving a two-step equation is isolating the
variable on one side of the equation. In which of the
following equations is the variable isolated?
A.x = 9/2 + 4
B.2X=8
C.3x = 8 +5
D.x = 5x - 4
Answer:
A. x= 9/2+4
because the x is by itself
Be safe and have a day
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0.00000003 in scientific notation
Answer:
3×[tex]10x^{-8}[/tex]
Step-by-step explanation:
0.00000003
Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the
10 . If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.
4a+3=15 Hi what is the answer and how do I get it?
Answer:
4a+3=15
Step-by-step explanation:
Let's solve your equation step-by-step.
4a+3=15
Step 1: Subtract 3 from both sides.
4a+3−3=15−3
4a=12
Step 2: Divide both sides by 4.
4a
4
=
12
4
a=3
Answer:
a=3
Kristen runs a website that helps people learn programming. Every month, Kristen receives a subscription fee of $10 from each of the subscribers to a website. Last month, the website had 100 subscribers. This month, 30 new members join the website, and 10 members cancel the subscription. How much money were Christians online business and this month
Answer:
$1,200
Step-by-step explanation:
Last month was $10 x 100 = $1,000
This month was $10 x 30 = $300
This month loss was $10 x 10 = $100
$1,000 + $300 = $1,300 - $100 = $1,200
Madison has three jobs. This week she earned $236 waitressing, $68 delivering packages, and $96 babysitting. What percent of her money earned this week came from waitressing?
Answer: 59%
Step-by-step explanation:
First, you should add all of the money together.
= $268 + $68 + $96
= $400
Now, put it into a fraction. Remember to have a percentage, you have to multiply the division by 100.
= [tex]\frac{268}{400}[/tex] x 100
= 59%
Which value is represented by point P?
A. sqrt11
B. sqrt21
C. sqrt114
D. sqrt121
Square root 114 represents the point p.
Given,
The point P value in the given figure is between 10 and 11.
We need to find which value in the option is represented by point P.
Given options are :
Sqrt 11 = 3.31
Sqrt 21 = 4.58
Sqrt 114 = 10.67
Sqrt 121 = 11
We need to see which option gives a value between 10 and 11.
We have,
Sqrt 114 = 10.67.
We also know that point P lies between 10 and 11.
Sqrt 114 gives a value between 10 and 11.
Thus Sqrt 114 represents the point p.
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Find the area of a circle with a radius of 8.
units?
Answer:
16
Step-by-step explanation:
Look at the attached picture
Hope it will help you
The 5th term in a geometric sequence is 140. The 7th term is 35. What are the possible values of the 6th term of the sequence?
Answer:
±70
Step-by-step explanation:
Using a geometric sequence, it is found that the possible values of the 6th term of the sequence are -70 and 70.
What is a geometric sequence?A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.
The nth term of a geometric sequence is given by:
[tex]a_n = a_1q^{n-1}[/tex]
In which [tex]a_1[/tex] is the first term.
The nth term can also be written as a function of the mth term, as follows:
[tex]a_m = a_1q^{n-m}[/tex]
In this problem, considering that we have the 5th and the 7th term, we have that:
[tex]a_7 = a_5q^2[/tex]
Since [tex]a_5 = 140, a_7 = 35[/tex]:
[tex]q^2 = \frac{a_5}{a_7}[/tex]
[tex]q^2 = \frac{35}{150}[/tex]
[tex]q^2 = \frac{1}{4}[/tex]
[tex]q = \pm \frac{1}{2}[/tex]
[tex]\pm \frac{1}{2}[/tex] of 140 is [tex]\pm 70[/tex], hence the possible values of the 6th term of the sequence are -70 and 70.
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which which division problem does the diagram below best illustrate?
60 points
Answer:
Step-by-step explanation:
32 divide 4 = 8
Answer:
B- 32 divided by 4 = 8
Step-by-step explanation:
Desenhe em uma folha dois quadrados de lado 1dm. Trace uma diagonal em cada um e recorte-os
Answer:
The given question is
Draw two 1 dm squares on a sheet of paper. Draw a diagonal on each one and cut them out.
So, you need to draw square with sides of 1 dm. However, first, you need to transform from dm to cm.
We know that 1 decimenter (dm) equals 10 centimeters (cm).
That means the square sides are 10 centimerers long. So, you need to draw two squares like the first image attached shows.
Then, to draw their diagonals, you need to draw a line segment from one corner to its opposite corner, you should have an inclined line acroos each square. As the second image attached shows.
There you have it. Two squares of 1 dm side with on diagonal each.
A bag contains 7 red marbles, 4 blue marbles and 5 green marbles. If three marbles are drawn out of the bag, what is the probability, to the nearest 1000th, that all three marbles drawn will be green?
The probability of drawing three green marbles consecutively without replacement from a bag containing different colored marbles is approximately 0.018 when calculated step by step.
Explanation:The question is about calculating the probability of drawing three green marbles in a row from a bag that contains multiple colored marbles. To find this probability, we need to use the concept of probability without replacement.
First, calculate the probability of drawing one green marble. There are 5 green marbles out of a total of 16 (7 red + 4 blue + 5 green), so the probability is 5/16. When we draw a green marble, we do not replace it, so there are now 4 green marbles left out of 15 total marbles. The probability for the second draw is then 4/15. Lastly, for the third draw, there are 3 green marbles out of 14, making the probability 3/14.
To find the overall probability of all three events occurring, calculate the product of the individual probabilities: (5/16) * (4/15) * (3/14). This gives us 60/3360, which simplifies to 1/56. To the nearest thousandth, that is approximately 0.018.
So the probability that all three marbles drawn will be green, to the nearest thousandth, is 0.018.
What is the factored form of
z^2 - 2z - 3
Answer:
z=1 z=-3
Step-by-step explanation:
take z^2 times it to -3 then factor for -2 and reverse the answer
The horizontal cross-sectional shapes of the given prism are all congruent.
Answer:
true
Step-by-step explanation:
This is for geometry and I need help...
Answer:
I would say C but i am not sure
Step-by-step explanation:
sorry if I am wrong
the circumference of a circular pool cover is about 88 meters what is the measure of the length of the radius of the pool cover round your answer to the nearest whole number
Answer: The length of radius of a circular pool is 7 meters
Step-by-step explanation:
Given that the circumference of a circular pool cover is about 88 meters
To find the length of radius
As we know circumference of a circle is given by
[tex]C=2\pi r[/tex] where C is circumference , and r is radius of the circle
Now as according to question we have
[tex]88= 2\pi r\\\\\Rightarrow 88= 2\times \dfrac{22}{7} r\\\\\Rightarrow r= \dfrac{88\times 7}{2\times 44} = 7 m[/tex]
Hence,the length of radius of a circular pool is 7 meters
can you help out with this
A dart is tossed and hits the dart board shown.
The dart is equally likely to land on any point on
the dart board. Find the probability, as a percent
to the nearest tenth, that the dart lands in the
ring surrounding the bullseye.
The probability that dart lands on ring surrounding bull eye to the nearest tenth is: 4.9%
Area of ring surrounding bulleye :
πr² ; r = 2 inArea = π×2² = 12.56 in²
Total area of dart board :
Area of square = s²Area = 16² = 256
The probability of dart landing in ring surrounding bull eye :
12.56 / 256 = 0.004906Expressing as a percentage:
0.004906 × 100% = 4.9%Tina brought six times as many shirts as Maria. She then purchased five more while
shopping. Tina's total number of shirts by the end of the day was twenty-three. How
many did Maria bring?
3 shirts
6 shirts
11 shirts
15 shirts
Answer:
3 shirts
Step-by-step explanation:
23 - 5 = 18
18 divided by 6 = 3