From a window 20m above the ground, a person could see the top of the house across the street at an angle of elevation of 5 degrees. The angle of depression to the base of the house was 15 degrees. What is the height of the house?
if u can draw an illustration, thanks
Answers
The height of house is 26.53 m
What is angle of elevation?The angle of elevation and angle of depression are opposites of each other. In an angle of elevation, the object is placed above the observer, while in the case of the angle of depression, it is placed below the observer.
If you are standing at your terrace and looking at the sun, then the angle of elevation will be formed. On the other hand, if you will look at the dog standing on the road from your terrace, then the angle of depression will be formed. In both cases, we use trigonometry angles to find the heights and distances.
Given:
Window height = 20 m
angle of elevation =5
angle of depression= 15
Using trigonometry
tan 15 = P/B
0.2679= 20/B
B= 74.654 m
Again
tan 5 =P/B
0.0874 = P/ 74.645
P= 6.5305 m
Hence, height of the tree is 6.53 + 20= 26.53 m
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Related Questions
Ben wants to buy a new car stereo and he has already saved some money. He used this inequality to represent the amount he still has to save to be able to buy the stereo, where a represents the amount still left to save. A + 212 greater-than-or-equal-to 365 If Ben saves $15 a week for the next 10 weeks, will he be able to buy the stereo and why? No, because he needs to save at least $153, and he will only save $150 over the next ten weeks. No, because he needs to save $577, and he will only save $150 more. Yes, because he has already saved $365, and the stereo cost $212. Yes, because he has already saved $212, and he will save another $150.
Answers
Answer:
No, because he needs to save at least $153, and he will only save $150 over the next ten weeks.
Step-by-step explanation:
In case when ben wants to save $15 for a week and the total number of weeks is 10 so the total saving amount is $150. Now if the cost of a stereo is less than the total of saving amount so he is confident to purchase the stereo.
Now if the amount that required to be saved is represented by a is more than $150 so he is unable to purchase a stereo
Hence, the correct option is a.
Answer:
Step-by-step explanation:
Using the equation, A + 212 ≥ 365
No, because he needs to save at least $153, and he will only save $150 over the next ten weeks.
A cylinder has a height of 5.3 cm and a diameter of 3.0 cm. What is its volume? (Hint: Volume of a cylinder = r2h ) 25.0 cm3 66.2 cm3 149.9 cm3 37.5 cm3
Answers
Answer:
37.5 cm³ .
Step-by-step explanation:
h = 5.3 cm
diameter = 3 cm
r = 3/2 = 1.5 cm
Volume of cylinder = πr²h {Plug in the values of h & r }
= 3.1428 * 1.5 * 1.5 * 5.3
= 37.5399
= 37.5 cm³
Answer:
37.5cm3
Step-by-step explanation:
Diameter = 3cm
Radius = 3cm÷2
= 1.5cm
Volume of cylinder= πr²h
= π(1.5²)+5.3
= 37.5 (3 S.F.)
When two fair 6-sided dice are tossed, the numbers $a$ and $b$ are obtained. What is the probability that the two digit number $ab$ (where $a$ and $b$ are digits) and $a$ and $b$ are all divisible by 3?
Answers
=================================================
Explanation:
If either a or b (or both) are multiples of 3, then so is a*b
Consider 'a' being a multiple of 3. This means a = 3k for some integer k. Multiply both sides by b to get ab = 3k*b, and we see that 3 is a factor of ab, making ab to be a multiple of 3.
----------
There are six sides to the dice and those sides are {1,2,3,4,5,6} of which only {3,6} are multiples of 3.
If we want both dice to be multiples of 3, then the possible outcomes are
(3,3)(3,6)(6,3)(6,6)There are four outcomes. This is out of 6*6 = 36 total outcomes overall.
Dividing the values gives 4/36 = 1/9 as the probability we want
----------
Side note: for a roll like (a,b) = (6,3) we see that a*b = 6*3 = 18, which is a multiple of 3. The same happens with the other three (a,b) pairings mentioned above.
Write 830,040 in expanded form with exponents.
830,040 = (8 x 105) +
(Use the operation symbols in the math palette as needed.)
Answers
Answer:
See below
Step-by-step explanation:
[tex]830040 \\ = (8 \times 100000) + (3 \times 10000) + (4 \times 10) \\ = 8 \times {10}^{5} + 3 \times {10}^{4} + 4 \times {10}^{1} \\ [/tex]
A bat and ball cost $1.10.
The bat costs one dollar mire than the ball.
How much does the ball cost?
Answers
Answer: Hi!
We already know that we can subtract a dollar from the total, because the bat is a dollar more than the ball. However, there's one more step! We have to divide the cost left, 10 cents, by 2 as well, because the bat is a dollar more than the ball, and if we said that the answer was a dollar, we would be wrong, because there would be 10 cents left as the cost of the ball - and if the bat was a dollar more than the ball, then the bat would be $1.10 and the total cost would be $1.20. 10 divided by 2 is 5, so the ball is 5 cents and the bat is $1.05.
Hope this helps!
5 cents
as the ball costs 5 cents the bat costs $1.05
Simplify the following Questions. (IMPORTANT NOTE!!! #'s 2 AND 7 MUST BE IN SCIENTIFIC NOTATION!!!!!) 1.) (x)²(2xy³)^5 2.) (4x10^8)^2 3.) (-h^4)^5 4.) (3xy³)²(xy)^6 5.) (p^9)^-2 6.)(5k²)³ 7.)(7x10^5)² 8.)(x)³(-x³y)² 9.)w^5(w²)^-4 10.) (2x^5)^4
Answers
Answer:
Step-by-step explanation:
Hint :
[tex](a*b)^{m}= a^{m}b^{m}\\\\\\(a^{m})^{n}=a^{mn}\\\\\\a^{m}*a^{n}=a^{m+n}\\[/tex]
[tex]1)x^{2}(2xy^{3})^{5}=x^{2}*2^{5}*x^{5}*(y^{3})^{5}\\\\\\=x^{2}*2^{5}*x^{5}*y^{3*5}\\\\=x^{2}*2^{5}*x^{5}*y^{15}\\\\=2^{5}*x^{2+5}*y^{15}\\\\=2^{5}x^{7}y^{15}[/tex]
[tex]2) (4x10^{8})^{2}=4^{2}*x^{2}*(10^{8})^{2}\\\\=16*x^{2}*10^{8*2}\\\\=1.6*10*x^{2}*10^{16}\\\\=1.6x^{2}*10^{16+1}\\\\=1.6x^{2}10^{17}[/tex]
[tex]3)(-h^{4})^{5}=(-h)^{4*5}=-h^{20}\\\\\4)(3xy^{3})^{2}(xy)^{6}=3^{2}x^{2}(y^{3})^{2}x^{6}y^{6}\\\\=9x^{2}y^{3*2}x^{6}y^{6}\\\\\\=9x^{2}y^{6}x^{6}y^{6}\\\\=9x^{2+6}y^{6+6}\\\\=9x^{8}y{12}\\\\\\[/tex]
[tex]5) (p^{9})^{-2}=p^{9*-2}=p^{-18}\\\\\\6)(5k^{2})^{3}=5^{3}(k^{2})^{3}=625k^{6}\\\\7)(7x10^{5})^{2}=7^{2}x^{2}(10^{5})^{2}\\\\=49x^{2}10^{5*2}\\\\=4.9*10^{1}x^{2}10^{10}\\\\=4.9x^{2}10^{10+1}\\\\=4.9x^{2}10^{11}[/tex]
[tex]8)x^{3}(-x^{3}y)^{2}=x^{3}*(-x^3})^{2}y^{2}\\\\\\=x^{3}*(-1)^{2}*x^{2*3}y^{2}\\\\=x^{3}*1*x^{6}y^{2}=x^{3+6}y^{2}\\\\=x^{9}y^{2}\\\\\\9)w^{5}(w^{2})^{-4}=w^{5}w^{2*-4}\\\\=w^{5}w^{-8}\\\\=w^{5-8}=w^{-3}\\\\=\frac{1}{w^{3}}\\\\\\10) (2x^{5})^{4}=2^{4}x^{5*4}\\\\=2^{4}x^{20}\\\\=16x^{20}[/tex]
Will Give Brainliest. Answer ASAP please
Answers
Answer:
1) Arc length = 2πr ( Ф/360)
= 2 × 22/7 × 15 (120/360)
= 44/7 × 15 (1/3)
= 44 × 5/7
= 31.428 in
2) Arc length = 2πr ( Ф/360)
= 2 × 22/7 × 14 (90/360)
= 44/7 × 14 ( 1/4)
= 616/7 × (1/4)
= 88 (1/4)
= 22 yards
Hope it helps!!!
PLEase help please help
Answers
Answer:
10 m
Step-by-step explanation:
490[tex]\pi[/tex]=[tex]\pi[/tex](7²)h
490[tex]\pi[/tex]/[tex]\pi[/tex]49=h
10=h
Josh is at the airport and calls for a Uber. He knows the driver will charge $10 to pick
him up and $3 per mile he will drive from the airport to home . if T(x) is the total cost
which equation models this situation
T(x) = 10 + 3x
The answer is not
here
T(x) =13x
T (X) = 10x + 3
Answers
Answer:
the answer is 10 +3x
Step-by-step explanation:
"the answer is not here" what do you mean
What is the purpose of multiplying by the conjugate of a complex denominator when finding the quotient of complex numbers?
Answers
Answer: To have a real number in the denominator
Step-by-step explanation:
Ok, a quotient between two complex numbers can be written as:
[tex]\frac{A + Bi}{C+Di}[/tex]
Now, when we do these types of divisions, we multiply and divide by the same number (so in essence we are multiplying by one) that is the conjugate of the denominator.
Remember that for a complex number:
Z = A + Bi
the conjugate is = A - Bi.
Then, wen we multiply the denominator by it's conjugate, we have:
(C + Di)(C - Di) = C^2 + D*C*i - D*C*i + (D*i)*(-D*i) = C^2 + D^2
So now we have a real number in the denominator (the imaginary part of this number is equal to zero)
So the answer to the question is:
"To have a real number in the denominator"
20 POINTS! A book sold 39,200 copies in its first month of release. Suppose this represents 7.1% of the number of copies sold to date. How many copies have been sold to date? Round your answer to the nearest whole number.
Answers
A video game was discounted and now costs two thirds of its original
price. If it originally cost $45, how much does it cost now?
Answers
The original price is 45.
It now costs 2/3 of 45.
[tex]\frac{2}{3} * \frac{45}{1} = \frac{90}{3}[/tex] or 30
♡ Hope this helps! ♡
❀ 0ranges ❀
Answer:
The video game will now cost $30
Step-by-step explanation:
Original price: $45
45 ÷ 3 = $15
15 x 2 = $30
Hope this helps!
is this a rhombus? see attachment
Answers
Answer: No, it is not a rhombus
Why not? This is because we do not have all four sides the same length.
DE is longer than EF, due to the opposite angles being larger. The rule is: the larger the angle, the longer the opposite side will be.
A box contains 4 red pencils, 3 blue pencils, and
3 yellow pencils. What is the probability that a
student randomly selects a blue pencil, keeps it,
and then a second student randomly selects a
yellow pencil? *
Answers
Step-by-step explanation:
Red=4
Blue=3
Yellow=3
Total=10
Pr(BY) without replacement= 3/10 *3/9
=6/90
=1/15
Section B
1. In the adjoining figure find out perpendicular, base and
hypotenuse from the given right-angled triangle with a and
B as the reference angles. Also give your reason.
a
nto
B
С
B.
D
Answers
Answer/Step-by-step explanation:
Using α as reference angle:
Perpendicular side = BC (one of the legs that adjoins to form a right angle. It is opposite to the reference angle.)
Base side = AB (The other leg that forms a right angle with the perpendicular side at the adjoining point. It is adjacent to the reference angle)
Hypotenuse = AC (the side opposite to the right angle, 90°)
Using β as reference angle:
Perpendicular side = AB (one of the legs that adjoins to form a right angle. It is opposite to the reference angle.)
Base side = BD (The other leg that forms a right angle with the perpendicular side at the adjoining point. It is adjacent to the reference angle)
Hypotenuse = AD (the side opposite to the right angle, 90°)
3/5 + (-1/5)
A. -2/5
B. 4/5
C. 2/5
Answers
Answer:
C
Step-by-step explanation:
3/5 + (-1/5) =(3-1)/5=2/5
3/5-1/5
3-1/5
2/5
C.2/5 ✔️
Solve using the Addition Method.
5x/6 + y/3 = 4/3
2x/3 - y/2 = 11/6
Answers
Answer:
x = 2
y = - 1
Step-by-step explanation:
5x/6 + y/3 = 4/3
2x/3 - y/2 = 11/6
Multiply the above equation by 6 to express in linear form
6 × (5x/6 + y/3 = 4/3)
5x + 2y = 8.... (1)
6 × (2x/3 - y/2 = 11/6)
4x - 3y = 11.... (2)
Thus, the equation are:
5x + 2y = 8.... (1)
4x - 3y = 11.... (2)
Next, multiply equation (1) by 3 and equation (2) by 2. This is illustrated below:
3 × (5x + 2y = 8)
15x + 6y = 24 ..... (3)
2 × (4x - 3y = 11)
8x - 6y = 22 ... (4)
Next, add equation 3 and 4 together. This is illustrated below:
.. 15x + 6y = 24... (3)
+ 8x - 6y = 22 .... (4)
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
23x = 46
Divide both side by 23
x = 46/23
x = 2
Next, substitute the value of x into any of the equation. Here, we shall substitute the value of x into equation (3). This is illustrated below:
15x + 6y = 24... (3)
x = 2
15(2) + 6y = 24
30 + 6y = 24
Collect like terms
6y = 24 - 30
6y = - 6
Divide both side by 6
y = - 6/6
y = - 1
Therefore, the value of x and y is
x = 2
y = - 1
what is the change in each term of the sequence? 1,4,13,40,121,....
Answers
the pattern is by multiples of 3 added to the preceding number;
example, 1+3= 4 that's 3
4+9=13 because 3*3 is 9
13+27=40 coz 9*3 is 27
40+81=121 coz 27*3 is 81
121+243=364 coz 81*3 is 243
and so on and so forth..
hope this helps!
What is the coefficient of y in the expression 1 ⋅ 4 + 7y?
Answers
Answer:
7
Step-by-step explanation:
The coefficient of a variable is simply the number it's being multiplied by or the number that is in front of it. In this case, the coefficient of y is 7.
Which is 65% of 35??
Answers
Answer:
22.75 .
Step-by-step explanation:
65 x 35 / 100 = 22.75.
The percentage expression 65% of 35 is 22.75
How to evaluate the percentage expressionFrom the question, we have the following parameters that can be used in our computation:
65% of 35
Express as products
So, we have the following representation
65% of 35 = 65% * 35
Express 65% as 0.65
So, we have the following representation
65% of 35 = 0.65 * 35
Evaluate the products
So, we have the following representation
65% of 35 = 22.75
Hence, the solution is 22.75
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b)[3x-7)2 by using identities note:the 2 is a square
Answers
Answer:
9x² - 42x + 49
Step-by-step explanation:
Given
(3x - 7)² = (3x - 7)(3x - 7)
Each term in the second factor is multiplied by each term in the first factor, that is
3x(3x - 7) - 7(3x - 7) ← distribute both parenthesis
= 9x² - 21x - 21x + 49 ← collect like terms
= 9x² - 42x + 49 ← in expanded form
Please help ASAP PLEASE
Jane is trying to decide between two savings account plans. Plan A offers a
quarterly compounded interest rate of 0.15%, while Plan B offers 0.5% interest
compounded annually. Which is the better plan? By how much?
Answers
Answer:
The answer is below
Step-by-step explanation:
The compound interest is given by the formula:
[tex]A=P(1+\frac{r}{n} )^{nt}\\\\Where\ A \ is\ the\ final \ amount, P\ is\ the \ principal\ or \ initial\ amount,r\ is\ the\ rate\\n\ is\ the\ number\ of \ times\ compounded\ per\ period\ and \ t\ is\ the\ number\ of\ periods.\\[/tex]
For the same amount of principal (P) for both plan A and B:
Plan A offers a quarterly compounded interest rate of 0.15%. That is r = 0.15% = 0.0015, n = 4. Therefore:
[tex]A_a=P(1+\frac{0.0015}{4} )^{4t}\\\\A_a=P(1+0.000375)^{4t}\\\\A_a=P(1.000375)^{4t}[/tex]
Plan B offers annual compounded interest rate of 0.5%. That is r = 0.5% = 0.005, n = 1. Therefore:
[tex]A_b=P(1+\frac{0.005}{1} )^{t}\\\\A_b=P(1.005)^{t}\\\\The\ ratio\ of\ their\ interest:\\\\\frac{A_a}{A_b} =\frac{P(1.000375)^{4t}}{P(1.005)^{t}} \\\\\frac{A_a}{A_b} =\frac{(1.000375)^{4t}}{(1.005)^{t}} \\\\For\ the\ same\ time\ period\ of\ one\ year(t)=1\\\\\frac{A_a}{A_b} =\frac{(1.000375)^{4(1)}}{(1.005)^{1}} \\\\\frac{A_a}{A_b} =\frac{1.0015}{1.005} \\\\A_b=\frac{1.005A_a}{1.0015}\\ \\A_b=1.003A_b[/tex]
Plan B is the better plan, it is greater by a factor of 1.003
Miguel Rodriguez borrowed $300 from his brother Julio to pay for books and tuition. He agreed to pay Julio in 6 months with simple annual interest at 6.5%.
Answers
Answer:
Simple Interest = 9.75
Total Amount needed to payback = 309.75
Step-by-step explanation:
SI = P x R x T / 100
SI = Simple Interest
P = Principal
R = Rate in years
T = Time
SI = 300 x 1/2 x 6.5 /100
=> SI = 3 x 1/2 x 6.5
=> 1.5 x 6.5
=> 9.75
Total Amount needed to payback = Principal + Simple Interest
=> Total Amount needed to payback = 300 + 9.75
=> Total Amount needed to payback = 309.75
Ben earns $13 per hour at Starbucks. When he works overtime, he earns time and a half. What is his regular pay for 40 hours of work?
Answers
Answer:
$520
Step-by-step explanation:
Ben earns $13 per hour of regular work
He gets for 40 hours of regular work:
$13*40 = $520Answer is $520
Overtime is (time+half) = $13 + $13/2 = $13 + $6.5 = $19.5
So, his regular pay (40 h/week) would be = $2,253.67
Using the equation F = ma, find the acceleration (a) of a 15 kg mass (m) that is acted on by 3 Newtons of Force (F). Group of answer choices
Answers
Answer:
Step-by-step explanation:
Yes
Answer:
a = 0.20 m/s²
Step-by-step explanation:
F = 3 N
m = 15 kg
F = m * a
find mass m:
3 = 15 * a
a = 3 / 15
a = 0.20 m/s²
2. What is the area of the shaded region below? Notice
that the angle is 120 degrees and the radius of the
circle is 8 inches.
8
120
Answers
Answer:
Approximately 67 square inches.
Step-by-step explanation:
The area of a circle is given by the formula:
[tex]A=\pi r^2[/tex]
And the sector area of a circle is given by the formula:
[tex]A=\frac{x\textdegree}{360\textdegree}(\pi r^2)[/tex]
Where x is the degree measurement of the sector.
We want to find the sector of the circle with a radius of 8. The degree measurement of the sector is 120. Therefore, plug 8 in for r and 120 for x:
[tex]A=\frac{120\textdegree}{360\textdegree}(\pi(8)^2)[/tex]
The fraction reduces to 1/3. 8^2 is 64:
[tex]A=\frac{1}{3}(64\pi)[/tex]
This is equivalent to:
[tex]A=\frac{64}{3}\pi\\ A\approx67.0206 \text{ in}^2[/tex]
f(2)= can someone let me know what the answer is
Answers
Answer:
-2
Step-by-step explanation:
f(2) is the value of the function when x = 2.
Look in the graph. When x = 2, the point on the graph has coordinates (2, -2).
f(2) = -2
what is the answer to this exponent 6*6*6*6*6
Answers
Answer:
6^5 or 7776
Step-by-step explanation:
6^5 because 6 is multiplied with 6, 5 times. So, it is 6^5.
We can also simplify this number.
=> 6 x 6 x 6 x 6 x 6
=> 36 x 36 x 6
=> 36 x 216
=> 7776
the expression 12xyz-45 is a a. monomial b. binomial c. trinomial d. constant
Answers
Answer:
Hey there!
12xyz-45 is a binomial. A binomial contains two terms.
Let me know if this helps :)
Solve these two equations using the Addition Method (also known as the elimination method).
3/4x + 1/3y = -1/2
1/2x - 5/6y = -7/2
Answers
Answer:
(-2, 3)
Step-by-step explanation:
5/2(3/4x + 1/3y = -1/2)
1/2x - 5/6y = -7/2
15/8x + 5/6y = -5/4
19/8x = -19/4
x = -2
1/2(-2) - 5/6y = -7/2
-1 -5/6y = -7/2
-5/6y = -5/2
y = 3