Answer:
Given 3:5 = 3+5=10,
400*3/8=150,
400*5/8=250.
The angle of elevation of the top of a pole as seen from a point 13 ft away from the base is double its angle of elevation as seen from a point 47 ft farther from the pole. Find the height of the pole above the level of the observer's eyes. 10) A) 34 ft B) 86 ft C) 60 ft D) 45 ft
The height of the pole above the level of the observer's eyes is 31.42 ft
Let the angle of elevation of the top of the pole from a point 47 ft away be α.
Let the angle of elevation of the top of the pole from the point 13 ft away be β.
Since the angle of elevation of a point 13 feet away is twice that from 47 ft away, we have that β = 2α.
If the height of the pole above the level of the observer's eye is h, we have that
tanβ = tan2α = h/13 and tanα = h/47
From trigonometric identities tan2α = 2tanα/(1 - tan²α)
Substituting the values of the variables into the equation, we have
tan2α = 2tanα/(1 - tan²α)
h/13 = 2h/47 ÷ [1 - (h/47)²]
Dividing through by h, we have
1/13 = 2/47 ÷ [1 - (h/47)²]
Cross-multiplying, we have
1/13 = 2/47 ÷ [1 - (h/47)²]
1 - (h/47)² = 2/47 × 13
1 - (h/47)² = 26/47
(h/47)² = 1 - 26/47
(h/47)² = (47 - 26)/47
(h/47)² = 21/47
Taking square-root of both sides, we have
h/47 = √(21/47)
Cross-multiplyng, we have
h = √(21/47) × 47
h = √(21 × 47)
h = √987
h = 31.42 ft
The height of the pole above the level of the observer's eyes is 31.42 ft
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PLEASE NEED THIS ASAP
Answer:
The answer is in the above attachment.
Express 405 1/3 in simplest radical form.
Answer:
3 cube root of 15
Step-by-step explanation:
theres your simple radical form
8(152/3) is 405 1/3 in simplest radical form.
What is simplification?Simplifying procedures is one way to achieve uniformity in job efforts, expenses, and time. It reduces diversity and variation that is pointless, harmful, or unneeded. Parenthesis, exponents, multiplication, division, addition, and subtraction are all referred to as PEMDAS. The order of the letters in PEMDAS informs you what to calculate first, second, third, and so on, until the computation is finished, given two or more operations in a single statement.
405 1/3 is equivalent to (405*3 + 1)/3 = 1216/3.
To express 1216/3 in simplest radical form, we can first simplify it by dividing both the numerator and denominator by their greatest common factor, which is 8.
1216/3 = (8*152)/3 = 8(152/3)
Now, we can see that 152/3 cannot be simplified any further, so the simplest radical form of 405 1/3 is: 8(152/3)
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According to this diagram, what is sin 23°?
67°
13
5
Сл
23°
90°
12
O A.
13
5
12
O B.
B. 13
12
13
O c.
c.13
O D.
D.
5
13
O E.
13
12
5
OF.
Using relations in a right triangle, it is found that the sine of 23 degrees is given by:
D. 5/13.
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.Looking at the graph, the side opposite to the angle of 23º is of 5, while the hypotenuse is of 13, hence the sine is given by:
sin(23º) = 5/13.
Which means that option D is correct.
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In what time will $1000 amount to $1331 at 10% per annum, compounded annually?
3 Years
Step-by-step explanation:Compound interest is a multiplier that affects the new value each time.
If the compound interest is 10% per annum, the multiplier each year is 1.1.
Year 1: $1000 * 1.1 = $1100
Year 2: $1100* 1.1 = $1210
Year 3: $1210* 1.1 = $1331
This means that it will take 3 years for $1000 to amount to $1331 at 10% per annum.
Alternatively, you can use a logarithm. The calculation can be written as:
1000 * [tex]1.1^n[/tex] = 1331, where n is the number of years.
Rearranged, this gives [tex]1.1^n[/tex] = 1331/1000 or [tex]1.1^n[/tex] = 1.331.
A logarithm can work out the value of n, and is written in the form log1.1(1.331), which gives a value of 3.
A room is 15 feet long and 12 feet wide. A scale drawing of the room is 10 inches by 8 inches. What is the scale of inches in the drawing to inches in the actual room?
Enter the correct answer in the box.
Answer:
The scale is 1:18 for the entire room, 1 inch in the diagram for 18 inches IRL
Step-by-step explanation:
12 inches = 1 foot
Convert the feet to inches, then divide both sides of the ratio by the # of inches in the diagram
So for length:
10:(15*12)
10:180
1:18
And for width:
8:12(12)
8:144
1:18
Answer:
18 inches
Step-by-step explanation:
The question asks for scale of inches in the drawing and the actual room, so first convert 15 ft and 12 ft into inches.
1 foot= 12in x 1ft= 12 inches
15 feet= 12in x 15ft = 180 inches
12 feet= 12in x 12ft = 144 inches
The room is 180 inches long and 144 inches wide.
To find the scale, set up a proportion to the drawing to the room.
[tex]\frac{10}{8} =\frac{180}{144}[/tex]
You can see that the scale is 18 inches because to get from 180 to 10, you multiply by 18, and the same thing as 8, you would multiply 8 by 18 to get to 144.
All 5-digit zip codes in the United States are assigned by region. In Texas, all zip codes begin
with the number 7 while the second digit is restricted to numbers from 5 to 9. There is no
restriction on the remaining digits. How many zip code combinations are possible in Texas?
4,000
5, 000
6, 000
7,000
Answer:
5,000
Step-by-step explanation:
[tex]\frac{1}{7}*\frac{5}{5-9} \frac{10}{0-9} *\frac{10}{0-9} * \frac{10}{0-9}[/tex]
PLS HELP FIND GRADIENT PLSSS DUE TMRW GIVING BRAINLIEST FOR FIRST ANSWER
Whats the question?......................
Answer:
For a;
The answer will be 3
For b;
The answer will be -4
Step-by-step explanation:
To find the gradient of the lines, you must pick 2 points on the line and then find [tex]dy/dx[/tex]
I hope this helped!
Can I have brainliest?
Have a great day/night/afternoon!
(I already went to the other question you posted, do not worry.)
- ❤ 7272033Alt ❤
I need answers ASAP
Answer:
Simplifying
6r + r + -5r = 0
Combine like terms: 6r + r = 7r
7r + -5r = 0
Combine like terms: 7r + -5r = 2r
2r = 0
Solving
2r = 0
Solving for variable 'r'.
Move all terms containing r to the left, all other terms to the right.
Divide each side by '2'.
r = 0
Simplifying
r = 0
7r-5r < this is the answer
6r+r=7r
Hey everybody! Not a super hard question here! Anybody think they can help me out?
Identify the correct domain and range.
Answer
B, the second choice
Step-by-step explanation:
the domain is defined as all possible x values of a function and the range is defined as all possible y values, so the domain would be all real numbers since x can be any value, and the range cannot be more than 3, since y=3 is the vertex of the parabola.
Suppose we have a linear equation relating y and x defined by
3y + 9x = 18,
where x is an independent variable and y is a dependent variable. Which of the following is a correct function notation
representation of y?
Select the correct answer below:
Answer:
(a) f(x) = -3x +6
Step-by-step explanation:
Solve for y, then write as a function.
3y +9x = 18 . . . . . . given
y +3x = 6 . . . . . . . . divide by 3
y = -3x +6 . . . . . . . subtract 3x
f(x) = -3x +6 . . . . . written using function notation
simplify by expressing with radicals n√x^3^n
We can work with the exponents to simplify our expression, and we will get:
[tex]\sqrt[n]{x^{3n}} = x^3[/tex]
How to simplify the expression?Remember that a root of degree n is equivalent to an exponent of 1/n.
This means that we can rewrite a root of degree n as:
[tex]\sqrt[n]{x} = x^{1/n}[/tex]
Then our expression:
[tex]\sqrt[n]{x^{3n}}[/tex]
Can be rewritten as follows.
[tex]\sqrt[n]{x^{3n}} = (x^{3n}})^{1/n}[/tex]
Now we have the exponent of an exponent, that means that we just need to take the product between the two exponents.
Now we can take the product of the exponents to get.
[tex]\sqrt[n]{x^{3n}} = (x^{3n}})^{1/n} = x^{3n*1/n} = x^3[/tex]
You can see that in the third step the exponents n and 1/n cancell eachother, so we end only with the exponent 3.
That is the expression simplified.
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Use the slope formula to determine the slope of the line containing the two points. Type your answer as an integer or reduced fraction in improper form if necessary.
Answer:
The slope is:
[tex] \binom{1}{2} [/tex]
In slope-intercept form the equation is:
[tex]y = \binom{1}{2} x - 3[/tex]
: Một khu đất 20 ha người ta trồng hai loại cây ngô và khoai. Năng suất của ngô tính theo x ha được (5-x/4) tấn trên 1 ha và năng suất của khoai tính theo y ha được (7-y/4) tấn trên 1 ha. Xác định diện tích trồng từng loại cây để sản lượng thu được là lớn nhất.
I have more question
Answer:
you would need three wholes because each whole would represent a loaf of pumpkin bread
The graph of f(x) = x² is transformed to create the graph of g(x) = f(x + 6). Which
statement is true?
A The graph of g(x) reflects the graph of f(x) across the x-axis.
B The graph of g(x) reflects the graph of f(x) across the y-axis.
CThe vertex of the graph of g(x) is 6 units to the left of the vertex of the graph of f(x).
DThe y-intercept of the graph of g(x) is 6 units above the y-intercept of the graph of f(x).
Answer:
Given a function \displaystyle f\left(x\right)f(x), a new function \displaystyle g\left(x\right)=-f\left(x\right)g(x)=−f(x) is a vertical reflection of the function \displaystyle f\left(x\right)f(x), sometimes called a reflection about (or over, or through) the x-axis.
Given a function \displaystyle f\left(x\right)f(x), a new function \displaystyle g\left(x\right)=f\left(-x\right)g(x)=f(−x) is a horizontal reflection of the function \displaystyle f\left(x\right)f(x), sometimes called a reflection about the y-axis.
Step-by-step explanation:
1/5 divided by 2/3 input the answer as a fraction
Answer:
Three tenths/ 3/10
Step-by-step explanation:
1/5 divided by 2/3 is 0.3 which is equal to 3/10
of the three lines in the graph one has slope m = 1 one has slope m = 2, and one has slope m = 1/5.
Put the lines in order from greatest to least slope.
Answer:
1/5 1 2
Step-by-step explanation:
. To do the ham số y = 3x - 3
Step-by-step explanation:
subject arts and architecture what primary
given: AC is parallel to DF, m<1 = m<4
prove: AE is parallel to BF
plz help:(
Answer:
..
Step-by-step explanation:
Gomenosai
Given that X varies directly as Y³ and X = 54, Y = 3. find X 10 Y = 5 what is the relationship between X and Y?
Answer:
x=6y3
Step-by-step explanation:
we first find the constant of proportionality where by we say; x= ky3
we're given x = 54
and y = 3
so
54=k(3cubed)
therefore
54= 9k
divide be 9 both sides to get k which is the constant
k=6
now rewrite the equation replacing k with 6
it will be...
X=6Y3
Ernie deposits $9,800 into a pension fund. The fund pays a simple interest rate of 7%. What will the balance be after four years?
Answer:
$12,845.80
Step-by-step explanation:
take the first number and go +7%. repeat four times
hope this helps :-)
$10.25 per hour x 25 hours round to the nearest cent
Answer:
256.25
Step-by-step explanation:
$10.25 not taxed x 25
The scatter plot shows the relationship between the average number of nightly customers and the number of mouths since a restaurant opened. The equation represents the linear model for this date
y = 5x + 120
what does the number 5 in the equation mean in this context?
A: There were 5 customers per night when the restaurant opened
B: The average number of costumers per night increased by 5 each month
C: The average number of customers per night decreased by 5 each month
D: The restaurant has been open for 5 months
Which ratio is equivalent to the given ratio? 8: 16 Select each correct answer. 16/31 1/3 1/2 12/24
[tex]8:16\implies \cfrac{8}{16}\implies \cfrac{1}{2}\implies 1:2 \\\\[-0.35em] ~\dotfill\\\\ \cfrac{16}{31}\qquad \bigotimes~\hfill \cfrac{1}{3}\qquad \bigotimes~\hfill \cfrac{1}{2}\qquad \textit{\large \checkmark}~\hfill \cfrac{12}{24}\implies \cfrac{1}{2}\qquad \textit{\large \checkmark}[/tex]
Answer:
1/2. and 12/24
they are both halves just as the ratio is half of the given number
Which claim supports this graph?
A- Students Never use social media.
B- Students mostly use social media 0-3 times a day.
C- Students mostly use social media 8-11 times per day.
D- Students are not using social media enough.
Answer:
The answer is C.
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
a function is given, 2^x + 3. find f(-2)
Answer:
2_3_4_4/547767()9897568. thank
On a family trip to Oman, Tarek drove 300 km in 5 hours. This is an example of a unit rate or a rate? Please tell the correct answer.
Answer:
300 km in 5 hours is the rate
unit rate is how much in one unit
in this case the unit is one hour
60km / hour
A. Determine the value of each function
1. For p(x)=-2x + 5, determine:
a. p(5)
b. p(0)
c. p(-1/2)
Answer:
a= -5
b=5
c=6
substitue each value as x
Han rides his bike for 50 miles over 4 hours.How long will it take him to ride 75 miles?
Answer:
6 hours.
Step-by-step explanation:
This is directly proportional, meaning if you multiply one side by a number, you multiply the other side by the same number. For the ratio 50:4, you would have to multiply 1.5 to 50 to get 75 miles, so you would also have to multiply 4 by 1.5. This would get you 6 hours.
