HELP FAST PLEASE
A six-feet-tall man looks off the roof of a five-story hotel. He sees a statue that is 75 ft. away from the hotel. If he is looking at the base of the statue, what angle does his sight line form with the side of the hotel? Assume that each complete story of the hotel is 12 ft. tall.
32.6 degrees
43.9 degrees
48.7 degrees
54.2 degrees
Answers
Answer: 48.7 degrees
Step-by-step explanation:
Let [tex]\theta[/tex] is the angle between the his sight line form with the side of the hotel,
Since, the building is of 5-story and a men having height 6 feet is in the fifth-story.
Thus, the total length from the eyes of the man and foot of the building = 6 + 12 × 5 = 6 + 60 = 66 feet
Also, the distance of the statue from the foot of the building = 75 feet.
Then by the below diagram,
[tex]tan\theta = \frac{75}{60+6}[/tex]
[tex]tan\theta = \frac{75}{66}[/tex]
[tex]\theta=48.6522227803\approx 48.7\text{ degree}[/tex]
Related Questions
Lindesy wants a new bike that costs $230. Her father says that if she saves up 30% of the cost he will pay the rest. How much money does Lindesy need to save?
Answers
Find two positive real numbers who's product is a maximum and whose sum is 156.
Answers
The sum of two numbers is 156, so we can write:
x+ y = 156
or
y = 156 - x
The product of two numbers = xy
Using the value of y in previous equation we can write:
Product = x(156 - x) = - x² + 156x
The above equation is a quadratic equation and results in a parabola. The maximum value of parabola with negative coefficient of x² lies at its vertex.
The x component of vertex will be = [tex] \frac{-b}{2a} [/tex]
Here b is the coefficient of x term, and a is the coefficient of x² term.
So,
a = -1
b = 156
Using the values in the formula we get the x component of vertex x = [tex] \frac{-156}{-2}=78 [/tex]
So x = 78
and
y = 156 - x = 156 - 78 = 78
Thus, the two numbers whose sum is 156 and which result in maximum product are 78, 78
Final answer:
To maximize the product of two numbers with a fixed sum of 156, we set up an equation for the product, differentiate, and find that the maximum product is obtained when both numbers are 78.
Explanation:
To find two positive real numbers whose product is a maximum and whose sum is 156, we need to use the concept of optimization in calculus. This involves taking the derivative of the function representing the product of the two numbers and setting it equal to zero to find the critical points. Since the sum of the numbers is fixed at 156, we can express one number in terms of the other, for example, x and 156 - x. The product of these two numbers is x(156 - x). To find the maximum product, we differentiate this function with respect to x:
[tex]\frac{d}{dx} [x(156 - x)] = 156 - 2x[/tex]
Setting this derivative equal to zero gives us 156 - 2x = 0, solving for x we find-
x = 78.
This gives us the two numbers as 78 and 78, because the sum must be 156 and the other number would be 156 - 78. To confirm that this gives a maximum, we would test the second derivative or use the first derivative test. However, by symmetry, when the sum of two numbers is fixed, their product is maximized when the two numbers are equal. In this case, both numbers are 78.
a cone is not a polyhedron. true or false?
Answers
Answer:
The answer is true
Step-by-step explanation:
we know that
A polyhedron is is a solid with flat faces and a cone is a solid with a curved side
therefore
A cone is not a polyhedron ( Is true)
A horse race has 14 entries and one person owns 5 of those horses. assuming that there are no ties, what is the probability that those five horses finish first comma second comma third comma fourth comma and fifth (regardless of order)
Answers
entries------------ > 14 in total.
the owner has-----------> 5 horses.
if each horse has the same probability of winning, then the probability that the owner's horses will come in first, second, third, fourth and fifth will be as follows:
we have 5 spots.
the probability that one of those 5 horses will be first is 5/14
the probability that one of the remaining 4 horses will be second is 4/13.
the probability that one of the remaining 3 horses will be third is 3/12.
the probability that one of the remaining 2 horses will be fourth is 2/11.
the probability that the remaining horse will be fifth is 1/10.
the total probability is [5/14 * 4/13 *3/12 *2/11 *1/10]
(120/240240)=1/2002=0.0004995
the answer is 0.0004995
Final answer:
The probability that the five horses finish first through fifth in any order is 0.0004995 or 0.04995%.
Explanation:
The probability that the five horses owned by one person finish first through fifth, regardless of order, in a horse race with 14 entries can be calculated using combinatorics. First, we determine the number of ways to choose 5 horses out of 14 to finish in the top 5 positions, which is C(14,5). Then we calculate the number of favorable outcomes, which, since the order doesn't matter for the set of horses owned by the person, is just 1. To find the probability, we divide the number of favorable outcomes by the total number of possible outcomes, resulting in 1/C(14,5). Using the formula for combinations C(n,r) = n! / (r! * (n-r)!), where n is the total number of entries and r is the number of horses owned by the person, we can calculate the exact probability.
The formula gives us C(14,5) = 14! / (5! * (14-5)!) = 14! / (5! * 9!) = 2002. Therefore, the probability is 1/2002, which simplifies to 0.0004995 or 0.04995%.
Joseph wants to cover a rectangular box with wrapping paper. The length of the box is 2 feet, its width is 1 foot, and its height is 1 foot. The cost of wrapping paper is $0.80 per square foot. How much will it cost Joseph to cover the box with wrapping paper?
Answers
Let's find it with plugging it in.
2(2×1) + 2(2×1) + 2(1×1)
4+4+2=10
Now the surface area is 10 ft², let's just multiply .8 by that to find the price.
.8×10= 8
It'll cost $8 for Joseph to cover the box with wrapping paper.
Tell me if this helps!!
x^2-15=0 Find the number of real number solutions for the equation.
Answers
1.1 Factoring: x2-15
Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)
Proof : (A+B) • (A-B) =
A2 - AB + BA - B2 =
A2 - AB + AB - B2 =
A2 - B2
Note : AB = BA is the commutative property of multiplication.
Note : - AB + AB equals zero and is therefore eliminated from the expression.
Check : 15 is not a square !!
Ruling : Binomial can not be factored as the difference of two perfect squares.
2.1 Solve : x2-15 = 0
Add 15 to both sides of the equation :
x2 = 15
When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:
x = ± √ 15
The equation has two real solutions
These solutions are x = ± √15 = ± 3.8730
Final answer:
Explaining the number of real number solutions for the given quadratic equation x²-15=0.
Explanation:
x²-15=0
To find the number of real number solutions for the equation, we start by setting the expression to zero:
x² - 15 = 0
x² = 15
x = ±√15
Therefore, the equation has two real number solutions, which are ±√15.
What is the approximate area of the shaded sector in the circle shown below
A.30.7 in^2
B.246 in^2
C.15.4 in^2
D.491 in^2
Answers
Answer: IT WAS B. -_-
Answer:
246 in^2
Step-by-step explanation:
just took the test
NEED HELP ASAP PLEASE HELP
What are the measures of the two angles in the figure below?
Select one:
a. 95° and 85°
b. 100° and 80°
c. 105° and 75°
d. 110° and 70°
Answers
This means we can say that:
(5x + 20) + (4x +25) = 180
Now we have an equation that we can solve:
(5x + 20) + (4x +25) = 180
9x + 45 = 180 (we collected the terms : 4x + 5x = 9x, and 20 + 25 = 45)
9x = 135 (we subtracted both sides by 45, to get the x values alone on one side)
x = 15 (we divided both sides by 9, to get what just x is)
-------------------------------------------------------------------------------------------------------------
Now that we know the value of x, we can substitute it into the equations given in the diagram:
5x + 20 = 5 * 15 + 20
= 95°
4x + 25 = 4 * 15 + 25
= 85°
-------------------------------------------------------------------------------------------------------------
Answer:
So the measure of the two angles are:
A) 95° and 85
The equation y = 8.1x models the relationship between the number of hours Alexander works, x, and the dollar amount he earns, y. Which is the graph of the equation y = 8.1x? Image for option 1 Image for option 2 Image for option 3
Answers
Answer with explanation:
⇒ y=8.1 x
This is a Linear equation depicting linear relationship between y and x which is between the number of hours Alexander works, x, and the dollar amount he earns, y.
To determine a line you need two points.
→Put, x=0,in y=8.1 x, gives y=0 gives a Point (0,0).
→Put,x=1 gives , y=8.1 × 1→y=8.1 gives another point (1,8.1).
→So, Drawn a line passing through (0,0) and (1, 8.1),which is the required image of the equation given.
Kite QRST has sides RS, ST, TQ and QR. What are the diagonals of this figure? Select all that apply.
Answers
A real estate broker sold your house for $72,000. The broker's commission was 6% of the selling price. How much would you get for the house after the commission is paid? A. $70,800 B. $76,320 C. $67,680 D. $73,200
Answers
=72,00-72000*0.06=$67,680
=94%
$72000 x 94%
=$67680
Write a real world problem that you would represent with the equation 4x+5=37.
Answers
4x + 5 = 37
4x + 5 (-5) = 37 (-5)
4x = 32
4x/4 = 32/4
x = 8
It will take Bob ~8 seconds to reach 37 feet*
*Problem & answer
hope this helps
What is the area of this trapezoid? 44 in² 64 in² 168 in² 192 in² Trapezoid A B C D with parallel sides D C and A B. Points F and E are between D and C. F E B A form a rectangle with 4 right angles. D F is 2 inches, F E is 14 inches, E C is 2 inches, A B is 14 inches., and E B is 12 inches.
Answers
we know that
[the area of the trapezoid]=[area rectangle]+2*[area triangle]
[the area of the trapezoid]=[14*12]+2*[12*2/2]=192 in²
the answer is 192 in²
Answer:
the answer is 192in
Step-by-step explanation:
Suria has x apples and oranges.how many apples and oranges does suria have altogether? Give your answer in terms of x
Answers
Answer:
It is given that Suria has x apples and Oranges.
Which means ,total number of fruits which includes apple and Orange is equal to x.
Suppose, number of Oranges Suria has = A
And, Number of Apples Possessed by Suria= B
→Number of Oranges +Number of Apple=x
→ A + B =x
So,total number of apples and Oranges does Suria have altogether = x
Which expression is a rational number? A) ( 25 + 25 )2 B) ( 25 + 50 )2 C) ( 50 + 75 )2 D) ( 25 + 72 )2
Answers
All expressions given, A, B, C, and D, are rational numbers. This is because they all result in a number that can be expressed as the quotient of two integers when the operations are performed according to the order of operations and squared.
A rational number is a number that can be expressed as the quotient or fraction rac{p}{q} of two integers, a numerator p and a non-zero denominator q. To determine which expression represents a rational number, we look for an outcome that is expressible as such a fraction after carrying out any operations involved in the expression.
Let's evaluate whether the expressions given result in rational numbers when the operations are performed:
A) ( 25 + 25 )2 = [tex](5+5)^2[/tex] = [tex]10^2[/tex] = 100 which is a rational number.B) ( 25 + 50 )2 = [tex](5+10)^2[/tex] = [tex]15^2[/tex] which is a rational number.C) ( 50 + 75 )2 = [tex](2+3)^2[/tex] = [tex]5^2[/tex] which is a rational number.D) ( 25 + 72 )2= [tex](5+14.4)^2[/tex] = [tex]19.4^2[/tex] which is not a perfect square but still a rational number since 19.4 is a rational number and squaring it results in another rational number.Therefore, all given expressions A, B, C, and D result in rational numbers when squared.
Option A, B, C, and D is a rational number.All given expressions result in rational numbers, as each step of their calculations simplifies to integers. Each integer can be expressed as the quotient of two integers, confirming they are rational.
To determine which expression results in a rational number, let's evaluate each option step by step. A rational number is any number that can be expressed as the quotient of two integers.
(25 + 25)2: First, we simplify inside the parentheses: 25 + 25 = 50. Then we square the result: 502 = 2500.(25 + 50)2: Simplify inside the parentheses: 25 + 50 = 75. Then we square the result: 752 = 5625.(50 + 75)2: Simplify inside the parentheses: 50 + 75 = 125. Then we square the result: 1252 = 15625.(25 + 72)2: Simplify inside the parentheses: 25 + 72 = 97. Then we square the result: 972 = 9409.All the results are integers, which are rational numbers because any integer n can be expressed as n/1. Therefore, all given expressions result in rational numbers.
The graph of y=|x|y=∣x∣y, equals, vertical bar, x, vertical bar is reflected across the xxx-axis and then scaled vertically by a factor of \dfrac14 4 1 start fraction, 1, divided by, 4, end fraction. What is the equation of the new graph?
Answers
Justification:
The statement is confusing, so I will re-write it to avoid confusions:
"The graph of y=|x| is reflected across the x-axis and then scaled vertically by a factor of 1/4. What is the equation of the new graph? "
Answer
Solution:
1) Reflection acros the x-axis means (a,b) transforms into (a, -b). That is for the given x the reflected function will return the negative of the original value, that is:
y = - |x|
2) Scaling by a factor of 1/4 means that the new function is multiplied by 1/4
=> y = - (1/4) |x| which is the answer
PLEASE HELP!!!!! For the given quadratic equation convert into vertex form, find the vertex, and find the value for x = 6. Show your work.
y = -2x^2 + 2x +2
Answers
We are given this equation
[tex] y=-2x^{2} +2x+2 [/tex]
The vertex form is given by:
[tex] y=a(x-h)^{2} +k [/tex]
Now let us try to convert our equation into vertex form:
[tex] y=-2x^{2} +2x+2 [/tex]
Vertex form is given by:
[tex] y=-2(x-0.5)^{2} +2.5 [/tex]
comparing our equation with vertex form ,
The vertex (h,k) is (0.5, 2.5)
Next we have to find y when x=6, plugging x as 6 in the given equation,
[tex] y=-2(6)^{2} +2(6)+2 [/tex]
y=-58
So at x=6, y=-58.
Math help? One question?
Answers
_____
The law of cosines is usually used for this.
EF^2 = DE^2 +DF^2 -2*DE*DF*cos(D)
.. = 6^2 +11^2 -2*6*11*cos(40°)
.. ≈ 55.88
EF ≈ √55.88 ≈ 7.5 . . . ft
If the minute hand of a clock is 20 degrees behind the hour hand at this moment, then in 18 minutes, the minute hand will be how many degrees ahead of the hour hand?
Answers
Answer:
I got 79 degrees in my pocket, gonna solve this math problem, its just like a pick on a locket, no wonder your grades are gonna skyrocket.
Step-by-step explanation:
The number of degrees ahead of the hour hand will be 128 degrees.
What is an angle?The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.
If the minute hand of a clock is 20 degrees behind the hour hand at this moment.
We know that the rotation of the minute hand in each minute is 6°.
The angle when minutes shows 18 minutes is given as,
⇒ 18 x 6°
⇒ 108°
The number of degrees ahead of the hour hand will be given as,
⇒ 108° + 20°
⇒ 128°
The number of degrees ahead of the hour hand will be 128 degrees.
More about the angled link is given below.
https://brainly.com/question/15767203
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the longest side of an acute isosceles triangle is 8 centimeters. rounded to the nearest tenth, what is the smallest possible length of one of the two congruent sides?
A:4.0
B:4.1
C:5.6
D:5.7
Answers
I helped you so you're welcome
if the vertex angle is 90, then it is a 45-45-90 triangle, when the longest side (the hypotenuse) is 8, each leg is 8/√2=5.65685
Because the vertex angle needs to be smaller than 90, the two equal side is larger than 5.6568, I'd go with D.
The length of a rectangle is 3 m less than double the width, and the area of the rectangle is 65 m2 . find the dimensions of the rectangle.
Answers
What is the sum of 36 ounces and 4 pounds? 6 lb. 6 lb., 4 oz. 96 oz. 98 oz.
Answers
Answer:
6 lb 4 oz
Step-by-step explanation:
Since, 1 lb = 16 oz,
Here, the given phrase,
The sum of 36 ounces and 4 pounds,
[tex]= 36\text{ oz}+4\text{ lb}[/tex]
[tex]=36\text{ oz}+64\text{ lb}[/tex]
[tex]=100\text{ oz}[/tex]
Again,
1 oz = 1/16 lb,
[tex]100\text{ oz}=\frac{100}{16}=6.25\text{ lb} = 6\text{ lb}+0.25\text{ lb}=6\text{ lb }4\text{ oz}[/tex]
Hence, The sum of 36 ounces and 4 pounds is 6 lb 4 oz
Second option is correct.
Jamison takes a 20 foot board and props it up with a one foot block at the far end to make a daredevil jump ramp for his bike. What is the measure of the angle of elevation of the ramp to the nearest degree?
Answers
Answer:
[tex]3^{\circ}[/tex]
Step-by-step explanation:
Let x represent the angle of elevation.
We have been given that Jamison takes a 20 foot board and props it up with a one foot block at the far end to make a daredevil jump ramp for his bike.
Upon looking at our attached file, we can see that 20 feet board and 1 foot board forms a right triangle with respect to ground, where side of 1 foot is opposite side and 20 feet side is hypotenuse.
We know that sine relates the opposite side of right triangle to its hypotenuse, so we can set an equation as:
[tex]\text{sin}=\frac{\text{Opposite}}{\text{Hypotenuse}}[/tex]
[tex]\text{sin}(x)=\frac{1}{20}[/tex]
Using arcsin we will get,
[tex]x=\text{sin}^{-1}(\frac{1}{20})[/tex]
[tex]x=2.865983982599^{\circ}[/tex]
Upon rounding our answer to nearest degree we will get,
[tex]x\approx 3^{\circ}[/tex]
Therefore, the measure of the angle of elevation of the ramp is 3 degrees.
Emma, Steve, Maria, and George are comparing the solution of a math assignment problem below.
Select the student who correctly subtracted the rational expressions.
Answers
Answer:
A. Steve
Step-by-step explanation:
We are given the expression, [tex]\frac{1}{x-1}-\frac{3}{x^{2}+2x-3}[/tex].
So, upon simplifying the expression, we get,
[tex]\frac{1}{x-1}-\frac{3}{x^{2}+2x-3}[/tex]
implies [tex]\frac{1}{x-1}-\frac{3}{(x-1)(x+3)}[/tex]
i.e. [tex]\frac{1(x+3)-3}{(x-1)(x+3)}[/tex]
i.e. [tex]\frac{x+3-3}{(x-1)(x+3)}[/tex]
i.e. [tex]\frac{x}{(x-1)(x+3)}[/tex]
So, from the options, we see that,
Steve has correctly subtracted the rational expressions.
Thus, option A is correct.
Cesar is building a shelf at an angle so that it appears to be leaning against the wall. The shelf touches the wall 7 ft. above the floor and the distance between the floor from the wall to the front of the shelf is 1.5 ft. What is the angle the shelf makes with the floor?
A. 77.9 degrees.
B. 77.6 degrees.
C. 12.1 degrees.
D. 12.4 degrees.
A 15-ft. building casts a shadow of 12 ft. What is the approximate angle of inclination of the sun?
A. 51.3 degrees.
B. 53.1 degrees.
C. 36.9 degrees.
D. 19.2 degrees.
Answers
- The shelf touches the wall 7 feet above the floor.
-The distance between the floor from the wall to the front of the shelf is 1.5 feet
Then:
Tan^-1(α)=Opposite Leg/Adjacent leg
Opposite leg=7
Adjacent leg=1.5
When you substitute the values, you obtain:
Tan^-1(α)=7/1.5
α=77.9°
What is the angle the shelf makes with the floor?
The correct answer is: A) 77.9 degrees.
2) The problem says that the 15-feet building casts a shadow of 12 feet. Then:
Tan^-1(β)=Opposite Leg/Adjacent leg
Opposite leg=15
Adjacent leg=12
When you substitute, you obtain:
Tan^-1(β)=15/12
β=51.3°
What is the approximate angle of inclination of the sun?
The correct answer is: A) 51.3 degrees.
1) The angle the shelf makes with the floor is approximately 77.905°. (Choice A)
2) The approximate angle of inclination of the sun is approximately 51.340°. (Choice A)
How to apply trigonometric relations to determine angles
1) In this case we know that shelf has a vertical height ([tex]h[/tex]) of 7 feet and a horizontal distance between the floor from the wall to the front of the shelf ([tex]l[/tex]) is 1.5 feet. The angle ([tex]\theta[/tex]), in degrees, is determined by tangent function:
[tex]\theta = \tan^{-1} \frac{7\,ft}{1.5\,ft}[/tex]
[tex]\theta \approx 77.905^{\circ}[/tex]
The angle the shelf makes with the floor is approximately 77.905°. (Choice A) [tex]\blacksquare[/tex]
2) The length of the shadow ([tex]l[/tex]) is 12 feet and the height of the building ([tex]h[/tex]) is 15 feet. The angle of inclination of the sun is determined by tangent function:
[tex]\theta = \tan^{-1} \frac{15\,ft}{12\,ft}[/tex]
[tex]\theta \approx 51.340^{\circ}[/tex]
The approximate angle of inclination of the sun is approximately 51.340°. (Choice A) [tex]\blacksquare[/tex]
To learn more on trigonometric relations, we kindly invite to check this verified question: https://brainly.com/question/6904750
Mila graphs the point A
(
5
,
0
)
5,0 on a coordinate plane.
Which of the following statements are true?
Select all that apply.
A.
Point A is 5 units to the right of the origin and up 1 unit.
B.
The x-coordinate of point A is 5.
C.
The y-coordinate of point A is 5.
D.
Point A is on the y-axis.
E.
Point A is on the x-axis.
what are the answers
Answers
Answer:
B,E
Step-by-step explanation:
B,E
Your teacher took a survey of student’s eye colors. She found that 15 students have brown eyes, 6 students have green eyes, and 4 students have blue eyes. Make a table showing the frequency
Answers
Green- 6
Blue- 4
15+6+4= 25
green: 6/25 = 6/25 * 4/4 = 24/100 = 24%
blue: 4/25 = 4/25 * 4/4 = 16/100 = 16%
What do all members of the family of linear functions f(x)=1m(x+3) have in common?
Answers
1. Their highest exponent is 1.
2. The graphs of the equations are lines.
When finding things in common between different types of functions, you always have to look at the two sides of math; geometry and algebra. Geometry is all the graphs, and algebra is the equations.
I hope this helps!
All linear function has a constant slope and degree as 1.
What is a linear function?A straight line on the coordinate plane is represented by a linear function.
A linear function always has the same and constant slope.
The formula for a linear function is f(x) = ax + b, where a and b are real values.
Linear functions are lines in the coordinate and describe itself that the slope will be the same irrespective of the point.
A linear function is given by ;
y = mx + x where m is slope.
As we can see the degree of x and y both are 1 so the linear function has a degree of 1.
Hence "All linear function has a constant slope and degree as 1".
For more about the linear function,
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Which are solutions of the equation 4x2 – 7x = 3x + 24? Check all that apply. x = –4 x = –3 x = -3/2 x = 2/3 x = 2 x = 4
Answers
First we rewrite the quadratic equation:
4x2 - 7x - 3x - 24 = 0
4x2 - 10x - 24 = 0
The solutions to the quadratic equation in this case are:
x1 = 4
x2 = -1.5
Answer:
x = -3/2
x = 4
Answer: b. -3 or 2
Step-by-step explanation:
simplify:
...............
Answers
Exact form:
[tex] \sqrt{61 - 24}\sqrt{5} [/tex]
Decimal form:
2.70820393...
I hope this helps!
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