For a project in his Geometry class, Tyler uses a mirror on the ground to measure the height of his school building. He walks a distance of 14.65 meters from his school, then places a mirror on flat on the ground, marked with an X at the center. He then steps 0.8 meters to the other side of the mirror, until he can see the top of the school clearly marked in the X. His partner measures the distance from his eyes to the ground to be 1.15 meters. How tall is the school? Round your answer to the nearest hundredth of a meter.
Answers
Answer:
The height of the school building is approximately 21.06 meters
Step-by-step explanation:
The method of Geometry Tyler is using to determine the height of his school building is through the property that similar triangles have a common ratio of corresponding their sides
The given parameters for the triangle formed by Tyler and the mirror are;
The distance from Tyler's eyes to the ground = 1.15 meters
The horizontal distance between Tyler and the mirror at X = 0.8 m
The parameters of the triangle formed by the height, h, of the school building and the mirror at X are;
The horizontal distance between the school building and the mirror = 14.65 m
The height of the school building = h
Therefore, we have;
[tex]\dfrac{The \ distance \ from \ Tyler's \ eyes \ to \ the \ ground}{The \ height \ of the \ school \ building} =\dfrac{Tyler's \ horizontal \ distance \ from \ mirror }{The \ building \ to \ mirror \ horizontal \ distance }[/tex]Therefore;
[tex]\dfrac{1.15 \, m}{h} = \dfrac{0.8 \ m}{14.65 \ m}[/tex]
[tex]h = \dfrac{1.15 \, m \times 14.65 \, m }{0.8 \, m} = 21.059375 \ m[/tex]
The height of the school building h to the nearest hundredth meter ≈ 21.06 m.
Related Questions
mary stated that 2.01 x 10⁶ is less than 4.8 x 10⁴ because 2.01 is less than 4.8. what was mary's mistake ?
I'm horrible at scientific notation so some help would be nice. =]
Answers
Answer:
Step-by-step explanation:
Scientific notation is always written as a number between 1 and 9.9999999 repeating. There follows a power of 10. I'm not sure which answer would help you see it clearer but
4.8 * 10^4 the decimal is shifted 4 places the right which is 48000 where you have no numbers, you use zeros.
2.01 * 10^6 means that you shift the decimal 6 places to the right.
2010000
So 2 million is larger than 48 thousand.
The other way to do it is just to look at the power. 6 is more than 4. 6 describes the number of places you move. So does 4. 6>4 so that's the larger number.
Use the special angles to evaluate: a) cosec 60° cot 30° + cos 45º cosec 45° 2
Answers
Answer:
the required answer is 4√2+1/2√2
help please! how do I calculate the coordinates of point a so that at is an altitude?
Answers
Part (a)
Since we want segment AT to be an altitude, this means that point A is somewhere on segment RI such that angle TAI is 90 degrees. In other words, segments AT and RI are perpendicular. Check out the diagram below.
We'll need to find the slope of line RI, so we'll need the slope formula
R = (x1,y1) = (-2,-2)
I = (x2,y2) = (4,1)
m = slope of line RI
m = (y2-y1)/(x2-x1)
m = (1-(-2))/(4-(-2))
m = (1+2)/(4+2)
m = 3/6
m = 1/2
m = 0.5
The slope of line RI is 1/2 or 0.5
Now let's use point R(-2,-2) along with that slope we just found to find the equation of line RI.
Turn to point slope form
y - y1 = m(x - x1)
y - (-2) = 0.5(x -(-2))
y + 2 = 0.5(x + 2)
y + 2 = 0.5x + 1
y = 0.5x + 1 - 2
y = 0.5x - 1
This is the equation of line RI. We'll use it later.
----------
We found that the slope of line RI was 1/2.
The negative reciprocal involves us flipping the fraction and flipping the sign to get -2/1 or simply -2.
The perpendicular slope is -2. This is the slope of altitude AT.
We want line AT to go through T(-2,4), so we'll use this point along with the perpendicular slope we just found to calculate the equation of line AT.
We'll turn to the point slope form
y - y1 = m(x - x1)
y - 4 = -2(x - (-2))
y - 4 = -2(x + 2)
y - 4 = -2x - 4
y = -2x - 4 + 4
y = -2x
The equation of the line that goes through points A and T is y = -2x.
----------
To summarize so far, we have these two equations
y = 0.5x - 1 .... equation of line RIy = -2x .... equation of line ATApply substitution to solve for (x,y) to find the intersection point. This will determine where point A is located.
y = 0.5x - 1
-2x = 0.5x - 1
-2x-0.5x = -1
-2.5x = -1
x = -1/(-2.5)
x = 0.4
Then we can determine y like so
y = -2x
y = -2(0.4)
y = -0.8
Therefore, point A is located at (0.4, -0.8). Both coordinate values are exact. In fraction form, we can say that the point is (2/5, -4/5), but I find decimals easier to work with in this instance.
Answer: (0.4, -0.8)===============================================================
Part (b)
To find the length of segment AT, we can find the distance from A to T. As you can probably guess, we'll use the distance formula.
A = (x1,y1) = (0.4, -0.8) ... found back in part (a)
T = (x2,y2) = (-2, 4) ... given
[tex]d = \sqrt{ (x_2-x_1)^2+(y_2-y_1)^2 }\\\\d = \sqrt{ (-2-0.4)^2+(4 - (-0.8))^2 }\\\\d = \sqrt{ (-2-0.4)^2+(4 + 0.8)^2 }\\\\d = \sqrt{ (-2.4)^2+(4.8)^2 }\\\\d = \sqrt{ 5.76+23.04 }\\\\d = \sqrt{ 28.8 }\\\\d \approx 5.36656\\\\d \approx 5.37\\\\[/tex]
The distance from point A to point T is approximately 5.37 units. This means that segment AT is roughly 5.37 units long.
Answer: 5.37 unitsSolve the inequality. Graph the solution |x+11|>6.
Plz need help mathxl
Answers
Answer:
1x>6-11
1x>-5
1x<-5
1 <1
x<-5/1
x<-5
hello help please
Express
[tex] \frac{3}{5} [/tex]
of a right angle triangle to radian measure and can some anybody help me by looking one old question from my profile help please
Answers
a right angle is 90°, or 1/4 of a circle.
3/5 * 1/4 = 3/20
radian measure is the length of the circumference of this part of the circle.
a full circumference of a circle would be 2*pi*r, also expressed as 2 rad * r
now let's multiply the full thing with the 3/20 from earlier to just get the desired fraction:
6/20 rad * r
= 3/10 rad * r
of course a solution in cm or inch still depends on the radius here, wich could be just plugged in at will
Answer:
[tex]\frac{3\pi }{10}[/tex]
Step-by-step explanation:
To express degrees in radians
radian measure = degree measure × [tex]\frac{\pi }{180}[/tex]
[tex]\frac{3}{5}[/tex] of a right angle
= [tex]\frac{3}{5}[/tex] × 90° = 54° , then
radian = 54 × [tex]\frac{\pi }{180}[/tex] = [tex]\frac{54}{180}[/tex] × π = [tex]\frac{3}{10}[/tex] × π = [tex]\frac{3\pi }{10}[/tex]
trigonometric identities help
Answers
Answer:
Step-by-step explanation:
I just graphed this and used the "maximum value" capability to locate the max value. It occurs at (0.363, 3).
there are 108 flowers. 1/9 of them bloomed. How many did not bloom? How many did?
Answers
Answer:
96 flowers did not bloom and 12 did.
Explanation:
Total flower = 108
Number of flower that bloomed
= ⅑ of the total flowers
= ⅑ of 108
= ⅑ × 108
= 108/9
= 12
So, number of flowers that did not bloom
= Total flowers - Number of flowers that bloomed
= 108 - 12
= 96
So, 96 flowers did not bloom and 12 flowers did.
Which expression has been simplified INCORRECTLY? * 1 point - (-9) = 9 - (+9) = -9 + (-9) = -9 + (+9) = -9
Answers
Answer:
+ (+9) = -9
Step-by-step explanation:
- (-9) = 9 A negative times a negative is a positive
- (+9) = -9 A negative times a positive is a negative
+ (-9) = -9 A positive times a negative is a negative
+ (+9) = -9 A positive time a positive is a positive
Giải phương trình lượng giác cơ bản sinx=cos2x
Answers
Answer:
Step-by-step explanation:
Categorize the graph as linear increasing, linear decreasing, exponential growth, or exponential decay
Answers
Answer:
D. Exponential growth
Step-by-step explanation:
Hope this helps
Function that is similar to exponential.
Option (A) is correct.
What is exponential decay?Exponential decay describes the process of reducing an amount by a consistent percentage rate over a period of time. It can be expressed by the formula [tex]y=a(1-b)^{x}[/tex] wherein y is the final amount, a is the original amount, b is the decay factor, and x is the amount of time that has passed.
We can observe that
First, y increases as x increases
Last it is a function that is similar to exponential.
Function is an exponential decay.
Option (A) is correct.
Find out more information about exponential decay here
https://brainly.com/question/14355665
#SPJ2
Jessie brought 3 1/5?cups of water on
a hike. If he drinks 2/5 cup of water
each hour, how many hours will he
have water for?
Answers
Answer:
8 hours
Step-by-step explanation:
3 1/5 cups, he drinks 2/5 cups every hour
to find the number of hours he has water for, divide the 2 numbers
3 1/5 = 16/5
16/5 divided by 2/5 is equal to 16/5 times 5/2
80/10 equals 8, so he will have water for 8 hours
Which exponential function is represented by the graph?
Answers
Answer:
Answer is option (B)......
What is the difference of the rational expressions below?
Answers
Answer:
in the pic
Step-by-step explanation:
answer A
.....
Let V(x) = -x2 + 2x - 4 and W(x) = -~3 + 2x2 + x +, 5. Find
V(x) + W(x).
ASAP
Answers
Answer:
-x3+x2+3x+1
Step-by-step explanation:
V(x) + W(x) = -x2 + 2x - 4 + -x3 + 2x2 + x + 5= -x3+x2+3x+1
Using the Factor Theorem, which of the polynomial functions has the zeros 2, radical 3 , and negative radical 3 ?
f(x)= x3 - 2x2 - 3x + 6
f(x)= x3 - 2x2 + 3x + 6
f(x)= x3 + 2x2 - 3x + 6
f(x)= x3 + 2x2 - 3x - 6
Answers
Using the factor theorem, it is found that the polynomial is:
[tex]f(x) = x^3 - 2x^2 - 3x + 6[/tex]
Given by the first option
---------------------------
Given a polynomial f(x), this polynomial has roots [tex]x_{1}, x_{2}, x_{n}[/tex] using the factor theorem it can be written as: [tex]a(x - x_{1})*(x - x_{2})*...*(x-x_n)[/tex], in which a is the leading coefficient.
---------------------------
In this question:
[tex]x_1 = 2[/tex][tex]x_2 = \sqrt{3}[/tex][tex]x_3 = -\sqrt{3}[/tex]By the options, leading coefficient [tex]a = 1[/tex]Thus:
[tex]f(x) = (x - 2)(x - \sqrt{3})(x + \sqrt{3})[/tex]
[tex]f(x) = (x - 2)(x^2 - 3)[/tex]
[tex]f(x) = x^3 -2x^2 - 3x + 6[/tex]
Which is the polynomial.
A similar problem is given that: https://brainly.com/question/4786502
I need help ASAP!!! FIND THE SEGMENT Please explain how u got the answer
Answers
Answer:
x = 960
Step-by-step explanation:
Using the Altitude- on- Hypotenuse theorem
( leg of large triangle )² = ( part of hypotenuse below it) × ( whole hypotenuse), so
x² = 576 × (576 + 1024) = 576 × 1600 = 921600 ( take square root of both sides )
x = [tex]\sqrt{921600}[/tex] = 960
a student takes a rectangular piece of paper 30 cm long and 21 cm wide find the area of the biggest circle that can be cut out from the paper also find the area of the paper left after cutting out the circle
Answers
Answer:
Step-by-step explanation:
diameter of the circle=smallest of the length and width=21 cm
r=21/2
area of the circle=πr²=22/7 ×(21/2)²=(21×441)/(7×4)=1323/4=330.75 cm²
If there are:
6 red marbles
10 yellow marbles
5 green marbles
and 1 blue marble
What is the probability of picking 1 blue marble and 1 green marble?
(Once a marble is chosen it is NOT put back into the box).
(Write your answer in the form of a decimal, round to 2 places).
Answers
Answer:
0.02
Step-by-step explanation:
either picking a green then blue;
5/22 x 1/21= 5/462
or picking a blue then green;
1/22 x 5/21= 5/462
total is 10/462 which is approximately 0.02
since there was no specific order in the question i assumed you add them both.
4.
If you took a horizontal slice out of the three-dimensional shape, what two-
dimensional shape would you have?
1) rectangle
2) circle
3) square
4) triangle
Answers
Answer:
Square
Step-by-step explanation:
It got 4 sides like square and its form is looking like a square.
Dont give me wrong answers. please help though.
Answers
Answer:
24 in^3
Step-by-step explanation:
Volume of the figure= 3 * (Volume of a cube with side 2)
Volume of the figure= 3*2^3=24 in^3
Answer:
24 cubic inches
Step-by-step explanation:
The formula for finding volume is b*h*w.
b*h*w is base multiplied my height multiplied my width. Lets use this formula to find the volume of one of cubes.
Here is the information we know about the cubes:
the base is 2 inches
the height is 2 inches
the width is 2 inches
Lets put this information into the formula to find the volume of one of the cubes. I will show the work in steps so it is easy to follow.
Step one: plug the given information into the formula.
b*h*w = 2*2*2
Step two: Solve the equation.
2*2*2 = 4*2 = 8
Now we have the volume of one on the cubes. This is 8 cubic inches. However, to find the volume of all three of the cubes we must multiply 8 by 3.
Step three: multiply 8 by 3.
8*3 = 24
And there you have it! Our final answer is 24 cubic inches.
Here is a quick review of what we did to get our answer:
2*2*2 = 8
8*3 = 24
I hope this helps!
tìm tất cả giá trị thực của tham số m để đồ thị hàm số y=x³-mx²+4 cắt trục hoành tại ba điểm phân biệt
Answers
Answer:
실례합니다?
Step-by-step explanation:
질문이 뭔가요??? 이해가 안가요? 어느 언어?
6-
С
5
B
B
4-
3-
D
2-
A
А
1-
0
-7
-5
0
-6
.4
-3
-2
-1
2
3
4
5
6
-10
-2-
-3-
-4-
Which of the following sequences of transformations is used to obtain figure A'B'C'D' from ABCD?
Answers
Answer: -1
Step-by-step explanation:
Look at the patter it has
Given m||n, find the value of x.
t
(9x+23)
m
(10x+6)
an
Answer:
Submit Answer
attempt 1 out of 2
Pls help I’ve already got it wrong once
Answers
Answer:
x=17
Step-by-step explanation:
These are alternate interior angles and alternate interior angles are equal when the lines are parallel
9x+23= 10x+6
Subtract 9x from each side
9x+23 -9x= 10x-9x+6
23 = x+6
Subtract 6 from each side
23-6 = x+6-6
17 =x
Find the value of x. Round to the nearest tenth
Answers
Answer:
658ft
Step-by-step explanation:
you first have to calculate the angle next to that 28°angle,if you look at the two they form a 90° so to find that angle you have to subtract 90-28=62
the x is the opposite of angle 62 and the 350 si the adjacent so you can use the tan ratio to find the answer
tan62=opposite/adjacent
tan62=y/350
y=tan62×350
=658ft
I hope this helps
A shopkeeper allows 10% discount on the marked price of a bicycle. If a costomer pays Rs 4068 with 13% VAT find the marked price of the bicycle
Answers
[tex] \large{ \tt{❁ \: S \: O \: L \: U \: T \: I \: O \: N \: ❁}}[/tex]
We're provided - Discount % = 10 % , Cost with VAT [ SP with VAT ] = Rs 4068 & VAT % = 13%. We're asked to find out the marked price of the bicycle. Let's start :[tex] \large{ \tt{❇ \: FIND \: SP \: WITHOUT \: VAT \: / \: SP\: ❇}}[/tex]
[tex] \large{ \tt{❃ \: SP \: with \: VAT= SP + VAT\% \: of \: SP}}[/tex]
[tex] \large{ \tt{⇢ \: 4068 = SP + 13\% \: of \: SP}}[/tex]
[tex] \large{ \tt{⇢ \: 4068 = SP + \frac{13}{100} \: sp}}[/tex]
[tex] \large{ \tt{⇢ \: 4068 = \frac{100 \: \: SP + 13 \: SP}{100} }}[/tex]
[tex] \large{ \tt{⇢ \: 4068 = \frac{113 \: SP}{100} }}[/tex]
[tex] \large{ \tt{⇢ \: 113 \: SP = 406800}}[/tex]
[tex] \large{ \tt{⇢ \: SP = \frac{406800}{113} }}[/tex]
[tex] \large{ \tt{⇢ \: SP = 3600}}[/tex]
Hence , SP = Rs 3600[tex] \large{ \tt{✽ \: NOW , \: FIND \: THE \: MP \:✽ }}[/tex]
Let Marked Price [ MP ] be x.[tex] \large {\tt{❃ \: SP = MP - dis\% \: of \: MP}}[/tex]
[tex] \large{ \tt{⇾ \: 3600 = x - 10\% \: of \: x}}[/tex]
[tex] \large{ \tt{⇾ \: 3600 = x - \frac{10}{100} } \: x}[/tex]
[tex] \large{ \tt{⇾ \: 3600 = \frac{100x - 10x}{100} }}[/tex]
[tex] \large{ \tt{⇾ \: 3600 = \frac{90x}{100} }}[/tex]
[tex] \large{ \tt{⇾ \: 90x = 360000}}[/tex]
[tex] \large{ \tt{⇾ \: x = \frac{360000}{90} }}[/tex]
[tex] \large{ \tt{⇾ \: x = Rs \: 4000}}[/tex]
[tex] \large{ \boxed{ \boxed{ \tt{☂ \: OUR \: FINAL \: ANSWER : \boxed {\tt {\: Rs \: 4000}}}}}}[/tex]
Hope I helped! Let me know if you have any questions regarding my answer and don't hesitate to reach out to me if you need any assistance! :)Determine whether the statement below is true or false boxy is rectangle
Answers
Does this graph show a function? Explain how you know.
A. No; the graph fails the vertical line test.
• B. No; there are y-values that have more than one x-value.
• C. Yes; the graph passes the vertical line test.
D. Yes; there are no y-values that have more than one x-value.
Answers
Answer:
C. Yes; the graph passes the vertical line test.
Step-by-step explanation:
Reasons the others are wrong:
A. It does pass the vertical line test.
B. Y-values can have any x values. It is x-values that can't have multiple y-values.
D. There are y-values with more than one x-value on this graph so that's just false. Even if it were true, that still doesn't invalidate it due to the reasons given in Answer B.
Would the function ƒ(x) = 4 be considered a step function? Explain your reasoning.
Answers
Hey there! I'm happy to help!
A step function is a function that looks like stairs when you graph it. Normally the end of one line will be graphed as an open circle (less or greater than, not equal to) while the other end would be a closed circle. This allows for a new line of the function to start directly above it without it not being a function (an input cannot have two outputs)
The function f(x)=4 is just a horizontal line as it has a slope of 0 (there is no x on the right side of the equation), so this doesn't resemble a step function.
Have a wonderful day and keep learning! :D
15x + 45 = 15 (3 + x) always never one solution how do I do it
Answers
Answer:
0
Step-by-step explanation:
First, you need to try to get rid of the ().
To do this:
15 * 3 and 15 * x
This makes 45 and 15x after the = , so the formula is now:
15x + 45 = 45 + 15x
Now get the 15x to the left side. When a number switches sides, it becomes negative when positive and positive when negative. So in this case 15x will become -15x and the 45(on the left) becomes - 45
15x - 15x = 45 - 45
Answer: 0
15x - 15x = 45 - 45
0x = 0 (*)
If we plug any real numbers of x to equation (*) we will always get 0 = 0
So the set of solutions of this question is all real numbers
Please help me to solve this question as soon as possible. Thank you
1.6 is a common factor of 36 and y. Find the possible value of y.
A. 25
B. 48
C.57
D. 81
Answers
Answer:
the answer is B
Step-by-step explanation:
because only 48 is dividable by 6
