Mathematics High School

I WANT DIAGRAM
A vertical tower subtends a right angle on the top of 10m high flagstaff.if distance between them is 20m,find the height of the tower

Answers

Answer 1
Let us consider a triangle where AB to be the flagstaff of 10 m and BC to be of 20 m as the distance between the tower and the flag.  
Considering ABC and ADE as triangle
 AB = 10 = CE
 BC = 20 = AE 
 Calculating the values of ABC
 tan x = AB/BC
 tan x = 10/20
 10/tan x = 20..............(1) 
 Calculating the values of ADE
 tan(90-x) = DE/AE
 cot x = DE/20
 DE/cot x = 20 .............(2) 
 Solving equations 1 & 2
 10/tan x = DE/cot x
 DE = 40
 Hence the total height of the tower is DE+CE = 40+10= 50 m.

Related Questions

How are the functions y=x and y=x+5 related? How are their graphs related?

Answers

Final answer:

The functions y=x and y=x+5 have the same slope but different y-intercepts. Their graphs are straight lines.

Explanation:

The functions y=x and y=x+5 are related in that they have the same slope of 1. This means that for every increase of 1 in the value of x, the value of y will also increase by 1. However, they have different y-intercepts. The function y=x has a y-intercept of 0, while the function y=x+5 has a y-intercept of 5.

Their graphs are related in that they are both straight lines. The graph of y=x is a line passing through the origin (0,0), while the graph of y=x+5 is a line shifted upward by 5 units compared to the graph of y=x.

PLZ HELP!!!!!!! Can a kite be formed by drawing a triangle and then reflecting one or more times? Explain.

Select one:
a. Yes. Draw any triangle ABC. Reflect this triangle across the perpendicular bisector of line AB, creating triangle A'B'C' for which A'=B and B'=A. By the definition of a reflection, sides A'C and B'C' are congruent. In addition, sides B'C and A'C' are congruent. The quadrilateral CC'B'A' has two pairs of consecutive sides that are congruent and no congruent opposite sides. By definition, this is a kite.
b. Yes. Draw any triangle ABC. Reflect this triangle across the line AB, creating triangle A'B'C' for which A'=A and B'=B. By definition of a reflection, sides B'C and B'C' are congruent. In addition, sides A'C and A'C' are congruent. The quadrilateral CA'C'B' has two pairs of consecutive sides that are congruent and no congruent opposite sides. By definition, this is a kite.
c. No. Since the reflection of a triangle is always another triangle, there is no way to create a quadrilateral using a triangle or its reflection.
d. No. It is not possible to reflect a triangle in such a way that the result is quadrilateral with any consecutive sides that are congruent.

Answers

The answer is (B).

Draw any triangle ABC. Reflect this triangle across the line AB, creating triangle A'B'C' for which A'=A and B'=B. By definition of a reflection, sides B'C and B'C' are congruent. In addition, sides A'C and A'C' are congruent. The quadrilateral CA'C'B' has two pairs of consecutive sides that are congruent and no congruent opposite sides. By definition, this is a kite.

Hi guys can you help me factor these two equations?

5x^2-13x-6

4x^4 – 28x^3 + 48x^2

please show your work on both of them, and thank you so much!

Answers

A) 5x^2-13x-6

 1. First, you must find the roots of the quadratic equation, by applying the quadratic formula, which is:

 x=-b√(b²-4ac)/2a

 2. The roots are:

 x1=3
 x2=-2/5

 3. Then, you have:

 5(x-3)(x+2/5)

 4. When you simplify, you obtain:

 (x-3)(5x+2)

 B) 4x^4-28x^3+48x^2 

 1. First, you must factor the common term, which is 4x^2. Then:

 4x^2(x^2-7x+12)

 2. Now, you must apply the quadratic formula to obtain the roots of the quadratic equation: x^2-7x+12. Then, you have:

 x1=4
 x2=3

 3. Finally, you obtain:

 4x^2(x-4)(x-3)

Ninas car exponentially depreciates at a rate of 7 percent per year. If nina bought the car when it was 6 years old for 12000, what was the original price of the car

Answers

the original price of the car would be $17,040 brand new 
hope this helps 

Answer:

[tex] A(6) = 12000 = A_o e^{-0.07 *6}[/tex]

And solving for the initial amount [tex] A_o[/tex] we got:

[tex] A_o = \frac{12000}{e^{-0.07*6}}= 18263.539[/tex]

So then the original price for the car would be approximately 18263.539$

Step-by-step explanation:

For this case we can use the exponential model given by:

[tex] A(t) = A_o e^{bt}[/tex]

Where:

[tex]A_o[/tex] represent the initial amount for the car

[tex]b=-0.07[/tex] represent the exponential growth/decay rate

t represent the number of years. With t =0 at the begin

After 6 year we have that t =6, and we know this condition:

[tex] A(6) = 12000[/tex]

So then we can use the exponential model formula and the condition given and we have this:

[tex] A(6) = 12000 = A_o e^{-0.07 *6}[/tex]

And solving for the initial amount [tex] A_o[/tex] we got:

[tex] A_o = \frac{12000}{e^{-0.07*6}}= 18263.539[/tex]

So then the original price for the car would be approximately 18263.539$

What is 6/7 as a recurring decimal?

Answers

this is not actually a recurring decimal when you divide 6 by 7, you get .85714286

maxine hosted a dinner party at her favorite restaurant. she had to pay $12 per guest. the restaurant took $72 off the bill due to a mistake in the order. if the finale bill is $300, which equation will help the restaurant determine the number of guests at the dinner party

Answers

" $300 = $12g - $72 " .

A clock is constructed using a regular polygon with 60 sides. The polygon rotates everybody minute. How much has the polygon rotated after 7 minutes
•14 degrees
•21 degrees
•35 degrees
•42 degrees

Answers

360/60 = 6

6 minutes = 1 degree

6 X 7 = 42

42 degrees is your Answer

Verify that △ABC∼△DEF. Find the scale factor of △ABC to △DEF.

△ABC: AB = 10, BC = 16, CA = 20
△DEF: DE = 25, EF = 40, FD = 50
I really need someone to explain to me how to do this because i am so confused my teacher didn't give us notes and didn't explain this very well.

Answers

Answer:

2/3 i got it right

Step-by-step explanation:

Final answer:

To find the scale factor between △ABC and △DEF, compare their corresponding side lengths and calculate the scale factor as 2.5 or 5/2.

Explanation:

To verify that two triangles △ABC and △DEF are similar, you need to check if their corresponding angles are congruent and their corresponding sides are proportional.

Calculate the scale factor using the corresponding sides of the triangles: AB/DE = BC/EF = CA/FD.

Substitute the values: 10/25 = 16/40 = 20/50. Simplify to find the scale factor.

Therefore, the scale factor of △ABC to △DEF is 2.5 or 5/2.

Please solve these for me. I need them for a quiz.

Answers

4a)

I'm going to use the Substitution method

c = 160 + 67t 
55 + 82t = 160 + 67t .... replace c with 55+82t; solve for t
55 + 82t - 55 = 160 + 67t - 55
82t = 67t + 105
82t - 67t = 67t + 105 - 67t
15t = 105
15t/15 = 105/15
t = 7

Use t = 7 to find that
c = 160 + 67t
c = 160 + 67*7
c = 629
You can use the other equation as well to get the same answer for c.

It takes 7 months for the cost to be the same. That cost is $629

===========================================================
4b)

I'm going to use the Elimination method

Subtract the equations to get
x+y = 20
x-4y = -15
-----------
0x+5y = 35

If 5y = 35, then y = 7 after we divide both sides by 5

Plug y = 7 into the first equation and solve for x
x+y = 20
x+7 = 20
x+7-7 = 20-7
x = 13

So x = 13 and y = 7 are the solutions

Max exercises 13 hours a week while Sasha exercises 7 hours a week
===========================================================
4c)

I'm going to use the Substitution method

x = price for one adult ticket (in dollars)
y = price for one student ticket (in dollars)

Fact #1
4 adult tickets + 2 student tickets = 64 dollars
4x + 2y = 64

Fact #2
3 adult tickets + 3 student tickets = 60 dollars
3x + 3y = 60
3(x + y) = 60
3(x + y)/3 = 60/3
x + y = 20
x + y-x = 20-x ... subtract x from both sides
y = 20 - x

Plug that into the first equation
4x + 2y = 64
4x + 2(y) = 64
4x + 2(20-x) = 64 ... replace y with 20-x; solve for x
4x + 40-2x = 64
2x + 40 = 64
2x + 40-40 = 64-40
2x = 24
2x/2 = 24/2
x = 12

Use x = 12 to find y
y = 20 - x
y = 20 - 12
y = 8

In summary, x = 12 and y = 8, which means...
One adult ticket costs $12
One student ticket cost $8


A rhombus exists. This rhombus has 2 diagonals. The diagonals touch the side forming angles. These angles are in the ratio 4:5. Solve for all the angles in this rhombus based on the theorems for rhombuses and parallelograms.

Answers

as you know, the diagonals in a rhombus meet in the center at right-angles, check the picture below.

and the pair of angles at each opposite vertex, are twins.

now, since the diagonals center meeting point, makes 4 right-triangles, let's use the one on the upper-left, recall that a triangle has a sum of all interior angles to be 180°, so the missing angles in that triangle are "complementary angles", namely, they add up to 90°.

so, let's check 90 in a 4:5 ratio then, we simply divide 90 by (4+5) and distribute the pieces accordingly, let's do so,

[tex]\bf 90\qquad 4:5\qquad \cfrac{4}{5}\qquad \cfrac{4\cdot \frac{90}{4+5}}{5\cdot \frac{90}{4+5}}\implies \cfrac{40}{50}\implies 40:50[/tex]

so the ratio of 4 angle, is really 40°, and the ratio of 5 angle is really 50°.

since the diagonal is bisecting the vertex, the angle made at the vertex is twice as much as that in the triangle we used, thus, 2(40) are the angles at the top and bottom, and 2(50) are the angles at the left and right.

80°, 80° and 100° and 100°.

Which rule describes a translation that is 8 units to the right and 2 units up?

Answers

we know that

when we speak of right or left we refer to the x axis
x positive --------------> right
x negative--------------> left

when we speak of up or down we refer to the y axis
y positive --------------> up
y negative--------------> down

therefore

the rule is
(x,y)---------> (x+8, y+2)
The answer is 

x, y (x + 8, y + 2)

Which algebraic expression is equivalent to the expression below? (3x + 12) + 8x

A.
(3x + 8x) + 12
B.
(3x - 8x) + 12
C.
23x
D.
(3x + 12x) + 8

Answers

7(4x+4)+5x, 28x+28+5x, 33x+28. Answer: A.

helppppppppppppppppppppppppppppppppp

Answers

Answer:
Third choice is the correct one

Explanation:
We are asked to use the u substitution. Therefore, we will assume that:
u = x^2

Substitute with u in the given expression as follows:
9x^4 - 2x^2 - 7 = 0
9u^2 - 2u - 7 = 0
(u-1)(9u+7) = 0
either u = 1
or u = -7/9

Now, u = x^2, this means that:
at u = 1:
x^2 = 1
x = ± √1 = ±1

at u = -7/9
x = ±i√7/9 (the i indicates the imaginary value)

Hope this helps :)

Find the nth term of the sequence
-3, 0, 5, 12

Work out the reciprocal of 2 x 10(9,as a power). Give your answer in standard form.

Answers

Hello,


Adding 4 to each term we find 1,4,9,16,....
[tex]u_1=-3\\ u_2=0\\ u_3=5\\ u_4=12\\ Let's\ assume\ v_n=u_n+4\\ v_1=-3+4=1=1^2\\ v_2=0+4=4=2^2\\ v_3=5+4=9=3^2\\ v_4=12+4=16=4^2\\ ...\\ v_n=n^2\\ u_n=v_n-4\\\\ \boxed{u_n=n^2-4} [/tex]


Write an expression to show the sum of fourteen and triple eight.

Answers

14x8³

have a good day!! :)
hope this helps!!! :D
plz give brainliest!! XD

The original price of sn item is $25, but after the discount, you only have to pay $18.50. what is the discount (as a percent)?

Answers

The first thing that you have to do is subtract 18.5 from 25. Then you do 6.5/25 and that equals 0.26. To get a percentage you multiply that by 100. You get 26%

The discount is 26%.

What is Discount?

The discount equals the difference between the price paid for and it's par value. Discount is a kind of reduction or deduction in the cost price of a product.

Given:

Marked price = $25

Selling price = $18.50

So,

Discount = MP - SP

Discount = 25-18.50

Discount = 6.50

Now,

D% = D/MP *100

D% = 6.5 /25*100

D% = 26%

Hence, the discount percent is 26%.

Learn more about discount here:

https://brainly.com/question/3541148

#SPJ2

help me plsss i really need did that but still dont get it

Answers

see attached picture for the answers:



A field test for a new exam was given to randomly selected seniors. The exams were graded, and the sample mean and sample standard deviation were calculated. Based on the results, the exam creator claims that on the same exam, nine times out of ten, seniors will have an average score within 6% of 80%.

Is the confidence interval at 90%, 95%, or 99%? What is the margin of error? Calculate the confidence interval and explain what it means in terms of the situation.

Answers

The confidence interval would be 90% Probability that mean lies between 74% and 86% is 90% Prob( 74 <= X-bar<= 86) = 0.9 So the confidence interval is [74, 86] with 90% confidence that the actual population mean lies inside the interval. The error margin would be 6%. In 9 out of 10 the confidence interval for similar samples of seniors will have the true mean of the population of senior scores. 

Eight more than the quotient of a number and 4 equals 5

Answers

Well we can put that word problem into a equation so, 8+x/4=5. Now what I would do is move the 8 to the other side, and since it moved to the other side it becomes a -8 so now we have x/4 = -3. Now I would multiply both side by 4 to get x = -12

Answer= X = -12

HELP QUICK PLEASE!!!!!
A proof for the Corresponding Angles Theorem is shown below. Next to each reason, choose the statement to which it applies.

Answers

y2 -y1 over x2 - x1 i hoped it helped 
xoxo nikole

#1=Given
#2=Alternate interior
#3=Vertical angles
#4=Substitution

factor the following polynomial completely 30y^6+25y^5-10y^4

Answers

5y^4 * (6y^2 + 5y-2)

If the circumference of a circle is 11inches, which is closest to its area?a.380 square inchesb.95 square inchesc.17 square inchesd.35 square inches

Answers

C=2 pi r and 11=2*3.14*r
11=6.28*r
r=1.75
A=pi r^2
A=3.14* (1.75)^2=9.625
this number is closer to 17 square inches

What is the area of a sector with a central angle of π3 radians and a radius of 12.4 m? Use 3.14 for π and round your final answer to the nearest hundredth.

Answers

The answer to this is 80.47. 

Answer:

80.47

Step-by-step explanation:

This is correct! :D

How many sets of 7 questions can be chosen from a file of 25 questions?

Answers

If all 25 questions are different,

When order of selection counts:
P(25,7)
=25!/(25-7)!
=15511210043330985984000000/6402373705728000
=2422728000

When order of selection does not count count:
C(25,7)
=25!/(7!*(25-7)!)
=15511210043330985984000000/(6402373705728000*5040)
=480700

I need Geometry help!!!

Answers

Vertical angles are equal, so
.. 3x +8 = 5x -20
.. 28 = 2x . . . . . . . . add 20-3x
.. 14 = x . . . . . . . . . . divide by 2

Each of the vertical angles is 3*14 +8 = 50°, so the supplementary one is 130°.
.. 5*14 +4y = 130
.. 4y = 60 . . . . . . . . subtract 70
.. y = 15 . . . . . . . . . . divide by 4

The values of interest are
.. x = 14
.. y = 15

If the radius of the circle is doubled, by what number is the circumference multiplied?

Answers

circumference is also doubled (multiplied by 2)
Answer:

The number by which the circumference is multiplied is:

                               2

Step-by-step explanation:

We know that the circumference of the circle in terms of the radius r is given by:

        [tex]\text{Circumference}=2\pi r[/tex]

Now, if the radius is doubled.

i.e.

[tex]r'=2r[/tex]

Hence, the circumference of the new circle is given by:

[tex]\text{Circumference of new circle}=2\pi (2r)\\\\i.e.\\\\\text{Circumference of new circle}=2(2\pi r)[/tex]

i.e.

[tex]\text{Circumference of new circle}=2\times \text{Circumference of original circle}[/tex]

The constant by which the circumference is multiplied is: 2

The perimeter of the rectangle is 34 cm. Find the value of x.


A. 2

B. 17

C. [tex] \frac{34}{33} [/tex]

D. 20

Answers

2(3x + 11) = 34
3x + 11 = 34/2
3x + 11 = 17
3x = 17 - 11
3x = 6
x = 6/3
x = 2

6) Ethan uses the function f(x) = 2x2 + 2x + 4 to track the temperature of a substance over 8 hours. You know that f(3) = 28 meaning that the temperature of the substance is 28°C when you plug in a 3 for x. What is the domain of Ethan’s function?

Answers

Final answer:

The domain of Ethan's function f(x) = 2x² + 2x + 4  is all real numbers as it is a quadratic function.

Explanation:

The domain of a function is the set of all possible input values (x-values) for which the function produces a valid output (y-value). In this case, the function f(x) = 2x² + 2x + 4 represents the temperature of a substance over time. Since temperature is a physical quantity and cannot be negative, the domain of the function must be restricted to non-negative values of x.

To determine the exact domain of the function, we can analyze the expression 2x² + 2x + 4. This expression is always non-negative for any real number x. Therefore, the domain of f(x) = 2x² + 2x + 4 is all real numbers x ≥ 0.

In mathematical notation, the domain of the function can be expressed as:

{x ∈ ℝ | x ≥ 0}

This indicates that the function is defined for all real numbers (ℝ) as long as the value of x is greater than or equal to 0 (x ≥ 0).

Write an equation for the translation of y = 4 x that has the given asymptotes. 15. x = 0, y = 3

Answers

y = 4/x +3

____
We are a bit mystified regarding the role of "15." in this question. We suspect it is an irrelevant question number.

jake plans to use a ramp to make it easier to move a piano out of the back of his truck the back of the truck is 33 inches tall and the ramp is 65 inches long. what is the horizontal distance from the end of the ramp to the back of the truck

Answers

check the picture below.

Answer:

56 inches is the horizontal distance from the end of the ramp to the back of the truck.

Step-by-step explanation:

Height of the back of the truck =33 inches

Length of the ramp = 65 inches

Length of the end of ramp to the back of the truck =?

In triangle ABC:

AB = 33 inches

BC = ?

AC = 65  inches

[tex]AB^2+BC^2=AC^2[/tex] (Pythagoras theorem)

[tex](33 inches)^2+(BC)^2=(65 inches)^2[/tex]

BC = 56 inches

Other Questions
How does evaporation make water denser? An app developer projects that he will earn $22.00 for every 8 apps downloaded. Write an equation to represent the proportional relationship between the number of apps and the total earnings. Jane earns $7.50 an hour and time-and-a-half for overtime. How much does she earn for a 43.5-hour week? a. $300 b. $363.50 c. $333.75 d. $339.38 ANSWER ASAP AND GET BRAINEST(answer not c) Which of the following describes the Cloture Rule?A single senator can talk long enough to prevent the full Senate from voting on a bill.A bill must be given a number, read twice, and then sent to a standing committee.Senators are limited by a rule that allows only two speeches on a topic during a legislative day.Three fifths of senators can vote to limit debate on a subject to 30 hours of floor time. Figure 17-2 shows highest fitness toward the center of the curve. When individuals with an average form of trait have the highest fitness the result is A-not predicable B-disruptive selection C-directional selection D-stabilizing selection How did humans and animals adapt/survive to hurricane Katrina? AND Give examples of organisms that could not adapt/survive? PLS ANSWER HELP 100 POINTS What is the most important chemical property of amines? Would of the Members Please check my answers? Will become fan and write testimonal!1. Which factor has greatest importance in determining the characteristics of an aquatic ecosystem? (1 point)day lengthwater depthangle of sunlightaverage precipitation2. Which is one way that a freshwater wetland differs from a lake or pond? (1 point)Water flows in a lake or pond but never flows in a wetland.Wetlands are nesting areas for birds, but lakes and ponds are not.Water does not always cover a wetland as it does a lake or pond.Wetlands are salty, but lakes and ponds are fresh. what were the benefits and drawbacks of town life in medieval Europe Which of the following was NOT a negative consequence of the Civil War A.More than 620,000 men had died in the war. B.Many towns and villages were completed devastated or destroyed. C.Slavery had been abolished. D.Many in the nation held hard feelings from the war. Question 15 pleasePlease show work and Thank you for your time Holly sang along as the band played her favorite song.What kind of sentence is this? The plan de laguala was designed to guarantee A variable-ratio schedule reinforces behavior after a: A client is diagnosed with pancytopenia caused by chemotherapy. what should a nurse teach the client about this complication? The lower base of the frustum shown in the figure is a square 8 ft on each side. The upper base is a square 4 ft on each side. If the altitude is 6 ft, find the slant height. A. 6 ft B. 5.66 ft C. 6.32 ft D. 4 ft Sylvia has 3/4 of a yad of paper to wrap candles. It takes 1/8 of a yard of paper to wrap each candle. How many candles can Sylvia Wrap? Tommy was walking at a rate of 4 mileshour at noon and at 12:30 pm he was walking at a brisk rate of 6 mileshour. Two hours later Tommy was walking at a leisurely rate of 2 mileshour. Which statement about Tommy's accleration is true?A)Tommy had an accleration of zero the entire time.B)Tommy had a positive acceleration between noon and 12:30 pm.C)Tommy had a positive acceleration between 12:30 and 2:30 pm.D)Tommy had a negative acceleration between noon and 12:30 pm. Fe2O3(s)+3CO(g)2Fe(s)+3CO2(g) How many moles of Fe2O3 are necessary to produce 1.648 mol of CO2? The atomic mass of gold is 197 g/mole, and the density of gold is 19.3 g/cm3. using this information along with the measured value of young's modulus, calculate the speed of sound in gold.