Two trees are 120 m apart. From the point halfway between them, the angle of elevation to the top of the trees is 36 and 52. How much taller is one tree than the other.
Answers
One tree is 31.044 m taller than the other one in height.
Given Information and Formula Used:
The distance between the trees, BC (from the figure) = 120 m
Elevation of angles to the top of the trees,
∠AMB = 52°
∠DMC = 36°
In a right angled triangle,
tan x = Perpendicular/Height
Here, x is the angle opposite to the Perpendicular.
Calculating the Height Difference:
Let's compute the height of the taller tree first.
In ΔAMB,
tan 52° = AB / BM
Now, since M is the point halfway between the trees,
BM = CM = BC/2
BM = CM = 60 m
⇒ 1.2799 = AB / 60
AB = 1.2799 × 60
Thus, the height of the taller tree, AB = 76.794 m
Now, we will compute the height of the smaller tree.
In ΔDCM,
tan 36° = DC / CM
⇒ 0.7625 = DC / 60
DC = 0.7625 × 60
Thus, the height of the smaller tree, DC = 45.75 m
The difference in the heights of the trees, AP = AB - DC
AP = (76.794 - 45.75)m
AP = 31.044m
Hence one tree is 31.044m taller in height than the other.
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Related Questions
What is true about the triangles shown in the diagram? Select all that apply.
Answers
Answers:
Choice A) Segment AC = 2*sqrt(17)
Choice B) Segment BD is 32 units long
Choice F) Segment AB is approximately 33 units long.
==========================================================
Explanation:
The triangles are similar, so we can form this proportion
CD/DA = DA/BD
2/8 = 8/x
2x = 8*8
2x = 64
x = 64/2
x = 32
BD is 32 units long
This means one of the answers is choice B. It rules out choice D.
--------------
The legs of right triangle ABD are
AD = 8BD = 32Use the pythagorean theorem to find hypotenuse AB.
a^2 + b^2 = c^2
(AD)^2 + (BD)^2 = (AB)^2
8^2 + 32^2 = (AB)^2
(AB)^2 = 64 + 1024
(AB)^2 = 1088
AB = sqrt(1088)
AB = sqrt(64*17)
AB = sqrt(64)*sqrt(17)
AB = 8*sqrt(17)
AB = 32.984845
Segment AB is approximately 33 units long.
This tells us another answer is choice F. Choice C is false because 4*sqrt(5) = 8.94427
--------------
BC = BD + DC
BC = 32 + 2
BC = 34
BC is the hypotenuse of triangle ABC
Use the pythagorean theorem to determine AC.
a^2 + b^2 = c^2
(AB)^2 + (AC)^2 = (BC)^2
(sqrt(1088))^2 + (AC)^2 = (34)^2
1088 + (AC)^2 = 1156
(AC)^2 = 1156 - 1088
(AC)^2 = 68
AC = sqrt(68)
AC = sqrt(4*17)
AC = sqrt(4)*sqrt(17)
AC = 2*sqrt(17)
Another answer is Choice A. It rules out choice E because 2*sqrt(17) = 8.2462 approximately.
For what values of x does 5x^2+4x-4= 0
Answers
The values of x that satisfy the equation are x = (-4 + 2√6) / 5 and x = (-4 - 2√6) / 5
What values of x satisfy the given equation?The values of x that satisfy the equation 5x² + 4x - 4 = 0 can be determined using the quadratic formula given below:
x = (-b ± √(b² - 4ac)) / (2a)
From the equation:
a = 5, b = 4, and c = -4.
Substituting these values into the quadratic formula:
x = (-(4) ± √((4)² - 4(5)(-4))) / (2(5))
Simplifying to solve for values of x
x = (-4 ± √(16 + 80)) / 10
x = (-4 ± √96) / 10
x = (-4 ± 4√6) / 10
x = (-4 ± 2√6) / 5
Hence, x = (-4 + 2√6) / 5 or x = (-4 - 2√6)
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Safiya needs to find a number that can be multiplied by 3√18
to result in a rational product.Which values could she use?
Answers
Safiya can use either ∛12 or ∛(1/6) to find a rational product when multiplied by ∛18. So, correct options are e and f.
The cube root of 18 is an irrational number because it cannot be expressed as a fraction of two integers. Safiya needs to find a rational number that, when multiplied by ∛18, results in a rational product. To do this, she needs to look for cube roots of numbers that are perfect cubes of integers.
Option a) ∛4 is a rational number, but it is not a perfect cube of any integer. Therefore, it is not a valid choice.
Option b) ∛18 is the given number and is not a perfect cube of any integer. Therefore, it is not a valid choice.
Option c) ∛3 is a rational number, but it is not a perfect cube of any integer. Therefore, it is not a valid choice.
Option d) ∛(1/18) is a rational number, but it is not a perfect cube of any integer. Therefore, it is not a valid choice.
Option e) ∛12 is a rational number and it can be expressed as ∛(2³ × 3). Therefore, it is a valid choice.
Option f) ∛(1/6) is a rational number and can be expressed as ∛(1/216). Therefore, it is a valid choice.
So, correct options are e and f.
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PLEASE HELP ME!!!!! The cost that a carpet cleaning company charges is directly proportional to the number of rooms cleaned. The cost is $22 for each room.
(a) Write a direct variation equation to represent the cost.
(b) How many rooms can a hotel pay the company to clean for $200? Write and solve an equation.
(c) Suppose the hotel plans to tip the carpet cleaners $40, how many rooms can the hotel get cleaned for $200 now? Write and solve an equation.
Answers
Answer:
Step-by-step explanation:
A researcher at a major clinic wishes to estimate the proportion of the adult population of the United States that has sleep deprivation. What size sample should be obtained in order to be99 % confident that the sample proportion will not differ from the true proportion by more than 4%? Round up to the nearest whole number.
Answers
The required sample size for the confidence interval and given margin of error is given as follows:
n = 1037.
What is a confidence interval of proportions?A confidence interval of proportions has the bounds given by the rule presented as follows:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which the variables used to calculated these bounds are listed as follows:
[tex]\pi[/tex] is the sample proportion, which is also the estimate of the parameter.z is the critical value.n is the sample size.The margin of error is given as follows:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
The confidence level is of 99%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.99}{2} = 0.995[/tex], so the critical value is z = 2.575.
As we have no estimate, the parameter is given as follows:
[tex]\pi = 0.5[/tex]
Then the sample size for M = 0.04 is obtained as follows:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.04 = 2.575\sqrt{\frac{0.5(0.5)}{n}}[/tex]
[tex]0.04\sqrt{n} = 2.575 \times 0.5[/tex]
[tex]\sqrt{n} = \frac{2.575 \times 0.5}{0.04}[/tex]
[tex](\sqrt{n})^2 = \left(\frac{2.575 \times 0.5}{0.04}\right)^2[/tex]
n = 1037.
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I need help with this math
Answers
Answer:
500 and 4.3
Step-by-step explanation:
A decigram is one-tenth of a gram and a kilometer is one-thousandth of a meter. Using this information, we must multiply the given amounts by the values.
5000 × 0.1 = 500
4300 × 0.001 = 4.3
Thus, the answers [in order] are 500 and 4.3
Hope this helps and feel free to ask any questions.
here are five number cards
2,5,7,8,9
one of the cards is removed and the mean average of the remaining four number cards is 6
which card was removed
show your working
Answers
Answer:
7
Step-by-step explanation:
Since one card was removed:
6 = x/4
x = 6 X 4
x = 24
Then you sum the numbers on the five cards and subtract 24 from it
(2 + 5 + 7 + 8 + 9) - 24
= 31 - 24
= 7
Therefore card with number 7 was removed.
Which point would NOT be a solution to the system of linear inequalities shown below
Answers
The point (4, - 1) will not be a solution to the system of linear inequalities shown.
What is the solution of the linear inequalities?The solution of the linear inequalities is calculated by simplifying the linear inequalities as follows;
The given linear inequalities;
y ≥ -x/4 + 7
y > 4x + 4
Solve the linear inequalities as follows;
4x + 4 ≥ -x/4 + 7
Collect similar terms together;
4x + x/4 ≥ 7 - 4
4x + x/4 ≥ 3
Multiply through by 4;
16x + x ≥ 12
17x ≥ 12
divide through by 17;
x ≥ 12/17
x ≥ 0.7
The value of y is calculated as;
y ≥ -x/4 + 7
y ≥ - (0.25 x 0.7) + 7
y ≥ 6.8
Since y is greater than or equal to 6.8, the point (4, - 1) will not be a solution to the system of linear inequalities shown.
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At the farmers' market, Tom bought 11/12 of a pound of string beans and 1/2 of a pound of
lima beans. How many more pounds of string beans did Tom purchase?
Write your answer as a fraction or as a whole or mixed number.
pounds
Answers
Answer:
Step-by-step explanation:
5/12 pounds more
please answer all 3 and show work
Answers
The equation of the Damari's investment is B(x) = 30000 * 1.03ˣ
Sky's family should take the offer of $5000 for the boatThe rule of the function is f(x) = 8 * 0.6ˣCalculating the equations of the functionsDamari's investment
Given that
Initial value, a = 30000
B(3) = 32306.72
The function is calculated as
B(x) = a * bˣ
Using B(3), we have
30000 * b³ = 32306.72
So, we have
b³ = 1.077
Take the cube root of both sides
b = 1.03
So, we have
B(x) = 30000 * 1.03ˣ
So, the function is B(x) = 30000 * 1.03ˣ
The boat of Sky's family
Here, we have
Initial value = 6000
Rate of depreciation = 6%
So, the function is
f(x) = 6000 * (1 - 6%)ˣ
So, we have
f(x) = 6000 * (0.94)ˣ
In 2024, we have
x = 2024 - 2021
x = 3
So, we have
f(3) = 6000 * (0.94)³
Evaluate
f(3) = 4983.50
This value is less than the offered value of $5000
This means that Sky's family should take the offer
The rule of the function
Here, we have the graph
From the graph, we have
Initial value, a = 8
Rate, b = 4.8/8
So, we have
Rate, b = 0.6
So, the function is
f(x) = 8 * 0.6ˣ
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what is √5^9 written without using any radicals?
Answers
Step-by-step explanation:
the square root of 5 can be written as 5 ^ (1/2).
We can then multiply the exponents, so it's 9/2.
So the answer could be written as 5 ^ (9/2).
The domain of this emath equation is
Answers
Answer:
x ≥ 5
Step-by-step explanation:
You want the domain of the equation y = √(x -5) -1.
DomainThe domain of the function is the set of x-values for which it is defined. The square root is not defined for negative values, so the domain is ...
x -5 ≥ 0
x ≥ 5 . . . . . . the domain of this function
__
Additional comment
The range is the set of y-values the function may produce. Here, that set of values is y ≥ -1.
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A submarine dives to a depth of 3775 m. It then climbs to a depth of 1395 m before descending one more time to a depth of 2890 m. How many meters in total has the submarine dived? What is the total distance (up and down) it has travelled? (Include the first descent in your calculations).
Answers
Step-by-step explanation:
3775 + 2890-1395 = total diving meters = 5270 m
Total movement = 3775 + ( 3775 - 1395 ) + (2890 - 1395 ) = 7650 m
Please help me understand this problem!
Answers
The values of c on the interval [-5, 5] are c = -[tex]5^{1/4[/tex]) and c = [tex]5^{1/4[/tex].
According to the Mean Value Theorem for Integrals, if f(x) is continuous on the interval [a, b], then there exists a value c in [a, b] such that:
f(c) = 1/(b-a) . ∫(a to b) f(x) dx
For f(x) = x⁴ on the interval [-5, 5], we have:
∫(-5 to 5) x⁴ dx = (1/5) . (5⁵ - (-5)⁵)/5
= (1/5) . (3125 + 3125)
= 1250
So we need to find c such that f(c) = 1250/10 = 125.
f'(x) = 4x³, so we can use the Mean Value Theorem for Derivatives to find a value of c that satisfies the condition.
f'(c) = (1/(5-(-5))) . ∫(-5 to 5) f'(x) dx
= (1/10) . [f(5) - f(-5)]
= (1/10) . [(5⁴) - ((-5)⁴)]
= 100
Therefore, by the Mean Value Theorem for Derivatives, there exists a value c in [-5, 5] such that f'(c) = 100.
Now, we need to check if there exists a value c in [-5, 5] such that f(c) = 125.
f(c) = c⁴, so we need to solve the equation c⁴ = 125.
c = ±[tex]5^{1/4[/tex]
Both of these values are in the interval [-5, 5], so they satisfy the Mean Value Theorem for Integrals.
Therefore, the values of c that satisfy the Mean Value Theorem for integrals for f(x) = x⁴ on the interval [-5, 5] are c = -[tex]5^{1/4[/tex]) and c = [tex]5^{1/4[/tex].
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Use technology or a z-score table to answer the question. The odometer readings on a random sample of identical model sports cars are normally distributed with a mean of 120,000 miles and a standard deviation of 30,000 miles. Consider a group of 6000 sports cars. Approximately how many sports cars will have less than 150,000 miles on the odometer? O 300 951 O 5048 O 5700
Answers
Approximately 5048 sports cars will have less than 150,000 miles on the odometer
Mean = 120,000
Standard deviation = 30,000
Total group = 6000
Total Miles = 150,0000
An odometer is a device used to gauge how far a wheeled vehicle has driven. The tool might be mechanical, electrical, or a hybrid of the two.
Calculating the Z score -
z = x - u/a
= 15,0000 - 12,0000/30000
= 30000/30000
= 1
Using the standard normal table, to determine the value -
P ( Z<1) = 0.8413
Calculating the total number of cars -
= P value x total group of cars
= 6000 x 0.8413
= 5047.7 or 5048
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HELP Plsssssssssssss
Answers
Answer:
[tex]9^{\frac{1}{8}x }[/tex]
Step-by-step explanation:
The function in the question
[tex]\sqrt[4]{9} ^{\frac{1}{2}x }[/tex]
is equivalent to
[tex]9^{(\frac{1}{4})(\frac{1}{2} x) }[/tex]
where you multiply the powers and get the final answer
[tex]9^{\frac{1}{8}x }[/tex]
Need help in solving this problem I’m stuck on it. Pls help me?????? If you can see the numbers it’s 3ft, 7ft, 5ft, 4ft.
Answers
Answer:
area=20ft^2
Step-by-step explanation:
3ft×4ft=12ft^2
12ft÷2=6ft is the area of the smaller triangle
7ft×4ft=28ft^2
28ft÷2=14ft is the area of the larger triangle
6ft+14ft=20ft^2
Pretty sure x is 75 but what do i write for the reason?
Thank uu
Answers
Answer:
Step-by-step explanation:
Interior angle sum = 180
2x - 45 + x = 180
3x - 45 = 180
x - 15 = 60
x = 75
Please help me it’s due today!!!!
Answers
The value of x in trapezoid KFGJ is 40.
Given information:
KFGJ is a trapezoid.
KF = 20
JG = x
MN is midsegment of trapezoid KFGJ.
MN = 30
To find the value of x in trapezoid KFGJ, we can use the fact that the midsegment MN of a trapezoid is parallel to the bases and its length is equal to the average of the lengths of the bases.
In this case, MN is given as 30, and we know that KF is one of the bases with a length of 20. To find the length of the other base JG, we can use the formula for the midsegment of a trapezoid:
MN = (KF + JG) / 2
Substituting the given values, we have:
30 = (20 + x) / 2
To solve for x, we can multiply both sides of the equation by 2:
60 = 20 + x
Subtracting 20 from both sides:
x = 60 - 20
x = 40
Therefore, the value of x in trapezoid KFGJ is 40.
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Can someone answer this question
Answers
The coefficients used to perform the synthetic division are given by the first option in this problem.
How to apply the synthetic division algorithm?In the synthetic division algorithm, the coefficients of a polynomial, which is the dividend, are each divided by a value.This divisor is the goes into the far left box.The standard format of the polynomial in this problem is given as follows:
[tex]6x^4 - 7x^3 + x^2 + 3[/tex]
Considering that x has a coefficient of zero, the order of the coefficients of the polynomial function is given as follows:
6, -7, 1, 0 and 3.
The divisor is of:
x + 4.
Hence the term on the left box is of:
x + 4 = 0 -> x = -4.
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For positive acute angles A and B, it is known that SinA= 11/61 and tan B=4/3. Find the value of Cos(A-B) in simplest form.
Answers
For positive acute angles A and B, if it is known that SinA= 11/61 and tan B=4/3, cos(A-B) = 224/305.
We can use the trigonometric identity cos(A-B) = cosA cosB + sinA sinB to find the value of cos(A-B).
First, we need to find the value of cosA and sinB:
Since sinA = opposite/hypotenuse, we can draw a right triangle with opposite side 11 and hypotenuse 61, and use the Pythagorean theorem to find the adjacent side:
cosA = adjacent/hypotenuse = √(61² - 11²)/61 = 60/61
Since tanB = opposite/adjacent, we can draw another right triangle with opposite side 4 and adjacent side 3, and use the Pythagorean theorem to find the hypotenuse:
hypotenuse = √(4² + 3²) = 5
sinB = opposite/hypotenuse = 4/5
Now we can substitute these values into the formula:
cos(A-B) = cosA cosB + sinA sinB
= (60/61)(3/5) + (11/61)(4/5)
= 180/305 + 44/305
= 224/305
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Hellooo i’m pretty sure x is 30 but can someone tell me what im meant to write for the reason. Thank youuu
Answers
Answer:
2x and 180 - 5x are complementary angles.
2x + 180 - 5x = 90
-3x + 180 = 90
-3x = -90
x = 30
Hii please answer i would appreciate it thankssss
Answers
Reason of congruency for each of the triangle are :
(a) SAS rule
(b) Triangles are not congruent.
Given are some triangles where some of the angles and sides are given to be equal.
We have to find the reason of congruency.
(a) Given two sides are equal.
One of the triangle has an included angle of 110°.
Find the included angle of the other one.
Included angle = 180 - (40 + 30) = 110°
So two sides and included angle of one is equal to the corresponding sides and angle.
So congruency is SAS rule.
(b) Length of the hypotenuse of first triangle = √(2² + 4²) = √20 cm
Length of hypotenuse of other triangle = 4 cm
The lengths are not equal.
So they are not congruent.
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Please help me answer this question. Having a hard time with it.
(Sorry if it’s blurry)
Answers
The new price of the pants, after the discount is applied, is the one in option B:
P = $38.40
What is the price of the pants excluding the tax?We know that the original price of the pants is $64, and we have a discount of 40%.
Then to find the new price of the pants, we need to multiply the original price by a factor (1 - 40%/100%) = (1 - 0.4) = 0.6
Then the new price of the pants, exluding the taxes, we will get that the new price is:
P = $64*0.6
P = $38.40
Then we can see that the correct option is B.
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Can someone answer this question
Answers
Answer: x+2
Step-by-step explanation:
It is not factorable through grouping method. You can test for factors if you divide the factor and it goes in evenly (no remainder) then, it is a factor.
I will use synthetic division to test:
X-8:
8 | 1 -14 56 -64
| 8 -48 64
1 -6 8 0 =>no remainder so yes this is a factor
X+2:
-2 | 1 -14 56 -64
| -2 32 -176
1 -16 88 -240 => remainder so NOT factor
X-2:
2 | 1 -14 56 -64
| 2 -24 64
1 -12 32 0 =>no remainder so yes this is a factor
X-4:
4 | 1 -14 56 -64
| 4 -40 64
1 -10 16 0 =>no remainder so yes this is a factor
The radius of a circle is 14 yards. What is the circle's circumference?
Use 3.14 for .
pls help
Answers
Given the arithmetic sequence an with a1=−10 and d=−2, find a3.
Answers
The value of a3 in the Arithmetic sequence with a1 = -10 and d = -2 is -14.
The value of a3 in the arithmetic sequence, we can use the formula for the nth term of an arithmetic sequence:
an = a1 + (n - 1) * d
Where:
- an is the nth term in the sequence
- a1 is the first term of the sequence
- d is the common difference between consecutive terms
- n is the position of the term we want to find
In this case, we are given that a1 = -10 and d = -2. We want to find the value of a3, which corresponds to the third term in the sequence (n = 3).
Plugging in the values into the formula, we have:
a3 = a1 + (3 - 1) * d
= -10 + 2 * (-2)
= -10 - 4
= -14
Therefore, the value of a3 in the arithmetic sequence with a1 = -10 and d = -2 is -14.
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Mrs. Sarfo is now three times as old as his daughter Joyce. If the sum of their ages 8 years ago was 48, find the girls present age
Answers
If the sum of their ages 8 years ago was 48 then the present age of girl is 16 years.
Mrs. Sarfo is three times as old as her daughter, so her present age would be 3J years.
8 years ago, Joyce's age would have been J - 8, and Mrs. Sarfo's age would have been 3J - 8.
The sum of their ages 8 years ago was 48:
(J - 8) + (3J - 8) = 48
Simplifying the equation:
4J - 16 = 48
Adding 16 to both sides:
4J = 64
Dividing both sides by 4:
J = 16
Therefore, the present age of Joyce is 16 years.
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HELP!
To keep fish in an aquarium healthy, the aquarium must maintain an average water temperature of 67°F. For 14 hours of the day, no hearing is required as the aquarium is naturally at 69°F. However, if left unheated for the remaining hours the temperature would drop to 50°F. How many degrees (during heating hours) should the tank temperature increase to maintain the average temperature?
Answers
Answer:
Step-by-step explanation:
To find out how many degrees the tank temperature should increase during the heating hours to maintain the average temperature, we need to calculate the temperature difference between the target average temperature of 67°F and the temperature during the unheated hours (50°F).
The difference in temperature is:
67°F - 50°F = 17°F
Since the heating hours account for the remaining hours of the day, which is 24 hours minus the 14 hours when no heating is required, we have:
24 hours - 14 hours = 10 hours
To maintain the average temperature of 67°F, the tank temperature should increase by 17°F during the 10 hours of heating.
To find the increase per hour, we divide the total temperature increase by the number of heating hours:
17°F / 10 hours = 1.7°F
Therefore, the tank temperature should increase by 1.7°F per hour during the heating hours to maintain the average temperature of 67°F.
A 3-D jigsaw puzzle becomes a cube with a volume of 1 cubic foot when it is solved. Mr. Ruiz stores several of these puzzles in a storage nook in his classroom. The nook is shaped like a rectangular prism and has a height of 3 feet. A layer of 8 puzzles will completely cover the floor of the nook. What is the volume of the storage nook?
Answers
The volume of the storage nook is 24 cubic feet.
How to find the volume of the storage nookTo find the area of 8 puzzles, we multiply the area of one puzzle by 8:
Area of 8 puzzles = 1 square foot * 8 = 8 square feet
Now, to find the volume of the storage nook, we multiply the area of the floor by its height:
Volume of the nook = Area of the floor * Height
= 8 square feet * 3 feet
= 24 cubic feet
Hence, the volume of the storage nook is 24 cubic feet.
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