Let's call the height of the second building "x". We can use trigonometry to solve for x.
First, let's draw a diagram to help visualize the problem:
A B
\ /
\ /
\ / x
\/
C
Where:
A is the top of the 200 meters high building
B is the bottom of the second building
C is the point from which the angles of depression and elevation are measured
x is the height of the second building
From the diagram, we can see that:
angle BCA = 20 degrees (angle of depression)
angle BAC = 10 degrees (angle of elevation)
AB = 200 meters
Using the tangent function, we can write:
tan(20) = x / AB (tangent of angle BCA)
tan(10) = x / (AB + x) (tangent of angle BAC)
We can solve these equations for x:
x = AB * tan(20) (multiply both sides by AB)
x = (AB * tan(10)) / (1 - tan(10)) (multiply both sides by 1 - tan(10), then simplify)
Plugging in the values we know:
x = 200 * tan(20)
x = (200 * tan(10)) / (1 - tan(10))
Using a calculator:
x ≈ 67.35 meters
Therefore, the height of the second building is approximately 67 meters (to the nearest hundred meters).
Select the correct answer. Which statement correctly describes this expression? |X^3| +5 A. the absolute value of three times a number added to 5 B. the cube of the sum of a number and 5 C. 5 more than the absolute value of the cube of a number D. the sum of the absolute value of three times a number and 5
The statement that correctly describes the expression |x^3|+5 is 5 more than the absolute value of the cube of a number.
Given this expression: |x^3|+5
| | = This sign means Absolute value,
x^3 = x³ = x × x × x
Hence, the statement that correctly describes the expression |x^3|+5 is : 5 more than the absolute value of the cube of a number.
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Calculator
What is the volume of this figure?
Enter your answer in the box.
ft³
4
3 ft
5 ft
6 ft
7 ft
2 ft
The volume of the solid figure is 75 ft³
How to solve an equation?An equation is an expression that can be used to show the relationship between two or more numbers and variables using mathematical operators.
The area of a figure is the amount of space it occupies in its two dimensional state.
The volume of a figure is the amount of space it occupies in its three dimensional state.
To get the surface area:
Area of base = (6 ft * 2 ft) + (7 - 6)ft * 3 ft = 15 ft²
Volume of figure = area of base * height = 15 ft² * 5 ft = 75 ft³
The volume of the figure is 75 ft³
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For questions 11-12, divide. Use synthetic division, if possible.
11. (x² +6x²-x² - 5x+1)+(x-2)
12. (x³ +9x² -5x +11)+(x² + 2)
Question 11 seems to have strange typos in it. Please double-check to make sure it has been typed correctly.
I'm not sure how to answer that one.
----------
I'll focus on Question 12.
The long division scratch work is shown in the image attachment below.
The answer to problem 12 is x+9 remainder -7x-7
Please let me know if you have questions about any step of the polynomial long division process.
Solve for circle theorem
The requried measure of the angles is given as:
(1) ∠OLQ = 32, (2) ∠NQP = 38°, (3) ∠NLP = 38°, and (4) ∠NPL = 52°.
As shown in the figure,
(1) Following the property of angle subtended by an arc on the center of the circle and at a point on the circumference of a circle,
∠OLQ = ∠OQL = 64/2 = 32°.
(2)
Following the figure,
∠NQP = ∠LQP - ∠LQN
= ∠LQP-[∠OQL+∠MQN]
= 90 - [32+20]
= 38°
Similarly,
∠NLP = 38°
∠NPL = 52°
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Find the dot product for the pair of vectors
The result of -3u + 5v is the vector (12, -34).
Let's start by defining the two given vectors u and v:
u = (1, 3)
v = (3, -5)
To find the dot product of two vectors, we need to multiply their corresponding components and then add up the results. The formula for the dot product of two vectors can be written as:
u · v = u₁v₁ + u₂v₂ + ... + uₙvₙ
where u₁ and v₁ are the first components of vectors u and v, u₂ and v₂ are the second components, and so on up to un and vₙ, which are the nth components.
Using this formula, we can find the dot product of u and v as follows:
u · v = (1)(3) + (3)(-5)
= 3 - 15
= -12
So, the dot product of vectors u and v is -12.
Next, we need to calculate -3u + 5v. To do this, we need to multiply each component of vector u by -3 and add it to the corresponding component of vector v multiplied by 5. We can write this as follows:
-3u + 5v = (-3)(u₁, u₂) + (5)(v₁, v₂)
= (-3)(1, 3) + (5)(3, -5)
= (-3, -9) + (15, -25)
= (12, -34)
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Jerry had 35 big stickers and 20 small stickers at first. He exchanged 10 small stickers for 5 big stickers. What percentage of his sticker are big stickers in the end?
(1) 10% (2) 20% (3) 40% (4) 80%
Answer:
80%
Step-by-step explanation:
After all the trade he got 50 stickers
40 Big
10 small
50 stickers is 100%
40B stickers is ??
WE multiply 40 by 100 then divide by 50
so 80%
Lisa is putting colored 11 light bulbs into a string of lights. There are 3 red light bulbs, 2 yellow light bulbs, and 6 pink light bulbs. How many distinct orders of light bulbs are there if two light bulbs of the same color are considered identical (not distinct)?
The distinct orders of light bulbs are there if two light bulbs of the same color are considered identical = 4,620
Here, the total number of bulbs = 11
The number of red light bulbs = 3
The number of yellow light bulbs = 2
and the number of pink light bulbs = 6
We know that the formula for the permutation with repetition is:
n! / (n1! × n2! x ... × nk!)
We use this formula to find the required number of light bulbs.
Here, two light bulbs of the same color are considered identical
We divide by 3! in order to adjust for overcounting, because we have 3 red light bulbs.
simmilarly for the 2 yellow light bulbs, we divide with 2!.
and for the 6 pink light bulbs, we divide by 6!
Thus, the total number of distinct orders of bulbs will be:
11! / (3! × 2! × 6!) = 4,620
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Two stores are selling the same video game and both are having a sale. Store 1 is selling the game for $45.99 with a 15% discount. Store 2 is selling the game for $ 52.99 with a 20% discount. Which store should you purchase the game from to get the best deal?
well, presumably the best deal is the cheaper one, so let's check how much is it for each
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{15\% of 45.99}}{\left( \cfrac{15}{100} \right)45.99} ~~ \approx ~~ 6.90\hspace{5em}\underset{ Store~1 }{\stackrel{ 45.99~~ - ~~6.90 }{\approx\text{\LARGE 39.09}}}\checkmark \\\\[-0.35em] ~\dotfill[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em} \stackrel{\textit{20\% of 52.99}}{\left( \cfrac{20}{100} \right)52.99} ~~ \approx ~~ 10.60\hspace{4em}\underset{ Store~2 }{\stackrel{ 52.99~~ - ~~10.60 }{\approx\text{\LARGE 42.39}}}[/tex]
Jessica wants to make a ramp using a board so that she can ride her bike onto the front porch. The ramp must reach from the ground to the floor of the porch, which is 212
ft above the ground. Jessica has decided that the ramp cannot have an incline of more than 35°.
What length board should Jessica buy if she uses the maximum angle of incline?
Enter your answer in the box. Round only your final answer to the nearest tenth
Length of board should Jessica buy is 4.4 feets.
Step-by-step explanation:
Height of the ramp =
Distance of the porch from the ground = x
Inclination of the ramp,θ = 35°
In triangle ABC,
AB =
AC = x
θ = 35°
According trigonometric ratios:
Length of board should Jessica buy is 4.4 feets.
Find the surface area of the cylinder in terms of Pi. The diameter is 14 cm and the height is 18 cm
The surface area of the cylinder in terms of pi is:
S = pi*301 cm²
how to find the surface?We know that for a cylinder of radius R and height H the surface area is:
S = pi*( 2RH + R²)
Here the height is 18 cm and the diameter is 14cm, then the radius is.
R = 14cm/2 = 7cm
Then the surface area will be:
S = pi*(2*7cm*18cm + (7cm)*7cm)
S = pi*301 cm²
That is the surface area in terms of pi.
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Please help me i need the answer and im so confused just tell me if its a b c or d please
Answer:
The answer would be option A
Step-by-step explanation:
-14 times 8=-122
Sum of vectors a+b pick one of answer choices
Answer:
< - 1, 5 >
Step-by-step explanation:
a = < - 5, 2 >
b = < 4, 3 >
a + b
= < - 5, 2 > + < 4, 3 >
add corresponding elements
= < - 5 + 4, 2 + 3 >
= < - 1, 5 >
what two numbers multiply to 48 and add to -7?
Thus the numbers that we are looking for are 8 and -6.
What are the numbers?We would have to use a method in which we would call the numbers that we want to find x and y.
We know that we have to solve the problem as a simultaneous equation so that we can be able to obtain the numbers that we seek.
If
xy = -48 ---(1)
x + y =2 --- (2)
y = -48/x ---(3)
Substitute (3) into (2)
x - 48/x = 2
x^2 - 48 = 2x
x^2 -2x - 48 = 0
x = 8 and x = -6
Thus;
8 + y = 2
y = -6
Or
-6 + y = 2
y = 8
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Missing parts:
What numbers multiply to -48 and add to 2 at the same time
Create a Venn diagram to illustrate each of the following: 26. (D ⋃ E) c ⋂ F
The Venn diagram for (D ⋃ E) ⋃ F will be the ovarlapped region of D,E and F.
To represent the sets D, E, and F in the Venn diagram, we first construct three overlapping circles. Then, beginning with the innermost operation and moving outward, we shade the regions corresponding to the set operations in the expression.
We shade the area where the circles for D and E overlap because the equation (D ⋃ E) denotes the union of the sets D and E. All the elements in D, E, or both are represented by this area.
The union of (D ⋃ E) with F is the next step. This indicates that we darken the area where the circle for F crosses over into the area that we shaded earlier. All the components found in sets D, E, F, or any combination of these sets are represented in this region.
The final Venn diagram should include three overlapping circles, with (D ⋃ E) ⋃ F shaded in the area where all three circles overlap.
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i need help please help its easy
The solutions for the inequality, in order from smallest to largest, are:
-7, -4, -2, 0, 0.9, 0.99, 0.999, 1
Which values make the inequality true?Here we have the inequality:
y ≤ 1
All the values that make the inequality true are the values equal or smaller than 1.
So we just need to list these in order from smaller to larger.
The correct order will be:
-7, -4, -2, 0, 0.9, 0.99, 0.999, 1
These are the solutions in order.
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what does it mean by "the quantity" in a scatter plot
Answer:
how many or how much or what is the amount
Step-by-step explanation:
quantity means
the amount or number of a material or immaterial thing not usually estimated by spatial measurement.
if I were to ask you " How many apples are in that bag" Im basically asking what is the quantity of apples in that bag. So, in scatter plots it's asking you, how many points are on this graph of scatter points
In the figure to the right, you are given a square ABCD. Each of its sides is divided into two segments, such that AE = BF = CG = DH. Prove that quadrilateral EFGH is a square.
First to answer gets brainliest
Answer:proving that EFGH is a square: points E,F,G,H
separate the sides of the square ABCD into two lines. if AE=BF=CG=DH then
AH=DG=EB=FC and it shows that if we connect the points E,F,G,H to each other with line we will have a square
HAE~EBF~FCG
solve. y=2x^2+8 for the axis of symmetry and the vertex
Carl went grocery shopping. He weighed his apples and they have a mass of 2450g. He measured the mass of the pineapple and found it was 3547g. How much more mass does the pineapple have?
The pineapple has 1097g more mass than the apples.
We have,
The difference between two values is the result of subtracting one value from the other.
In this case, we want to find the difference between the mass of the pineapple and the mass of the apples.
To do this, we subtract the mass of the apples from the mass of the pineapple.
The equation for this is:
Pineapple mass - Apple mass = Difference
Substituting the given values:
3547g - 2450g = 1097g
Therefore,
The pineapple has 1097g more mass than the apples.
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Please help I need this asap
The inequality given that the function f is increasing over it s domain
f(x²-2)<f (7x-8), Df = (-∞,2) is: x ∈ (-∞,1) U (6,2).
What is the inequality?We know the values of x within the domain by setting the intersection points of the two functions f(x2-2) and f(7x-8).
f (x²-2) = f (7x-8)
So,
x²-2 = 7x-8
Simplify and find x
x² - 7x + 6 = 0
(x - 1)(x - 6) = 0
x = 1 or x = 6
The domain (-,2) is divided into the intervals (-,1), (1,6), and (6,2). Now let assess the interval endpoints because f is rising:
For x < 1:
x² - 2 < 7x - 8
x² - 7x + 6 < 0
(x - 1)(x - 6) < 0
For 1 < x < 6:
x² - 2 < 7x - 8
x² - 7x + 6 < 0
(x - 1)(x - 6) > 0
For x > 6:
x² - 2 < 7x - 8
x² - 7x + 6 < 0
(x - 1)(x - 6) < 0
Since f is rising across its domain the inequality f(x2-2) f(7x-8) has the following solution: x ∈ (-∞,1) U (6,2).
Therefore the inequality is x ∈ (-∞,1) U (6,2).
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What is the range of the function f(x) = |x| + 5?
R: {f(x) ∈ ℝ | f(x) < 5}
R: {f(x) ∈ ℝ | f(x) ≥ 5}
R: {f(x) ∈ ℝ | f(x) > 5}
R: {f(x) ∈ ℝ | f(x) ≤ 5}
The range of the function f(x) = |x| + 5 include the following; B. R: {f(x) ∈ ℝ | f(x) ≥ 5}.
What is a domain?In Mathematics and Geometry, a domain is the set of all real numbers for which a particular function is defined.
Additionally, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.
By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:
Domain = {-∞, ∞} or -∞ ≤ x ≤ ∞.
Range = {5, ∞} or 5 ≤ f(x) ≤ ∞.
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Victoria wants to figure out if she can run faster than
an elephant. She reads that an elephant can run 100
yards in 20 seconds. She knows she can run 60 feet in
10 seconds. Victoria says, "Since 60/10 = 6 and 100/20 = 5,
my speed is faster than an elephant's!" Does her
statement make sense? Explain why or why not.
20
Answer and explanation:
Victoria's statement that her running speed is faster an elephant's does not make sense because it is based on the comparison of unlike units of measurement.
How the above conclusion is reached:Elephant's running speed = 100 yards in 20 seconds
= 5 yards per second (100 ÷ 20)
Units of Measurement:1 yard = 3 feet
5 yards = 15 feet (5 x 3)
The elephant's running speed = 15 feet per second.
Victoria's running speed = 60 feet in 10 seconds
= 6 feet per second (60 ÷ 10)
Thus, we conclude that the elephant's running speed is 15 feet per second, while Victoria does 6 feet per second, making her claim untrue.
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Some easy math i totally cant solve it
Answer:
correct answer is D
Step-by-step explanation:
Cindy has a new job offer but will need a new car for the job. After planning a budget, they determine that they can afford to pay at most $215 per month for a 6-year car loan. If an annual percentage rate of 2.1% is available to finance the car loan, calculate the value of the most expensive car loan that Cindy can afford. Round to the nearest whole
number
The value of the most expensive car loan that Cindy can afford is $13,712
We are given that;
Amount= $215
Percentage= 2.1%
PMT = 215 i = 0.021 / 12 = 0.00175 (the annual interest rate divided by 12 months) n = 6 × 12 = 72 (the number of months in 6 years)
Now,
The formula for the present value of an annuity is:
PV = PMT × (1 - 1/(1 + i)^n) / i
where:
PV = present value PMT = payment amount i = interest rate per period n = number of periods
Plugging these values into the formula, we get:
PV = 215 × (1 - 1/(1 + 0.00175)^72) / 0.00175 PV = 215 × (1 - 0.888) / 0.00175 PV = 215 × 0.112 / 0.00175 PV = 13,712
Therefore, by the percentage the answer will be $13,712.
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Brenda's class took a field trip to the science museum. It took them 50 minutes to drive to the museum. They stayed at the museum for 3 hours and 45 minutes, and it took them 56 minutes to drive back to school. When the class arrived back at school, it was 3:47 P.M. What time did Brenda's class leave for the field trip?
Brenda's class left for the field trip at 10:16 A.M.
We have,
Let's break down the time of Brenda's class field trip:
50 minutes to drive to the museum
3 hours and 45 minutes (or 225 minutes) at the museum
56 minutes to drive back to school
Adding up all of these times, we get:
50 + 225 + 56 = 331 minutes
So the field trip took a total of 331 minutes.
If the class arrived back at school at 3:47 P.M., and we subtract 331 minutes from 3:47 P.M., we can determine the time they left for the field trip:
3:47 P.M. - 331 minutes
= 10:16 A.M.
Therefore,
Brenda's class left for the field trip at 10:16 A.M.
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If two angles are complementary then the sum of their measures is _______.
(Answer with a number ONLY)
If the two angles are complementary, then their sum is 90 degrees.
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°.
Complementary angle - Two angles are said to be complementary angles if their sum is 90 degrees.
If the two angles are complementary, then their sum is 90 degrees.
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There are 40 boxes of lamps in the storage room. Twenty-four of the boxes contain green lamps. What percent of the boxes contain green lamps? A. 25% B. 50% C. 60% D. 75%
The percentage of boxes with green lamps is 60%, the correct option is C.
We are given that;
Number of boxes= 40
Green lamp boxes= 24
Now,
To calculate the percentage of boxes that contain green lamps, you need to divide the number of boxes with green lamps by the total number of boxes and then multiply by 100. This is according to the formula for finding a percentage of a number12.
=(24 / 40) x 100 = 60%
Therefore, by percentage the answer will be 60%.
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The sum of a certain infinite geometric series is $2.$ The sum of the squares of all the terms is ${}5.$ Find the common ratio.
The common ratio between the sum of a certain infinite geometric series is 2. the sum of the squares of all the terms is 3 is, - 1/9
Now, We can formulate;
⇒ { a/ 1-r} = 2
And, a²/ (1 - r²) = 5
⇒ 2a/ ( 1+r ) = 5
⇒ 2(2 - 2r)/ 1 + r = 5
⇒ 4 - 4r = 5 + 5r
⇒ 9r = - 1
⇒ r = - 1/9
Thus, The common ratio between the sum of a certain infinite geometric series is 2. the sum of the squares of all the terms is 3 is, - 1/9
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Sarah's bird feeder holds 1/2 of a cup of birdseed. Sarah is filling the bird feeder with a scoop that holds 1/4 of a cup. How many scoops of birdseed will Sarah put into the feeder?
The number of scoops of birdseed Sarah puts in the feeder n = 2
Given data ,
Let the number of scoops of birdseed Sarah puts in the feeder be n
While utilizing a scoop that can contain 1/4 cup of birdseed, Sarah's bird feeder holds 1/2 cup of birdseed. We must divide the capacity of the bird feeder by the capacity of the scoop to determine how many scoops Sarah will add to the feeder.
On simplifying the equation , we get
1/2 ÷ 1/4 = n
n = 1/2 x 4/1
n = 4/2
n = 2 scoops
Hence , the equation is solved and n = 2
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Determine the relationship between the lengths of AB and BC. Please help
The relation between lengths of AB and BC are,
⇒ Lenght of AB and BC are different.
We have to given that;
Triangles ABD and BDC are given.
Here, All the angles of a triangle ABD are different from angles of BDC.
Hence, We get;
Both triangle ABD and BDC are congruent.
So, All the sides of ΔABD are different from the sides of different from ΔBDC.
Hence, Lenght of AB and BC are different.
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