From his eye, which stands 1.61 meters above the ground, Jacob measures the angle
of elevation to the top of a prominent skyscraper to be 25°. If he is standing at a
horizontal distance of 281 meters from the base of the skyscraper, what is the height
of the skyscraper? Round your answer to the nearest tenth of a meter if necessary.
Step-by-step explanation:
we have a right-angled triangle, that is "hovering" 1.61 m above the ground.
the Hypotenuse (the side opposite of the 90 degree angle) is the line of sight from the eye to the top of the skyscraper.
one leg is the height of the skyscraper (minus the 1.61 m).
the other leg is the ground distance from Jacob to the skyscraper (281 m).
we know already 2 angles : the 90° angle between the ground distance and the skyscraper height. and the 25° between the ground distance and the line of sight.
and as we know that the sum of all angles in a triangle is always 180°, we know that the third angle (between the line of sight and the skyscraper height) is
180 - 90 - 25 = 65°
now we can use the law of sines
a/sin(A) = b/sin(B) = c/sin(C)
(the ratio between a side and its opposing angle)
to get all missing side lengths.
the 25° angle is opposite of the skyscraper height, and the 65° angle is opposite of the ground distance (the only side length we know so far).
so,
height/sin(25) = 281/sin(65)
height = 281 × sin(25)/sin(65) = 131.0324519... m
to get the full height of the skyscraper, we need to add the 1.61 m that the described triangle was "hovering" above ground.
therefore, the height of the skyscraper is
131.0324519... + 1.61 = 132.6424519... ≈ 132.6 m
explain why the area of the large rectangle is 2a + 3a + 4a
Answer:
The area of the large rectangle = the sum of the areas of the three smaller rectangles
areas of the smaller rectangles are : 2a, 3a, and 4a respectively
Therefore the area of the lage rectangle = 2a + 3a + 4a
The sum of the area of all the rectangles will be 2a + 3a + 4a.
What is the area of the rectangle?Let W be the rectangle's width and L its length.
The area of the rectangle is the multiplication of the two different sides of the rectangle. Then the rectangle's area will be
Area of the rectangle = L×W square units
The dimensions of the rectangle are 2 by a, 3 by a, and 4 by a.
The area first rectangle is given as,
⇒ 2 × a
⇒ 2a
The area second rectangle is given as,
⇒ 3 × a
⇒ 3a
The area third rectangle is given as,
⇒ 4 × a
⇒ 4a
The total area of the rectangle will be given as,
A = 2a + 3a + 4a
More about the area of the rectangle link is given below.
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100 points!! ASAP do all problems with steps to your answer
Answer:
11. 10
12. -9v + 7
13. 1-10b
14. 5n+10
15. 12v
16. 0
17. 0
18. -4n+10
19. 9b - 9
20. 5v-8
Hope it help.
Answer: 13: 1-10b
14: 5n +10
15: 12v
16: nothing
17 0
18: 10 -4n
19: 11 + 5b
20: 5x + -8
Step-by-step explanation:
13: 6b + 4b = 10b
1-0=1
1-10b
14: n+4n = 5n
5n+10
15: 10v + 2v = 12v
16: 6v - 6v = 0
17: -2 +2 =0
18: 9 + 1 = 10
5n + n = 4n
10 - 4n
19: 10 + 1 = 11
7b-2b = 5b
11 + 5b
20: 1 -9 = -8
5x + -8
John has decided to get in shape for the new year. He is planning to joining the local fitness club. The fitness club charges customers a $14.95 monthly fee plus a one time joining fee $110.00.
What is the total cost John will pay for a 12-month membership at the fitness club?
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Please find the range of these numbers
Answer:7
Step-by-step explanation:range is highest number subtracted by lowest
Answer:
17
Step-by-step explanation:
The formula for range is max-min.
The max is 91 and the min is 74
91-74=17
Which triangle congruence postulates can be used to prove that Triangle ABD is congruent to Triangle CDB in Rectangle ABCD?
Answer:
SSS, SAS, ASA, AAS, HL
Step-by-step explanation:
1. SSS (side side side) says if 3 sides of one triangle are congruent to 3 sides of another triangle, then the 2 triangles are congruent.
2. SAS (side angle side) says if 2 sides and the included angle of a triangle are congruent to 2 sides and the included angle of another triangle, then the 2 triangles are congruent.
3. ASA (angle side angle) says if 2 angles and the included side of a triangle are congruent to 2 angles and the included side of another triangle, then the 2 triangles are congruent.
4. AAS (angle angle side) says if 2 angles and the none included side of one triangle are congruent to the corresponding parts of another triangle, then the 2 triangles are congruent.
5 HL (hypotenuse leg) says if 2 right triangles that have a congruent hypotenuse and a corresponding congruent leg, then the 2 triangles are congruent.
Because it is a rectangle, the sides are equal, and they share the same hypotenuse.
Simplify the expression. Write your answer as a power.
4.5^5/4.5^3
The simplified expression is
In a set of bivariate data, an additional point is added near the regression line but far away from the rest of the data. this
will the slope of the regression line and the correlation coefficient.
A slightly change, strengthen
B greatly change, weaken
C slightly change, weaken
D greatly change, strengthen
E not change, not change
Answer:
C. is the answerStep-by-step explanation:
CARRY ON LEARNINGAND REMEMBER DO ALWAYS READ AND WRITE
What are the coordinates of C if translated 5 units upward?
(6, 11)
hope this helps!
−3.6−1.9t+1.2+5.1t ////////////////////////////////////////////////////////////
Answer:
3.2t -2.4
Step-by-step explanation:
Combine like terms then solve (-1.9t +5.1t)+(-3.6+1.2)
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Answer:
Step-by-step explanation:
a (2³)² = 2³ˣ² = 2⁶
b (7⁰)¹ = 7⁰ˣ¹ = 7⁰ = 1
c (5⁶)³ = 5⁶ˣ³ = 5¹⁸
d (6²)⁴ = 6²ˣ⁴ = 6⁸
e (8³)⁴ = 8³ˣ⁴ = 8¹²
f (4³)² = 4³ˣ² = 4⁶
g (9¹)² = 9¹ˣ² = 9² = 81
h (3⁷)² = 3⁷ˣ² = 3¹⁴
i (10²)³ = 10²ˣ³ = 10⁶
j (11²)⁴ = 11²ˣ⁴ = 11⁸
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Answer:
Y-intercept: (0, -10)
X-intercepts: (5,0), (1,0)
Axis of symmetry: (3,0)
Step-by-step explanation:
You can tell what the y-intercept is by looking at the function. At the end there is a “-10”, which indicates that it’s the y-intercept.
There are many ways to find x-intercepts. You can factor the function, use the quadratic formula, or complete the square.
By factoring it, you get
-2(x-5)(x-1)=0
If one part of it equals zero, than the whole function equals zero.
So it can be split up like this
(x-5)=0
(x-1)=0
So...
x=5 and x=1 are the the zeros or (5,0) and (1,0)
Finally, you convert the function from standard form to vertex form. By doing -b/2a, you can find the x-coordinate of the vertex, which is the axis of symmetry. The answer is 3 or (3,0) because -12/2(-2)= 3.
after the outbreak of a mysterious disease, the average wait time at a hospital by 70%. Before the outbreak, the average wait time at a hospital is m minutes
Answer:
1.7m
Step-by-step explanation:
Given that 'm' was the waiting time before the outbreak
After the outbreak, waiting time increased by 70%.
This implies that :
70% of m increase
m + 70% of m
m + 70/100 of m
m + ( 70÷100 ) × m
m + 0.7m
= 1.7m
Step-by-step explanation:
Calculate the average speed of an airplane, in miles per hour, if it travels 1,000 miles in 2
2 1 2
hours.
The average speed of the airplane which travels the given distance and time is 400mph.
SpeedSpeed is simply defined as distance traveled per unit of time. It is the change of position of a moving object per unit of time.
It is expressed as;
s = distance / time = d / t
Given the data in the question;
Distance travelled d = 1000miTime taken t = 2 and 1/2 hrs = 2.5hrsAverage speed; s = ?To determine the average speed of the airplane, we substitute our given values into the expression above.
s = d / t
s = 1000mi / 2.5hrs
s = 400mph
Therefore, the average speed of the airplane which travels the given distance and time is 400mph.
Learn more about Speed and Velocity here: https://brainly.com/question/10566304
patrick said that the product of any number and 4 is always double the product of that number and 2. Is patrick correct. explain
Patrick is correct, since the two parts of the statement are equal.
From the question,
Patrick said that the product of any number and 4 is always double the product of that number and 2. We are to investigate if Patrick is correct.
First, let the number be x,
From the first part of the statement
The product of any number and 4
That is,
4 × x = 4x
And
The second part of the statement,
double the product of that number and 2
That is,
2(x × 2) = 2(2x)
Now, we will investigate if
4x = 2(2x)
Expand the right hand side of the equation
That is,
4x = 2 × 2x
Then, we get
4x = 4x
Since the two parts of the statement are equal, then Patrick is correct.
Hence, Patrick is correct, since the two parts of the statement are equal.
Learn more here: https://brainly.com/question/14176303
Equations that represent a line parallel to y=8x+4
y=8x+b, b being any number, is parallel to y=8x+4.
For example:
y=8x+2
y=8x+(1/2)
y=8x+937382
y=8x-4
State what information is required to know that the triangles are congruent.
-GEOMETRY
[tex]\huge \bf༆ Answer ༄[/tex]
The additional information needed to prove that the triangles are congruent is ~ A
[tex] \sf\angle M \cong \angle V \: \: or \: \: \angle N \cong\angle U[/tex]What is the factored form of n3+512 (pleas help fast)
A- (n-8)(n^2+8n+64)
B- (n+4)(n^2-4n+128)
C- (n-4)(n^2+4n+128)
D- (n+8)(n^2-8n+64)
Answer:
Since both terms are perfect cubes, factor using the sum of cubes formula,
a³+b³=(a+b)(a²-ab+b²) where
a=n and b=8
(n+8)(n²-8n+64)
Answer
(n+8)(n²-8n+64)
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Carryonlearing
Answer:
Step-by-step explanation:
The only one that has a chance of being correct is D. That's because the first term is correct and you have to assume that the second one is as well.
cubrt(512) = 8
The first term is (n + 8)
The second term is (n^2 - 8*n + 8^2) = n^2 - 8n + 64
All the other answers have the wrong first term
A: it should be n + 8 not n - 8
B and C are both wrong because the cube root of 512 is 8 not 4.
Mrs. Rainer would like to buy 28
composition notebooks for her math class.
If they are on sale for $0.94 each, how
much will she spend, not including tax?
Answer:
$26.32
Step-by-step explanation:
0.94x28 = 26.32
(Meeting character limit)
Which of these actions would decrease heat transfer between two objects?
increasing the temperature of the warmer object
increasing the area of their contact
reducing the thermal energy of the cooler object
reducing the time of their contact
(Fr ran out of free answers)
Answer:
increasing the area of their contact
Jill takes 2 hours to paint a room, Jim takes 3 hours to paint a room. How long (in minutes) will it take both of them to paint a room
Answer:
72 minutes
Step-by-step explanation:
The sum of the rates of work in rooms per hour is ...
Jill's rate + Jim's rate
= (1/2 room/hour) +(1/3 room/hour) = (3/6 +2/6 room/hour) = 5/6 room/hour
__
Then the combined rate in hours per room is ...
1/(5/6 room/hour) = 6/5 hours/room = (6/5 hours/room)(60 minutes/hour)
= 72 minutes per room
Jill and Jim can paint the room in 72 minutes when they work together.
radius=12 round up to the nearest tenth
Answer:
12.0
Step-by-step explanation:
Answer:
452.4
Step-by-step explanation:
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consider a sequence with the common difference of 5 and whose fiftieth term is 259. what are the first three terms of this sequence?
A- 15,20,25
B- 13,18,23
C- 9,14,19
D- 14-19,24
E- 10,15,20
Here is a free 100 points annnnd brainliest
This question is about strategy
Skill
Precision
Alr here it is:
Problem one: Molly bought and infinite amount of bottles of dish soap. She had an infinite amount of money. When she bought the dish soap, she lost all of it.
How is this possible?
Problem one (part two): Molly then called her friend Blitzo over. Blitzo then gave Molly and infinite amount of money without losing all of his money.
How is this possible
If you have questions or want hints, ask in comments below this question
1. She bought the infinite dish soap with her money
2. you can't lose anything infinite
3. remeber our deal? brainliest pls.
Find a quadratic model in standard form for the set of values.
(-2, 18), (0, 4), (4, 24)
4x^2 + 2x - 4
Hope this helps
3) A straight line passes through points (0,7) and (2, -1).
What is its equation?
Answer:
y=-x+A
Step-by-step explanation:
Answer:
y=-4x+7
Step-by-step explanation:
1) find the slope first between the two points
m= y2-y1/x2-x1
m= -1-7/2-0
m=-8/2
m=-4
2) use the linear equation y=mx+c
using the slope we find earlier and the coordinate
to substitute into the equation which is,
y=mx+c
7=-4(0)+c
c=7
3) the answer
y=-4x+7
(0, 2), (1,7) create a equation that passes through each pair of points
Answer:
y = 5x + 2
Step-by-step explanation:
Given the equation 5x + 2
Plug in 0
y = 5(0) + 2
y = 2
(0,2)
Given the equation 5x + 2
Plug in 1
y = 5(1) + 2
y = 7
(1,7)
Hi Guys,
I am Revising for Exams.
I don't get the Topic:
PERCENTAGES OF AN AMOUNT.
Please help me to find out the Answer/Equation etc
Thank You All.
What is the measurement of pie?
Answer: 3.14159
Step-by-step explanation: