Answer:
x = 48
Step-by-step explanation:
To solve this problem, one must assume that the segment with a length of (7) bisects the segment with a length of (x).
It is given that the segment with a length of (7) is perpendicular (forms a right angle with) the segment that has a length of (x). This is indicated by the box around one of the angles, signifiying that it is a right angle, or (90) degree angle. Therefore, the triangle with sides measuring (25) and (7) is a right triangle. Thus, one can use the Pythagorean theorem to solve for the base length. Then multiply it by (2) to find the total length of (x).
The Pythagorean theorem states the following:
[tex]a^2+b^2=c^2[/tex]
Where (a) and (b) are the legs, or sides adjacent to the right angle, and (c) is the hypotenuse or side opposite the right angle.
[tex]a^2+(7)^2=(25)^2[/tex]
Simplify,
[tex]a^2+49=625[/tex]
Inverse operations,
[tex]a^2=576\\\\a=24[/tex]
Multiply this value by (2) to find the total side length of the segment (x),
2(a)
Substitute,
2(24)
Simplify,
48
A truck is traveling at a constant speed. The diagram represents the truck's distance and time. What is the speed of the truck?
Answer:
distance divided by time
Step-by-step explanation:
distance is the speed of the moving object multiplied by the time taken to complete a certain distance therefore the speed is the distance covered divided by the time taken.
this is the question
Answer:
Step-by-step explanation:
From her eye, which stands 1.69 meters above the ground, Penelope measures the angle of elevation to the top of a prominent skyscraper to be 16∘. If she is standing at a horizontal distance of 200 meters from the base of the skyscraper, what is the height of the skyscraper? Round your answer to the nearest hundredth of a meter if necessary.
Answer: 59.04
Step-by-step explanation:
tan 16= x/200
tan16/1=x/200
200 tan 16=x
x=57.349077...
x=57.349077...
Add 1.69, the distance from the ground to her eye:
57.349077...+1.69= 59.039077...
≈ The skyscraper is 59.04 meters tall.
You can use right triangles to get the height of the skyscraper.
The height of the skyscraper is 59.04 meters approximately.
What is angle of elevation?You look straight parallel to ground. But when you have to watch something high, then you take your sight up by moving your head up. The angle from horizontal to the point where you stopped your head is called angle of elevation. See the figure where angle DCE is the angle when Penelope saw the skyscraper. It is measured from the horizontal line DC.
How to use right triangles to find the height of the specified sky scrapper?Remember that we assume that building is vertical to the ground. This means, there is 90° formation.
Since the distance from the base of the building is given and the angle of elevation is given, we have enough data to construct a specific right triangle where the vertical line opposite to the angle of elevation is of the measure of the height of the building.
And then we can use tangent ratio which relates perpendicular and base to the considered angle.
Remember that trigonometric ratios are defined for right triangles only(those triangles who have one of the angle as of 90 degrees).
See the diagram attached below, where the length AE is the building's height. AD is same as CB which is height of Penelope(a person who is watching the top of that given skyscraper).
For the right angle triangle EDC, and for the angle considered ∠ECD, we have the perpendicular as side opposite to the angle ∠ECD which is ED and the base is DC. Thus, the tangent ratio of ∠ECD is given by
[tex]tan(\angle ECD) = \dfrac{Perpendicular \: to \: \angle ECD}{Base \: to \: \angle ECD } = \dfrac{ED}{DC} = \dfrac{h - 1.69}{200}\\tan(16^\circ) = \dfrac{h - 1.69}{200}\\[/tex]
DC = AB and DA = CB because of ABCD being a rectangle because of building and person both standing vertical to the ground and the line DC being parallel to the ground, thus all angles being right angle(of 90 degrees).
From the calculator, the value of tan(16°) is approx 0.2867
Thus, putting this value in the obtained equation, we get:
[tex]tan(16^\circ) = \dfrac{h - 1.69}{200}\\0.2867 = \dfrac{h-1.69}{200}\\\\0.2867 \times 200 = h - 1.69 \\57.35 + 1.69 = h\\h = 59.04 \: \rm meters[/tex]
Thus, the height of the specified skyscraper is approx 59.04 meters.
Learn more about trigonometric ratios here:
https://brainly.com/question/22599614
Do the ratios 4:18 and 2:9 form a proportion?
yes
no
Answer:
Yes. A propotion is to check if two things are equivelent. The ratios 4:18 and 2:9 are equivelent.
Which fraction is equal to a whole number? 10/4. 8/4. 3/6. 7/8
plz help
Answer:
[tex]\frac{8}{4}[/tex] = 2
Step-by-step explanation:
Divide numerator by denominator
[tex]\frac{10}{4}[/tex] = 2.5 ← not a whole number
[tex]\frac{8}{4}[/tex] = 2 ← a whole number
[tex]\frac{3}{6}[/tex] = 0.5 ← not a whole number
[tex]\frac{7}{8}[/tex] = 0.875 ← not a whole number
calculate the area of the rectangle with length 9cm and breadth 4cm
Answer:
36cm^2
Step-by-step explanation:
the answer is
area of rectangle =l×b
=9×4.
=32
Please help me with this geometry question
These are the answer choices
1) 8
2)7
3)6
4)4
Answer:
7 is the correct answer
Step-by-step explanation:
Hope this answer helps you :)
Have a great day
Mark brainliest
Solve for x. Round to the nearest tenth, if necessary.
Answer:
Step-by-step explanation:
take 69 degree as reference angle
using sin rule
sin 69=opposite/hypotenuse
0.93=7.2/x
x=7.2/0.93
x=7.74
x=7.7
Find the solution(s) of the system of equations.
y = –x2 + 2
y = x2 + 4x + 4
A rectangle has an area of 75.2m2.
One of the sides is 0.8m in length.
Work out the perimeter of the rectangle.
Answer:
189.6m
Step-by-step explanation:
Area of reactangle= side₁ ×side₂
Let the other side of the rectangle be x meters.
Area of rectangle= 75.2m²
0.8x= 75.2
x= 75.2 ÷0.8
x= 94
Perimeter of rectangle
= 2(side₁ +side₂)
= 2(0.8 +94)
= 189.6 m
Which equation is correct?
please help me :((
Answer:
sin x° = opposite ÷ hypotenuse
Step-by-step explanation:
Cosine is represented by the expression adjacent ÷ opposite and sine is represented by opposite ÷ hypotenuse. Only the fourth option lines up with the functions defined above.
If you are having trouble remembering the ratios for each trig function, you can use the acronym SohCahToa. This stands for:
S - sine
o - opposite
h- hypotenuse
C - cosine
a - adjacent
h - hypotenuse
T - tangent
o - opposite
a - adjacent
Identify the imaginary part of this complex number:
10 - 5i
Answer:
-5i is the imaginary portion
Step-by-step explanation:
a+bi
a is the real part bi is the imaginary part
-5i is the imaginary portion
Alright, I am getting annoying at this point but who can help me with this one?
Answer:
A
Step-by-step explanation:
F(x) = 4x^2 + 1
G(x) = x^2 - 5
(F-G)(x) = (4x^2+1 - x^2-5)
collect like terms
(F-G)(x) = (4x^2-x^2 + 1-5)
= (3x^2 - 4)
Help with these two questions
Answer:
11. = D) x is greater than or equal to -1
12. = A) x is less than -2
Step-by-step explanation:
Answer:
11. -1 ≤ x
or
x ≥ -1, D
Because it is starting at -1, and the arrow is pointing up showing that x is greater than. BUT the circle is not hallow and is filled meaning that is is greater than, OR EQUAL TOO.
12. X < -2, A
Because it is starting at -2 and is going down showing that -2 is greater, and since the circle is hallow it just means X is less than NOT OR EQUAL TOO.
How many yards are in 18 feet?
Answer:
it is 6 yards
Step-by-step explanation:
since 1 yard is equal to 3 feet, 18 feet divided by 3 is 6
hope this helped :D
solve y= -2^(-x-3)= -4
HELP!!! ME!!!! PLEZ!!!
Answer:
option 2, because g-h and j -k is congruent
please help imfailing my math class and this is the only way for me to not attend summer school
Answer:
This is too long to explain I am just gonna write the correct answers
18.=c
19.=d
20.?
21.=a
22.=a
23.=b
24.=a
25.=a
26.=c
27.=c
28.=c
29.=a
30.=d
31.=maybe a
32.=c
33.=a
Step-by-step explanation:
The results of a national survey showed that on average, adults sleep hours per night. Suppose that the standard deviation is hours. Round your answers to the nearest whole number. a. Use Chebyshev's theorem to calculate the percentage of individuals who sleep between and hours. At least b. Use Chebyshev's theorem to calculate the percentage of individuals who sleep between and hours. At least c. Assume that the number of hours of sleep follows a bell-shaped distribution. Use the empirical rule to calculate the percentage of individuals who sleep between and hours per day. At least
Answer:
Following are the solution to the given question:
Step-by-step explanation:
For point a:
[tex]6.5 - 4.9 = 2.4 \\\\\frac{2.4}{1.2} = 2 \\\\\sigma \ \ so \ k = 2[/tex]
For point b:
[tex]\frac{3}{1.2}\ \ \sigma\ \ so \ k =\frac{3}{1.2} \ \ so\ \ 1- \frac{1}{k ^2} = 0.84[/tex]
For point c:
Once again, we have k = 2 though with Chebyshev discrepancy of witness numbers in the same number of standard deviations off mean = at least 75 percent.
given: XZ/MZ=YZ/NZ Prove XZ/MZ=XY/MN
Answer:
By trigonometric ratio;
XZ/sin(b) = XY/sin(c) = YZ/sin(a)
MN/sin(c) = NZ/sin(f) = MZ/sin(d)
∴ XZ/MZ = XY/MN × (sin(b)/(sin(d))
XY/MN = XZ/MZ × (sin(b)/sin(d))
Where (sin(b)/(sin(d)) = V;
(XZ/MZ)/(XY/MN) = (XY/MN × V)/(XZ/MZ × V)
(XZ/MZ)/(XY/MN) = (XY/MN)/(XZ/MZ)
∴ (XZ/MZ)² = (XY/MN)²
∴ XZ/MZ = XY/MN QED
Step-by-step explanation:
Whereby the shapes in the question are triangles ΔXYZ and ΔMNZ, and given that we have;
XZ/MZ = YZ/NZ, and from the attached drawing, we have;
∠XZY = ∠NZM
By trigonometric ratio, we have;
XZ/sin(b) = XY/sin(c) = YZ/sin(a)
∴ XZ = sin(b)×XY/sin(c)
MN/sin(c) = NZ/sin(f) = MZ/sin(d)
MZ = sin(d)×MN/sin(c)
∴ XZ/MZ = sin(b)×XY/sin(c)/(sin(d)×MN/sin(c)) = XY/MN × (sin(b)/(sin(d))
XY = sin(c) × XZ/sin(b), MN = sin(c) × MZ/sin(d)
XY/MN = sin(c) × XZ/sin(b)/(sin(c) × MZ/sin(d)) = XZ/MZ × (sin(b)/sin(d))
Let 'V' represent (sin(b)/(sin(d)), we have;
XZ/MZ = XY/MN × V...(1)
XY/MN = XZ/MZ × V...(2)
Dividing equation (1) by (2) gives;
(XZ/MZ)/(XY/MN) = (XY/MN × V)/(XZ/MZ × V) = (XY/MN)/(XZ/MZ)
(XZ/MZ)/(XY/MN) = (XY/MN)/(XZ/MZ)
∴ (XZ/MZ)² = (XY/MN)²
∴ XZ/MZ = XY/MN
what is the surface area?
Answer:
30.
3×4=12
12×5=60
60÷2=30
i will make you a BRAINLEST! please help pretty easy!
Answer:
The volume is 942.478
Step-by-step explanation:
Which of the following is a factor of x3 + 2x2 - 25x – 50?
Answer:
(x - 5)(x + 2)(x + 5)
Step-by-step explanation:
x³ + 2x² - 25x - 50
x³ + 7x² - 5x² - 35x + 10x - 50
x(x² + 7x + 10) - 5(x² + 7x + 10)
(x - 5)(x² + 7x + 10)
(x - 5)(x² + 2x + 5x + 10)
(x - 5)(x(x + 2) + 5(x + 2))
(x - 5)(x + 2)(x + 5)
determine the equation of the line with slope 3/4 passing through the point 4,0
Answer:
[tex]y = \frac{3}{4}x - 3[/tex]
Step-by-step explanation:
If it has a slope of 3/4, then it will look like this:
[tex]y = \frac{3}{4}x + b[/tex]
If it passes through (4, 0), than y = 0 when x = 4
[tex]y = \frac{3}{4}(4) + b[/tex]
[tex]y = 3 + b[/tex]
[tex]b = -3[/tex]
Therefore, the equation is [tex]y = \frac{3}{4}x - 3[/tex].
HELP VERY URGENT!!!!!!
Answer:
Step-by-step explanation:
D is greater than -2
Answer:
A, C, D
Step-by-step explanation:
All of them have a larger x-coordinate than -2.
A = .5
C = -1
D = -1.5
Hope that this helps!
find the value of X to the nearest tenth.
Answer:
i don't know ok thank you bye
Gus has a fish tank that holds 4710 inches^3 of water. He is using a cylinder shaped bucket with a radius of 5 inches and a height of 20 inches to fill the tank.
Answer:
3
Step-by-step explanation:
How many times will Gus need to fill the bucket to completely fill the fish tank if he doesn’t spill a drop? Use 3.14 for pi
Number of times = volume of tank /volume of cylinder
volume of cylinder = πr²h
3.14 x 5² x 20 = 1570
4710 / 1570 = 3 times
what is the answer to this?
Answer:
I think n = 7
Step-by-step explanation:
I might be wrong but I looked carefully and I think n is 7.
Answer:
the answer is n=7 so it
Step-by-step explanation:
is7
Find the volume of this cylinder.
Round to the nearest tenth.
17 ft
8ft
[ ? ) ft3
Enter
Answer:
The answer is 3418.1 ft rounded to the nearest tenth.
Step-by-step explanation:
The total volume of the cylinder can be defined by the Area of circular base * Perpendicular height.
The area of the circular base can be calculated as
[tex]\pi \times {r}^{2} [/tex]
where r is the radius of the circular base, which is 8 ft.
The area of the circular base is
[tex]\pi \times {8}^{2} = 64\pi[/tex]
We also know the height of the cylinder is 17 ft.
Hence, the volume of the cylinder is
[tex]64\pi \times 17 = 1088\pi = 3418.0528...[/tex]
This will be rounded up to 3418.1 with the nearest tenth
Which of the following is the correct graph of the equation y = –2x + 10?
Step-by-step explanation: Er there's no graph but I'll help. Look in the file! :) Have a nice day!
Answer:
Step-by-step explanation:
There's no graph but I'll draw a graph and screen shot it for u.