Answers
Given , A right angled triangle with an interior angle measuring 35 and a side measuring 20.
To calculate the value of x, we use the trigonometric ratio.
We have been given the measurement of hypotenuse and have to find the measurement of the opposite side of angle 35. Here we use sine ratio to find the measurement of opposite side.
[tex] sin (\theta) = \frac{opposite}{hypotenuse} [/tex]
measurement of hypotenuse = 20 and [tex] \theta [/tex] = 35,
[tex] sin(35)=\frac{x}{20}\\\\x=20 \times sin(35)\\\\ value\: of \:sin (35) = 0.57\\\\x= 20 \times 0.57 = 11.48 \approx 11.5 [/tex]
Hence , value of x = 11.5
Related Questions
Why do elephants have ivory tusks?
Answers
Elephants have ivory tusks, which are elongated incisor teeth, primarily for digging, stripping bark, and defense, and they may have evolved for sexual selection and competitive interactions among males.
Elephants have ivory tusks because they are actually elongated incisor teeth. These tusks are composed of dentine and are covered by a layer of enamel, just like our teeth. Elephants use their tusks for various purposes, such as digging for water, stripping bark from trees, and as a weapon for defense. However, the primary reason they have tusks is not entirely understood. It's believed that tusks might have evolved for sexual selection and display, as well as for competitive interactions among male elephants.
What is the total cost or sale price to the nearest cent 20$ haircut; 15% tip
Answers
The answer is $23.00
whats a prime number
Answers
A prime number is a number that can't be divided by any whole number but one.
For example, 3, 7, 11, and 29 are prime numbers because they can't be divided by a whole number (excluding 1).
Hope this helps!
What is the square root of 25p^3 expressed in simplified form?
Answers
estimate the value of this expression by rounding each number to the nearest
whole unit. (1.94)(7.51)(3.74)
A. 21
B. 42
C. 56
D.64
Answers
First, we need to round each number to the nearest whole unit:
1.94 ≈ 2
7.51 ≈ 8
3.74 ≈ 4
Now, we multiply:
2 * 8 * 4 = 64
So, our answer is D.
Hope this helps!
What is the average speed in miles per hour of a car that’s travels 956.4 miles in 15.9 hours? Round the answer to nearest tenth , explain step by step how to solve it
Answers
rounded = 60.2
Greg started with a certain number of quarters. He then decided on a number of quarters he would save each day. He added the quarters he saved to the amount with which he started. At the end of day 2, Greg had a total of 26 quarters saved. At the end of day 5, he had a total of 35 quarters saved.
A. How many quarters does Greg start with? Show or explain your work.
B. Write an equation to model the number of quarters Greg has saved, y, after x days.
C. Using the rate at which Greg is saving, explain why he can never have exactly 100 quarters saved by the end of any given day.
Answers
Final answer:
Greg started with 20 quarters. The equation for the number of quarters saved after x days is y = 20 + 3x. With Greg's savings rate of 3 quarters per day, he cannot have exactly 100 quarters on any day since 100 is not a multiple of 3 plus the 20 starting quarters.
Explanation:
To determine how many quarters Greg started with, let 's' be the number quarters Greg started with, and 'd' be the number of quarters he saves each day. After 2 days, he had a total of 26 quarters saved, and after 5 days, he had a total of 35 quarters saved. These can be written as two equations:
s + 2d = 26s + 5d = 35Subtracting the first equation from the second gives:
3d = 9
From which we find that d = 3 (Greg saves 3 quarters a day). Plugging this value back into the first equation:
s + 2(3) = 26
s + 6 = 26
s = 20
Greg started with 20 quarters.
B. The equation to model the number of quarters Greg has saved, y, after x days is:
y = 20 + 3x
C. With the savings rate of 3 quarters a day, Greg's total will always be a multiple of 3 plus the 20 he started with. 100 is not a multiple of 3, meaning he can never save exactly 100 quarters by the end of any given day since 100 minus the 20 quarters he started with leaves 80, which is not divisible by 3.
Final answer:
Greg started with 20 quarters and saves 3 quarters every day afterward. The equation to model the number of quarters saved after x days is y = 20 + 3x. It is impossible for Greg to have exactly 100 quarters saved by the end of any given day because 100 cannot be reached by adding multiples of 3 to the starting amount of 20 quarters.
Explanation:
To solve for the number of quarters Greg started with and the number of quarters he saves each day, we can set up a system of equations. Let's designate q as the number of quarters Greg started with and d as the number of quarters he saves each day. From the problem, we have two points of data: On day 2, Greg has 26 quarters, and on day 5, he has 35 quarters.
The equations representing these two data points are:
q + 2d = 26q + 5d = 35Subtracting the first equation from the second gives us:
3d = 9
Dividing both sides by 3 gives us:
d = 3
Now that we have the value for d, we can substitute it back into the first equation:
q + 2(3) = 26
q + 6 = 26
Subtracting 6 from both sides gives us:
q = 20
Greg started with 20 quarters.
For the equation to model the number of quarters saved, y, after x days, we have:
y = q + dx
This simplifies to:
y = 20 + 3x
To address part C, let's analyze the possibility of Greg having exactly 100 quarters saved. If we set y to 100 in the equation y = 20 + 3x and solve for x, we get:
100 = 20 + 3x
80 = 3x
x = 80/3
x ≈ 26.67
Since x must be an integer because Greg cannot save a fraction of a day, he cannot have exactly 100 quarters by the end of any given day. This is because 100 is not a multiple of 3 (the daily amount Greg saves) when starting from 20. Thus, it's impossible for Greg to have exactly 100 quarters saved by the end of any given day.
△ABC is similar to △DEF .
AB=5 inches, BC=9 inches, and DE=7.5 inches.
What is EF ?
Answers
AB/BC = DE/EF
5/9 = 7.5/EF
5(EF) = 9 * 7.5
5(EF) = 67.5
EF = 13.5
Please help meeeeeeeee
Answers
2*22=44
:) I hope this helps!
Double a penny every day for 30 days. How many dollars do you have
Answers
If I have this correct it is just 2 pennies which is each one cent multiplied by 30
A right triangle is drawn on a coordinate plane. Two vertices of the triangle are points A(−2,4) and B(3,−2) . The third vertex of the triangle is point C, which lies in the third quadrant of the coordinate plane.
What is the distance from point A to point C?
Enter your answer in the box
Answers
To find the distance between point A and point C, just subtract the y-values.
[tex]\sf 4-(-2)=\boxed{\sf 6}[/tex]
It takes 24 cups of chicken broth to make chicken soup recipe. How much is this in quarts?
Answers
for which data representation is the median the better measure of center
Answers
The median is the better measure of center when dealing with data sets that have outliers or extreme values.
The median is the better measure of center when a data set contains several outliers or extreme values. It is less sensitive to measurements with extreme values, providing a more robust estimation of central tendency. The median can be thought of as the middle number in a series, where 50% of the measurements are above it and 50% are below.
PLEASE HELP ME!! A right circular cone has a radius of 6 inches and a volume of 180 cubic inches. What is the height of the cone? Please answer without using pi. Thank you
A. 5 in.
B. 15 in.
C. 25 in.
D. 90 in.
Answers
Given that the volume is 180 cubic inches
[tex] \frac{1}{3} \pi r^{2} h[/tex] = [tex]180[/tex]
Given that the radius is 6m
[tex] \frac{1}{3} \pi 6^{2} h[/tex] = [tex]180[/tex]
Evaluate
[tex] \frac{1}{3} \pi (36) h[/tex] = [tex]180[/tex]
[tex] 12\pi h[/tex] = [tex]180[/tex]
[tex] h[/tex] = [tex]180[/tex] ÷ ([tex] 12 \pi [/tex])
[tex] h[/tex] = 4.77 ≈ 5 inches (Answer A)
Option B.The height of a cone is 15 inches.
To find the height of the cone, we will use the formula for the volume of a cone:
V = (1/3) * π * r² * h
We know the volume (V) is 180 cubic inches and the radius (r) is 6 inches.
We need to solve for the height (h).
First, let's plug in the known values:
180 = (1/3) * π * (6)² * h
180 = (1/3) * π * 36 * h
540 = π * 36 * h
540 / 36π = h
We can simplify this further, h = 15/π. Since we do not use π for the answer:
By rational observation of given options, B. 15 in. seems accurate.
A sign in front of a roller coaster says ''you must be 40 inches tall to ride'' what percentage of this height is A 34 inches and B 54 inches. Please answer both questions if you can.
Answers
34/40 x 100 = 85%
Percentage of B
54/40 x 100 = 135%
Ans: A) 85% B) 135%
I would rather to help 6th and 7th grade math
Answers
i need to find the area
there are 3 rectangles and a trapezoid
show how plz
Answers
20 x 5 = 100
100 yd²
15 x (20-14) = 90
90 yd²
14 x 10 = 140
140 yd²
The area of a trapezoid is 1/2(b1+b2)h
In this problem:
b1=25-15-5
b1=5
b2=10
h=20-14
h=6
We can then plug this into the formula:
A = 1/2(5+10)(6)
A = 1/2(15)(6)
A = 45 yd²
We can then get the area of the whole polygon by adding up the areas of the three rectangles and trapezoid:
A = 100+90+140 + 45
A = 375 yd²
I need help figuring out when to use law of sine or law of cosine?
These are some examples of problems.
Please Help!
Answers
when you have two sides and angle between them, this is law of cos, problem 6,8
problem 7 you can use both, but if you can use both better to use law of sin, it is just easier
Final answer:
Use the law of sines when you have two angles and one side, or two sides and a non-inclusive angle. Use the law of cosines when you have two sides and the included angle or all three sides. Apply trigonometric identities for vector addition and resolving forces.
Explanation:
Deciding when to use the law of sines or the law of cosines depends on the information given in a triangle problem. The law of sines is most useful when you know either two angles and one side (AAS or ASA) or two sides and a non-enclosed angle (SSA). The law states that the ratio of the length of a side to the sine of its opposing angle is consistent for all sides and angles in a triangle, often written as a/sin A = b/sin B = c/sin C.
The law of cosines is handy when you have either two sides and the included angle (SAS) or when you have all three sides (SSS). This law relates the lengths of the sides of a triangle to the cosine of one of its angles, following the formula c² = a² + b² - 2ab cos C.
For vector addition problems or when decomposing forces into components, trigonometric identities involving sine and cosine are employed. If you're resolving a weight into components, you may use sine to find the component opposite the angle and cosine for the component adjacent to the angle.
HELP ASAP!!!
1: What is the surface area of a sphere with a radius of 4 meters rounded to the nearest square meter
A: 50 m^2
B: 101 m^2
C: 201 m^2
D: 268 m^2
2: What is the volume of a sphere with a radius of 6 meters rounded to the nearest square meter?
A: 905 m^3
B: 679 m^3
C: 452 m^3
D: 226 m^3
Answers
the surface area of the sphere can be calculated using the following equation
Area = 4πr²
where r = radius
π = 3.142
radius of the sphere = 4 m
substituting radius in the area equation
Area = 4 x 3.142 x 4²
= 201.08 m²
when rounded off to nearest sq.meter , 201.08 ≈ 201
answer is C. 201 m²
Q2)
volume of the sphere can be calculated from the following equation
V = 4/3 πr³
radius of sphere = 6 m
π = 3.142
V = 4/3 x 3.142 x 6³
= 904.8 m³
rounded off to nearest sq. meter
904.8 ≈ 905 m³
correct answer is A
is 2x-5y=0 a direct variation
Answers
Answer: Yes
107=5x+17 simplify your answer as much as possible
Answers
90divided 5=18
18*5=90+17=107
I did the work ♥♥♥♥
5*18=90
90+17=107
what value of c makes x^2 - 24x + c a perfect square trinomial?
Answers
The answer is 144
Answer:
Step-by-step explanation:
Quadratic equation is given by x²-24x+c
This is in the form expansion of (a-b)², that is a²-2ab+b²
Comparing
a² = x², a = x
-2ab = -24x
-2xb = -24x
b = 12
c = b² = 12² =144
x²-24x+144 = (x-12)²
Option D is the correct answer
BRAINLIEST if right!
A cone has a diameter of 9 inches and a height of 12 inches. Find the volume of the cone to the nearest cubic inch.
972 in³
113 in³
324 in³
254 in³
Answers
v = 3.14 x 4.5^2 x 12/3
v = 3.14 x 20.25 x 4
v = 254.34
Answer = 254 in^3
Smoked salmon is being sold for $15.50 per pound. What is the cost of 6 ounces of salmon?.
Answers
15.50 / 16 = 0.96875 per ounce
0.96875 * 6 = $5.81
what she got to school she saw that the school has nine buildings each Heaven 30 classrooms how many classrooms does the school have
Answers
Final answer:
To find the total number of classrooms in the school, we multiply the number of buildings (9) by the number of classrooms in each building (30), resulting in a total of 270 classrooms.
Explanation:
The question asks how many classrooms are there in total if a school has nine buildings, each with 30 classrooms. To find the answer, we need to multiply the number of buildings by the number of classrooms in each building. This calculation is straightforward:
Multiply the number of buildings (9) by the number of classrooms in each building (30).
This gives us: 9 buildings x 30 classrooms/building = 270 classrooms in total.
Therefore, the school has a total of 270 classrooms.
Convert 3 feet to inches.
A) 4 inches
B) 9 inches
C) 12 inches
D) 36 inches
Answers
3 feet x 12 inches = 36 inches
answer is D
3•12=36
D), there are 36 inches in 3 feet.
i need this rotated 270 degrees clockwise
Answers
D(1, 2) ⇒ D'(-2, 1)
F(2, 3) ⇒ F'(-3, 2)
G(4, 1) ⇒ G'(-1, 4)
When a number x is multiplied by 5, it gives the same result as when 48 are added to twice the number. Form an equation in terms of x. Hence, find the number x
Answers
-2x. -2x
3x=48
3. 3
x=16
What is the circumference of the circle? Round your answer to the nearest foot
Answers
Where "C" is circumference and "d" is diameter.
Substituting your values in, we have:
Which, when rounded, is 37.7.
thats my work but when you do your work for your question you get 78.58 and you would round to the nearset tenth and you get 78.5
Hope this helps:) please mark branliest would really apperciate it thx
what is the answer to this question ?
Answers
So for F the third angle for each of the pairs is
left side: 180 - (51 + 30) = 180 - 81 = 99
right side: 180 - (109 + 30) = 180 - 139 = 41
This is not the answer.
G
180 - (92 + 70) = 180 - 162 = 18
180 - (28 + 70) = 180 - 98 = 82
This is not the answer either.
H
180- (58 + 30) = 180 - (88) = 92
180 - (90 + 58) = 180 - 148 = 32
Not at all.
180 - (35 + 82) = 180 - 117 = 63
180 - (82 + 63) = 180 - 145 = 35
This pair has a third angle that is equal to the other triangle's pair. This is your answer.