The problem involves using trigonometry to find the height of a mast given the hypotenuse of a right-angled triangle and an angle. The sine function is used in this case, providing an approximate mast height of 30 meters.
Explanation:This question involves the application of trigonometry. The wires form right-angled triangles with the mast and the ground, and the measure provided, 57m, is the hypotenuse of these triangles. The question asks for the height of the mast (opposite side) and the angle provided is 32° with the horizontal.
To solve this, the function of sine can be used, where the sine of an angle is equal to the opposite/hypotenuse. This can be rearranged to the formula: Opposite (height of the mast) = Hypotenuse * Sin(angle).
Therefore, the height of the mast = 57 meters * sin(32°) = 29.96 meters, approximately 30 meters mast height.
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Final answer:
Using the tangent function with the given angle of 32 degrees and the distance from the base of the mast to the attachment points of the wires (57 metres), the height of the mast is calculated to be approximately 35.64 metres.
Explanation:
To find the height of the mast, we can use trigonometry, specifically the tangent function, because we have an angle and the opposite side, which in this case is the distance from the ground to the point where the wire is attached to the mast. The tangent of an angle in a right-angled triangle is the ratio of the opposite side to the adjacent side (tan(θ) = opposite/adjacent).
In this scenario, we have the angle (32°) and the adjacent side (57 metres), and we want to find the opposite side, which is the height of the mast. The formula we will use is:
height = adjacent × tan(angle)
Let's put the values we know into this formula:
height = 57 × tan(32°)
To calculate the height, you will need a calculator that can compute the tangent of an angle. The height will then be found as follows:
height = 57 × 0.6249 (tan(32°))
height = 35.6393 metres, which can be rounded to 35.64 metres.
The mast is therefore approximately 35.64 metres tall.
PLZZZ HELP AND HURRY MARK BRAINLIST IF CORRECT
What is due to acids formed when atmospheric and volcanic gases mix with water
A chemical weathering
B mechanical weathering
C root- pry
D pedalfer
Plzz and thank youu
Answer:
Answer is D
Step-by-step explanation:
Due to the pedalfer by the formation of the acid at the time when atmospheric and volcanic gases mix with water.
What is a pedalfer?Pedalfer should be comprise of the aluminum and iron oxides. It should be considered as the subdivision of the order of zonal soil that contains the wide range of soils where sesquioxides increase with respect to the silica at the time of forming the soil. Also it should be arise when the area is humid.
Therefore, we can conclude that the option d is correct.
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Joan receives a 9% commission on appliances she sells. Last month she sold $18,500 worth of appliances. How much did Joan earn in commissions last month?
Answer:
She earned $1,665.
Step-by-step explanation:
x / 18500 = 9/100
What did you do to transform 18500 into 100? Divide by 185
Since you divided the denominator 185, you must do the same to the numerator.
x / 185 = 9 OR 9 * 185 = x
x = 1665
Estimate a 15% tip on a dinner bill of $31.86 by first rounding the bill amount to the nearest ten dollars.
Estimated tip:
Becky and Cathy are sisters. Becky is four years older than Cathy. The following shows how Becky's age, y, changes as Cathy's age, x, changes.
Answer:
the answer would be B.
Step-by-step explanation:
Study island I did this one
GIVING BRAINLIEST BRAINLIEST!!!! Easy mathhh DO NUMBER 4
Answer:
I got 1/2
Step-by-step explanation:
Which statements about this system of equations are true? Check all that apply
.
2x - 7y=-13
- 2x + 11y = 1
The x-variable will be eliminated when adding the system of equations.
The y-variable will be eliminated when adding the system of equations.
The sum of the system of equations is 4y = -12.
Ox=17
y=-3
There are infinitely many solutions to the system of equations.
Answer:
the x-variable will be eliminated when the adding the system of equations. The sum of the system of equations is 4y = -12.
x= - 17
y= - 3
Step-by-step explanation:
Find the value of x
A pizza has a circumference of 37.68 inches. What is the area of the pizza?
Answer:
118.31
Step-by-step explanation:
because the circumference is 3.14 and you have to do 37. 68 x 3.14 and you get your answer
The net of a cylinder is shown. The area of one base of the cylinder is 9Pi in.2. The circumference of a base is 6Pi in., and the height of the cylinder is 10 in. Which expression can you use to find the lateral area plus two bases of the cylinder? A--6Pi + 9Pi(10) in.2 B--9Pi + 6Pi(10) in.2 C--6Pi + 6Pi + 9Pi(10) in.2 D--9Pi + 9Pi + 6Pi(10) in.2
Answer:
The answer is D.
Step-by-step explanation:
The expression can be used to find the lateral area plus two bases of the cylinder is (D) 9[tex]\Pi[/tex] + 9[tex]\Pi[/tex] + 6[tex]\Pi[/tex](10) [tex]in^2[/tex] .
Mathematically, an expression is a combination of numbers, variables, operations, and functions that are combined according to specific rules to represent a mathematical computation or relationship. It can be thought of as a mathematical phrase or formula.
The sum of lateral area and the two bases of the cylinder
= lateral area + sum of the area of two bases.
The lateral area = 6[tex]\Pi[/tex](10) [tex]in^2[/tex].
So, The sum of the lateral area and the two bases of the cylinder
= 9[tex]\Pi[/tex] + 9[tex]\Pi[/tex] + 6[tex]\Pi[/tex](10) [tex]in^2[/tex].
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Solve the system. -3x + 4y = -22 2x + 7y = 5 A) (6, -1) B) (-1, 6) C) (-6, 1) D) (-1, -6)
Answer:
A
Step-by-step explanation:
We have the system of equations:
-3x + 4y = -22
2x + 7y = 5
Let's solve this using elimination, so multiply the first equation by 2 and the second equation by 3:
2 * (-3x + 4y = -22) ⇒ -6x + 8y = -44
3 * (2x + 7y = 5) ⇒ 6x + 21y = 15
Our equations are now:
-6x + 8y = -44
6x + 21y = 15
Add these two together to eliminate the x term:
-6x + 8y = -44
+ 6x + 21y = 15
______________
0x + 29y = -29
y = -29/29 = -1
Plug this back into one of the equations to find x:
-3x + 4y = -22
-3x + 4 * (-1) = -22
-3x - 4 = -22
-3x = -18
x = -18/(-3) = 6
The answer is (6, -1) or A.
Answer:
A. (6,-1)
Step-by-step explanation:
-3x + 4y = -22
2x + 7y = 5
x = (5 - 7y)/2
-3[(5 - 7y)/2] + 4y = -22
-15/2 + 21y/2 + 4y = -22
29y/2 = -29/2
y = -1
x = (5 - 7(-1))/2
x = 12/2
x = 6
How do you calculate probability?
Step-by-step explanation:
write it as a fraction.
Example:
What is the probability of drawing a diamond from a deck of cards?
The number on the bottom of the fraction is the total number of objects/possibilities.There are 4 suits in a deck of cards (spades, clubs, hearts, diamonds) so that is the number that goes on the bottom of the fraction (the denominator)?/4
diamonds is only 1 of the four suits so the number on the top of the fraction (the numerator) will be 11/4
you can express this in many ways such as a fraction or percentageI HOPE THIS WAS HELPFUL :-)
To calculate the probability of an event A when all outcomes in the sample space are equally likely, count the number of outcomes for event A and divide by the total number of outcomes in the sample space.
Explanation:To calculate the probability of an event A when all outcomes in the sample space are equally likely, count the number of outcomes for event A and divide by the total number of outcomes in the sample space. This is known as the theoretical probability of A.
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Question 5 (5 points)
To the nearest hundredth, what is the value of m?
15
08.66
12.99
2.31
7.50
Answer:
m = 12.99
Step-by-step explanation:
cos30° = m/15
√3/2 = m/15
2m = 15√3
m = 15√3/2
m = 15·1.73/2
m = 25.95/2
m = 12.99
Sana maka tulong plss rate and love
Caren has 6 oranges to share. If she
gives one third of an orange to each
person, how many people can share
Caren's oranges?
Answer:
6/ 1/3
6 x 3/1
6 x 3 = 18
Hope this helps Your answer is 18
Step-by-step explanation:
Answer:
she can share with 18 people
Solve the system of equations :
2x -5y=-22
X+7y=27
Answer:
x=−1 y=4
Step-by-step explanation:
Let's solve your system by substitution.
2x−5y=−22; x+7y=27
Rewrite equations:
x+7y=27;2x−5y=−22
Step: Solve x+7y=27for x:
x+7y=27
x+7y+−7y=27+−7y(Add -7y to both sides)
x=−7y+27
Step: Substitute−7y+27 for x in 2x−5y=−22:
2x−5y=−22
2(−7y+27)−5y=−22
−19y+54=−22(Simplify both sides of the equation)
−19y+54+−54=−22+−54(Add -54 to both sides)
−19y=−76
−19y
−19
=
−76
−19
(Divide both sides by -19)
y=4
Step: Substitute 4 for y in x=−7y+27:
x=−7y+27
x=(−7)(4)+27
x=−1(Simplify both sides of the equation)
Irina wants to build a fence around a rectangular vegetable garden so that it has a width of at least 10 feet. She can use a maximum of 150 feet of fencing. The system of inequalities that models the possible lengths, l, and widths, w, of her garden is shown. w ≥ 10 2l + 2w ≤ 150 On a coordinate plane, 2 solid straight lines are shown. The first line is horizontal to the y-axis at y = 10. Everything above the line is shaded. The second line has a negative slope and goes through (0, 75) and (75, 0). Everything to the left of the line is shaded. Which length and width are possible dimensions for the garden? l = 20 ft; w = 5 ft l = 20 ft; w = 10 ft l = 60 ft; w = 20 ft l = 55 ft; w = 30 ft
Answer:
In option a, w < 10
in option b, w = 10 and 2(20) + 2(10) = 40 + 20 = 60 < 150
in option c, w > 10 but 2(60) + 2(20) = 120 + 40 = 160 > 150
In option d, w > 10 but 2(55) + 2(30) = 110 + 60 = 170 > 150
Therefore the corect answer is option b.
Step-by-step explanation:
MATH HELP PLEASE !50 POINTS!
Answer: 108
Step-by-step explanation: You take the x and the 2/3x and combine them to get 1 2/3x, so 1 2/3x=180. 180 divided by 5 is 36, and 36 times three is 108
Answer:
108
Step-by-step explanation:
Angles on a line add up to 180 degrees.
x + 2/3x = 180
5/3x = 180
x = 180 × 3/5
x = 108
The height of a tree increases by 60% each year. When planted the tree was 40cm tall. How tall will the tree be in 5 years time.
Answer:
≈419.4 cm.
Step-by-step explanation:
To solve this problem, you will need to set up an exponential graph as shown:
y= 40 ·[tex](1.6)^{x}[/tex]
The 40 represents the initial height of the tree, while (1.6) represents the annual growth rate. 'x' represents the amount of years elapsed.
We can simply solve this by substituting 5 for x:
y= 40· [tex](1.6)^{5}[/tex]
y ≈ 419.4 cm.
After decoding the clues on the map, they found out that they needed to go to the
Island of Mysteries which was 120 miles away. To get there, they could either
take a plane for $600 or a boat for $254. How much money can they save if they
took a boat to the island?
Answer:
$346.00
Step-by-step explanation:
We know that the price to take a plane to the Island of Mysteries is $600 and the price to take a boat is $254.
To find how much money they will save if they were to take a boat, you would subtract the cost of the boat ride from the plane ride to find the difference.
$600 - $254 = $346.00
Leeza’s aquarium holds 55 gallons of water. She is filling the tank and has already put in 22 gallons. Write and solve an inequality to find out how many more gallons she might put in the tank.
Step-by-step explanation:
the answer is 55 is less than or equal to 22
In ΔIJK, the measure of ∠K=90°, KJ = 77, IK = 36, and JI = 85. What ratio represents the cosine of ∠I?
We have been given that in ΔIJK, the measure of ∠K=90°, KJ = 77, IK = 36, and JI = 85. We are asked to find the ratio that represents the cosine of angle I.
First of all, we will draw a right triangle as shown in the attachment.
We know that cosine relates adjacent side of right triangle with hypotenuse.
[tex]\text{cos}=\frac{\text{Adjacent}}{\text{Hypotenuse}}[/tex]
We can see that adjacent side to angle I is IK and hypotenuse is IJ.
[tex]\text{cos}(\angle I)=\frac{IK}{IJ}[/tex]
[tex]\text{cos}(\angle I)=\frac{36}{85}[/tex]
Therefore, the ratio of cosine of angle I is [tex]\frac{36}{85}[/tex].
Answer:
the ratio of cosine of angle I is 36/85.
Step-by-step explanation:
1 1/3 x 6/7 (the 1 in the front is a whole)
Look at the attached picture
Hope it will be helpful to you
Answer:
well it would be 9 over 14 hope this helps
Step-by-step explanation:
Julio drives 2.5 hours at 45 miles per hour. Kilgore drives 4 hours at 35 miles per hour. Who drives farther? How much
farther?
Kilgore, 27.5 miles
Julio: 28.5 miles
Julio: 112.5 miles
Kilgore; 140 miles
Answer:
kilgore, 140 miles
Step-by-step explanation:
Kilgore drives farther than Julio with a difference of 27.5 miles. Julio drives 112.5 miles while Kilgore drives 140 miles.
To determine who drives farther, we need to calculate the distance driven by Julio and Kilgore.
Julio: Julio drives 2.5 hours at 45 miles per hour. Using the formula distance = speed × time, Julio's distance is 45 miles/hour × 2.5 hours = 112.5 miles.Kilgore: Kilgore drives 4 hours at 35 miles per hour. Applying the same formula, Kilgore's distance is 35 miles/hour × 4 hours = 140 miles.Kilgore drives farther. The difference in the distance is 140 miles - 112.5 miles = 27.5 miles.
Simplify the expression:Two-thirds divided by (negative 4) minus (one-sixth minus StartFraction 8 over 6 EndFraction)
1
StartFraction 29 over 24 EndFraction
StartFraction negative 24 over 17 EndFraction
StartFraction 23 over 24 EndFraction
we have been given an expression [tex]\frac{\frac{2}{3}}{-4}-\left(\frac{1}{6}-\frac{8}{6}\right)[/tex]. We are asked to simplify our given expression.
Using quotient rule [tex]\frac{\frac{a}{b}}{c}=\frac{a}{bc}[/tex], we will get:
[tex]\frac{2}{3\cdot -4}-\left(\frac{1}{6}-\frac{8}{6}\right)[/tex]
[tex]\frac{2}{-12}-\left(\frac{1}{6}-\frac{8}{6}\right)[/tex]
Now, we will combine like terms:
[tex]\frac{2}{-12}-\left(\frac{1-8}{6}\right)[/tex]
[tex]\frac{2}{-12}-\left(\frac{-7}{6}\right)[/tex]
[tex]-\frac{2}{12}+\frac{7}{6}[/tex]
[tex]-\frac{1}{6}+\frac{7}{6}[/tex]
Let us combine like terms:
[tex]\frac{-1+7}{6}[/tex]
[tex]\frac{6}{6}=1[/tex]
Therefore, our expression simplifies to 1.
Answer:
1
Step-by-step explanation:
Brainliest please
Devaughn's age is three times Sydney's age. The sum of their ages is 76. What is Sydney's age?
Answer:
22
Step-by-step explanation:
Basically you can think of Devaughn as 3x and Sydney as 1x, which gives you 4x=88. 88/4= 22, so Sydney is 22
You roll a six sided die. What is the
probability of rolling an even number
three times in a row?
Answer:
50
Step-by-step explanation:
The probability of rolling an even number three times in a row is; 1/27.
What is the probability of rolling an even number three times in a row?It follows from the task content that the six sided die is rolled thrice.
With each roll, it follows that the probability of rolling an even number is 2/6 = 1/3.On this note, upon rolling the dice thrice, it follows that the probability of rolling an even number all three times is;
P = 1/3 × 1/3 × 1/3 = 1/27.Read more on probability;
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It took 4 hours to drive 240. At this rate,how long does it take to drive 90 miles?
The required time that it takes for 90 miles is 1.5 hour.
What is the difference between average and instantaneous speed?The average speed is calculated for a period of time while instantaneous speed is calculated at certain instant of time. For instantaneous speed and average speed are equal for an object moving with constant speed.
The total distance is given as 240 miles.
And, the time taken is 4 hours.
Now, the speed can be calculated by taking the ratio of the distance and time as below,
Speed = Distance ÷ Time
⇒ Speed = 240 ÷ 4 = 60
Thus, the time taken to drive 90 miles is calculated as,
Time = Distance ÷ Speed
⇒ Time = 90 ÷ 60 = 1.5
Hence, the time taken to cover 90 miles is 1 hour.
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8x-72=2x-36
I need the answer
Answer: [tex]x=6[/tex]
Subtract 2x from both sides
[tex]8x-72-2x=2x-36-2x\\6x-72=-36[/tex]
Add 72 to both sides
[tex]6x-72+72=-36+72\\6x=36[/tex]
Divide both sides by 6
[tex]6x/6=36/6\\x=6[/tex]
Answer:
x=6
Step-by-step explanation:
first thing first you always need to get x alone and since you have an X on both side we need to move one of them to the same side as the other one.
8x-72=2x-36
add 72 on both sides ( the opposite of subtracting is adding)
8x=2x-36+72
8x=2x+36
then we subtract 2x on both sides to get X alone
8x-2x=36
6x=36
then we divide 36 by 6 to get our answer for x
X= 6
and that's your answer, hope this helped
1) During skating practice, Sasha landed 7 out of 12 jumps. What is the experimental
probability that she will land her next jump?
Answer:
14 maybe
Step-by-step explanation:
With a stratified random sample, a population is broken up into different
subgroups and then simple random samples are conducted within each of
these subgroups.
A. True
B. False
Answer:
True
Step-by-step explanation:
This is true. In a stratified random sample, the overall population is broken up into smaller groups by a certain factor that pertains to the survey they are conducting. They will then choose a simple random sample in each of these groups to determine who is going to be surveyed. Based on this, the definition is true.
a length of clothesline is 3 1/3 ft long. how would you report its length in inches?
Answer:
40 inches
Step-by-step explanation:
Simply multiply the length value by 12
1 foot = 12 inches