A guy-wire is attached from the ground to the top of a pole for support. If the angle of elevation to the pole is 67° and the wire is attached to the ground at a point 137 feet from the base of the pole, what is the height of the pole (round to 2 decimal places)?
Answer:
The height of the pole is 322.75 feet.
Step-by-step explanation:
Let the triangle Δ ABC with AC be the length of wire and AB be the Height of the pole
Length between the point of attachment of wire from base of the pole = BC = 137 feet
Angle of elevation to the pole = θ = 67°
We have to find the length of the pole that is AB Let the height of pole be h feet.
According to trigonometry :
[tex]\tan C=\frac{\text{perpendicular}}{\text{base}}[/tex]
Here, C = 67° , perpendicular = AB = h , base = BC = 137
Substitute the values,
[tex]\tan 67^{\circ}=\frac{AB}{BC}[/tex]
[tex]\tan 67^{\circ}=\frac{h}{137}[/tex]
[tex]h=\tan 67^{\circ} \times 137[/tex]
[tex]h=322.75[/tex]
Thus, the height of the pole is 322.75 feet.
Answer:60.1
Step-by-step explanation:
cos
y = -16x2 + 32x - 10 This parabola has x-intercepts, representing the times when the dolphin's height above water is feet.
Answer:
2
0
two real solutions
Step-by-step explanation:
from edge!!
To find the x-intercepts of the quadratic equation representing the height of a dolphin's jump, we can use the quadratic formula by plugging in the coefficients from the equation y = -16x^2 + 32x - 10. The intercepts indicate the times when the dolphin's height above water is zero feet.
Explanation:The question involves finding the x-intercepts of a quadratic equation, which represent the points where a parabola crosses the x-axis. In this context, the x-intercepts correspond to the times when the dolphin's height above water is 0 feet. To find the x-intercepts, we can use the quadratic formula:
x = −b ± √(b² − 4ac) / (2a)
For the equation y = −16x² + 32x − 10, the coefficients are a = −16, b = 32, and c = −10. By substituting these values into the quadratic formula, we can calculate the times when the dolphin is at the water level (y=0). Since this is a mathematical problem involving a real-world scenario, it is essential to check that the resulting times make sense within the context. Negative values for time, for example, would not be physically meaningful.
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Cheryl paid $3.00 for a pair of socks and eight times as much for a pair of shoes. Her brother Kevin also bought socks and shoes but paid twice as much as Cheryl did for each. How much money did they spend together ?
Choose the graph that represents the time for which the velocity of the ball will be between –90 and –58 ft/s.
The answer is c because t must be less than 2.5 and more than 1.5.
Find this by separating the inequality into:
-90 < -32t - 10
&
-32t - 10 < -58
Simplify and you get 2.5 and 1.5
Graph (C) represents the time for which the velocity of the ball will be between –90 and –58 ft/s option (C) is correct.
What is a number line?It is defined as the representation of the numbers on a straight line that goes infinitely on both sides.
We have:
The velocity of the ball will be between –90 and –58 ft/s.
Let v be the velocity of the ball:
v lies between -90 and -58
-90 < v < -58
The above expression represents the inequality:
Or
-90 < -32t - 10
t < 2.5
And
-32t - 10 < -58
t > 1.5
The number line will be:
Open the circle on the number 1.5 and open circle at 2.5 and a line was drawn between this point.
Thus, graph (C) represents the time for which the velocity of the ball will be between –90 and –58 ft/s option (C) is correct.
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Two rectangular prisms have the same volume. The area of the base of the blue prism is 216 square units. The area of the base of the red prism is one third that of the blue prism. Which statement is true?
a) The height of the red prism is one-third the height of the blue prism.
b) The height of the red prism is the same as the height of the blue prism.
c) The height of the red prism is six times the height of the blue prism.
d) The height of the red prism is three times the height of the blue prism.
Answer:
D
Step-by-step explanation:
This list shows the age at which 43 U.S. Presidents began their terms. 57 61 50 54 54 54 56 54 61 54 48 49 42 51 61 57 68 65 50 51 60 52 57 51 52 47 56 62 69 58 49 56 55 55 43 64 57 64 46 55 51 55 46 Before you can make a frequency table, you need to decide how to set up the age intervals. What is the BEST way to group these ages into six intervals?
The best way to group these ages into six intervals is from 40-44 to 65-69.
What is a Frequency Distribution Table ?A frequency distribution table gives an idea about the data point or interval and its frequency.
The age of the Presidents given as
57 61 50 54 54 54 56 54 61 54 48 49 42 51 61 57 68 65 50 51 60 52 57 51 52 47 56 62 69 58 49 56 55 55 43 64 57 64 46 55 51 55 46
The smallest number ( age) is 42 and the largest number (age ) is 69
To make 6 intervals in this gap of 27 , each interval should be of length 5
Therefore the intervals will be
40-44
45-49
50-54
55-59
60-64
65-69
This is the best way to group into intervals.
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Final answer:
The best way to group the ages of U.S. Presidents into six intervals for a frequency table is by intervals of five years each, starting at age 42 and ending at age 71, to cover the entire range and maintain equal width for all intervals.
Explanation:
When grouping ages into intervals for a frequency table, it's best to have intervals that are of equal width and cover the entire range of data without overlap. For the ages of U.S. Presidents starting their terms, which range from 42 to 69, we could divide this range into six intervals in a way that makes sense for this data set.
First, find the range by subtracting the youngest age from the oldest: 69 - 42 = 27. Next, divide this range by the number of desired intervals (6), which gives us 4.5. We can round this to 5 to make the intervals more practical. Thus, each age interval will span 5 years. Starting at 42, the six intervals would be: 42-46, 47-51, 52-56, 57-61, 62-66, and 67-71.
This grouping covers all the ages and each interval is of equal width, making it easy to interpret the frequency table.
Use the expression below to complete the following tasks. (3a2 - 5ab + b2) - (-3a2 + 2b2 + 8ab) What is the additive inverse of the polynomial being subtracted?
Answer:
Option 3
Step-by-step explanation:
edge 2020
find the difference of the least common multiple and the greatest common factor of 12 and 32 show your work please
Describe the test grades using the measures of center
Lexi's bulletin board is 40 centimeters wide. each of her ribbons is 4 centimeters wide, and her photos are 12 centimeters wide. what combination of ribbons and photos will fit side by side with no overlap on Lexi's bulletin
In a line of students ,Jenna is number 8.The teacher says the rule for a number pattern is add4.The first term 7.What number should Jenna say?
Cream filled chocolates are $3.59 a pound Billy bought 1/2 pound of vanilla creams what was the cost round your answer
NEED HELP ASAP!! WILL GIVE BRAINLIEST
5. Marco wrote the equation below.
cos(-pi/2)=cos(3pi/2)
which statement best describes marcos equation?
a. it is true because the cosine function is odd
b. it is false because the cosine function is even
c. it is true because the cosine function has a period of 2pi
d. it is false because the cosine function has a period of pi.
The given equation is represented below:
cos(-pi/2)=cos(3pi/2)
The value of cos(-pi/2) is 0 and the value of cos(3pi/2) is also 0
Further a function is defined as an even function if f(x) = f(-x)
Cosine function is an even function.
Therefore it is true and the correct option is c
It is true because the cosine function has a period of 2pi
Hope it helps ..!!
Answer:
Option C - It is true because the cosine function has a period of [tex]2\pi[/tex].
Step-by-step explanation:
Given : Marco wrote the equation below.
[tex]\cos (-\frac{\pi}{2})=\cos (\frac{3\pi}{2})[/tex]
To find : Which statement best describes Macro equation?
Solution :
Since, the period of the given cos function is 360°
So, it holds the property of trigonometric :
[tex]\cos \theta=\cos (2\pi+\theta)[/tex] then the function is an even function.
Taking [tex]\theta =-\frac{\pi}{2}[/tex]
Then , [tex]2\pi+\theta = 2\pi-\frac{\pi}{2}[/tex]
[tex]2\pi+\theta = \frac{4\pi-\pi}{2}[/tex]
[tex]2\pi+\theta = \frac{3\pi}{2}[/tex]
So, the given function is a even function in a period of [tex]2\pi[/tex].
Therefore, Option C is correct.
It is true because the cosine function has a period of [tex]2\pi[/tex].
Brooke earns $7 an hour at her job now. She can represent the total she makes in a week using the expression 7r. Brooke has asked for a $1 an hour raise. Which expressing would represent the amount Brooke would make in a week after the raise?
Jack purchased a box of 1,000 candy guitar lollipops to sell in the bakery for $20.00. How much did he pay for each lollipop?
Noah makes ceramic pots for the market. On the weekends he makes 11 more pots than he does during the week. Noah represented the number of pots he makes on weekends using the expression p + 11. Which expression represents the total mumber of pots Noah made one weekend if he made 14 more than his usual number?
Kens turtle competed in a 0.50- meter race. His turtle had traveled 49/100 meter when the winning turtle crossed the finish line. What is 49/100 written as a decimal
Well, to make it simple it's 0.49. Hope it helps!
Which of the following would NOT be a deduction from a paycheck?
Select the best answer from the choices provided.
taxes
FICA
hourly wages
health insurance
Box i contains 4 red and 8 blue marbles while box ii contains 5 red and 3 blue marbles. an unfair coin is tossed –whose probability of turning up heads is 40%. if the coin comes up heads box i is chosen and a random marble is chosen, otherwise if it is tails the marble is chosen from box ii.(a)find the probability a red marble is chosen.(b)if a red marble is chosen, what is the probability it came from box i? (c)if a blue marble is chosen, what is the probability it came from box i?
Jeannie's restaurant served 58 customers on Monday. After the first day the amount of customers served decreases at a rate of 2.5% each day.
What is the explicit rule for this situation and approximately how many customers will be served on the 6th day?
Round to the nearest customer.
Drag and drop the answers into the boxes to match the situation.
Explicit rule
Number of customers on the 6th day.
A n = 58 x (0.975) n - 1, A n = 58 x (0.025) n - 1, A n = 58 (1.025) n - 1, 51, 49, 48, 46,
Answer:
51 customers
Step-by-step explanation:
Jeannie's restaurant served 58 customers on Monday.
Rate of decrement r =2.5 % = 0.025
Formula : [tex]y=a(1-r)^{n-1}[/tex]
A is the initial amount
r is the rate
n is the no. of days
So, Substitute the values
[tex]y=58(1-0.025)^{n-1}[/tex]
[tex]y=58(0.975)^{n-1}[/tex]
So, explicit rule : [tex]A_n=58(0.975)^{n-1][/tex]
Now to find the no. of customers will be served on the 6th day
Substitute n = 6
[tex]A_6=58(0.975)^{6-1}[/tex]
[tex]A_6=51.1035[/tex]
So, 51 customers will be served on the 6th day
The value of the digit in the hundreds place in the number 653,841 is 1/10 the value of the digit in the thousands place in which number?
The answer is 0.5.
To find the answer, understand the place value system in numbers.
The value of the digit in the hundreds place in the number 653,841 is 1/10 the value of the digit in the thousands place in which number.
To find the answer, we need to understand the place value system. In the number 653,841, the digit in the hundreds place is 8, and the digit in the thousands place is 5. Therefore, 1/10 of the digit in the thousands place is 0.5.
So, the answer is 0.5.
if c is the incenter of AMD, AMC=3x+6 AND dmc = 8X-49, FIND EACH MEASURE
Answer:
[tex]m\angle AMC = 39\°[/tex] and [tex]m\angle DMC = 39\°[/tex].
Step-by-step explanation:
As you can observe in the image attached, angles AMC and DMC are congruent, because if point C is the incenter of AMD, that means each line the forms such point is a bisector.
Remember that a bisector is a line that equally divides an angle.
So,
[tex]\angle AMC = \angle DMC\\3x+6=8x-49[/tex]
Solving for [tex]x[/tex], we have
[tex]6+49=8x-3x\\5x=55\\x=11[/tex]
Then, we substitute this value in each expression to find the angles.
[tex]\angle AMC = 3x+6 = 3(11)+6=33+6=39[/tex]
[tex]\angle DMC = 8(11)-49=88-49=39[/tex]
Therefore, the measures of those angles are [tex]m\angle AMC = 39\°[/tex] and [tex]m\angle DMC = 39\°[/tex].
4x. (2x^3 — x^2–18x+15) Standard Form
The range of F(x) = 6 * 3x is all positive real numbers.
8pints compared to 15 cups
Lines l and m are parallel and intersected by transversals t and s as shown in the figure below.
What is m
A) 180 degrees
B) 360 degrees
C) 540 degrees
D) 720 degrees
find the domain of
[tex]f(x) = \frac{ \sqrt{x + 2} }{ {x}^{2} - 25 } [/tex]
Brent was looking at his cell phone bill and saw that the total number of texts he has sent is tracked, as shown below:
Month
Texts
1
120
2
237
3
354
4
471
The function representing Brent's texting per month is f(m) = 117m + 3. What does the 117 represent?
It should be the additional texts per month or D
Answer:
The number of texts he sends per month
Step-by-step explanation:
The function f(m) = 117m + 3 is a linear function, which is in the form f(x) = mx+b. In this form, m (the number beside our variable) is the slope, or rate of change, and b (the number added or subtracted) is the y-intercept.
In our function, 117 is the number beside the variable, which makes it the slope. This is the rate of change of this function; it describes how the dependent variable (number of texts) changes for every change in the independent variable (months).
In other words, it tells how many texts he sends per month.
John always wears a shirt, pants, socks, and shoes. He owns 12 pairs of socks, 3 pairs of shoes, 5 pairs of pants, and 5 shirts. How many different outfits can John make?
Answer:
900
Step-by-step explanation:
Khan academy
Given a circle with a diameter of 4, which equation expresses π as the ratio of the circumference of a circle to its diameter?
C /4 = π
Took the test myself, this is the answer.