A telephone pole cast a shadow that is 34 m long find the height of the telephone pole if a statue that is 36 cm tall cast a shadow 77 cm long ?
Answer:
16 cm approximately
Step-by-step explanation:
We are given that a telephone pole cast shadow that is 34 m long .We are given that a statue that is 36 cm long and shadow of statue is 77 cm long.
We have to find the length of telephone pole
Let height of pole
Using direct proportion
[tex]\frac{x}{34}=\frac{36}{77}[/tex]
By multiply property of equality then we get
[tex]x=\frac{36}{77}\times 34[/tex]
x=[tex]\frac{1224}{77}[/tex]
x=15.896 cm
Hence, the height of telephone pole=15.896 cm=16 cm approximately
Which number is greater? 0 -1 -25 -50?
What's 10⁄12 written as a fraction in simplest form?
A. 5⁄6
B. 10⁄6
C. 3⁄5
D. 5⁄12
What key features of a polynomial can be found using the fundamental theorem of algebra and the factor theorem?
Answer:
The key fundamental theorem of algebra says that degree of polynomial is equal to number of zeros in a function.The Factor Theorem states that a first degree binomial is a factor of a polynomial function if the remainder, when the polynomial is divided by the binomial, is zero.Based on the table, which statement best describes a prediction for the end behavior of the graph of f(x)? As x → ∞, f(x) → –∞, and as x → –∞, f(x) → ∞ As x → ∞, f(x) → ∞, and as x → –∞, f(x) → ∞ As x → ∞, f(x) → ∞, and as x → –∞, f(x) → –∞ As x → ∞, f(x) → –∞, and as x → –∞, f(x) → –∞
Answer: The correct option is B, i.e., "As x → ∞, f(x) → ∞, and as x → –∞, f(x) → ∞".
Explanation:
From the table it is noticed that the first row represents the value of x and the second row represents the value of f(x).
The value of f(x) is 14 at x = -5, after that the value of f(x) is decreased as the value of x increases.
The value of f(x) remains unchanged when the value of x approaches to 0 from 1.
The value of f(x) is -6 at x = 0, after that the value of f(x) is increased as the value of x increases.
From the table it is noticed that as the value of x approaches to positive infinity the value of f(x) is also approaches to positive infinity.
[tex]f(x)\rightarrow\infty \text{ as }x\rightarrow\infty[/tex]
From the table it is noticed that as the value of x approaches negative infinity the value of f(x) is also approaches to positive infinity.
[tex]f(x)\rightarrow\infty \text{ as }x\rightarrow-\infty[/tex]
These statement are shown in second option, therefore the second option is correct.
Answer:
The end behavior of the graph of the function f(x) is:
f(x) → ∞, and as x → –∞, f(x) → ∞ As x → ∞,
Step-by-step explanation:
Based on the table we could observe that the function f(x) is increasing to the left of -1 as well to the right of -1 and it attains the minimum value to be -6.
Hence, it can be predicted that the end behavior of the graph of the function f(x) goes to infinity in the left and also it goes to infinity in the right.
Hence, the statement that best describes the end behavior of the graph of f(x) is:
f(x) → ∞, and as x → –∞, f(x) → ∞ As x → ∞.
Guess the value of the limit (correct to six decimal places). (if an answer does not exist, enter dne.) lim hâ0 (4 + h)5 â 1024 h
Margaret plans to deposit $500 on the first day of each of the next five years, beginning today. if she earns 4% compounded annually, how much will she have at the end of five years?
Determine the order in which an inorder traversal visits the vertices of the given ordered rooted tree.
Solve the equation by graphing. x^2+14x+45=0 First, graph the associated parabola by plotting the vertex and four additional points, two on each side of the vertex. Then, use the graph to give the solution(s) to the equation. If there is more than one solution, separate them with commas.
Points:
Solution(s):
a total of 321 tickets were sold for the school play. They were either adult tickets or student tickets. The number of student tickets sold was two times the number of adult tickets sold. How many adult tickets were sold
4. Meagan invests $1,200 each year in an IRA for 12 years in an account that earned 5%
compounded annually. At the end of 12 years, she stopped making payments to the
account, but continued to invest her accumulated amount at 5% compounded annually for
the next 11 years.
a. What was the value of the Ira at the end of 12 years?
b. What was the value of the investment at the end of the next 11 years?
c. How much interest did she earn?
a. The value of the Ira at the end of 12 years is $19,100.55.
b. The value of the investment at the end of the next 11 years is $32,668.43.
c. Interest earn is $18,288.43.
a. Using this formula to determine the value of the Ira at the end of 12 years
A=Pmt [(1+r)^n-1]/r
Let plug in the formula
A=1,200[(1+0.05)^12-1]/0.05
A=1,200[(1.05)^12-1]/0.05
A=$1,200(0.795856)/0.05
A=$955.02759/0.05
A=$19,100.55
b. The value of the Ira at the end of 11 years is:
$19,100.55(1+0.05)^11
=$19,100.55(1.05)^11
=$19,100.55(1.710339358)
=$32,668.43
c. Interest earn
Total investment=1200(12)
Total investment= $14,400
Now let calculate the interest earned
Interest earned = $32,668.43 - $14,400
Interest earned= $18,288.43
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What is a non example of a rate
write an expression for the area of the rectangle
The blades of a windmill turn on an axis that is 40 feet from the ground. The blades are 15 feet long and complete 3 rotations every minute. Write a sine model, y = asin(bt) + k, for the height (in feet) of the end of one blade as a function of time t (in seconds). Assume the blade is pointing to the right when t = 0 and that the windmill turns counterclockwise at a constant rate.
a is the .
The vertical shift, k, is the... length of a blade, height of a windmill, or numbers of rotations per minute.
a =
k =
20
5
30
Step-by-step explanation:
A total of 279 tickets were sold for the school play. they were either adult or student tickets. the number of student tickets sold was two times the number of adult tickets sold. how many adult tickets were sold?
Final answer:
The number of adult tickets sold for the school play is 93, calculated by setting up an equation based on the information that the total tickets sold were 279 and student tickets were two times the number of adult tickets.
Explanation:
The question asks us to determine the number of adult tickets sold when a total of 279 tickets were sold for the school play, and the number of student tickets is two times the number of adult tickets sold. We can set up an equation to solve this problem.
Let A be the number of adult tickets, and S be the number of student tickets. The problem gives us two equations:
S = 2A (The number of student tickets is two times the number of adult tickets)
A + S = 279 (The total number of tickets sold is 279)
Substituting the first equation into the second gives us:
A + 2A = 279
3A = 279
A = 279 / 3
A = 93
Therefore, 93 adult tickets were sold for the school play.
The perimeter of a rectangle is 56 feet. Describe the the possible lengths of a side if the area of the rectangle is not to exceed 132 square ft
The possible lengths of sides of the rectangle will be [tex](6,22)[/tex] or [tex](22,6)[/tex] .
What is area ?Area is the space which is occupied by any [tex]2D[/tex] surface.
Area of rectangle [tex]=Length\ *\ Breadth[/tex]
Perimeter of rectangle [tex]=2(Length\ +\ Breadth)[/tex]
We have,
Perimeter of rectangle [tex]=56[/tex] feet
Area of rectangle [tex]=132[/tex] squared feet
Let,
Length of rectangle [tex]=x[/tex]
Breadth of rectangle [tex]=y[/tex]
So,
Perimeter of rectangle [tex]=2(Length\ +\ Breadth)[/tex]
[tex]56=2(x+y)[/tex]
[tex]28=(x+y)[/tex]
⇒ [tex]x=28-y[/tex] [tex]........(i)[/tex]
Now,
Area of rectangle [tex]=Length\ *\ Breadth[/tex]
[tex]132=x\ *\ y[/tex] [tex]........(ii)[/tex]
Now substitute value of [tex]x[/tex] in [tex](ii)[/tex],
[tex]132=(28-y)y[/tex]
[tex]132=28y-y^2[/tex]
⇒[tex]y^2-28y+132=0[/tex]
Now using Middle term split method;
[tex]y^2-28y+132=0[/tex]
[tex]y^2-22y-6y+132=0[/tex]
[tex]y(y-22)-6(y-22)=0[/tex]
[tex](y-6)(y-22)=0[/tex]
⇒
[tex](y-6)=0[/tex]
⇒ [tex]y=6[/tex]
[tex](y-22)=0[/tex]
⇒ [tex]y=22[/tex]
So,
Now if we take [tex]y=6[/tex], then
[tex]x=28-6[/tex]
[tex]x=22[/tex]
And,
if we take [tex]y=22[/tex], then
[tex]x=28-22[/tex]
[tex]x=6[/tex]
So, the possible lengths of sides of the rectangle are [tex](6,22)[/tex] or [tex](22,6)[/tex] .
Hence, we can say that he possible lengths of sides of the rectangle are [tex](6,22)[/tex] or [tex](22,6)[/tex] .
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The probability that you will win a game is 0.18. if you play the game 504 times, what is the most likely number of wins?
If, on average, Bob can make a sale to every 3rd person that comes into his store, how many people must come into Bob�s store if he wanted to make approximately fifteen (15) sales?
Find the length of the third Angelou a triangle given that the first two angels are 35 and 70 show your work
angles in a triangle = 180 degrees
70 +35 = 105 degrees
180-105 = 75 degrees
3rd angle = 75 degrees
Which of the following are vertical asymptotes of the function y=3cot(1/2x)-4? A. 3pi B. 2pi C. pi/2 D. 0
Answer:
B and D
Step-by-step explanation:
Find the percent equivalent to the ratio 8 to 20
divide the ratio:
8/20 = 0.4
0.4 = 40%
What is the median of the data set given below? 19, 22, 46, 24, 37, 16, 19, 33
Line segment AB is congruent to line segment CD.
A.AB overbar similar to CD overbar
B.AB overbar congruent to CD overbar
C. AB overbar equal to CD overbar
D. AB overbar element to CD overbar
When two line segments are congruent, what it really means is that the length of the line segments are equal. Congruent is usually interchanged with the word equal since it means the same: equal lengths. However, congruent is very specific in the sense that it means “equal lengths”. When we say equal alone, it may refer to different properties, congruent however is very specific.
Now the answer to this question should be:
B. AB overbar congruent to CD overbar
Not similar, not equal, and definitely not element. What we mean in this case is “equal lengths”, therefore the perfect word is congruent.
An ellipse has vertices along the major axis at (0, 8) and (0, –2). The foci of the ellipse are located at (0, 7) and (0, –1). What are the values of a, b, h, and k, given the equation below? (y-k)^2/a^2+(x+h)^2/b^2=1
Answer: The values for a, b, h, and k are a = 5, b = 3, h = 0, k = -3.
Step-by-step explanation: In this problem, we know ellipse has vertices along the major axis at (0, 8) and (0, -2). The foci of the ellipse are located at (0, 7) and (0, -1). We are asked to determine the values of a, b, h, and k.
We were also then provided with the equation for vertical eclipse:
[tex]\frac{(x-h)^2}{b^2} + \frac{(y -k)^2}{a^2}[/tex]
Before we begin, we need to first define our values for a, b, h, and k.
a - distance to vertices from the centerb - distance to co-vertices from the center(h, k) - represents the center of the eclipseThe first step, we need to determine the center of the eclipse. We can use the midpoint formula to determine the midpoint between the vertices along the major axis: (0, 8) and (0, -2).
[tex]M = (\frac{x_{1} +x_{2} }{2} , \frac{y_{1} + y_{2} }{2} )[/tex]
[tex]M = (\frac{0 + 0}{2} , \frac{-2 + 8}{2} )\\M = (0, 3)[/tex]
We now know that our center (h, k) is (0, 3). Which means our values for h and k are 0 and 3. Next, we have to determine our values for a and b. Considering the center of our eclipse is not at the center, we can use one of our vertices to determine our value for a.
[tex]V_{1}[/tex] = (h, k±a)
(0, 8) = (0, 3±a)
3 ± a = 8
±a = 5
Now, we know that a = 5. For us to get b, we need to use this formula: [tex]c^2 = a^2 - b^2[/tex]. Let's rewrite this formula, so we can focus on getting our b-value.
[tex]c^2 - a^2 = -b^2[/tex]
For us to use this formula, we need to determine our c value. To find our c-value, we have use of our foci points: (h, k±c). C is the units away/further from the center towards our foci points.
(0, 3±c) = (0, 7)
3 + c = 7
7 - 3 = c
4 = c
Now, we know that our value for c is 4. Now, let's plug into the formula.
[tex](4)^2 - (5)^2 = -b^2\\16 - 25 = -b^2\\\frac{-9}{-1} = \frac{-b^2}{-1} \\\sqrt{b^2} = \sqrt{9} \\b = 3[/tex]
Our value for b is 3. If we put into our eclipse formula:
[tex]\frac{(x-0)^2}{3^2} + \frac{(y -(-3))^2}{5^2}[/tex]
Bob drove from home to work at 50 mph. After work the traffic was heavier, and he drove home at 30 mph. His driving time to and from work was 1 hour and 4 minutes. How far does he live from his job?
The adult child radio at a local daycare center is 3 to 16.at the same rare how many adults are needed for 48 children?
To find the number of adults needed for 48 children at a daycare with an adult to child ratio of 3:16, we set up a proportion and solve for the unknown number of adults. We cross-multiply and divide to find that 9 adults are required.
The question asks us to calculate how many adults are needed for 48 children in a daycare center given an adult to child ratio of 3:16. To solve this, we need to set up a proportion based on the ratio and solve for the number of adults needed.
We have the ratio of adults to children as 3:16, which means for every 3 adults, there are 16 children. To find out how many adults are needed for 48 children, we set up the proportion:
3 adults / 16 children = x adults / 48 children
Now we cross-multiply and solve for x:
(3 adults) / (48 children) = (16 children)
144 = 16x
x = 144 / 16
x = 9
Therefore, 9 adults are needed to take care of 48 children at the daycare center.
M(5, 7) is the midpoint of rs The coordinates of S are (6, 9). What are the coordinates of R?
(5.5, 8)
(7, 11)
(10, 14)
(4, 5)
How many outfits are possible from 4 pairs of jeans 6 shirts and 2 pairs of shoes? Assume that outfit consists of 1 pair of jeans, 1 shirt, and 1 pair of shoes
multiply jeans by shirts by shoes
so 4 x 6 x 2 = 48 different combinations
A store is offering a 20% discount on all sales over $50 if you purchase a T-shirt and a pair of jeans for $62.50 what is the amount of the discount you would receive
The discount on the purchase of a T-shirt and a pair of jeans costing $62.50 with a 20% discount policy is $12.50.
A store's discount policy offers 20% off for purchases over $50. The question involves calculating the discount amount when a T-shirt and a pair of jeans are purchased together for $62.50. To determine the discount, we simply multiply the total purchase amount by the discount rate.
Step-by-Step Calculation:
First, confirm the purchase amount qualifies for the discount. The combined cost of the T-shirt and jeans is $62.50, which is above $50, so the purchase qualifies for the discount.
Calculate the discount by multiplying the total purchase amount by the discount rate: $62.50 × 0.20 (which is the same as 20%).
Discount Amount = $62.50 × 0.20 = $12.50.
Therefore, the amount of the discount the customer would receive on the purchase of the T-shirt and jeans is $12.50.
How many different committees can be formed from 10 teachers and 41 students if the committee consists of 2 teachers and 2 students?