Answer:
about 15/16
Step-by-step explanation:
two poles are connected by a wire that is also connected to the ground. the first pole is 30 ft tall and the second pole is 15 ft tall. there is a distance of 45 ft between the two poles. where should the wire be anchored to the ground (in ft, from the shorter pole) to minimize the amount of wire needed?
At 30 ft the wire is anchored to the ground (in ft, from the shorter pole) to minimize the amount of wire needed.
What is the quadratic equation?
Any equation in algebra that can be written in standard form as where x stands for an unknown value and a, b, and c stand for known values is said to be a quadratic equation. In general, it is assumed that a > 0; equations with a = 0 are regarded as degenerate since they become linear or even simpler.
Let x (ft) be the distance from the base of the left pole to the anchor point. Since 2 poles has a distance of 45 ft, the distance from the anchor point to the right pole is 45 - x
The wire length from the top of the left pole to the anchor point is
[tex]L^{2} _l = 30^{2} + x^{2}[/tex]
= x² + 900
Similarly for the 2nd part of the wire
[tex]L^{2} _r = 15^{2} + (45-x)^{2}[/tex]
= 256 + 2025 - 45x + x²
= x² + 2281 - 45x
We want to minimize the length of the wires, or [tex]L_l + L_r[/tex]
√x² + 900 + √ x² + 2281 - 45x
we can take the first derivative of this and set it to 0
[tex]\frac{x}{\sqrt{ x^2 + 900} } + \frac{45 - x}{\sqrt{x^2 + 2281 - 45x} } = 0[/tex]
x = 30
Hence, at 30 ft the wire is anchored to the ground (in ft, from the shorter pole) to minimize the amount of wire needed.
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Which is the best estimate of the
solution for the system of linear
equations graphed below?
A.(0.5,2)
B. (1.5, 2)
C. (2,1.5)
D. (2.5, 1.5)
Answer:
B. (1.5, 2)
Step-by-step explanation:
Hope it helps!
Answer:
B
Step-by-step explanation:
The intersection of the two lines looks to be about (1.5 , 2)
PLS HELP ASAP!!!! 50 PTS
Answer: x=4
Step-by-step explanation:
6x + 10 = 5x + 14
x + 10 = 14
x = 4
the difference of vidya's age and 15 is 66 use the variable v to represent vidya's age
Answer:
[tex]\huge\boxed{\sf v = 81}[/tex]
Step-by-step explanation:
Let Vidya's age be v.
Given condition:v - 15 = 66
Add 15 to both sides
v = 66 + 15
v = 81[tex]\rule[225]{225}{2}[/tex]
Simplify: 8x62x4
A.6x2
B.4x2
C.8x10
D.10x10
I would like to create a rectangular vegetable patch. The fencing for the east and west sides costs $4 per foot, and the fencing for the north and south sides costs only $2 per foot. I have a budget of $96 for the project. What are the dimensions of the vegetable patch with the largest area i can enclose?.
The dimensions of the vegetable patch with the largest area we can enclose are
length = 12 feet and breadth = 6 feet.
Given, a rectangular vegetable patch.
The fencing for the east and west sides costs $4 per foot, and the fencing for the north and south sides costs only $2 per foot.
We have a budget of $96 for the project.
Let the length of the rectangle be, l
and breadth of the rectangle be, b
according to the ques,
4l + 8b = 96
l + 2b = 24
l = 24 - 2b
Now, area of the rectangle be,
Area = length×breadth
Area = l×b
A = (24 - 2b)b
A = 24b - 2b²
On differentiating both sides, we get
A' = 24 - 4b
b = 6
l = 24 - 12 = 12
So, the dimensions of the vegetable patch with the largest area we can enclose are
length = 12 feet and breadth = 6 feet.
Hence, The dimensions of the vegetable patch with the largest area we can enclose are
length = 12 feet and breadth = 6 feet.
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9 2 8 7 6 5 1 4 3 show the contents of the array above each time an insertion sort changes it while sorting the array into ascending order.
The array that has been sorted using insertion sorting 1 2 3 4 5 6 7 8 9.
A straightforward sorting algorithm called insertion sort functions like how you might arrange playing cards in your hands.
Initial Pass: 2 9 8 7 6 5 1 4 3
The array's first two members are initially compared using an insertion sort.
Since 9 is bigger than 2, they are not arranged in ascending order, and 2 is not in the proper place. So, switch 9 and 2.
Therefore, 2 is currently kept in a sorted sub-array.
Second Pass: Continue with the next two elements and compare them.
2 8 9 7 6 5 1 4 3
Here, 9 is bigger than 8, therefore both items appear to be in ascending order; as a result, there won't be any switching. Along with 8, 9 is also kept in a sorted sub-array.
Third pass: Currently, the sorted sub-array has two entries, which are 2 and 8.
Moving on to the following two components, which are 9 & 7,
2 7 8 9 6 5 1 4 3
Continue sorting similarly; the results would be 1 2 3 4 5 6 7 8 9.
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Two towns have accumulated different amount of snow. IN town 1, the snow depth is increasing by 3 1/2 inches every hour, and currently has 5 inches of snow. IN town 2, the snow depth is increasing by 2 1/4 inches every hour, and currently has 6 inches of snow. In how many hours will the snowfall of both towns by equal.
The snowfall of both towns by equal in 4/5 hours or 48 minutes.
What is a linear equation?A linear equation is an algebraic equation of degree one. In general, the variable or the variables(in the case of a linear equation in two variables) the variables are x and y.
Assuming the no. of hours to be x, therefore the expression for town 1 is
y = (7/2)x + 5 and the expression for town 2 is y = (9/4)x + 6.
The snowfall of both towns by equal when,
(7/2)x + 5 = (9/4)x + 6.
(7/2)x - (9/4)x = 6 - 5.
[(14 - 9)x]/4 = 1.
(5/4)x = 1.
x = 4/5 hours Or (4/5)×60 = 48 minutes the snowfall of both towns by equal.
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Graph the equation.
y = x
Answer:
Slope: 1
__________
y-intercept: (0,0)
Step-by-step explanation:
33, 25, 42, 25, 31, 37, 46, 29, 38 what is the interquartile range of the data?
The interquartile range of the data will be 13
When arranged from lowest to highest, the IQR reflects the median 50% of values. To calculate the interquartile range (IQR), firstly compute the median (middle value) of the data's lower and upper halves. All those are quartile 1 (Q1) and quartile 3 (Q3) values (Q3). The interquartile range is the difference between quarters three and then one.
first, let us sort the data from lowest to highest
25,25,29,31,33,37,38,42,46
Q1- median of the lower half of the data=(29+25)/2=27
Q3-median of the upper half of the data=(38+42)/2=40
the interquartile range of the data will be Q3-Q1
40-27= 13
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An initial population of 20 fish is introduced into a lake. This fish population grows according to a continuous exponential growth model. There are 52 fish in the
lake after 7 years.
A pizza shop needs 5 ounces of cheese and 3 ounces of sauce to make one pizza. after 4 hours of being open one evening, the pizza shop has used 192 ounces combined of sauce and cheese. how many pizzas were made so far that evening?
The total number of pizzas were made in 4 hour in pizza shop is 24.
Describe the term unitary method?The unitary approach involves calculating the value of an individual unit, from which we can calculate the values of the necessary number of units. A single or distinct unit is referred to by the word unitary. Therefore, the goal of this strategy is to establish values in reference to a separate unit.For the stated question-
For one pizza-
Ounce of cheese required = 5.
Ounces of sauce required = 3.
Total requirement = 8 ounces.
After 4 hours,
Total ounces combined of sauce and cheese used = 192.
Thus,
Number of pizza = 192 / 8
Number of pizza = 24
Thus, the total number of pizzas were made in 4 hour in pizza shop is 24.
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the base of the first booth is the shape of a triangle. write a polynomial that represents the area of the booth. write your answer in descending order. please use the palette below to enter your answer.
The polynomial that represents the area of the booth is 3[tex]t^3[/tex]-12t.
How to calculate polynomial for triangle area?Polynomial is a expression of variable, coefficients, and constants with mathematics operation of subtraction, addition, multiplication, and powers (only positive integers) of variable.
So, basically to calculate polynomials is the same as normal calculations except that the numbers are changed to variables.
Base length = 2[tex]t^2[/tex]-8
Height length = 3t
Calculate the area of triangle. So,
Area of triangle = (1/2) × base × height
= (1/2) × 2[tex]t^2[/tex]-8 × 3t
= (1/2) × 6[tex]t^3[/tex]-24t
= 3[tex]t^3[/tex]-12t
Thus, the area of the booth can be written by this polynomial 3[tex]t^3[/tex]-12t.
Your question is incomplete, but most probably your full question was (image attached).
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Given AB, find C which is 1/3 of the distance from A to B. A(1,2) B(-5,8)
Answer: (2,0)
Step-by-step explanation:
question: 14. which of the following shapes replaces the question mark to complete the series? ? 8 oo aa
Pattern Recognition is defined as the pattern is a number, shape, or something repeated in a particular way. Analysis of patterns should consider on different basis. The correct option is option (d).
The main basis of Pattern Recognition are the following:
1. Color change
2. Shape change
3. Rotation change
4. Size change
we have given three shapes pattern and we have to find out the perfect shape for forth place and the required shape follow the order like others.
After examine the pattern, we can see that the first figure is a filled triangle and the second figure is a hollow circle. This pattern is maintained alternately. The last figure(3rd place) is an open circle, so the next figure is a filled triangle.
So, the correct option is d.
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State whether the following statement is true and explain why or why not: A trinomial is always a higher degree than a monomial. Give an example proving your answer is correct.
Grading: 2 points: Correct Answer; 2 points: Explanation; 1 point: Example
The given statement that a trinomial is always a higher degree than a monomial is false because greater number of terms does not means higher degree.
A monomial is an algebraic expression with only one term. Or we can say that the representation of a single concept is a monomial.
An example of an unary expression is: 12
A trinomial is an algebraic expression containing three terms. An example of a ternary is: x + y + 7
A trinomial is always of higher degree than a monomial is false statement .
A counterexample can be used to explain why this is wrong. Suppose we have a monomial, 8⁵ and then a trinomial x² + 2x + 3 . This is just a random example. This monomial has a higher degree because 5 is greater than 2. So basically it doesn't matter what the monomial is, if the degree is higher it is just a term than the maximum degree of the trinomial. Just because this has three terms does not mean that the highest degree term is greater than his one term in the monomial.
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The average waiting time at a drive-in window of a local bank is 10. 3 minutes, with a standard deviation of 2. 7 minutes. Assume the variable is normally distributed. If a customer arrives at the bank, find the probability that the customer will have to wait between 4 and 9 minutes.
29.78% of customers will most likely probability be waiting between 4 and 9 minutes.
Explain the term z-score of the normal distribution?An observation's Z score indicates however many standard deviations it deviates from the mean. The standard normal distribution's mean is zero. Positive Z scores are those above the mean, while negative Z scores are those below the mean.The formula for the z score is-
z = (x - μ)/σ
In which,
μ = mean of 10. 3 minutes
σ = standard deviation of 2. 7 minutes.
z score for the x = 4 minutes.
z = (4 - 10.3)/2.7
z = -2.33
z score for the x = 9 minutes.
z = (9 - 10.3)/2.7
z = -0.48
Thus,
Probability that the customer will have to wait between 4 and 9 minutes.
P(4 < x < 9) = P(-0.48 < z < -2.33)
Use z score table-
P(4 < x < 9) = 0.3085 - 0.0107
P(4 < x < 9) = 0.2978
P(4 < x < 9) = 29.78%
Thus, 29.78% of customers will most likely be waiting between 4 and 9 minutes.
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a tower that is 106 feet tall casts a shadow 135 feet long. find the angle of elevation of the sun to the nearest degree.
The angle of elevation of the sun is [tex]tan^{-1}[/tex](106/ 135).
The angle of elevation:
The angle is formed by the line of sight and the horizontal plane for an object above the horizontal.
Here we have to find the angle of elevation of the sun.
Data given:
length of the tower = 106 feet
shadow form by the tower = 135 feet
The formula for the angle of elevation = height/base
tanФ = height/base
= 106/ 135
Ф = [tex]tan^{-1}[/tex](106/135)
Therefore the angle of elevation is [tex]tan^{-1}[/tex]( 106/ 135).
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Can someone please help me
Answer:
6
Step-by-step explanation:
Perimeter = 2l + 2w
48 = 2(18) + 2(w)
48 = 36 + 2w
12 = 2w
w = 6
Could you please give me brainliest for this? Thank you!
Find the area of the composite figure. I got 78 but my teacher said that it is incorrect. WILL MARK BRAINLIEST! Thanks!
Answer:
44
Step-by-step explanation:
Essentially there are 3 triangles
The top left has a base of 5 and a height of 4
Its area is 1/2 x b x h = 1/2 x 5 x 4 = 10
Then there are two triangles with the same base of 2.5 + 6 = 8.5 and same height of 4 feet. So each of the triangles has the same area as the other.
Total area of both triangles = 2 (1/2 x b x h) = bh = 8.5 x 4 = 34
Total area = 10 + 34 = 44
Answer:
44 ft²
Step-by-step explanation:
Here's how I divided the parts of the composite figure:
1. There is a triangle at the left with the vertex pointing down and base above. The base is 5 ft. The height is 4 ft.
2. There are 4 triangles left. I divided them into two triangles like this:
An upper triangle which has a base of 2.5 ft + 6 ft, and a height of 4 ft with a horizontal base on the bottom and a vertex on the upper side.
A lower triangle that is a mirror image of the triangle just above. The dimensions are the same.
Triangle on upper left:
base = 5 ft
height = 4 ft
Triangles at right (2 triangles with the same dimensions)
base = 2.5 ft + 6 ft = 8.5 ft
height = 4 ft
area of triangle = base × height / 2
Total Area = (5 ft)(4 ft)/2 + 2 × (8.5 ft)(4 ft)/2
Total Area = 10 ft² + 34 ft²
Total Area = 44 ft²
Helppppppppppppppppppppppppp
Answer:
-[tex]\frac{16}{49}[/tex]
Step-by-step explanation:
First do: (-[tex]\frac{4}{7}) ^{2}[/tex], which is -[tex]\frac{4}{7}[/tex]*-[tex]\frac{4}{7}[/tex] which is [tex]\frac{16}{49}[/tex] and then add in the other negative: -[tex]\frac{16}{49}[/tex]
Olivia has has read 40 pages of a 70 page book, 60 pages of an 85 page book, and 43 pages. What is the percentage f pages that Olivia has not read?
Answer:
Below
Step-by-step explanation:
Total pages read = 40 + 60 +43 = 143 pages read
Total pages of all of the books = 70 + 85 + x
percentage READ = (143) / ( 70 + 85 + x) * 100% = ???
percentage NOT read = 100 - ???
(since 'x' was not given in the question post)
Read pages:
40+60+43=143
All pages:
70+85+43=198
198-143=55
55/198=0,2778
0,2778×100%=27.78%
What is the average rate of change of the function f(x)=2(3)xfrom x = 2 to x = 4?.
The average rate of change of the function f(x)=2(3)x from x = 2 to x = 4 = 72
How do functions work?The term "function" refers to the relationship between a collection of inputs and outputs with one each. Simply described, a function is an association of inputs where each input is coupled with exactly one output. Every function has an associated domain, codomain, or range. The most common way to represent a function is as f(x), where x represents the input.
To calculate the average rate of change, use the slope formula:
y2−y1/x2−x1=m
f(4)−f(2)/4−2=m
Finding the values of f(4) and f(2) will help us to simplify this.
f(4)=2(3)4=2(81)=162
f(2)=2(3)2=2(9)=18
m=162−18/2
m=144/2
m=72
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The equation of a line is 2y = 8x + 10
find the SLOPE of a line that is
a) parallel to the line
b) perpendicular to the line
c) neither parallel or perpendicular
Solve 3x² - x = 10
A.X=2 and X=-15
B. X=-5 and X= 2/3
C. X=-5/3 and X=2
D. X=-3 and X=10
Answer:
C. x = -5/3 and x = 2
Step-by-step explanation:
Bring the 10 over to the other side of the equation.
3x² - x - 10 = 0
Factorise.
(3x + 5)(x - 2) = 0
3x + 5 = 0 or x - 2 = 0
3x = -5 or x = 2
x = -5/3 or x = 2
In two or more complete sentences, describe how to determine if the function f(x)=2cos(x) is even by looking at a graph.
The given function f(x) = 2 cos (x) is an even function because the result of the cosine of negative angles are the same with those of positive angles.
How to determine an Even Function?
To check if a function is odd or even, we have to calculate f(−x).
The function is even if f(-x) = f(x)
The function is odd if f(-x) = -f(x)
We are given the function as; f(x) = 2 cos (x)
f(-x) = 2 cos (-x)
Now, we know that the cosine of a negative angle always gives the same value as the cosine of the positive angle and as such, we can say that;
2 cos (-x) = 2cos (x)
The same result as f(x) which tells us that it is an even function
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3x + 4x +5x = 4(x + 2) Please write as the actual answer and a decimal
Answer: 1
Step-by-step explanation:
We can rewrite the equation as
12x = 4x +8
8x= 8
x=1
Triangle PQR has the following measures: p= 16.2 m, q = 35.0 m, and m/R = 75°.
What is the area of triangle PQR?
After solving the area of the triangle PQR obtained will be equal to 273.6 m²
What is a triangle?
The basic polygonal shape of a triangle has three sides & three interior angles. This is one of the fundamental shapes in geometry and is particularly associated. It has three connected vertices. Triangles can be divided into a variety of categories according to their sides and angles.
As per the given information given in the question,
p= 16.2
q = 35.0 m and,
m ∠R = 75°
Find x by cosine rule,
cos 75° = (16.2² + 35² - x²)/(2 × 16.5 × 35)
x = 34.5 m
The value of r is 34.5 mm then the third side of the triangle pqr will be,
Use heron's formula,
s = (16.2 + 35 + 34.5)/2
s = 42.85
Area = [tex]\sqrt{s(s-p)(s-q)(s-r)}[/tex]
A = √42.85(42.85 - 16.2)(42.85 - 35)(42.85 - 34.5)
A = 273.6 m²
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Francisco is building a window seat below a bay window in the shape of an isosceles trapezoid. His blueprint for the window seat is shown below.
What is the area of the window seat?
Answer:
56
Step-by-step explanation:
Danni placed $5700 in a savings account which compounds interest continuously at a rate of 2. 1%. How much will she have in the account after 4 years? round your answer to the nearest whole number. Do not include a $ in your answer.
Using the compound interest method, we can calculate that Danni will have $6,194.09 in her account after 4 years.
What is compound interest?Compound interest, also known as interest on principal and interest, is the practice of adding interest to the principal amount of a loan or deposit.
Compound interest works by periodically adding collected interest to your main, which is the sum you first deposited into the savings account so that interest can then be earned on both.
In essence, your interest begins to generate interest of its own.
Compound interest formula: [tex]A=P\left(1+\frac{r}{100}\right)^{n t}[/tex]
Now, calculate the amount Danni will have after 4 years:
[tex]A=P\left(1+\frac{r}{100}\right)^{n t}[/tex]
A = 5700(1+0.021)⁴
A = 5700(1.0210⁴
A = $6,194.09
Therefore, using the compound interest method, we can calculate that Danni will have $6,194.09 in her account after 4 years.
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Answer:
A=6199.48
Step-by-step explanation:
Use the formula for calculating compound interest A=P0ert where A is the unknown, P0=5700, r=0.021, and t=4. Substitute the values into the formula and simplify.
A=5700e0.021⋅4
A=5700e0.084
A=5700(1.0876...)
A=6199.48
The amount in the account after four years is A≈6199, to the nearest dollar.