Answers
Area of the rectangle
LB92(40)3680ft²Area of trapezoid
1/2(sum of parallel sides)(Height)1/2(5+92)(40-5)1/2(97)(35)3395/21697.5ft²Total
3680-1697.51982.5ft²Related Questions
30-32 sketch the region enclosed by the given curves and find its area.
31. [tex]y=\cos ^{2} x \sin x, \quad y=\sin x, \quad 0 \leqslant x \leqslant \pi[/tex]
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Check the picture below.
so hmmm for the sake of completion, let's check where they intersect
[tex]cos^2(x)sin(x)=sin(x)\implies cos^2(x)sin(x)-sin(x)=0 \\\\\\ sin(x)[cos^2(x)-1]=0\implies \begin{cases} sin(x)=0\\ cos^2(x)-1=0 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ sin(x)=0\implies x=sin^{-1}(0)\implies \boxed{x=0} \\\\[-0.35em] ~\dotfill\\\\ cos^2(x)-1=0\implies cos^2(x)=1\implies cos(x)=\sqrt{1} \\\\\\ cos(x)=1\implies x=cos^{-1}(1)\implies \boxed{x=\pi}[/tex]
now, notice, in the picture the function that is "above" or the "ceiling" function is the sin(x), so we'll get the area under the curve by using "above" - "below" functions.
[tex]\stackrel{above}{sin(x)}~~ - ~~\stackrel{below}{cos^2(x)sin(x)} \implies sin(x)-[1-sin^2(x)]sin(x) \\\\\\ sin(x)-[sin(x)-sin^3(x)]\implies ~~\begin{matrix} sin(x)-sin(x) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ +sin^3(x)\implies sin^3(x)[/tex]
now let's use the triple angle identity of sine
[tex]\stackrel{\textit{triple angle identity}}{sin(3x)=3sin(x)-4sin^3(x)}\implies 4sin^3(x)=3sin(x)-sin(3x) \\\\\\ sin^3(x)=\cfrac{3sin(x)-sin(3x)}{4}\implies sin^3(x)=\cfrac{3}{4}sin(x)-\cfrac{1}{4}sin(3x) \\\\[-0.35em] ~\dotfill\\\\ \displaystyle\int\limits_{0}^{\pi }~sin^3(x)dx\implies \int\limits_{0}^{\pi }~\left[ \cfrac{3}{4}sin(x)-\cfrac{1}{4}sin(3x) \right]dx[/tex]
[tex]\displaystyle \cfrac{3}{4}\int\limits_{0}^{\pi }sin(x)dx-\cfrac{1}{4}\int\limits_{0}^{\pi }sin(3x)dx\implies \left. \cfrac{3}{4} \cdot -cos(x) \right]_{0}^{\pi }-\left. \cfrac{1}{4} \cdot \cfrac{-cos(3x)}{3} \right]_{0}^{\pi } \\\\\\ \cfrac{3}{2}~~ - ~~\cfrac{1}{6}\implies \implies \blacktriangleright \cfrac{4}{3} \blacktriangleleft[/tex]
Solve the following using inverse matrix also indicate the inverse matrix A-1 that was used to solve the system
7X+8Y=3
4X+6Y=-2
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Laura is a single taxpayer, she has $35,000 in ordinary taxable income and $5,000 in capital gains on an investment she held for 2 years. use the tables to complete the statement
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Going by the information given above, Laura is most likely going to belong to the tax bracket where the rate payable is 12%. This is because she is a single filer and her income is between $10,276 and $41,775.
What is a tax bracket?Tax brackets are a series of income and tax layers by which people are defined based on how much they earn per annum.
The tax rates range from 10% to 37%. The rate applicable to a person or group of persons depends on
whether or not they are singleIf married, whether they are filing jointly; andhow much their annual income is subject to deductibles.It is to be noted that a general answer was provided here due to insufficient details in the question.
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PLEASE HELPPP!!!!
Which of the following is the best buy?
3 lb. for $5.13
2 lb. for $3.37
3.25 lb. for $5.53
1.5 lb. for $2.52
Answers
Answer:
3.25\
Step-by-step explanation:
Answer:
$2.52
Step-by-step explanation:
u have to at the lb. and the $ and which will give u more for a less price so we x out $5.53 and then 5.13.now all you have left is 2.52 and 3.37 and 3.37 is more than 2.52 and 2 lb. is more ik but u save more money by buying 1.5 lb.
hope this helps:)!!
Which is the slope of the line that passes through the points (-3, 1) and (4, -2)?
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change in y/change in x
-2-1/4-(-3)
Write the Inequality shown in the diagram below
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Answer:
-1 ≤ x < 3
Hope this helps ;)
The scores of a recent test taken by 1200 students had an approximately normal distribution with a mean of 225 and a standard deviation of 18. determine the number of students who scored between 200 and 245
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If the probability will be 0.7842. Then the number of students who scored between 200 and 245 will be 941.
What is a normal distribution?The Gaussian Distribution is another name for it. The most significant continuous probability distribution is this one. Because the curve resembles a bell, it is also known as a bell curve.
The z-score is a statistical evaluation of a value's correlation to the mean of a collection of values, expressed in terms of standard deviation.
The scores of a recent test taken by 1200 students had an approximately normal distribution with a mean of 225 and a standard deviation of 18.
Then the number of students who scored between 200 and 245 will be
Then the z-score for x = 200
[tex]z = \dfrac{200-225}{18}\\\\z = -1.389[/tex]
Then the z-score for x = 245
[tex]z = \dfrac{245-225}{18}\\\\z = 1.1111[/tex]
Then we have
[tex]\begin{aligned} P(-1.39 < z < 1.11) &= P(z < 1.11) - P(z < -1.389)\\\\&= P(z < 1.11)- [1-P(z > -1.389)] \\\\&=0.8665 - (1-0.9177) \\\\&=0.7842 \end[/tex]
Then the number of students who scored between 200 and 245 will be
→ 0.7842 × 1200
→ 941.04 ≅ 941
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NEED HELPP ASAPP SOMEONE HELP
Answers
Answer:
[tex]\textsf{C)}\quad g(x)=\dfrac{1}{2}(x-8)^2-8[/tex]
Vertex = (8, -8)
Step-by-step explanation:
Standard form: [tex]y=ax^2+bx+c[/tex]
Vertex form: [tex]y=a(x-h)^2+k[/tex]
where (h, k) is the vertex
Intercept form: [tex]y=a(x-p)(x-q)[/tex]
where p and q are the x-intercepts
Therefore, the form that most quickly reveals the vertex is
[tex]g(x)=\dfrac{1}{2}(x-8)^2-8[/tex]
The vertex is (8, -8)
Another path in the community is 2.1 miles long. It also has benches at 1/3 and 2/3 of the distance from the beginning to the end of the path. How far in miles, is each from the beginning of the path?
PLEASE HURRY
Answers
Answer:
0.7 miles
1.4 miles
Step-by-step explanation:
Distance of the first bench from the path = 1/3 x 2.1 miles = 0.7 miles
Distance of the second bench from the path = 2/3 x 2.1 miles = 1.4 miles
What's the importance of statistics in real life
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Answer:
Statistics are incredibly important in real life. For example, we use statistics for weather forecasting. Probability (which is a form of statistics) is used by weather forecasters to figure out how likely it is that there will be rain, snow, sun, etc. on a given day in a certain area.
Step-by-step explanation:
'*•.¸♡ hope i helped, have a great day ♡¸.•*'
2 angles that are supplementary are always linear pair true or false?
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Answer: true
Step-by-step explanation: The answer is true. As a linear pair is a pair of adjacent, supplementary angles. Adjacent means next to each other, and supplementary means that the measures of the two angles add up to equal 180 degrees.
Answer:
true
Step-by-step explanation:
A spinner is divided into 15 identical sectors and labeled 1 through 15.
How many spins are expected for a multiple of 4 to be spun 30 times?
Select from the drop-down menu to correctly complete the sentence
The spinner is expected to have to spin approximately Choose times for a multiple of 4 to be spun 30 times.
A. 113
B. 120
C. 150
D. 225
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Find the slope between the two given points:
5. (3,4) and (6,7) 6. (-2,-6) and (-1,-4)
Please show Work Due Tommorow!!!!
I will give brainiest if it's right
Answers
Answer:
5.1 6.2
Step-by-step explanation:
5.y2-y1/x2-x1
7-4/6-1=1
6.y2-y1/x2-x1
-4+6/-1+2=2
#46 will give brainliest
Answers
Answer:
50
Step-by-step explanation:
This is the equation:
x = 5 + 3y
We know that:
x - y = 35
Meaning we only need to solve for y now:
(5 + 3y) - y = 35
5 + 2y = 35
2y = 30
y = 15
Meaning the final formula is
x = 5 + 3(15)
x = 50
Let's set some variables before we solve:
First number ⇒ xSecond number ⇒ yOkay's lets read the question
'x' is 5 more than three times 'y'⇒ [tex]x = 3y +5[/tex]
⇒ [tex]x-3y=5[/tex]
Their difference is 35⇒ [tex]x - y = 35[/tex]
Let's put the two equations together and solve
[tex]x-3y=5 --equation1\\[/tex]
[tex]x-y=35 -- equation2[/tex]
(equation2) - (equation1)
[tex]2y = 30\\y = 15 -- equation 3[/tex]
(equation 3)'s value of y into (equation2)
[tex]x - 15= 35\\x = 50[/tex]
Thus: [tex]x = 50[/tex] and [tex]y = 15[/tex]
The larger number is 50
Answer: 50 or Choice 3
Hope that helps!
Which is a graph of =3−1 y = 3 x - 1 ?
Answers
Answer:
The one on the top right
Step-by-step explanation:
first, look at the y-intercept:
two of the graphs (top-right and bottom-left) have the correct y-intercept of (0, -1).
(The y-intercept is 0 and then the last term of the equation in this form)
next, look at the slope:
slope is in the form of rise/run
the slope for this equation is 3, or 3/1
so look at the graphs, find the y-intercept point and go up three cells and over one.
Only one of the graph's lines goes through this point, and that is the top-left one
A recipe for bread uses 5 cups of white flour and 3 cups
of wheat flour. How many more cups of white flour than
wheat flour are used in the recipe? Write an equation and
complete the bar diagram to solve.
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The water usage at a car wash is modeled by the equation w(x) = 3x3 4x2 − 18x 4, where w is the amount of water in cubic feet and x is the number of hours the car wash is open. the owners of the car wash want to cut back their water usage during a drought and decide to close the car wash early two days a week. the amount of decrease in water used is modeled by d(x) = x3 2x2 15, where d is the amount of water in cubic feet and x is time in hours. write a function, c(x), to model the water used by the car wash on a shorter day. c(x) = 2x3 2x2 − 18x − 11 c(x) = 3x3 2x2 − 18x 11 c(x) = 3x3 2x2 − 18x − 11 c(x) = 2x3 2x2 − 18x 11
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A function, c(x), that models the water used by the car wash on a shorter day is C(x) = 4x³ + 7x² − 14x - 6
Calculations and Parameters:Given:
The amount of water used in normal days:
W(x) = 5x³ +9x²-14x +9 -----(i)The amount of decrease in water used is modeled by the equation;
D(x)= x³+2x² +15--------(ii)To find the function C(x), we would have to subtract eq(ii) from eq(i)
5x³ +9x²-14x +9
- x³+2x² +15
= C(x) 4x³+7x²-14x-6
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A piece rate worker is paid _____.
Answers
Answer:
The answer is on the quantity they produce per hour.
Step-by-step explanation:
If they produce more, they will be paid more, based on the rate per finished item
The stem-and-leaf plot shows test scores for students in Math 7. How many students earned more than a 65 on their test? Key 4|5 = 45 A) 58 students B) 28 students C) 60 students D) 65 students
Answers
Answer:
68 studentsStep-by-step explanation:
Count the number of scores greater than 65
60's ⇒ 8 (2 of 66, 4 of 68, 2 of 69)70's ⇒ 18 (4 of 72, 2 of 74, 2 of 75, 2 of 76, 2 of 78, 6 of 79)80's ⇒ 10 (2 of 81, 2 of 85, 2 of 86, 2 of 87, 2 of 88)90's ⇒ 22 (6 of 90, 2 of 92, 2 of 93, 2 of 94, 6 of 95, 2 of 98, 2 of 99)Total number is
8 + 18 + 10 + 10 + 22 = 68Note: none of answer choices reflect this
Answer:
68 student hope that helps
Find the values of x and y from the given equal ordered pair (2x, 3y) = (32,81)
Answers
Answer:
here,comparing the corresponding elements,
2x = 32 3y = 81
or x = 32/2= 16 or y = 81/3 = 27
x = 16
y = 27
i hope my answer is helpful to you and please mark me as brainliest
If rosetta sells her house and pays off the mortgage, how much should she receive (assuming there are no other costs associated with selling the house)? $42,000 $50,000 $52,000 $60,000
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Based on the amount that Rosetta sells her house and the mortgage she had before she did, the amount she will recieve is $50,000.
How much will Rosetta receive?Rosetta owes a total of $150,000 for her mortgage payment and was able to sell the house for $200,000.
This means that the amount she will recieve is:
= Selling price - Mortgage
= 200,000 - 150,000
= $50,000
In conclusion, option B is correct.
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Answer:
B. $50,000
Step-by-step explanation:
The diameter of a cylindrical construction pipe is 3 ft. If the pipe is 12 ft long,
what is its volume?
Use the value 3.14 for π, and round your answer to the nearest whole
number.
Be sure to include the correct unit in your answer.
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Work Shown:
d = 3 = diameter
r = d/2 = 3/2 = 1.5 = radius
h = 12 = height or length of the pipe
pi = 3.14 approximately
V = volume of the cylinder pipe
V = pi*r^2*h
V = 3.14*(1.5)^2*12
V = 84.78
V = 85
The cylindrical pipe's volume is about 85 cubic feet.
help ME solve please
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The area of a circle is 12.56 square kilometers. What is the circle's radius?
Answers
Answer:
[tex]r = 2km[/tex]
Step-by-step explanation:
Area =
[tex]area = \pi {r}^{2} [/tex]
[tex]12.56 = 3.14 \times {r}^{2} [/tex]
[tex] {r}^{2} = \frac{12.56}{3.14} [/tex]
[tex] {r}^{2} = 4[/tex]
[tex]r = \sqrt{4} [/tex]
[tex]r = 2km[/tex]
the average of two numbers is 41. If one of the numbers is 27, what is the other number?
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The other number if the average of two numbers is 41 and one is 27 is 55
How to calculate the average of numbers?Average of number is also known as the mean.
Let the unknown number be "x" such that:
x +27/2 = 41
Determine the value of x
x + 27 = 2(41)
x + 27 = 82
x = 82 - 27
x = 55
Hence the other number if the average of two numbers is 41 and one is 27 is 55
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A builder uses parallelogram-shaped stones as decoration around a building’s windows. The stones come in many different sizes. Each stone has a base length of x inches and a height of (3x − 5) inches. Write a polynomial to describe the area of a stone. Then find the area of a stone that has a length of 6 inches.
Answers
The polynomial that describes the area of the stone is: 3x² - 5x
Area of the stone with a base length of 6 in. is: 78 sq. in.
What is the Area of a Parallelogram?Area of Parallelogram = base length × height
Given the following:
Base length = x in.Height = (3x - 5) in.Area of the parallelogram-shaped stone = x(3x - 5) = 3x² - 5x
To find the area of the stone with a base length (x) of 6 inches, substitute x = 6 into 3x² - 5x:
Area = 3(6)² - 5(6) = 78 sq. in.
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1-4) Choose Yes or No to tell if the fraction 3/4 will make each equation true. (You are putting the 3/4 in each blank and multiplying to see if it will give you the product given.)
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2. No
3. Yes
4. Yes
Enter the solution (x, y) to the system of equations shown.
Answers
Answer:
(2, 5 )
Step-by-step explanation:
y = 2x + 1 → (1)
3y = 4x + 7 → (2)
substitute y = 2x + 1 into (2)
3(2x + 1) = 4x + 7 ← distribute parenthesis on left side
6x + 3 = 4x + 7 ( subtract 4x from both sides )
2x + 3 = 7 ( subtract 3 from both sides )
2x = 4 ( divide both sides by 2 )
x = 2
substitute x = 2 into (1) for corresponding value of y
y = 2(2) + 1 = 4 + 1 = 5
solution is (2, 5 )
Which equation represents a linear function?
Answers
Answer:
y = x-3
step by step explanation:
The equation of a linear function has no exponents higher than 1
On a coordinate plane, an exponential function decreases from quadrant 2 into quadrant 1 and approaches y = 0. it crosses the y-axis at (0, 4). what is the initial value of the exponential function shown on the graph? 0 1 2 4
Answers
Answer:
its 4
Step-by-step explanation:
trust me bro im a geinus
The initial value of the exponential function shown on the graph should be 4.
What is an exponential function?The exponential function represents a dependency relationship. In this type of mathematical operation there is a variable in the exponent and the real number in the base.
In this case, the exponential function is:
F(X)=Y
Knowing that the given points correspond to X=0 and Y= 4, when placing in the formula of the function, one finds:
F(0)=4
F(4)=0
So, the initial value of the exponential function shown on the graph should be 4.
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