Answers
= 34 degrees
Related Questions
please help! (listing BRAINLIST and giving points) :)
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Answer:
(a) = 60
(b) = 70
Step-by-step explanation:
(a) Sum of all the angles of a triangle is 180
This is an equilateral Triangle
which means all the sides are equal since all the sides are equal that means all the angles are equal
[tex]x + x + x = 180 \\ 3x = 180 \\ x = \frac{180}{3} \\ x = 60[/tex]
(b) this is an isosceles triangle with two equal sides that means the two opposite angles are equal
[tex]40 + x + x = 180 \\ 40 + 2x = 180 \\ 2x = 180 - 40 \\ 2x = 140 \\ x = 70[/tex]
Kern Shipping Inc. has a requirement that all packages must be such that the combined length plus the girth (the perimeter of the cross section) cannot exceed 99 inches. Your goal is to find the package of maximum volume that can be sent by Kern Shipping. Assume that the base is a square.
a. Write the restriction and objective formulas in terms of x and y. Clearly label each.
b. Use the two formulas from part (a) to write volume as a function of x, V(x). Show all steps.
Answers
Answer:
Step-by-step explanation:
From the given information:
a)
Assuming the shape of the base is square,
suppose the base of each side = x
Then the perimeter of the base of the square = 4x
Suppose the length of the package from the base = y; &
the height is also = x
Now, the restriction formula can be computed as:
y + 4x ≤ 99
The objective function:
i.e maximize volume V = l × b × h
V = (y)*(x)*(x)
V = x²y
b) To write the volume as a function of x, V(x) by equating the derived formulas in (a):
y + 4x ≤ 99 --- (1)
V = x²y --- (2)
From equation (1),
y ≤ 99 - 4x
replace the value of y into (2)
V ≤ x² (99-4x)
V ≤ 99x² - 4x³
Maximum value V = 99x² - 4x³
At maxima or minima, the differential of [tex]\dfrac{d }{dx}(V)=0[/tex]
[tex]\dfrac{d}{dx}(99x^2-4x^3) =0[/tex]
⇒ 198x - 12x² = 0
[tex]12x \Big({\dfrac{33}{2}-x}}\Big)=0[/tex]
By solving for x:
x = 0 or x = [tex]\dfrac{33}{2}[/tex]
Again:
V = 99x² - 4x³
[tex]\dfrac{dV}{dx}= 198x -12x^2 \\ \\ \dfrac{d^2V}{dx^2}=198 -24x[/tex]
At x = [tex]\dfrac{33}{2}[/tex]
[tex]\dfrac{d^2V}{dx^2}\Big|_{x= \frac{33}{2}}=198 -24(\dfrac{33}{2})[/tex]
[tex]\implies 198 - 12 \times 33[/tex]
= -198
Thus, at maximum value;
[tex]\dfrac{d^2V}{dx^2}\le 0[/tex]
Recall y = 99 - 4x
when at maximum x = [tex]\dfrac{33}{2}[/tex]
[tex]y = 99 - 4(\dfrac{33}{2})[/tex]
y = 33
Finally; the volume V = x² y is;
[tex]V = (\dfrac{33}{2})^2 \times 33[/tex]
[tex]V =272.25 \times 33[/tex]
V = 8984.25 inches³
Here are the population figures of five different cities. 371,265 635,155 226,710 468,920 724,435 What is the difference between the largest population and the smallest population?
Answers
Answer:
497,725
just subtract smallest from largest to get the difference
724,435 - 226,710
Answer:
largest population 724,435Smallest population 226,710Use the order of operations to simplify the expression
(5.4)² - 5.4²
Answers
Answer:
0
Step-by-step explanation:
(5.4)^2 - 5.4^2
= 5.4^2 - 5.4^2
= 5,4^2(1 - 1)
= 5.4^2(0)
= 0
The pyramid shown below has a square base, a height of 7, and a volume of 84 cubic units.
What is the length of the side of the base?
12
36
6
18
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Which system of equations can be used to find the roots of the equation 4x2 = x3.
ly=-4x²
ly=x²+2x
(y = x² - 4x² + 2x
»
O
ly=0
0
o y
Jy = 4x²
Lva-x-2x
ly=44²
ly=x²+2x
o
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Answer:
The second answer
Y=X³-4X²+2X
Y=0
The system of equations can be used to find the roots of the given equation is y = 4x², y = x³+2x
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
For example, 3x – 5 = 16 is an equation.
Given is an equation, 4x² = x³+2x, we need to identify the system of equations can be used to find the roots of this,
An equality can be transformed in a system of equations by making each side equal to a new variable. In this case the variable y was made equal to each side.
See that may find the solution of such system by graphing both functions in a same coordinate system, where the intersection of the functions would show the solution of the system.
The attached image. In such graph, the red curve is the function y = x² and the blue function is y = x³ + 2x.
The intersection point is (0,0) meaning that the solution is x = 0, y = 0.
Hence, the system of equations can be used to find the roots of the given equation is y = 4x², y = x³+2x
Learn more about equations, click;
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question : Suppose you have VND 100 million to save orspend. If you lend, you will receive 112 million after a year. Inflation is 14% / year.
a. What is the nominal interest rate you get?
b. What is the real interest rate?
c. Should you save or spend that money?
d. Question (c) how will be answered if inflation is 10% / year, nominal interest rates do not change?
Answers
Answer:
Step-by-step explanation:
The company has only two division division eight and division be last year division a made 60% of the companies total revenue and division be made 40% of the total revenue this year division as revenue has decreased by 35% and division bees revenue has decreased by 5% which division had higher revenue this year?
Answers
9514 1404 393
Answer:
Division A
Step-by-step explanation:
Suppose last year's revenue for the company was 100 units.
Last year's Division A revenue was 0.60×100 = 60. This year's revenue is 1-35% = 65% of last year's, so is ...
60 × 0.65 = 39 . . . . units
__
Last year's Division B revenue was 0.40×100 = 40. This year's revenue is 1-5% = 95% of last year's, so is ...
40 × 0.95 = 38 . . . . units
__
At 39 units this year, Division A still has the higher revenue than Division B at 38 units.
help answer please help
Answers
Answer:
The best was to display a set of data with a wide range would be
a histogram.
Step-by-step explanation:
It's a graphical display of bars which will help you measure the central tendency.
Which of the following values could be an absolute value?
Answers
Answer:
Step-by-step explanation: It could be 8,7, or 2. Because these are all positive
:)
Levers are not a problem in the mechanical system. But, if you put two different simple machines that do not cooperate, they will be able to make the question that you need to. T or F
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Answer:
True
Step-by-step explanation:
I am assuming that you are asking if two different simple machines that do not cooperate will work or not.
The answer to that is True.
Two things that do not work together will not work together. The two simple machines can not work with each other.
So, the answer is True. Best of Luck!
Three consecutive integers have a sum of 30. Which equation can be used to find x, the value of the smallest of the three numbers? (x + 1) + (x + 2) = 30 x + (x + 1) + (x + 2) = 30 x (x + 1) (x + 2) = 30 3 x (x + 1) (x + 2) = 30
Answers
Answer:
X+(X+1)+X+2)=30
Step-by-step explanation:
Find the length of the third side. If necessary, round to the nearest tenth.
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Answer: 14.4
Step-by-step explanation:
Which inequality has the solution shown below?
-18 -17 -16 -15 -14 -13 -12
Answers
Answer:
0.2x+5>2
Step-by-step explanation:
0.2 is the same as 2/10;
(2/10)x>2-5
(2/10)x>-3
2x>-30
X>-15( since -15 is lesser than -14,-13,-12 and so on. the sign should be >
Please help a girl out, math is not my forte
Answers
Answer:
80 ft²
Step-by-step explanation:
You are given the formula
a = (1/2)bh
Just plug in the base and height, then multiply
a = (1/2) * 8 *20
a = (1/2) * 160
a = 80 ft²
Answer:
80 [tex]ft^{2}[/tex]
Step-by-step explanation:
Area = [tex]\frac{1}{2} bh[/tex]
Area = [tex]\frac{1}{2}[/tex] 8 · 20
Area = [tex]\frac{1}{2}[/tex] 160
Area = 80 [tex]ft^{2}[/tex]
[tex] {x}^{2} + \sqrt{x} + \sqrt[5]{x} [/tex]
what is f'(3) of this equation?
Answers
Answer:
[tex]3 + \frac{1}{2\sqrt{3} } + \frac{1}{5\sqrt[5]{81} }[/tex]
Step-by-step explanation:
Just to make it easier to see, [tex]\sqrt{x} = x^{\frac{1}{2} }[/tex] and [tex]\sqrt[5]{x} = x^{\frac{1}{5} }[/tex] This way we could more easily use the power rule of derivatives.
So if f(x) = [tex]x^{2} +x^{\frac{1}{2} } +x^{\frac{1}{5} }[/tex] then f'(x) will be as follows.
f'(x) = [tex]x^{1} +\frac{1}{2} x^{-\frac{1}{2} } +\frac{1}{5} x^{-\frac{4}{5} } = x +\frac{1}{2x^{\frac{1}{2} }} +\frac{1}{ 5x^{\frac{4}{5} }} = x +\frac{1}{2\sqrt{x}} +\frac{1}{ 5\sqrt[5]{x^4} }[/tex]
to find f'(3) just plug 3 into f'(x) so [tex]3 + \frac{1}{2\sqrt{3} } + \frac{1}{5\sqrt[5]{81} }[/tex]
A license plate begins with three letters. If the possible letters are A, B, C, D and E, how many different permutations of these letters can be made if no letter is used more than once?
Answers
Answer:
60 different permutations of these letters can be made.
Step-by-step explanation:
Permutations formula:
The number of possible permutations of x elements from a set of n elements is given by the following formula:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]
How many different permutations of these letters can be made if no letter is used more than once?
3 letters from a set of 5. So
[tex]P_{(5,3)} = \frac{5!}{(5-3)!} = \frac{5!}{2!} = 5*4*3 = 60[/tex]
60 different permutations of these letters can be made.
PLEASE HELP ME!!! I need to simplify these equations, not answer them.
Answers
Answer:
Step-by-step explanation:
a= 2qr^3 quotent 6p^2
7) Point P is located at (4,8) on a coordinate plane. Point P will be relfected over y = x. What will bee
the coordiantes of the image of point P?
A. (28,4)
B. 24,8)
C. (4,28)
D. (8,4)
Answers
Answer to the question?
Answers
Answer:
35
Step-by-step explanation:
AEC and AEB form a straight angle(180°)
180-40=140
AEV and AED are equal
140 divided by 4 = 35
The Centers for Disease Control and Prevention Office on Smoking and Health (OSH) is the lead federal agency responsible for comprehensive tobacco prevention and control. OSH was established in 1965 to reduce the death and disease caused by tobacco use and exposure to secondhand smoke. One of the many responsibilities of the OSH is to collect data on tobacco use. The following data show the percentage of U.S. adults who were users of tobacco for a recent 11-year period
Year Percentage of Adults Who Smoke
1 22.9
2 21.7
3 21
4 20.3
5 20.3
6 19.9
7 19.4
8 20.7
9 20.7
10 19
11 18.8
What type of pattern exists in the data?
Use simple linear regression analysis to find the parameters for the line that minimizes MSE for this time series. Do not round your interim computations and round your final answers to three decimal places. For subtractive or negative numbers use a minus sign. (Example: -300)
y-intercept, b0 =
Slope, b1 =
MSE =
One of OSH’s goals is to cut the percentage of U.S. adults who were users of tobacco to 12% or less within nine years of the last year of these data. Does your regression model from part (b) suggest that OSH is on target to meet this goal?
Use your model from part (b) to estimate the number of years that must pass after these data have been collected before OSH will achieve this goal. Round your answer to the nearest whole number.
years.
Answers
Answer:
1.) A negative linear pattern
2.) Y = - 0.298X1 + 22.241
3.) slope = - 0.298 ; intercept = 22.241
Kindly check explanation
Step-by-step explanation:
Fitting the time series data using technology, the regression equation obtained is :
Y = - 0.298X+ 22.241
Where ; y = percentage of adults who smoke
x = year
Comparing with the linear equation model :
y = b1x + b0
y = - 0.298x + 22.41
-0.298 = slope
22.41 = intercept
The mean squared error, MSE = 0.512
To achieve, percentage users of 12% or less :
y = 12
Y = - 0.298X+ 22.241
12 = - 0.298X + 22.241
12 - 22.241 = - 0.298X1
-10.241 = - 0.298X
X = 10.241 / 0.298
X = 34.365
X = 35 years
From the model OSHA is not on target to meet it's goal as it will take 35 - 11 = 24 years from the last year of the data to achieve a smoker percentage less Than 12%
Let f(x)=x2+10x+37 .
What is the vertex form off(x)?
What is the minimum value off(x)?
Enter your answers in the boxes.
Vertex form: f(x)=
Minimum value of f(x):
Answers
Answer:
f(x) = (x+5)^2 +12
The minimum value is 12
Step-by-step explanation:
f(x)=x^2+10x+37
The vertex will be the minimum value since this is an upwards opening parabola
Completing the square by taking the coefficient of x and squaring it adding it and subtracting it
f(x) = x^2+10x + (10/2) ^2 - (10/2) ^2+37
f(x) = ( x^2 +10x +25) -25+37
= ( x+5) ^2+12
Th is in vertex form y = ( x-h)^2 +k where (h,k) is the vertex
The vertex is (-5,12)
The minimum is the y value or 12
Write the simplified expression that represents the perimeter of the triangle below.
X - 3
4x + 4
2x + 1
Show Work
Answers
Answer:
Just plus everything together
X-3+4X+4+2X+1
Step-by-step explanation:
The radius of a circle is 10 cm. Find its circumference in terms of \piπ.
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[tex]{ \bf{ \underbrace{Given :}}}[/tex]
Radius of the circle "[tex]r[/tex]" = 10 cm.
[tex]{ \bf{ \underbrace{To\:find:}}}[/tex]
The circumference of the circle.
[tex]{ \bf{ \underbrace{Solution :}}}[/tex]
[tex]\sf\orange{The\:circumference \:of\:the\:circle\:is\:20\:π\:cm.}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]
We know that,
[tex]\sf\purple{Circumference\:of\:a\:circle \:=\:2πr }[/tex]
[tex] = 2 \: \pi \times 10 \: cm \\ \\ = 20 \: \pi \: cm[/tex]
Therefore, the circumference of the circle is 20 π cm.
[tex]\huge{\textbf{\textsf{{\orange{My}}{\blue{st}}{\pink{iq}}{\purple{ue}}{\red{35}}{\green{♡}}}}}[/tex]
The retail cost of a TV is 50 % more than its wholesale cost. Therefore, the retail cost is ____ times the wholesale cost.
Answers
Answer:
Let the retail cost be x and the wholesale cost be y
Step-by-step explanation:
x = y + 0.50y
x = 1.50y
Therefore the retail cost is 1.50 times the wholesale cost.
33. Given the following algebraic expression 5x² + 10 Which statement is true?
a. The coefficient is 5
b. The constant is 2
C. The power is 10
d. The constant is 5
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Answer:
Given the following algebraic expression 5x² + 10 Which statement is true?
a. The coefficient is 5. ( true)
b. The constant is 2
C. The power is 10
d. The constant is 5
hope this helps
The amount of bleach a machine pours into bottles has a mean of 36 oz. with a standard deviation of 0.55 oz. Suppose we take a random sample of 56 bottles filled by this machine. So, 75% of the sample means will be less than what value
Answers
Answer:
0.9836
Step-by-step explanation:
Determine the value of x.
Answers
The answer to this question is B) 44.78
Answer:
Step-by-step explanation:
x = 44.78
A ramp is in the shape of a triangle
Answers
Answer:
Step-by-step explanation:
Is this the correct answer?
Answers
Answer:
Correct.
Step-by-step explanation:
It looks good to me.
Good job!
