Answers
Given the rectangle ABCD, you can identify that it is divided into two Right Triangles:
[tex]\begin{gathered} \Delta ACD \\ \Delta ABD \end{gathered}[/tex]• You can find the length of the rectangle by applying the following Trigonometric Function:
[tex]\cos \alpha=\frac{adjacent}{hypotenuse}[/tex]In this case, you can set up that:
[tex]\begin{gathered} \alpha=30\degree \\ adjacent=CD=AB=l \\ hypotenuse=AD=9 \end{gathered}[/tex]Then, substituting values and solving for "l", you get:
[tex]\begin{gathered} \cos (30\text{\degree})=\frac{l}{9} \\ \\ 9\cdot\cos (30\text{\degree})=l \\ \\ l=\frac{9}{2}\sqrt[]{3}ft \end{gathered}[/tex]• In order to find the width of the rectangle, you can use this Trigonometric Function:
[tex]\sin \alpha=\frac{opposite}{hypotenuse}[/tex]In this case, you can say that:
[tex]\begin{gathered} \alpha=30\degree \\ opposite=AC=BD=w \\ hypotenuse=AD=9 \end{gathered}[/tex]Therefore, substituting values and solving for "w", you get:
[tex]\begin{gathered} \sin (30\degree)=\frac{w}{9} \\ \\ 9\cdot\sin (30\degree)=w \\ \\ w=\frac{9}{2}ft \end{gathered}[/tex]• Now you need to use the following formula for calculating the area of a rectangle:
[tex]A=lw[/tex]Where "l" is the length and "w" is the width.
Substituting the length and the width of the given rectangle into the formula and evaluating, you get:
[tex]A=(\frac{9}{2}\sqrt[]{3}ft)(\frac{9}{2}ft)[/tex][tex]A\approx35.1ft^2[/tex]Hence, the answer is: Option C.
Related Questions
Please answer correctly and explain how you got it please don't have but it would help.
Answers
Answer: Linear
Step-by-step explanation:
Each time [tex]x[/tex] increases by [tex]1[/tex], [tex]y[/tex] decreases by [tex]8[/tex]. Since the value of y changes at a constant rate, the relationship is linear.
Does anyone understand this geometry question
Answers
Answer:
This is an isosceles right triangle, so
x = 45°.
P(6, -3); y =1/2 x + 2
Write an equation for the line in point-slope form.
Answers
Equation for the line in point-slope form is 5x + 6y = 6.
What is point slope form?The equation of a straight line that passes through a particular point and is inclined at a specific angle to the x-axis can be found using the point slope form.
Given Data
P(6, -3)
y =1/2 x + 2
When the equation has been solved for y, the line in slope intercept form with slope = m = 1/2 = the coefficient of the x term is represented by the equation y= (1/2)x + 2. 2 represents the y coordinate of the location (0, 2) where the line intersects the y axis as the y intercept.
So, the points are (6,-3) and (0,2)
Formula
y₂ - y₁ = m(x₂ - x₁)
slope of the line (m) = [tex]\frac{x-x}{y-y}[/tex]₁¹
m= [tex]\frac{2-(-3)}{0-6}[/tex]
m = -[tex]\frac{5}{6}[/tex]
Equation
y- (-3) = -[tex]\frac{5}{6}[/tex](x- 6)
y +5 = -[tex]\frac{5}{6}[/tex]x + 6
y + 5 = -[tex]\frac{5+36 }{6}[/tex]
6y + 30 = -5x + 36
5x + 6y = 6
Equation for the line in point-slope form is 5x + 6y = 6.
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Please explain the steps you would take to solve this derivative (gr 12 calc)
Answers
First step, derivative of the constant:
[tex]f^{\prime}(x)=\frac{1}{2}\frac{d(e^{-3x^2+tan(3x+5)})}{dx}[/tex]Second step, the chain rule:
[tex]\begin{gathered} =\frac{1}{2}e^{-3x^2+tan(3x+5)}*\frac{d(-3x^2+tan(3x+5))}{dx} \\ =\frac{1}{2}e^{-3x^2+tan(3x+5)}*\frac{(-6x+sec^2(3x+5)*3)}{} \end{gathered}[/tex]Where we applied that the derivative of tangent is the secant^2.
Hence the answer is:
[tex]\frac{1}{2}e^{-3x^2+tan(3x+5)}*\frac{(-6x+3sec^2(3x+5))}{}[/tex]Which expression is equivalent to the given expression? \frac{\left(ab^{2}\right)^{3}}{b^{5}}
Answers
The expression which is equivalent to the given expression; (ab²)³/b⁵ as given in the task content is; a³b.
Which expression is equivalent to the given expression; (ab²)³/b⁵ as in the task content?It follows from the task content that the expression which is equivalent to; (ab²)³/b⁵ be determined.
Hence, since the given expression is; (ab²)³/b⁵.
By first applying the power of power law of indices; we have;
(ab²)³/b⁵ = a³b⁶/b⁵.
Also, by applying the quotient of powers rule of indices; we have;
a³ b^(6 - 5)
= a³b¹
= a³b
Ultimately, the expression which is equivalent to; (ab²)³/b⁵ as required in the task content is; a³b.
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HELP ME WITH IS PROBLEM THANK YOU
Answers
The given algebraic expression would be equivalent to the expression [tex]\dfrac{1}{4(x)^\frac{2}{9} }[/tex] which is the correct answer would be an option (B)
What is the algebraic expression?Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.
The given algebraic expression is:
[tex](64x^{\frac{2}{3} })^{-\frac{1}{3} }[/tex]
Apply the property of a⁻ˣ = 1/aˣ in the above term,
[tex]\dfrac{1}{ (64x^{\frac{2}{3} })^{\frac{1}{3} }}[/tex]
Here 64 = 4×4×4 = 4³
[tex]\dfrac{1}{ (4^3x^{\frac{2}{3} })^{\frac{1}{3} }}[/tex]
Apply the cube root property and Multiply the exponent of the variable x to 1/3
[tex]\dfrac{1}{ 4x^{\frac{2}{3} }^\times^{\frac{1}{3} }}[/tex]
Apply the multiplication operation to the exponent of the variable x to get the solution.
[tex]\dfrac{1}{4(x)^\frac{2}{9} }[/tex]
Hence, the correct answer would be an option (B)
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From the diagram below, if the sides AD = 3 and DC = 27, and BD = X + 3, find x.
Answers
Given:
• AD = 3
,• DC = 27
,• BD = x + 3
Let's solve for x.
To solve for x, apply the altitude formula:
[tex]\frac{AD}{BD}=\frac{BD}{DC}[/tex]Where BD is the altitude.
Cross multiply:
[tex]BD^2=AD*DC[/tex]Plug in the values and solve for x:
[tex]\begin{gathered} (x+3)^2=3*27 \\ \\ (x+3)^2=81 \end{gathered}[/tex]Take the square root of both sides:
[tex]\begin{gathered} \sqrt{(x+3)^2}=\sqrt{81} \\ \\ x+3=9 \\ \\ \text{ Subtract 3 from both sides:} \\ x+3-3=9-3 \\ \\ x=6 \end{gathered}[/tex]Therefore, the value of x is 6 .
ANSWER:
d. 6
1. What is the domain of the graph?84-8O{x | -3 SXS3)all real numbers{x | xs-3 or x 2 3}y 1-3 sy s 3)
Answers
From the graph below, the domain is
[tex]x\colon\text{ x }\leq\text{ -3 or x }\ge\text{ 3}[/tex]5 Guess my rule: X Y 1 9 IN min OUT
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1) Looking at that table, we can pick the points
(1,9) (3,23)
2) Note that every time x increases by 2 units y increases by 14
3) Considering this a linear function we can find the rule by plugging in
23-9/3-1=14/2 = 7
9=7(1)+b
9=7 +b
2 =b
So we can write the rule as y =7x+2
how much money must be loaned to receive 15,000 if the money is loaned for 5 years at 12% interest
Answers
Step-by-step explanation:
i don't know if this is right
Write the equation of the perpendicular bisector of XY if endpoint X is at (-9,1) and endpoint Y is at (3,5). A) y = -X B) y = 3x - 6 C) y = -3x - 6 D) y = 3x + 12
Answers
A perpendicular bisector is a segment which intersects another segment on its midpoint and with a right angle.
First, we have to find the midpoint between X(-9,1) and Y(3,5), as follows
[tex]\begin{gathered} M=(\frac{-9+3}{2},\frac{1+5}{2}) \\ M=(\frac{-6}{2},\frac{6}{2}) \\ M=(-3,3) \end{gathered}[/tex]This means the perpendicular bisector must pass through (-3,3). Now, with the given points we find the slope of XY
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{5-1}{3-(-9)}=\frac{4}{3+9}=\frac{4}{12} \\ m=\frac{1}{3} \end{gathered}[/tex]Then, we apply the rule of perpendicularity to find the slope of the perpendicular bisector.
[tex]\begin{gathered} m_1\cdot m=-1 \\ m_1=\frac{-1}{m} \\ m_1=-\frac{1}{\frac{1}{3}}=-3 \end{gathered}[/tex]Now, we use the slope-point formula to find the equation for the perpendicular bisector.
[tex]y-y_1=m(x-x_1)[/tex]Where we replace the slope -3 and the point (-3,3).
[tex]\begin{gathered} y-3=-3(x-(-3)) \\ y-3=-3x-9 \\ y=-3x-9+3 \\ y=-3x-6 \end{gathered}[/tex]Therefore, the right answer is C.Find the mean, mode, and range Mean_______ show all workRange_______show all workExplain how you find thisMode_________
Answers
To answer this question, it is a good practice to order the data in ascending order as follows:
[tex]9,\: 10,\: 10,\: 10,\: 10,\: 11,\: 11,\: 11,\: 11,\: 11,\: 11,\: 12,\: 12,\: 12,\: 12,\: 12,\: 13,\: 13,\: 13,\: 14,\: 14,\: 15,\: 15,\: 15,\: 15,\: 15,\: 15,16,17,17[/tex]We need to check for the total number of data. In this case, we have 30 observations.
Finding the meanTo find the mean, we need to find the sum of all the observations and then divide this result by the total of observations (30). Then, we have:
[tex]\frac{9+\: 10+\: 10+10+\: 10+\: 11+\: 11+\: 11+\: 11+\: 11+\: 11+\: 12+\: 12+\: 12+\: 12+\: 12+\: 13+\: 13+\: 13+\: 14+\: 14+15+\: 15+\: 15+15+15+_{}15+16+17+17}{30}[/tex]Then, the value for the mean is:
[tex]\text{mean}=\frac{382}{30}=12.73333333\ldots[/tex]Finding the rangeThe range is the result of subtracting the greatest number and the lowest number in the data:
[tex]\text{Range}=17-9=8[/tex]Finding the modeThe mode is the observation that is repeated the most (appears the most).
We can see that we have two values that appear six times in the list: 11 and 15.
Therefore, we can see that there is not a unique element, so there is no mode.
In summary, we have:
• Mean = 12.73333...
,• Range = 8
,• Mode = None.
Predict the amount of tips that would be collected if 100 customers were served at the restaurant on a given day Explain your reasoning. Answer is $178 explain your answer thank you! 40 points if answered correctly!!
Answers
Answer:
$194.69
Step-by-step explanation:
The best way to predict the amount of tips is using this formula:
[tex]100(\frac{Tips(total)}{Customers(total)} )[/tex]
This finds the average tip per customer with all of the data, and multiplies it by 100 to get the predicted amount of tips for 100 customers.
Plugging in the data from the table gives you this equation:
[tex]100(\frac{1174}{603} )[/tex]
This equals $194.69.
Please help!
The volume of a sphere is 36 in³. What is the surface area?
Answers
Answer:
Step-by-step explanation:
V = 4/3.pi.r^3
36 = 4/3 pi r^3
8.6 = r^3
r = 2 in
---------------------
Area of sphere :
A = 4.pi.r^2
A = 4 . Pi . 2^2
A = 16 Pi
A = 50.26 in
45. Write an inequality that represents the graph. Explain it step by step please.
Answers
Answer: x < -4
Step-by-step explanation:
➜ First thing we notice is the open circle. This means we will use either < or >
➜ The next thing we notice is that the values are pointing to the left of the circle, this means we will be using <
➜ The last part we notice is that the dot is on -4. This is the value we'll use to write our inequtliy.
The last thing to do is to write the inequality using the parts we pointed out above:
x < -4
what is 4x-2=3(x-3)
Answers
4x -2 = 3(x-3)
4x - 2 = 3x - 9
bring like terms together
4x-3x = -9 +2
x = -7
I need help with this question but no one is helping me! Can someone please help me
Answers
Answer:
the probability is 2/8
Step-by-step explanation:
A tank has 120 gallons of water and is being drained at a rate of 1/2
gallon each second. Another tank has 100 gallons of water and is being drained at a rate of 1/4
gallon each second. Which equation could be used to determine x, the number of seconds, when the two tanks have the same amount of water?
Answers
It will take 80 seconds for both tank 1 and tank 2 to have the same amount of water
Water in the tank 1 = 120 gallons
Drainage rate of tank 1 = 1/2 gallon each second
Water in tank 2 = 100 gallons
Drainage rate of tank 2 = 1/4 gallon each second
Let x represent the number of seconds it will take for both tanks to have the same amount of water
Formulating the equation we get the following:
Water in tank 1 - Drainage rate of tank 1*x = Water in tank 2 - Drainage rate of tank 2*x
120 - 1/2x = 100 - 1/4x
20 = 1/2x - 1/4x
20 = 1/4x
x = 80
So, it will take 80 seconds
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Describe a series of transformations Matt can perform to decide if the two windows are congruent
Answers
Answer:
See below
Step-by-step explanation:
Rotate rectangle A 90 ° clockwise with the center being the lower right hand corner. Then translate down and right until rectangle A in over rectangle B
Jenny is designing a pen for a cow in the shape of a right triangle. Because of space limitation on the farm, the first side of the pen should measure 10 feet and form a right angle with the second side, which should be 14 feet long. How many feet of fencing does Jenny need to make the whole pen? Round to the nearest tenth.
Answers
Answer:
70
Step-by-step explanation:
14 x 10 is 140.
Since a triangle is just half a square, we multiply the two sides we have and then divide it.
140 ÷ 10 = 70.
Answer = 70.
P.S If it is correct, pls give Brainliest, thanks!
Prime Factorization
(See attachment for more info)
Thank you.
Answers
Daniyar paid his April FlashCard bill in full. His May bill shows an average daily balance of $270.31 and a monthly periodic rate of 1.65%. What is the finance charge on Daniyar's May statement?
Answers
The finance charge on Daniyar's May statement is $4.45.
What is finance charge?
The cost of consumer credit expressed as a dollar amount is the financing charge. It includes any fee imposed by the creditor as an incident to or a requirement of the credit extension that is directly or indirectly payable by the customer. It excludes any fee that would be paid in an equivalent cash transaction.
The finance charge is equal to the product of the average daily balance and the monthly periodic rate.
So,
$270.31 x 1.65%
= $270.31 x 0.0165
= $4.45
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help
A) What is true about each multiple of 3 other than that it is a multiple of 3?
B) What is true about each number with a factor of 7 other than that it is a factor of 7?
Answers
Every other multiple of 3 is even.
The answer is 7. Seven is a prime number, which means that its multiples are 1 and itself (7): 7 = 1 * 7
The digits in multiples of 3 add up to a multiple of 3 (36 = 3 + 6, 111 = 1 + 1 + 1, etc.) All EVEN multiples of 3 are also a multiple of 6 (the even multiples of 3 are the 6 “count by's”).
The answer is 7. Seven is a prime number, which means that its multiples are 1 and itself (7): 7 = 1 * 7. To find out which one is a factor of 7, we should divide each of them by 7. 1/7 will be a decimal number and 7/7 = 1, which is a whole number. Thus, 7 will be a multiple of 7 and also a factor of 7.
A whole number higher than 1 whose only elements are 1 and itself is referred to as a prime number. A whole number that may be split evenly into another number is referred to as a factor. 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29 are the first few prime numbers. Composite numbers are those that have more than two components.
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Kubin Company’s relevant range of production is 18,000 to 22,000 units. When it produces and
sells 20,000 units, its average costs per unit are as follows:
Required:
1. Assume the cost object is units of production:
a. What is the total direct manufacturing cost incurred to make 20,000 units?
b. What is the total indirect manufacturing cost incurred to make 20,000 units?
2. Assume the cost object is the Manufacturing Department and that its total output is 20,000 units.
a. How much total manufacturing cost is directly traceable to the Manufacturing Department?
b. How much total manufacturing cost is an indirect cost that cannot be easily traced to the
Manufacturing Department?
3. Assume the cost object is the company’s various sales representatives. Furthermore, assume
that the company spent $50,000 of its total fixed selling expense on advertising and the
remainder of the total fixed selling expense comprised the fixed portion of the company’s
sales representatives’ compensation.
a. When the company sells 20,000 units, what is the total direct selling expense that can be
readily traced to individual sales representatives?
b. When the company sells 20,000 units, what is the total indirect selling expense that
cannot be readily traced to individual sales representatives?
4. Are Kubin’s administrative expenses always going to be treated as indirect costs in its internal
management reports?
Answers
For 18000 units the calculated sum is $150,000.
The following are the company's production and period costs:
The product costs $ 350,000 for 20,000 units.
20,000 units = $150,000 in cost period
The product costs $ 385,000 for 22,000 units.
18,000 units each period = $ 135,000
The corporation incurs two major costs while creating an item: production costs and period costs.
Production costs are expenses directly connected to the manufacturing process. These expenses include labor, raw materials, and overhead.
While period costs are expenses incurred for the company's activities such as administrative and selling/sales charges,1. The cost of making 20,000 units is
Existing unit manufacturing costs are as follows:
Direct labor costs $7.00. Manufacturing variable overhead of $4.00 Fixed manufacturing overhead of $1.50 $ 5.00
Total product cost per unit = $7.00 + $4.00 + $1.50 + 5.00 = $17.5
So, for 20,000 units, the calculation is: 20,000 x $17.5 = $350,000
The time required to produce 20,000 units is
Each unit's cost period is as follows:
$ 3.50 in fixed selling expenses, $ 2.50 in fixed administration expenses, and $ 1.00 in variable administrative expenses.
Total period cost per unit = $ 3.5+ $ 2.5+ $ 1.00+ $ 0.5 = $ 7.5
So, for 20,000 units, the calculation is: 20,000 x $ 7.5 = $150,000
The cost of making 22,000 units is
Existing manufacturing costs per unit: $ 17.5
So, for 20,000 pieces, the cost is 22,000 x $17.5 = $ 385,000
The total period cost / unit for generating 18,000 units is $ 7.5.
So, for 18,000 units, the calculation is: 18,000 x $ 7.5 = $ 135,000
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Two buses leave Dallas at the same time traveling in opposite directions. One bus travels at 59 mph and the other at 54 mph. How soon will they be 791 miles apart?
Answers
Let t be the time, in hours, elapsed till the buses are 791 miles apart, then we can set the following equation:
[tex]59mph\cdot t+54\text{mph}\cdot t=791\text{ miles.}[/tex]Solving the above equation for t we get:
[tex]\begin{gathered} 113\text{ mph}\cdot t=791miles, \\ t=\frac{791}{113}\text{hours,} \\ t=7\text{ hours.} \end{gathered}[/tex]Answer: 7 hours.
six times the sum of four and a number is 7. what is the number?
Answers
Step-by-step explanation:
6×(4 + x) = 7
24 + 6x = 7
6x = -17
x = -17/6 = -2.833333333... = -2 5/6
What is the length of a rope if the mass of a rope is 4.25
Answers
Using a regression calculator, the line of best fit for the given set of data is:
[tex]y=0.34121x+0.168088[/tex]where y = mass of the rope and x = length of the rope.
To estimate the length of the rope if its mass is 4.25 kilograms, let's replace "y" in the equation above with 4.25, and then solve for x.
[tex]4.25=0.34121x+0.168088[/tex]Subtract 0.168088 on both sides of the equation.
[tex]4.25-0.168088=0.34121x+0.168088-0.168088[/tex][tex]4.081912=0.34121x[/tex]Then, divide both sides of the equation by 0.34121.
[tex]\frac{4.081912}{0.34121}=\frac{0.34121x}{0.34121}[/tex][tex]\begin{gathered} 11.963049=x \\ 11.96\approx x \end{gathered}[/tex]Therefore, the length of the rope having a mass of 4.25 kilograms is approximately 11.96 meters.
What system of linear inequalities is shown in the graph?
Enter your answers in the boxes.
Answers
Answer: [tex]y < \frac{1}{3}x+2, y < -2x+2[/tex]
Step-by-step explanation:
The equations of the lines are [tex]y=\frac{1}{3}x+2[/tex] and [tex]y=2-2x[/tex].
Since the line [tex]y=\frac{1}{3}x+2[/tex] has a dotted boundary and is shaded below, it represents the inequality [tex]y < \frac{1}{3}x+2[/tex].
Since the line [tex]y=2-2x[/tex] has a dotted boundary and is shaded below, it represents the inequality [tex]y < 2-2x[/tex].
PLEASE HURRY ASAP PLEASE HURRY
The value of a stock decreases by an average of 10 dollars each week. Which of the following represents the total average decrease in the stock after 8 weeks?
Answers
The stock witness an total average decrease in stock of $80 in the 8 weeks
How to determine the total average decrease in the stockThe given parameters are:
Average decrease per week = 10 dollars
Also, we have the number of weeks to be
Number of Weeks = 8 weeks
So, the total average decrease in the stock is calculated using the following equation
Total = Average decrease per week x Number of weeks
Substitute the known values in the above equation
So, we have the following equation
Total = 10 x 8
Evaluate the products in the above equation
So, we have the following equation
Total = 80
Hence, the total average decrease in the stock is $80
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vinny has decided to order high tops in black and white at a 5.8 ratio. he beleives he will need a total of 169 pairs. how many black high tops will he order
Answers
Answer:
65 pairs
Step-by-step explanation:
Black makes up 5/(5+8) = 5/13 of the total order, so ...
(5/13)(169 pairs) = 65 pairs
Vinny will order 65 pairs of black high tops.