Answer:
See belowStep-by-step explanation:
Part BAssumed the dimensions of the top and bottom parts are identical.
Since the cylindrical part has total height of 1.8 cm and the hemisphere volume is transferred to bottom part and the cone part is still full, the value of h is the difference of the total height of cylinder and full part of the top section of cylinder:
h = 1.8 cm - 0.3 cm = 1.5 cmPart CFind the volume of sand in the bottom part. It consists of a hemisphere and a cylinder of 1.5 cm height.
V(cylinder) = πr²h = 3.14*(2.6/2)²*1.5 ≈ 7.96 cm³V(hemisphere) = 2/3πr³ = 2/3*3.14*(2.6/2)³ ≈ 4.6 cm³Total sand in the bottom part:
7.96 + 4.6 = 12.56 cm³Time taken:
12.56 / 0.05 = 251.2 seconds = 4 min 11.2 secondsMarissa is painting her rectangular patio, with the exception of a bench that does not need to be painted:
rectangle with a length of x plus 15 and width of x plus 10 with a rectangle in the bottom right corner labeled bench that has a length of 5 and width of 1
Write an equation to determine the area, A, of the patio that will be painted.
A = (x + 20)(x + 11)
A = (x + 15)(x + 10) + 5
A = (x + 15)(x + 10) − 5
A = (x + 9)(x + 10)
The equation A = (x + 15)(x + 10) − 5 represents the area of the patio that will be painted, where A is the total area.
Option C is the correct answer.
We have,
The equation A = (x + 15)(x + 10) − 5 represents the area of the patio that will be painted.
The dimensions of the rectangular patio are given as (x + 15) for the length and (x + 10) for the width.
These values account for the extra length and width added to the original dimensions (x) to include the bench area.
To determine the total area of the patio that will be painted, we calculate the product of the length and width, which is (x + 15)(x + 10).
However, we need to subtract the area of the bench, which has a length of 5 and a width of 1.
Hence, we subtract 5 from the product to exclude the bench area.
Therefore,
The equation A = (x + 15)(x + 10) − 5 represents the area of the patio that will be painted, where A is the total area.
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Answer:
C
Step-by-step explanation:
i took the test :)
have a great day.!
The frequency distribution representing the number of frequent flier miles accumulated by employees at Brumley Statistical Consulting Inc. is repeated froFrequent Flier Miles (000) Frequency0 up to 3 53 up to 6 126 up to 9 239 up to 12 812 up to 15 2Total 50a. How many employees accumulated less than 3,000 miles?b. Convert the frequency distribution to a cumulative frequency distribution.c. Portray the cumulative distribution in the form of a cumulative frequency polygon.d. Based on the cumulative frequency polygon, about 75% of the employees accumulated how many miles or less?
Answer:
a. How many employees accumulated less than 3,000 miles?
The number of employees accumulated less than 3,000 miles= 5
So the number of employees accumulated less than 3,000 miles is 5.
d. Based on the cumulative frequency polygon, about 75% of the employees accumulated how many miles or less?
8.5 thousands of miles, found by starting at 75 percent on the vertical axis on the right, over to the polygon and then down to the horizontal axis.
Step-by-step explanation:
The given frequency distribution representing the number of frequent flier miles accumulated by the employees in a company.
Frequent Flier Miles (000) Frequency
0 up to 3 5
3 up to 6 12
6 up to 9 23
9 up to 12 8
12 up to 15 2
Total 50
a. How many employees accumulated less than 3,000 miles?
The number of employees accumulated less than 3,000 miles= 5
So the number of employees accumulated less than 3,000 miles is 5.
b. Convert the frequency distribution to a cumulative frequency distribution.
We make the cumulative frequency distribution from the frequency distribution by adding up a frequency and all other frequencies below it.
Frequent Flier Miles Frequency Cumulative frequency
0 up to 3 5 5
3 up to 6 12 17
6 up to 9 23 40
9 up to 12 8 48
12 up to 15 2 50
Total 50
d. Based on the cumulative frequency polygon, about 75% of the employees accumulated how many miles or less?
8.5 thousands of miles, found by starting at 75 percent on the vertical axis on the right, over to the polygon and then down to the horizontal axis.
What is the probability a student scored less than 75%. The μ=75 and the σ=10
P (x < 75) = ____ + _____ = ______
PLEASE FILL IN THE BLANKS!
On solving the provided question we can say that As a result, the probability of a student P(x < 75) = 75 + (-75 ) = 0 .
What is probability?Probability is a measure of how likely an event is to occur. It is represented by a number between 0 and 1, with 0 representing a rare event and 1 representing an inescapable event. Switching a fair coin and coin flips has a chance of 0.5 or 50% since there are two equally likely outcomes. (Heads or tails). Probabilistic theory is an area of mathematics that studies random events rather than their attributes. It is applied in many disciplines, including statistics, economics, science, and engineering.
z = (x - μ) / σ
z = (75 - 75) / 10 = 0
That is, a raw score of 75 equates to a z-score of 0.
P(z < 0) = 0.5
As a result, the likelihood of a student scoring less than 75% is 0 or 0%.
So, P(x < 75) = 75 + (-75 ) = 0
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Using lexicographic ordering of 4-sets, select the two inequalities that are both correct. O {2,1,4,5}<{1,16,67,4} {1,5,7,8}<{1,6,67,8} O {2,1,4,5}>{1,16,67,4} {1,5,7,8}<{1,6,67,8} O{2,1,4,5}<{1,16,67,4} {1,5,7,8}>{1,6,67,8} O {2,1,4,5}>{1,16,67,4} {1,5,7,8}>{1,6,67,8}
Using lexicographic ordering of 4-sets, the two correct inequalities are {2,1,4,5}<{1,16,67,4} {1,5,7,8}<{1,6,67,8}
Lexicographic ordering, also known as a dictionary or alphabetical order, is a method of comparing sequences of elements. In this case, we are comparing 4-sets. When comparing two sets, we start by comparing the first elements of each set. If they are equal, we proceed to compare the second element, and so on until we find a pair of elements that are different. The set with the smaller element at that position is considered smaller in lexicographic order.
1. In the first inequality, {2,1,4,5}<{1,16,67,4}, we can see that the first element of the first set (2) is greater than the first element of the second set (1). Therefore, the second set is smaller in lexicographic order, making the inequality correct.
2. In the second inequality, {1,5,7,8}<{1,6,67,8}, the first elements are equal (1). So, we proceed to compare the second elements. The second element of the first set (5) is smaller than the second element of the second set (6), so the first set is smaller in lexicographic order, making the inequality correct.
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creating and solving inequality
Answer:
I decided to take a picture since it was easier for me that way. Hope you don't mind. Oh and if my number line isn't clear, the answer is the first number line
A movie theater has a seating capacity of 257. The theater charges $5.00 for children, $7.00 for
students, and $12.00 of adults. There are half as many adults as there are children. If the total ticket
sales was $ 1870, How many children, students, and adults attended?
The attendance at the movie theatre is;
Children = 142
Students = 44
Adults = 71
What is arithmetic?
Arithmetic is an elementary part of mathematics that consists of the study of the properties of the traditional operations on numbers—addition, subtraction, multiplication, division, exponentiation, and extraction of roots.
Here, we have
Given:
Seating capacity = 257
Charges: Children = $5.00; Students = $7.00; Adults = $12.00
Total sales of ticket = $1870
A number of children, students, and adults were present in the theatre.
Let A, C, and S represent adults, children, and students respectively.
There are half as many adults as there are children; this means that
A = ½C
If the total seat capacity is 257, then
A + C + S = 257
Also, if the total sales of tickets are $1870, then
12A + 7S + 5C = 1870
So, we have two equations to be solved simultaneously.
A + C + S = 257 --- (1)
12A + 7S + 5C = 1860 --- (2)
Substitute ½C for A in (1) and (2)
½C + C + S = 257
Multiply both sides by 2
2(½C + C + S) = 2 * 257
C + 2C + 2S = 514
3C + 2S = 514 ----- (3)
12(½C) + 7S + 5C = 1870
6C + 7S + 5C ,= 1870
6C + 5C + 7S = 1870
11C + 7S = 1870 --- (4)
Make S the subject of the formula in (3)
2S = 514 - 3C
S = ½(514 - 3C)
S = 257 - 1.5C
Substituton 257 - 1.5C for S in (4)
11C + 7(257- 1.5C) = 1870
11C + 1799 - 10.5C = 1870
Collect like terms
11C - 10.5C = 1870 - 1799
0.5C = 71
Multiply both sides by 2
2 * 0.5C = 2 * 71
C = 142
Recall that
S = 257 - 1.5C
S = 257 - 1.5(142)
S = 257 - 213
S = 44
Also, recall that
A = ½C
A = ½ * 142
A = 71
Hence, the attendance at the movie theatre is;
Children = 142
Students = 44
Adults = 71
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an expression is given -2y+3/2x+7/4 which are equivelent to the given expression
The equivalent value of the expression is A = ( -16y + 12 + 7 ) / 8x
Given data ,
Let the equation be represented as A
Now , the value of A is
A = -2y+ 3/2x + 7/4
On simplifying , we get
A = ( -4y + 3 )/2x + 7/4
Taking LCM on both sides , we get
A = ( -16y + 12 + 7 ) / 8x
Hence , the expression is A = ( -16y + 12 + 7 ) / 8x
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At a local ballpark a team charges $10 per ticket the team must pay its players $4000 it costs the owner $6 for each souvenir they gave away how many tickets must be sold to break even
Answer:400
Step-by-step explanation:it didn’t say it gives away and souvenirs so the 6$ can be out the equation and 4000 divided by 10 is 400
The number of tickets that must be sold to break even is 1000 if at a local ballpark a team charges $10 per ticket the team must pay its players $4000.
What is linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
The question is incomplete.
The complete question is:
At a local ballpark, a team charges $10 per ticket. The team must pay its players $4000. It costs the owners $6 for each souvenir they give away.
How many tickets must be sold to break even.
Let x be the number of tickets.
Let y be the total cost
From the data given in the question we can frame the linear equation in two variables:
y = 6x + 4000
y = 10x
After solving the above two linear equations in two variables.
6x + 4000 = 10x
10x - 6x = 4000
4x = 4000
x = 1000
Thus, the number of tickets that must be sold to break even is 1000 if at a local ballpark a team charges $10 per ticket the team must pay its players $4000.
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Two girls divided $1.60 in the ratio 5 : 3. How much more does one girl get than the other?
let's convert those $1.60 to pennies, that's 160 pennies, now, let's divide those 160 by (5 + 3) and distribute between the girls accordingly
\(\stackrel{Girl1}{5}~~ : ~~\stackrel{Girl2}{3} ~~ \implies ~~ \stackrel{Girl1}{5\cdot \frac{160}{5+3}}~~ : ~~\stackrel{Girl2}{3\cdot \frac{160}{5+3}} ~~ \implies ~~ \stackrel{Girl1}{5\cdot 20}~~ : ~~\stackrel{Girl2}{3\cdot 20} \\\\\\ \stackrel{Girl1}{100}~~ : ~~\stackrel{Girl2}{60}\qquad \textit{one girl got \underline{40 more cents } than the other girl}\)
48+(-22) what’s the answer?.
Answer:
26
Step-by-step explanation:
A (+) and a (-) will always be a minus, so 48+(-22) becomes 48 - 22, which equals 26.
Answer:
26.
Step-by-step explanation:
48 - 22 = 26.
Will someone help me with this basic geometry?
The value of x in the right angle placed is equal to 16
Right AnglesA right angle is an angle that measures 90 degrees. It is the most commonly seen angle in our day-to-day life. It can be seen in the corners of a room, the edges of boxes, the screen of a mobile phone, and so on. The sides of a square and a rectangle always form a right angle with each other. In radians, it is represented as π/2. Let us discuss more about a right angle in this article.
A right angle is an angle of 90°. When two rays intersect and form a 90˚ angle or are perpendicular to each other at the intersection, they are said to form a right angle.
In the given question, we can set an equation and find the value of x
90 = 26 + 4x
Lets solve for x
4x = 90 -26
4x = 64
x = 16
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Which solution is the best estimate to the system of equations?{y=1/4x−2y=−2x+3 (0, −2)(1.5, 0)(2.2, −1.4)(0, 3)
given the equations,
y = 1/4x - 2
y = -2x + 3
the solution that best estimate the system equation is (2.2, -1.4)
that's the what the system would give from the graph
therefore that makes the third option the correct option which is (2.2, -1.4)
Somebody help me pls ♀️
1. The trigonometric ratios are given as follows:
Sine = opposite/hypotenuse.Cosine = adjacent/hypotenuse.Tangent = opposite/adjacent.2. The equation to solve for x is given as follows: sin(52º) = x/13.
3. Two equations to solve for m are given as follows:
n² + m² = l².m = square root (l² - n²).4. The length of the hypotenuse of the triangle is given as follows: 7.9 inches.
5. The lengths are given as follows:
BD = 4.3 cm.BC = 11.5 cm.What are the trigonometric ratios?The three trigonometric ratios are given as follows:
Sine of angle = length of opposite side divided by the length of the hypotenuse.Cosine of angle = length of adjacent side divided by the length of the hypotenuse.Tangent of angle = length of opposite side divided by the length of the opposite side.In the second problem, we have that the side x is opposite to the angle of 52º, while the hypotenuse is of 13, hence the equation to solve for x is given as follows:
sin(52º) = x/13.
In item 3, the Pythagorean Theorem is used to solve for m, as follows:
n² + m² = l².
m² = l² - n²
m = square root (l² - n²).
In item 4, we have that the angle opposite to the leg of length 7 inches is of 62º, hence the hypotenuse is given as follows:
sin(62º) = 7/h
h = 7/sin(62º)
h = 7.9 inches.
The length BD in item 5 is obtained as follows:
cos(30º) = BD/5
BD = 5 x cos (30º)
BD = 4.3 cm.
Then the length BC is calculated as follows:
sin(22º) = 4.3/BC
BC = 4.3/sin(22º)
BC = 11.5 cm.
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Miguel bought a shirt for $13.95, a pair of pants for $16.87, and a hat for $7.79. What was the total amount of money Miguel spent?
Answer:
they did not pay the same rate.
2 pairs for $50
50÷2=25
Miguel spent $25 on each pair of jeans
4 pairs for $90
90÷4=22.5
Han spent $22.50 on each pair of jeans
Therefore these two did not pay the same rate.
Step-by-step explanation:
Wanna chat add me as a friend OR COME TO Snap (ADAMBELAL839)
Answer:
38.61
Step-by-step explanation:
Each value added to gether to achieve your final value
11. If using the method of completing the square to solve
the quadratic equation x² + 13x - 32 = 0, which
number would have to be added to "complete the square"?
The number that needs to be added to complete the square is 169/4
The number to be added to "complete the square"?To complete the square for the quadratic equation x² + 13x - 32 = 0, we need to add (13/2)² = 169/4 to both sides.
This is because the coefficient of x in the quadratic term is 13, so half of that is 6.5, and the square of that is 42.25, which simplifies to 169/4.
The equation will then become:
x² + 13x - 32 + 169/4 = 0 + 169/4
So the number that needs to be added to complete the square is 169/4, or 42.25.
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Please help I can't stand word problems there are also more word problems in my account I need help with.
Answer:
15
Step-by-step explanation:
if you have them I'll be sure to answer 15 if it's on yours that's what I did for mine but everyone's questionnaire is different and that is where we need to multiply and divide them
It is always helpful to rewrite a quadratic equation in standard form as a first step in solving it.
A. FALSE
B. TRUE
Answer:
A
Step-by-step explanation:
Now when I think of solving it, I think of finding the zeros. Now if you start with the form, for example:
\((x+3)(x-3)\)
Then you can easily see the zeros are -3 and 3.
But if you start with the standard form:
\(ax^2+bx+c=0\\or\\x^2-9\)
It will be harder to find the zeros and you would do the eqation or factor it.
So if your in the factored form don't go to standard to find the zeros.
The given statement is False.
What is a quadratic equation?An equation with highest degree two, is considered as a quadratic equation.
In standard form, the right side of an equation should be 0 and every component on the left side should be 1.
For example, x² = 4; to express this in standard form, move the number 4 to the left side of the equation, resulting in x² - 4 = 0.
If you are asked to find x in this circumstance, there is no need to write the equation in standard form; simply take this same real number of both of the equation's sides to find x.
Hence, it is not always necessary to write the quadratic equation in standard form then solve.
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Write an integer to represent the situation.
paying a bill of $55
Answer:
I have 2
1)working for 2 hours and getting payed $55
2)you have $-55 in your bank
Step-by-step explanation:
The required integer that represents paying a bill of $55 would be "55".
What are Integers?Integers are defined as the collection of Whole Numbers Integers is represented by the symbol Z.
Integers are numbers that can be written without a fractional or decimal component, such as -3, -2, -1, 0, 1, 2, 3, and so on. They include the positive whole numbers (1, 2, 3, etc.), the negative whole numbers (-1, -2, -3, etc.), and zero.
We have to write an integer to represent the given situation.
As per the question, the integer represents the amount of money being paid in dollars.
Therefore, an integer that represents paying a bill of $55 would be "55".
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Professor A.B.C company opens his own company, Electronic Tutorial Services, and completes the following transactions in June:
6/1 A.B.C company invests 20,000 in the business.
6/3 Purchased 12,100 of equipment.
6/4 Paid 220 premium for an insurance policy.
6/6 Purchased office supplies on Account 140.
6/9 Purchased a new computer for 9,000. Paid 40% cash agreed to pay the remainder Later.
6/10 Billed student Omar 58 for tutorial services that were performed.
6/14 Paid for the supplies purchased on June 6th.
6/15 the owner suggested to purchased new Building for his company by 22,000
6/25 Received 85 cash from student Salim Ali for tutorial services performed.
6/30 Student billed on June 10 pays the amount due to A.B.C company.
6/30 A.B.C company withdraws 60 for personal use.
Required: Prepare the all Accounting Cycles
In June, A.B.C company invested $20,000, purchased equipment, paid insurance premium, bought office supplies, billed students for tutorial services, received cash, paid for supplies, withdrew personal funds.
Accounting Cycles:
1. June 1:
- A.B.C company invests $20,000 in the business.
- Prepare the journal entry:
- Debit: Cash ($20,000)
- Credit: Capital ($20,000)
2. June 3:
- Purchased equipment for $12,100.
- Prepare the journal entry:
- Debit: Equipment ($12,100)
- Credit: Cash ($12,100)
3. June 4:
- Paid $220 premium for an insurance policy.
- Prepare the journal entry:
- Debit: Insurance Expense ($220)
- Credit: Cash ($220)
4. June 6:
- Purchased office supplies on account for $140.
- Prepare the journal entry:
- Debit: Office Supplies ($140)
- Credit: Accounts Payable ($140)
5. June 9:
- Purchased a new computer for $9,000. Paid 40% in cash and agreed to pay the remainder later.
- Prepare the journal entry for the cash payment:
- Debit: Computer ($3,600) [40% of $9,000]
- Credit: Cash ($3,600)
- Prepare the journal entry for the remaining amount:
- Debit: Computer ($5,400)
- Credit: Accounts Payable ($5,400)
6. June 10:
- Billed student Omar $58 for tutorial services performed.
- Prepare the journal entry:
- Debit: Accounts Receivable ($58)
- Credit: Tutorial Services Revenue ($58)
7. June 14:
- Paid for the supplies purchased on June 6th ($140).
- Prepare the journal entry:
- Debit: Accounts Payable ($140)
- Credit: Cash ($140)
8. June 15:
- The owner suggested purchasing a new building for the company for $22,000.
- No journal entry is required at this point. It is a decision made by the owner.
9. June 25:
- Received $85 cash from student Salim Ali for tutorial services performed.
- Prepare the journal entry:
- Debit: Cash ($85)
- Credit: Accounts Receivable ($85)
10. June 30:
- Student billed on June 10 pays the amount due ($58).
- Prepare the journal entry:
- Debit: Cash ($58)
- Credit: Accounts Receivable ($58)
11. June 30:
- A.B.C company withdraws $60 for personal use.
- Prepare the journal entry:
- Debit: Withdrawals ($60)
- Credit: Cash ($60)
These transactions represent the accounting cycles for the given period.
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Harry is making cookies he needs one and 3/4 cup of flour for one batch but he wants to make one and a half batches right an equation that can be used to find how many cups of flour Harry will need.
Answer:
Step-by-step explanation:
1¾ cup/batch
1½ batches × 1¾ cup/batch = 1½×1¾ cups = 2⅝ cups
Answer: 2 5/8 cups of flour
Step-by-step explanation:
1 3/4 x 1 1/2 = 7/4 x 3/2 = 21/8 = 2 5/8 cups
PLEASE DO NOT BE NONSENSE
Answer:
7. 4- 4.5
8. 2- 4
9. 3- round 4 .94 then multiply by 7
10. 4-. 11.58
hope it helps (^^)# Cary on learningHow do I multiply a number and a half (3.5) with a whole number.
Answer:
Turn the decimal into a fraction and the whole number into a fraction
Step-by-step explanation:
Example: 7/2x56/1
find the value of X.
2+3x=62
3x=60
x=20
Hope this helps! Brainliest? :D
A scale drawing of Jacks living room is shown below. If each 2cm on the scale drawing equals 10 feet, what are the actual dimensions of the room. 4cm by 6cm
Answer:
Hope dis helps :> Have a great day
Step-by-step explanation:
Drawing : Actual
Scale
2 : 10
2 cm : 10 feet
Length
6 cm : 30 feet
Width
4 cm : 20 feet
The actual dimensions of the room are - Length=30 feet, Width=20 feet.
The answer is the second one.
what is the difference between -15-9?
Answer:
Step-by-step explanation:
-15-9 = -24
I would think about it as adding 15 and 9, but just make the answer negative.
A tank contains 5832 litres of water. Each day one-third of the water in the tank is removed and not replaced. How much water remains in the tank at the end of 6 days? [Hint: answer 512 litres] Show me the steps
Here is your answer.
A tank contains 5832 litres of water.
Total amount of water in tank = 5832 litres.
Each day one-third of the water in the tank is removed and not replaced.
Since one third of the water is removed for six days.
1st day = 1/3rd of 5832 litres is removed
\( = \dfrac{5832}{3} = 1944\)
Amount of water left = 5832 - 1944 = 3888 litres
2nd day = 1/3rd of 3888 litres is removed
\( = \dfrac{3888}{3} = 1296 \)
Amount of water left = 3888 - 1296 = 2592 litres
3rd day = 1/3rd of 2592 litres is removed
\( = \dfrac{2592}{3} = 864 \)
Amount of water left = 2592 - 864 = 1728 litres
4th day = 1/3rd of 1728 litres is removed
\( = \dfrac{1728}{3} = 576 \)
Amount of water left = 1728 - 576 = 1152 litres
5th day = 1/3rrd of 1152 litres is removed
\( = \dfrac{1152}{3} =384 \)
Amount of water left = 1152 - 384 = 768 litres
6th day = 1/3rrd of 768 litres is removed
\( = \dfrac{768}{3} = 256 \)
Amount of water left = 1768 - 256 = 512 litres
So, 512 litres water remains in the tank at the end of 6 days
Determine which of the following equations represents a circle with a real non-vero radius, a) x2 + y2 + 10x = -30
Given the equation of the circle ;
\(x^2+y^2+10x=-30\)Completing the square of the terms of x
so,
\(\begin{gathered} (x^2+10x+(\frac{10}{2})^2)+y^2=-30+(\frac{10}{2})^2 \\ \\ (x^2+10x+25)+y^2=-30+25 \\ \\ (x+5)^2+y^2=-5 \end{gathered}\)The general equation of the circle is :
\((x-h)^2+(y-k)^2=r^2\)Comparing the equations together :
\(\begin{gathered} r^2=-5 \\ \\ r=\sqrt[]{-5} \end{gathered}\)so, the given equation represents a circle with a non-real radius.
Select all the correct answers.
Brian set his compass equal to the radius of circle C and drew two circles centered at points A and B on circle C. He labeled the points of intersection of the two circles as shown.
To complete his construction, Brian only needs to use his straightedge to draw some chords of circle C.
Which figures could Brian be constructing?
equilateral triangle MNQ inscribed in circle C
equilateral triangle ANP inscribed in circle C
regular hexagon AMNBPQ inscribed in circle C
square MNPQ inscribed in circle C
square ANBQ inscribed in circle C
Answer: equilateral triangle ANP inscribed in circle C, regular hexagon AMNBPQ inscribed in circle C
Step-by-step explanation:
By looking through our choices, we can eliminate which choices could be wrong and which choices could be right.
Δ MNQ does form a triangle, however, it DOES NOT form a equilateral triangle.
Δ ANP does form a triangle and it is ALSO an equilateral triangle.
Hexagon AMNBPQ does form a hexagon and it is ALSO a regular polygon as we can see all the sides and angles within the polygon are congruent to one another.
MNPQ does form a quadrilateral, however, it DOES NOT form a square. It is instead a rectangle.
ANBQ does form a quadrilateral, however, it DOES NOT form a square. It is instead a rectangle.
A 65 ft. long swimming pool is to be constructed. The pool will be 4 ft. deep at one end and 11 ft. deep at the other. To the nearest degree, what will be the measure of the acute angle the bottom of the pool makes with the wall at the deep end
Answer:
Measure of the acute angle = 84°
Step-by-step explanation:
In the figure attached,
ABDE is a swimming pool having length 'AB' = 65 feet
Depth of one end of the pool is BE = 4 feet
And depth of the other end AD = 11 feet
Acute angle between the bottom of the pool (DE) and wall of the deep end (AD) is ∠ADE.
Now from ΔCDE,
tanx = \(\frac{EC}{DC}\)
tanx = \(\frac{7}{65}\)
x = \(\text{tan}^{-1}(\frac{7}{65})\)
x = 6.15°
Now measure of acute angle the bottom of the pool makes with wall at he deep end,
m∠ADE = (90 - 6.15)°
= 83.85°
≈ 84°
Find the missing side. 31° Z z = [?] Round to the nearest tenth. Remember: SOHCAHTOA 21
A²+B²= C²
31²+ 21²= z²
961+441 = z²
1402= z²
z= 37.443290454