Answers
In ∆ABC,
∠A = 60°∠B = 60°BC = 12 units∠BDC = 90°To Find :Area of ∆ABC = ?Solution :As, we have :
∠A = 60°∠B = 60°So, By angle sum property of triangle :
∠A + ∠B + ∠C = 180°
\( \tt : \implies 60\degree + 60\degree + \angle C = 180\degree\)
\( \tt : \implies 120\degree + \angle C = 180\degree\)
\( \tt : \implies \angle C = 180\degree - 120\degree\)
\( \tt : \implies \angle C = 60\degree\)
Now, we have :
∠A = 60°∠B = 60°∠C = 60°As, all angles are of same length, therefore it is a equilateral triangle.
We know that sides of equilateral triangle are equal.
\( \tt : \implies AB = BC = AC\)
Now, we have BC = 12 units.
Hence, all sides are of 12 units.
Now, we know that area of equilateral triangle is :
\( \large \underline{\boxed{\bf{Area_{(equilateral \: triangle)} = \dfrac{\sqrt{3}}{4} side^{2}}}}\)
\( \tt : \implies Area = \dfrac{\sqrt{3}}{4} \times (12 \: units)^{2}\)
\( \tt : \implies Area = \dfrac{\sqrt{3}}{\cancel{4}} \times \cancel{144} \: units^{2}\)
\( \tt : \implies Area = \sqrt{3} \times 36 \: units^{2}\)
\( \tt : \implies Area = 36\sqrt{3} units^{2}\)
So, Area of given triangle is 36√3 units².
Related Questions
What is the mean absolute deviation of the following data: 61, 63, 64, 68, 70, 76 ROUND TO THE NEAREST HUNDREDTH Single line text.
Answers
Answer:
4.33 infinity.
Step-by-step explanation:
The infinity should just be a line over the 3's
Answer:
4.33
Step-by-step explanation:
First, find the mean value.
Mean = 67
61 - 67 = |-6| = 6
63 - 67 = |-4| = 4
64 - 67 = |-3| = 3
68 - 67 = 1
70 - 67 = 3
76 - 67 = 9
Add: 6 + 4 + 3 + 1 + 3 + 9/6 = 4.33333333333
4.33333333333 rounded to the nearest hundredth = 4.33
Can some one solve 4 for me plz I’ll give a crown
Answers
Answer: I'm pretty sure it's the 3rd one
Step-by-step explanation:
The value of 4 : 40.01 is
Answers
Answer:
Sunglower I really want to help, but personally I do not know the answer, but if this answer is going percentage wise, the answer would be 1.6004
if multiple events have a 20% probability, what is the chance that two or more will happen simultaneously
Answers
The probability of two or more events happening simultaneously is 0.36.
The probability of two or more events happening simultaneously depends on the number of events and the type of relationship between them. If the events are independent, meaning that the occurrence of one event does not affect the probability of the other event happening.
The probability of two or more events happening simultaneously can be calculated using the formula for the sum of probabilities:
P(A or B) = P(A) + P(B) - P(A and B)
Where A and B are two events. If we have n independent events with the same probability of 20%, the probability of two or more events happening simultaneously can be calculated as follows:
P = 1 - P(none of them happen) = 1 - (1 - 0.2)ⁿ
For n = 2, we have:
P = 1 - (1 - 0.2)² = 1 - 0.64 = 0.36
So, the chance that two events with a 20% probability will happen simultaneously is 36%. The chance for three or more events is even higher.
It's important to note that if the events are dependent, the calculation will be different. The relationship between the events can significantly impact the final probability.
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The radius of a circle is 3 kilometers. What is the circle's circumference?
r=3 km
Use 3.14 for л.
Answers
Raoul is y years old . Kayla is 6 years older than raoul and lsaac is 4 years younger than raoul find kaylas age
Answers
Answer:
20
Step-by-step explanation:
Let Kayla's age be k.
Let Isaac's age be a.
Kayla is 6 years older than Raoul. This means that:
k = y + 6
lsaac is 4 years younger than Raoul. This means that:
a = y - 4
y = 12
=> k = 12 + 6 = 18
and
a = 12 - 4 = 8
The sun of Raoul's age and Isaac's age is:
12 + 8 = 20
does 3:3 or any full ratio equal 1:1?
Answers
Answer:
yes
_____________________________
you can look at 3:3 as 3/3 which is 1
and 1:1 = 1/1 which is also 1
the ratio sign also means divide.
_____________________________
hope this helps :)
A tank and a pail contained a total of 962 ml of water. When 250 ml of water was poured from the pail to the tank, the amount of water in the tank was 12 times the amount of water in the pail. How much water did the pail contain at first?
Answers
By solving a system of equations, we will see that the pail originally contained 382.9 ml.
How to write the system of equations?
First, we need to define the variables, we will use:
T = amount of water in the tank.P = amount of water in the pail.First, we know that the total amount of water is 962 ml, then we have:
P + T = 962 ml.
We also know that if we pour 250 ml from the pail to the tank, the amount of water in the tank will be 12 times the amount of water in the pail, this is written as:
T + 250ml = 12*(P - 250ml)
Then the system of equations is:
P + T = 962 ml
T + 250ml = 12*(P - 250ml)
To solve this, first, we need to isolate one of the variables in one of the equations, I will isolate T in the first one:
T = 962 ml - P
Now we replace this into the other equation to get:
(962 ml - P) + 250ml = 12*(P - 250ml)
Now we can solve this for P.
962 ml + 250 ml - P = 12*P - 12*250 ml
1,212 ml - P = 12*P - 3,000 ml
1,212 ml + 3,000 ml = 12*P - P
(4,212 ml)/11 = P = 382.9 ml
So the pail originally contained 382.9 ml
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qs 14-18 determining components of costs of goods manufactured
Answers
Cost of Goods Manufactured is an accounting term used to describe the total cost of producing and manufacturing goods. It includes all direct and indirect costs of production, including labor, materials, overhead, and other expenses. Below are the five components of the cost of goods manufactured.
Direct Materials: It includes the cost of raw materials used in manufacturing a product.
Direct Labor: It includes the wages paid to workers who directly worked on the production line or in manufacturing a product.
Factory Overhead: It includes all indirect costs of manufacturing a product such as depreciation on equipment, rent, insurance, utilities, etc. Work-in-Process
Inventory: It includes the cost of materials, labor, and overhead that has been incurred but has not yet been completed. Finished Goods Inventory: It includes the cost of goods that have been fully manufactured but have not yet been sold.
To calculate the cost of goods manufactured, the sum of all these five components is calculated. It helps manufacturers to determine the total cost of goods manufactured and the cost per unit of production. Cost of goods manufactured is essential in determining the pricing strategy for a product as it helps to ensure that the product is profitable.
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Xander is planning on building a house. The blueprints show a house that is 3 inches wide and 2 inches tall. The blueprints use a scale in which 14 inch represents 2 feet.
How wide and tall will the actual house be?
Drag and drop the height and width of the actual house into the boxes.
Answers
Answer:
16ft tall and 24ft wide
Step-by-step explanation:
Answer:
16ft 24ft
Step-by-step explanation:
i got the same qestion and its correct.
5. If the solution of an equation is a = -2, what could the original equation be?
-
OA. x+6=8
OB. x-6-8
O c. x+8 = 6
OD x 8-6
HELP PLEASEEEE
Answers
Answer:
C
Step-by-step explanation:
x + 8 = 6
x = 6-8
x = -2
.....
Evaluate the expression when x = 9.
x + 5(x + 2)
Answers
Answer:
64
Step-by-step explanation:
x + 5(x + 2)
Distribute
x + 5x+10
Combine like terms
6x+10
Let x = 9
6(9) +10
54+10
64
Answer:-10/13
Step-by-step explanation:
Please answer in an hour! You will get a thumbs up.
Question 1 (a)
Assume you purchase a new tractor on Jan 1, 2022 for a cost of $200,000. You estimate you will be able to use the tractor for 10 years, and it will have a salvage value of 10% of the original by the end of its useful life. Determine the book value at the end of the first year (December 31, 2022) using straight-line depreciation.
options:
$18,000
$180,000
$185,000
$182,000
Question 1 (b)
A balance sheet (using current and noncurrent assets and liabilities- no intermediate) shows that a farmer has current assets of $80,000 and owner equity of $100,000. Her current ratio is 2 and her debt/equity ratio is 1.0. Determine the farmer's noncurrent liabilities.
Question 1 (b) options:
$40,000
$60,000
$100,000
unable to determine
Answers
Question 1a
To calculate the book value at the end of the first year using straight-line depreciation, we need to determine the annual depreciation expense first. The straight-line method assumes that the asset depreciates by an equal amount each year over its useful life. Therefore, we can use the following formula to calculate the annual depreciation:
Annual Depreciation = (Cost - Salvage Value) / Useful Life
Substituting the given values, we get:
Annual Depreciation = ($200,000 - $20,000) / 10 years = $18,000 per year
This means that the tractor will depreciate by $18,000 each year for the next 10 years.
To determine the book value at the end of the first year, we need to subtract the depreciation expense for the year from the original cost of the tractor. Since one year has passed, the depreciation expense for the first year will be:
Depreciation Expense for Year 1 = $18,000
Therefore, the book value of the tractor at the end of the first year will be:
Book Value = Cost - Depreciation Expense for Year 1
= $200,000 - $18,000
= $182,000
So the book value of the tractor at the end of the first year, December 31, 2022, using straight-line depreciation is $182,000. so the answer is D
Question 1(b)
To determine the farmer's noncurrent liabilities, we need to use the information provided to calculate the total liabilities and then subtract the current liabilities from it. Here's the step-by-step solution:
Calculate the total current liabilities using the current ratio:
Current Ratio = Current Assets / Current Liabilities
2 = $80,000 / Current Liabilities
Current Liabilities = $80,000 / 2
Current Liabilities = $40,000
Calculate the total liabilities using the debt/equity ratio:
Debt/Equity Ratio = Total Liabilities / Owner Equity
1.0 = Total Liabilities / $100,000
Total Liabilities = $100,000 * 1.0
Total Liabilities = $100,000
Subtract the current liabilities from the total liabilities to get the noncurrent liabilities:
Noncurrent Liabilities = Total Liabilities - Current Liabilities
Noncurrent Liabilities = $100,000 - $40,000
Noncurrent Liabilities = $60,000
Therefore, the farmer's noncurrent liabilities are $60,000. so the answer is B.
A backpack that normally sells for $39 is on sale for $25. Find the
percent of change.
Answers
Answer: To find the discount, simply multiply the original selling price by the %discount:
ie: 39 x 33/100= $12.87
So, the discount is $12.87.
Step-by-step explanation: To find the sale price, simply minus the discount from the original selling price:
ie: 39- 12. 87= 26.13
So, the sale price is $26.13
what is the mass of x divided by 12
Answers
The value of expression is,
⇒ x ÷ 12
We have to given that;
The algebraic expression is,
⇒ x divided by 12
Hence, We can formulate;
The value of correct expression is,
⇒ x ÷ 12
⇒ x / 12
Thus, The value of expression is,
⇒ x ÷ 12
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Can someone help me with this math homework please!
Answers
Answer:
1/2
8
Step-by-step explanation:
When its talking about the result or output, look at the range, and then follow the line(s) back to the number(s) in the domain. Do the opposite when it's talking about the function of a certain number, e.g. f(4).
40 plus what equals 180
Answers
Answer:
140
Step-by-step explanation:
180 - 40 = 140
reverse operations
140 + 40 = 180
Applying algebra and assuming the unknown value is x, we can determine that 40 plus 140 equals 180.
How to Apply Algebra?To solve the equation "40 plus what equals 180," we can use algebraic notation. Let's denote the unknown value as "x." The equation can be represented as:
40 + x = 180
To find the value of x, we can isolate it on one side of the equation by performing the same operation on both sides. In this case, we subtract 40 from both sides:
40 + x - 40 = 180 - 40
x = 140
Therefore, 40 plus 140 equals 180.
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Suppose that five adjacent imperfections are located on a fiber.
(a) What is the distribution of the distance between the first imperfection and the fifth imperfection
Answers
Therefore, if the distance between adjacent imperfections follows an exponential distribution, we can model the distance between the first and fifth imperfections as the sum of five independent exponential random variables.
To determine the distribution of the distance between the first imperfection and the fifth imperfection, we need more information about the nature of imperfections on the fiber and their distribution. Different imperfections can have different distributions depending on the underlying process or mechanism that produces them. Without specific information about the distribution of imperfections, it is difficult to determine the exact distribution of the distance between the first and fifth imperfections.
However, if we assume that the imperfections are randomly distributed along the fiber, we can make an approximation. In this case, we can assume that the distance between adjacent imperfections follows a Poisson distribution.
The Poisson distribution is commonly used to model the number of events occurring in a fixed interval of time or space, given a known average rate of occurrence. If we assume that imperfections occur randomly with a certain average rate (λ) per unit distance along the fiber, then the distance between imperfections follows an exponential distribution.
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Please help me with this Geometry Question
Answers
The value of x from the given figure is 12 units.
What are similar triangles?Two triangles are similar if the angles are the same size or the corresponding sides are in the same ratio. Either of these conditions will prove two triangles are similar.
From the given figure,
Consider ΔADC and ΔABC,
∠C=∠C (Reflex property)
AC=AC (Reflex property)
∠BAC=∠CDA=90°
By AA similarity, ΔADC ~ ΔABC
So, AC/BC = DC/AC
x/36 = 4/x
x²=36×4
x²=144
x=12 units
Therefore, the value of x from the given figure is 12 units.
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x − y = 4
x − 2y = 10
Solve the following system using the elimination method.
Answers
Answer:
\(x - y = 4 \\ - ( x - 2y) = 10 \\ y = - 6 \\ \\ x - ( - 6) = 4 \\ x + 6 = 4 \\ x = - 2\)
check
\( - 2 - ( - 6) = 4 \\ - 2 + 6 = 4 \\ \\ - 2 - 2( - 6) = 10 \\ - 2 + 12 = 10\)
Answer:
(-2,-6)
Step-by-step explanation:
we have the two equations
x - y = 4 and x - 2y = 10
Notice how both equations have 1x.
This means that we can subtract the two equations, leaving us with a single variable ( because the 1x would cancel out ), we could then solve for that variable. This is known as the elimination method.
so subtract the two equations
x - y = 4
-(x -2y = 10) ( remove parenthesis and apply negative sign )
x - y = 4
-x +2y = -10
-------------------
y = -6
Now that we have found the value of y we simply plug in the value of y into one of the equations and solve for x.
x - y = 4
y = -6
x - (-6) = 4
remove parenthesis and change sign
x + 6 = 4
Subtract 6 from both sides
x = -2
We can conclude that the solution to the system of equations is (-2,-6)
3(x - 2) + 2 = 5(x - 3) + 9 por fa
Answers
Answer:
x = 1
Step-by-step explanation:
Given
3(x - 2) + 2 = 5(x - 3) + 9 ← distribute and simplify both sides
3x - 6 + 2 = 5x - 15 + 9
3x - 4 = 5x - 6 ( subtract 5x from both sides )
- 2x - 4 = - 6 ( add 4 to both sides )
- 2x = - 2 ( divide both sides by - 2 )
x = 1
Section 3: Translate from English into the language of Propositional Logic. Use the letters provided to stand for simple propositions.
17. Stacy will come with us to see the Gauguin exhibit only if Angelina and Jane don’t both go. (S, A, J)
18. If diamonds are not precious stones, then neither are sapphires. (D, S)
Section 5: Test the following arguments for validity using either the direct or
indirect truth-table method.
34. G ⊃ H / R ≡ G / ~H v G // R • H
Answers
The argument is valid. The argument is valid based on the direct truth-table method.
To test the validity of the argument, we can use the direct truth-table method. Let's break down the argument and construct the truth table for the given premises and the conclusion:
Premises:
G ⊃ H
R ≡ G
~H v G
Conclusion:
R • H
Constructing the truth table:
We have three propositions: G, H, and R. Each proposition can have two truth values, true (T) or false (F). Therefore, we need 2^3 (8) rows in the truth table to evaluate all possible combinations.
By evaluating the truth table, we find that in all rows where the premises (1, 2, 3) are true, the conclusion (R • H) is also true. There is no row where the premises are true, but the conclusion is false. Therefore, the argument is valid.
The argument is valid based on the direct truth-table method. This means that if the premises (G ⊃ H, R ≡ G, ~H v G) are true, then the conclusion (R • H) must also be true.
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The graph of f passes through (-2,7) and is perpendicular to the line whose equation is x= -16.
The equation of the function is
Answers
Answer:
y = 7
Step-by-step explanation:
x = -16 is a vertical line.
All lines perpendicular to a vertical line are horizontal lines. All horizontal lines have a slope of 0
so m = 0, y = 7, x = -2
y = mx + b
7 = 0(-2) + b
b = 7
so,
y = 0x + 7
y = 7
can you please help me
Answers
Answer:
C.
Step-by-step explanation:
Hi there!
To answer this, we must set it up as
\(3x(2x^4-12x^2+7)\)
Now we just use the distributive property to solve.
this becomes \(6x^5-36x^3+21x\)
I hope this helps!
Which is the simplified version of:
7x + 12 + 3x = -6 (x - 7) + 9x
A. 5x = -30
B. 7x = -54
C. 7x = 30
D. 7x = -19
PLEASE DON’T GUESS :(
Will mark brainliest if your rightƪ(˘⌣˘)ʃ
Answers
Answer:
The answer is letter D
Step-by-step explanation:
Answer:
7x+3x=10x
-6(x-7)= -6x+42
then 10x+12=-6x+42+9x
10x+12=3x+42
10-3=42_12
7x=30
then the correct answer is C
Warren wants to buy grass seed to cover his whole lawn, except for the pool. the pool is 5 3/4m by 3 1/2m. find the area the grass seed needs to cover
find the area the grass seed needs to cover
Answers
Grass Seed Area = L - 20 1/8
To help Warren determine the area of his lawn where grass seed is needed, we first need to know the total area of his lawn.
Unfortunately, you have not provided the dimensions of the entire lawn. However, I can guide you through the process using the information given about the pool.
First, let's find the area of the pool. The dimensions are 5 3/4m by 3 1/2m. To find the area, multiply the length by the width:
Area = (5 3/4) * (3 1/2)
Convert the mixed numbers to improper fractions:
Area = (23/4) * (7/2)
Multiply the fractions:
Area = (23*7) / (4*2) = 161/8
Now convert the improper fraction back to a mixed number:
Area = 20 1/8 square meters
This is the area of the pool. To find the area where grass seed is needed, subtract the pool's area from the total area of the lawn. Assuming the total area of the lawn is "L" square meters, the area to be covered with grass seed would be:
Grass Seed Area = L - 20 1/8
Once you provide the dimensions of the entire lawn, you can follow these steps to find the area where grass seed is needed.
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please help asap!!!look at the box
Answers
Answer:
y
Step-by-step explanation:
The sum of the interior angles of a regular pentangon
Answers
Answer:
540
Step-by-step explanation:
ARCHITECTURE The Pentagon in Washington, D.C. is shaped like a regular pentagon. Find the sum of the measures of the interior angles of the largest pentagon-shaped section of the Pentagon building. = 180(3) or 540 Simplify. The sum of the measures of the interior angles is 540.
Given a polynomial and one of its factors, find the remaining factors of the polynomial.
x^3+7x^2+7x-15 : x-1
Answers
Answer:
i think, im not sure
Step-by-step explanation:
options?.:
x=1
x=−3
x=−5
Your answer should be x^2 + 8x + 15
What i the equation of a line that i parallel to the line y =2x 7 and pae through the point -2,4
Answers
The equation of a line y=2x+8.
The equation of a straight line can be represented in the slope-intercept form, y = mx + c
Where c = intercept
Slope, m =change in the value of y on the vertical axis/change in the value of x on the horizontal axis
Looking at the given line,
y = 2x + 7
Compared with the slope-intercept equation,
Slope, m = 2
If a line is parallel to another line, it means that both lines have equal or the same slope. This means that the slope of the line passing through the point (-2, 4) is 2
Substituting m= 2, y = 4 and x = -2 into the equation, y = mx + c , it becomes
4 = 2 × - 2 + c
4 = - 4 + c
c = 4 + 4 = 8
The equation becomes y=2x+8.
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