Answers
The unknown angle of the triangle is as follows:
∠BCE = 65 degrees
How to find the angle of a triangle?A triangle is a polygon with three sides. The sum of angles in a triangle is 180 degrees.
Therefore, the angle ∠BCE can be found as follows:
∠BAC = 70 degrees
∠ABC = 60 degrees
∠ACB = 180 - 70 - 60
∠ACB = 180 - 130
∠ACB = 50 degrees
Hence, using exterior angle theorem,
The exterior angle theorem states that the measure of an exterior angle is equal to the sum of the measures of the two remote interior angles of the triangle.
∠BCD = 60 + 70 = 130 degrees
Hence,
∠BCE = 130 / 2 = 65 degrees
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Related Questions
2. Construct Arguments Explain why -7 has a
greater absolute value than the absolute value
of 6.
5.-9
7.1-5
9. --
11.-1
Answers
Answer:
See below
Step-by-step explanation:
Absolute value is the positive distance from 0, so |-7| = 7 because -7 is 7 from 0, whereas 6 is 6 away from 0. Because 7>6, then -7 has a greater absolute value than 6
How many days are in 800 hrs? Round your answer to the nearest tenth.
Answers
Explanation: 800/24 = 33.333333333
Rounded to the nearest tenth it is 33.3.
Answer:
800 hrs = 33.3 days
Step-by-step explanation:
1 day = 24 hours
800 hours = 800/24 = 33.33
Round to the nearest tenth:
33.3 days
A women went to Shopping.First she spent 4/5th of all money she had in her purse, and then she lost 2/3 of what was remaining. Now she has 10$ left. How much money did she spent?
Answers
The amount of money that was spent is $120.
How to illustrate the fraction?A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split.
In this case, the women went to Shopping and first she spent 4/5th of all money she had in her purse, and then she lost 2/3 of what was remaining.
The fraction of money left will be:
= 1 - 4/5 - (2/3 × 1/5)
= 1 - 4/5 - 2/15
= 1/15
Since she had $10 left the original amount will be:
= $10 ÷ 1/15
= $10 × 15
= $150
The amount spent will be:
= 4/5 × $150
= $120
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3 Dylan needs to buy new contact lenses. His ophthalmologist sells 8-lens boxes in
packs of 2 for $52 and 10-lens boxes in packs of 4 for $120. Which option is the
better deal?
Answers
Answer:
Dylan should purchase the 10-lens boxes in packs of 4 for $120, as this is the better deal. This option provides 40 lenses for $120, which works out to be $3 per lens. The 8-lens boxes in packs of 2 for $52 only provides 16 lenses for $52, which works out to be $3.25 per lens Therefore, the 10-lens boxes in packs of 4 is the better deal.
Step-by-step explanation:
Answer:
he should buy the 10-lens boxes in packs of 4 for $120
Step-by-step explanation:
the inaugural attendance of an annual film festival is 20,000. The attendance y increases by 5% each year
A. write a function that represents the attendance after t years.
B. about how many people will attend the festival in the fifth year?
Answers
A. A function that represents the attendance after t years can be written as y = 20,000(1 + 0.05t)
What does a math function mean?
a mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable).
This function represents the initial attendance of 20,000, multiplied by 1 + 5% increase each year (0.05) times the number of years (t).
B. To find out about how many people will attend the festival in the fifth year, we can substitute t = 5 into the function.
y = 20,000(1 + 0.05 * 5)
y = 20,000(1 + 0.25)
y = 20,000(1.25)
y = 25,000
So, approximately 25,000 people will attend the festival in the fifth year.
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Please define the following: Revenue, Cost and Profit VS
Marginal Revenue, Marginal Cost and Marginal Profit.
Answers
The additional expense brought on by reducing the quantity is known as the cost. An additional expense "at the margin" is another name for this. The extra income that results from raising the supply is known as the marginal revenue.
What is Cost and Profit?
Profit is defined as the difference of revenue and cost (determined by deducting cost from revenue. when revenue exceeds operational expenses, the difference between them is called the operating profit.
The additional money "at the margin" is another name for this.The money left over after a corporation pays its bills and expenses is known as its profit. Costs are the out-of-pocket expenditures comes to making, producing, and marketing the company's goods and services.
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Given that the polynomial x² - 10x + 14 leaves the same remainder when divided by x + 2b orx + 2c where 3b - 2c = 0 and b # c . Find the values of b and c.
Answers
Step-by-step explanation:
please refer to the 3 pages of sketch for details
The question is in the photo attached
Answers
Answer: 10,000
Step-by-step explanation: here's how I got my answer:
Since we are finding the decrease from 2005-2015, we need to multiply 1/20 by 10, since the timespan is 10 years worth of decreasing.
So, 1/2 * 10 =1/2
So, since we have 1/2 as the overall decrease in the population within the 10 years, we divide 20,000 by 1/2 or 20,000 by 2, and we get 10,000. I hope this helps.
A group of friends went to lunch. The bill before sales tax and tip was $37.50. A sales tax of 8% was added. The group then tipped 18% on the amount after the sales tax was added. What was the amount, in dollars, of the sales tax?
What was the total amount the group paid, including tax and tip?
Answers
Sales Tax = $3.00
The total amount paid by the group was $48.15
The amount of the sales tax can be calculated by multiplying the pre-tax bill of $37.50 by the sales tax rate of 8%:
Sales tax = $37.50 * 8% = $3.00
The total amount paid including tax and tip can be calculated by adding the amount of the sales tax to the pre-tax bill and then calculating the tip on the new total:
Total = $37.50 + $3.00 + ($37.50 + $3.00) * 18% = $37.50 + $3.00 + $7.65 = $48.15
So the total amount paid by the group was $48.15.
Shana wants to buy a music player. She has $100 cash.
1. Can she afford a $79 unit plus HST? Yes or No?
Provide an estimate or a calculation to support your answer:
Answers
Answer:
Yes
Step-by-step explanation:
A $79 unit plus HST will be 89.27
any help please - Simplify the expression 3(x + 2) –5(2x + 1). Factorise the expression 12x –18y and 2x2–5x –3. (3+6=9)
Answers
Simplifying the expression, the answer would be -7x+1
Solution
3 (x+2) - 5 (2x+1)
3x + 6 - 10x -5
COLLECT LIKE TERMS
3x - 10x + 6 - 5
= -7x+1
1. The following information relates to YANET PLC for the year ended 31 December, 2021 The statement of profit or loss for the year ended 31 December, 2021 Birr (000) 55,000 35,100 19,900 Revenue (net sales) Less: Cost of sales Gross profit Total expense EBIT Less: Interest Profit before tax Less: tax Profit for the year Assets Non-current assets Current assets Inventory Receivables Statement of Financial Position as at 31 December, 2021 2000 (Birr 000) 15,330 Cash Total Current assets Total Asset Equity and liabilities Equity Share capital Retained earnings Total Equity Non-current liabilities Long term- Loan Current liabilities 1. Rate of return on total asset 2. Profit Margin ratio 3. Current ratio 4. Inventory turnover ratio 5. Account receivable turnover ratio 1,908 4,362 2021 (Birr 000) 17,190 7,000 4,100 12,070 7,830 1,560 6,270 1,645 12,745 29,935 7,700 6,515 14,215 9,940 5,780 Total liabilities 15,720 Total equity and liabilities 29,935 Required: A) Calculate the following ratios for 2021. 22% 4% 2.5:1 6,930 3,675 2,110 12,715 28,045 6 13 40% 6 7,700 4,905 12,605 Industry Average 9,450 5,990 15.440 28,045 6. Debt ratio 7. Times interest earned B) Based on the above industry average, suggest the company profitability, liquidity and use of financial gearing.
Answers
A) The ratios for 2021 are as follows:
Rate of return on total asset = (Profit for the year / Total assets) * 100 = (12,605 / 29,935) * 100 = 42%
Profit margin ratio = (Profit for the year / Revenue) * 100 = (12,605 / 55,000) * 100 = 22.9%
Current ratio = (Current assets / Current liabilities) = (17,190 / 7,700) = 2.23:1
Inventory turnover ratio = (Cost of sales / Inventory) = (35,100 / 3,675) = 9.58
Accounts receivable turnover ratio = (Revenue / Receivables) = (55,000 / 4,905) = 11.22
Debt ratio = (Total liabilities / Total assets) = (15,720 / 29,935) = 52.6%
Times interest earned = (EBIT / Interest) = (12,715 / 1,560) = 8.14
B) Based on the above industry averages:
profitability: the company's profit margin ratio of 22.9% is lower than the industry average of 40%, which suggests that the company's profitability is lower than the industry average.
liquidity: the company's current ratio of 2.23:1 is lower than the industry average of 2.5:1, which suggests that the company's liquidity is lower than the industry average.
use of financial gearing: the company's debt ratio of 52.6% is higher than the industry average of 6%, which suggests that the company is more heavily leveraged than the industry average.
In summary, the company profitability is lower than the industry average, liquidity is lower than the industry average, and the company is more heavily leveraged than the industry average.
What is a company's profitability?
A company's profitability refers to its ability to generate a profit and return on investment. It is a measure of how well a company is able to generate revenue, control costs, and manage its assets and liabilities. Profitability ratios are used to evaluate a company's financial performance and to compare it to other companies in the same industry. Some of the most common profitability ratios include:
Gross profit margin: measures the percentage of revenue that remains after accounting for the cost of goods sold. It's calculated by dividing gross profit by revenue.
Operating profit margin: measures the percentage of revenue that remains after accounting for all operating expenses. It's calculated by dividing operating profit by revenue.
Net profit margin: measures the percentage of revenue that remains after accounting for all expenses, including taxes and interest. It's calculated by dividing net profit by revenue.
Return on assets (ROA): measures how efficiently a company is using its assets to generate a profit. It's calculated by dividing net income by total assets.
Return on equity (ROE): measures how efficiently a company is using shareholder's equity to generate a profit. It's calculated by dividing net income by shareholder's equity.
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Could someone help answer this? Thanks!
The limit of a function y=f(x) at x=a is sometimes best understood as the approximate height of the function around x=a based on the values around x=a whereas the value of the function f at x=a is the exact height of the function at that point. Consider two functions 1) f(x)=x+1 and g(x)=(x^2-1)/(x-1). Answer the following questions. (a) Discuss the process of finding the limit x->1 f(x). (b) How does it differ from f(1)?
Answers
a) The process to find the limit is given as follows:
f(x): simply replace x by 1.g(x): factor and then replacing.b) When a function does not have any discontinuity at x = 1, the procedure is the same as calculating f(1), however in the case of a discontinuity, such as for f(x), the discontinuity first has to be removed, if possible.
How to calculate the limit of a function?The first step in calculating the limit of a function is calculating the numeric value of the function at the value of x which the function approaches.
Hence:
lim x -> 1 f(x) = 1 + 1 = 2.lim x -> 1 g(x) = (1² - 1)/(1 - 1) = 0/0.For the case of g(x), there is a discontinuity, meaning that the function has to be factored to remove the discontinuity.
Applying the subtraction of perfect squares, we have that:
x² - 1 = (x - 1)(x + 1).
Then:
g(x) = (x - 1)(x + 1)/(x - 1) = x + 1.
Meaning that the limit is then calculated as follows:
lim x -> 1 g(x) = lim x->1 x + 1 = 1 + 1 = 2.
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5. Mariel volunteers at the
animal shelter 3 times a month.
After 6 months, how many
times has she volunteered at
the animal shelter?
Answers
For each order, the web site applies a 7.7% sales tax to the price of the cards, plus a one time mailing fee of 5.95. Based on the information in the table, what will be the total cost for an order for 280 cards?
Answers
Answer: $1794.28
Step-by-step explanation:
280*5.95= 1666
0.077*1666= 128.282
1666+128.282= 1794.282
We round cause its money
the mean of 100 nummerical observations is 51.82
Answers
If the mean of 100 nummerical observations is 51.82 then the value of all 100 numbers is 5182.
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
Given that mean of 100 nummerical observations is 51.82
We need to find the sum of all the observations
The formula to find mean is mean=Sum of observations/ Number of observation
From given mean=51.82
Number of observations =100
Let us take x as sum of all 100 numbers
So 51.82=x/100
Now apply cross multiplication
x=51.82×100
x=5182
Hence, if the mean of 100 nummerical observations is 51.82 then the value of all 100 numbers is 5182.
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What is the repeated addition of 9x0=
Answers
Answer:
The answer is zero
Step-by-step explanation:
Hope it helps
Exit ticket for geometry
Answers
Answer:
y = 10
Step-by-step explanation:
given DEFG = SPQR
QR = FG
=> 2x - 4 = 12
=> 2x = 16
=> x = 8
angle PQR = EFG
=> 6y + x = 68
=> 6y + 8 = 68
=> 6y = 60
=> y = 10
In the diagram below,
ZCAB≈ ZCDE. Solve for x. Round
your answer to the nearest tenth if
necessary.
14
A
D
X
с
18.7
E
9.3
B
Answers
Answer:14 a
Step-by-step explanation:
The explanation is that it is E
s/4 +5=13
How do i solve thissssssss
Answers
[tex]\dfrac{s}{4} +5=13[/tex]
Simplify:
[tex]\dfrac{1}{4} s+5=13[/tex]
Subtract 5 from both sides:
[tex]\dfrac{1}{4} s+5-5=13-5[/tex]
[tex]\dfrac{1}{4} s=8[/tex]
Multiply both sides by 4:
[tex]4\times(\dfrac{1}{4} s)=4\times(8)[/tex]
[tex]\fbox{s = 32}[/tex]
s = 32.
Step-by-step explanation:1. Write the expression.[tex]\frac{s}{4} +5=13[/tex]
2. Subtract 5 from both sides of the equation.[tex]\frac{s}{4} +5-5=13-5\\ \\\frac{s}{4} =8[/tex]
3. Multiply by "4" on both sides of the equation.[tex]\frac{s}{4}*4 =8*4\\ \\s=32[/tex]
4. Verify.If the result is correct, then the equation should return the same value of both sides of the equal symbol (=) when we substitute the variable "s" by it's calculated value, 32.
[tex]\frac{(32)}{4} +5=13\\ \\8+5=13\\ \\13=13[/tex]
As you can tell, the same number appears on both sides of the equal symbol, this means that the result is correct!
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Please help will mark Brainly
Answers
Step-by-step explanation:
1. Simplify -6y >= 12 by dividing both sides by -6 to get y alone. This results in y<=-2, because when dividing an inequality by a negative number the sign gets switched.
2. Mark the point (0, -2) because there is no x-value. Shade everything lower and equal to -2 because y can be equal to -2 or less than it.
Answer:
Y less than
Step-by-step explanation:
SUBJECT: GEOMETRY
Hello!! Could somebody please solve this for me asap, I'm having a bit of trouble? The problem is shown in the picture.
Answers
The length of the side CD is 5.195 cm and the Area of ΔABC is 31.17 cm²
How to use trigonometric ratios?
The basic trigonometric functions are;
sin θ = opposite/hypotenuse
cos θ = adjacent/hypotenuse
tan θ = opposite/adjacent
From the given triangle ABC, we can see that it is a right angle triangle where ∠ACD = 60°, and as such, ∠CAD = 30°.
Thus;
BC/AC = tan 30°
6/AC = 0.5774
AC = 10.39cm
Thus;
CD/AC = cos 60
CD = 10.39 * 0.5
CD = 5.195 cm
Formula for area of a triangle is;
Area = ¹/₂ * base * height
Area = ¹/₂ * 6 * 10.39
Area = 31.17 cm²
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Colton works in a department store selling clothing. He makes a guaranteed salary of $500 per week, but is paid a commision on top of his base salary equal to 10% of his total sales for the week. How much would Colton make in a week in which he made $1075 in sales? How much would Colton make in a week if he made xx dollars in sales?
Answers
Answer:
Step-by-step explanation:
If Colton makes a guaranteed salary of $500 per week, and he is paid a commission of 10% on top of that for a total of $1075 in sales, he would make an additional $107.50 in commission (1075 x .1 = 107.5). In total, Colton would make 500 + 107.5 = $607.50 in a week where he made $1075 in sales.
The crew on a fishing boat caught four fish that weighed a total of 1,032 pounds. The tarpon weighed twice as much as the amberjack and the white marlin weighed twice as much as the tarpon. The weight of the tuna was 5 times the weight of the amberjack.
Answers
Using equations, the weights of the four fish are as follows:
Amberjack = 86 poundsTarpon = 172 poundsWhite Marlin = 344 poundsTuna = 430 pounds.What are equations?Equations are mathematical statements showing the equality of two mathematical expressions.
Using the equation sign (=), equations depict that expressions are equal or equivalent.
The total weight of the four fish = 1,032
Let the weight of the Amberjack = x
Weight of the Tarpon = 2x
Weight of the White Marlin = 4x (2 x 2x)
Weight of the Tuna = 5x
x + 2x + 4x + 5x = 1,032
12x = 1,032
x = 86
Weights:Amberjack = 86 pounds (x)
Tarpon = 172 pounds (2x)
White Marlin = 344 pounds (4x)
Tuna = 430 pounds (5x)
Total weight = 1,032 pounds (86 + 172 + 344 + 430)
Thus, we solved the weight of each fish using equations.
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Question Completion:How much did each fish weigh?
The odometer of a car reads 35,467.219 the 5 stands for 5 x1,000 miles. Use expanded form to show what each of the other digits in the odometer reading means.
Answers
So the expanded form of the odometer reading 35,467.219 is:
5 x 1000 + 3 x 100 + 4 x 10 + 6 x 1 + 7 x 1/10 + 2 x 1/100 + 1 x 1/1000 + 9 x 1/10000
What is expanded form?A number is divided up into its place values, then expanded to represent the value of each digit. The enlarged form of 943 is shown as an example. 9 blocks of 100s Three blocks of ones, and four blocks of tens. Nine hundred increased to 4 tens, 3 ones. Form: 900 + 40 + 3.
Define Decimal Numbers.The accepted method for representing both integer and non-integer numbers is the decimal numeral system. It is the expansion of the Hindu-Arabic numeral system to non-integer values. Decimal notation is the term used to describe the method of representing numbers in the decimal system.
In expanded form, the odometer reading of 35,467.219 can be broken down into the value of each digit in the number.
5 stands for 5 x 1,000 miles
3 stands for 3 x 100 miles
4 stands for 4 x 10 miles
6 stands for 6 x 1 miles
7 stands for 7 x 1/10 of a mile
2 stands for 2 x 1/100 of a mile
1 stands for 1 x 1/1000 of a mile
9 stands for 9 x 1/10000 of a mile
So the expanded form of the odometer reading 35,467.219 is:
5 x 1000 + 3 x 100 + 4 x 10 + 6 x 1 + 7 x 1/10 + 2 x 1/100 + 1 x 1/1000 + 9 x 1/10000
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hello, i need helpw ith my math question
Answers
The three ways to purchase a vehicle include: (1) On lease (2) On hire purchased and (3) On cash basis
How to purchase a vehicle?A vehicle can be purchased on the following ways:
Lease: This involves granting the user access on the property over a period of time before he could make paymentHire purchase: In this method, the buyer deposits first initial money while he agrees with the seller to make the payment of the balance on installment basis Cash: In this method the buyer pays cash at prompt or on the point of purchaseAdvantages include:
It places the buyer on good life without cashHe enjoys the luxurious lifeDisadvantages:
He can run away with the vehicleThe seller looses in cash of accident taking the life of the buyerAdditional expenses include
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solve the system by elimination. show steps so i can write down please i will mark brainliest thank you!! :)
Answers
Answer:
(-2,5), refer to the step-by-step. Feel free to comment any questions you may have!
Step-by-step explanation:
Given the system of equation, [tex]\left \{ {{x+6y=28} \atop {2x-3y=-19}} \right.[/tex], solve by elimination.
[tex]\left \{ {{-2(x+6y=28)} \atop {2x-3y=-19}} \right.[/tex] , multiply the top equation by -2.
We get, [tex]\left \{ {{-2x-12y=-56} \atop {2x-3y=-19}} \right.[/tex]
[tex]+ {{-2x-12y=-56} \atop {2x-3y=-19}} \right.[/tex], add the equations together.
We get, [tex]-15y=75[/tex], we just eliminated the variable, x, we can now solve this equation for y.
[tex]-15y=-75 = > y=\frac{-75}{-15}[/tex], [tex]y=\frac{75}{15} = > y=5[/tex]
We just found the value y, which is y=5. Now we can take this value and plug it into y for either of the two original equations and solve for x. I will take the top equation...
[tex]x+6y=28 = > x+6(5)=28 = > x+30=28[/tex], subtract the value, 30, from both sides. We get, [tex]x=-2[/tex].
We found the value x, x=-2.
Thus the solution to the given system of equations is (-2,5).
Answer:
(-2, 5)
Step-by-step explanation:
Given linear system of equations:
[tex]\begin{cases}x+6y=28\\2x-3y=-19\end{cases}[/tex]
To solve by the method of elimination, first multiply the first equation by -2:
[tex]\implies -2 (x+6y=28)[/tex]
[tex]\implies -2x-12y=-56[/tex]
Add this to the second equation to eliminate the term in x:
[tex]\begin{array}{lrcrcr}& 2x & - & 3y & = & -19\\+\vphantom{\dfrac12}&(-2x & - & 12y & = & -56\\\cline{2-6}&\vphantom{\dfrac12}&- & 15y & = &-75\end{array}[/tex]
Solve the expression for y:
[tex]\implies -15y=-75[/tex]
[tex]\implies y=5[/tex]
Substitute the found value of y into the expression for x and solve for x:
[tex]\implies x=28-6(5)[/tex]
[tex]\implies x=28-30[/tex]
[tex]\implies x=-2[/tex]
Check by substituting the found values of x and y into both equations.
Equation 1
[tex]\implies -2+6(5)=-2+30=28[/tex]
Equation 2
[tex]\implies 2(-2)-3(5)=-4-15=-19[/tex]
Hence proving that the solution (-2, 5) is true.
whats 5x5? Maybe will mark brainiest
Answers
Answer:
25
Step-by-step explanation:
5x5 = 25
Answer:
25
Step-by-step explanation:
Let's go through our times tables really quick!
5x1 = 5 (5 + 0)
5x2 = 10 (5 + 5)
5x3 = 15 (5 + 5 + 5 [10 + 5])
5x4 = 20 (5 + 5 + 5 + 5 [15 (5x3) + 5)
As we can see, if we know 5x4, we can easily find 5x5! It's just 5x4 + 5
So, 5x5 is 25
Hope this helped!
Round 0.12406667 to the nearest hundredth
Answers
Answer:
Step-by-step explanation:
0.124
A rectangular playground area is 3,162 meters. The width is 51 meters. Find the length?
Answers
Work Shown:
area = length*width
length = area/width
length = 3162/51
length = 62 meters