13. Given: BC = DC, AC = ECProve: ABC = EDC

Answer:

BA = 36 cm

CA = 6 cm

Step-by-step explanation:

CB + AC = BA

26 + 10 = 36 cm

AB - CB = CA

22 - 16 = 6 cm

There was a total loss of $150.00 over those 6 days

1 - Simplify the word problem

A store makes a loss of $25 per day for 6 days

2 - Write a statement for it

d = days

t = total loss

25d = t

3 - Plug in the days for d

25(6) = t

150 = t

t = $150

There was a total loss of $150.00 over 6 days

Hope this helps :)

Answer:

x = 49

Step-by-step explanation:

The sum of angles is 360

(x + 84) + 80 + 3x = 360

x + 3x = 360 - 84 - 80

4x = 196

x = 196/4 = 49

Since then, it has spread to other rivers, colonized them, clogged the water intake pipes, and competed with local species for food. Zebra mussels are the method for removing a lot of plankton from the water column.

Here, we have,

The Caspian Sea in Asia is where zebra mussels, or Driessen polymorph, are found naturally.

They arrived in the Great Lakes region in the late 1980s via ballast water from a transatlantic ship.

The Great Lakes, Mississippi, Tennessee, Hudson, and Ohio river basins were all overrun by these mussels within ten years.

The lake's brilliant blue hue is a result of Tahoe's clean air and water.

There is more to this phenomenon than just the fact that Lake Tahoe's surface reflects the sky, which contributes to its blue color.

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complete question:

As you respond to Part A, Part B, and Part C, follow the directions below.

​

​Address all of the instructions in each prompt.

​Use evidence from the information provided and your own knowledge of science to support your responses.

Part A

​

Describe one way scientists near Lake Tahoe can detect if the lake has been impacted by zebra mussels.

Let's use the variable x to represent the spaces between posters.

So the spaces at the left and right of the group will be 3x.

Drawing the diagram, we have:

Writing an equation to solve for x, we have:

So the space between each pair of posters is 0.75 feet.

Solution

We have a point P=(a=7,b=6) and we need to rotate around C=(x= 4,y=1)

And we can use the following formula:

We can change the origin and the new coordinates are now:

C (0,0), P= (3 ,5)

Then the rotated point is:

Px' = (5, -3)

And the real value would be:

P' = (5+4, -3+1)= (9,-2)

For the second case the new coordinate is:

Px'' = (-5, -3)

And with the transformation we have:

P'' =(-5+4, -3+1)= (-1, -2)

Hence, in respοnse tο the prοvided questiοn, we can say that functiοn  B. The quοtient οf a number and twenty cοrrespοnds tο p ÷ 20.

Mathematicians research numbers and their variants, equatiοn and related structures, οbjects and their lοcatiοns, and prοspective lοcatiοns fοr these things. The term "mοdule" is used tο describe the cοnnectiοn that exists in between set οf inputs, each οf which has a cοrrespοnding οutput. A functiοn is an input-οutput cοnnectiοn in which each inputs results in sοmething like a single, distinct return.

A dοmain, cοdοmain, οr scοpe is assigned tο each functiοn. Functiοns are usually denοted by the letter f. (x). An x is used fοr entry. On capabilities, οne-tο-οne capabilities, multiple prοwess, in capabilities, and οn capabilities are the fοur majοr types οf accessible functiοns.

D. thirteen times a number squared cοrrespοnds tο 13b².

A. a number times eleven plus thirty-three cοrrespοnds tο 11n + 33.

C. twelve less than a number cοrrespοnds tο y - 12.

B. The quοtient οf a number and twenty cοrrespοnds tο p ÷ 20.

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A. x² - 200 gives the amount of money the interior designer will make decorating the house as a function of hours he works.

B. He will earn 1,875 if he works for 50 hours.

C. The difference quotient is equal to 2x.

The solution has been obtained by using functions.

What is a function?

Function is a kind of relation, or rule, that associates a single input with a single, predetermined output.

We are given two functions

f(x) = 49x² – 200

which represents the amount of money he earns per room decorated

g(x) = (1/7)x

which represents the number of rooms the interior designer decorates

A. The amount of money the interior designer will make decorating the house as a function of hours he works will be given by evaluating f(x) in g(x).

So,

f(g(x)) = 49((1/7)x)² – 200

f(g(x)) = x² - 200

B. Since, the house requires 50 hours of work, this means that x = 50.

Substituting this in f(g(x)) = x² - 200, we get

f(g(50)) = 50² - 200

f(g(50)) = 1,875

C. The difference quotient for the function is as follows

\(\lim_{h \to \ 0}\frac{f(x+h) -f(x)}{h}\)

\(\lim_{h \to \ 0}\frac{(x+h)^{2}-200-x^{2}+200}{h}\)

\(\lim_{h \to \ 0}\frac{x^{2} + 2xh + h^{2}-x^{2}}{h}\)

= 2x

Hence, x² - 200 gives the amount of money and he earns 1,875 if he works for 50 hours. The difference quotient is equal to 2x.

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Answer:

Step-by-step explanation:

Comment

The answer is answer to the question "What makes these factors equal zero?"  See the graph below for confirmation to the answer to the question.

x can be equal to zero. X = 0 can be one answer.

x + 2 = 0 so x can be equal to x +2 - 2 = - 2   or x = - 2

x^2 - 5 can be an answer. x = +/- the square root of 5

So now look at the graph.

Graph

I can't seem to get sqrt of 5 on the graph. The answer is about +/- 2.23. You can find those points yourself. The other two points are clear and are marked.

The the coefficient of variation for set a is 15.7% and the coefficient of variation for set b is 22.3%.

The formula for calculating the coefficient of variation is:

CV = (standard deviation / mean) x 100%

where standard deviation is a measure of the spread of the data around the mean. The CV expresses the standard deviation as a percentage of the mean.

To calculate the CV for set a, we first need to find the mean and standard deviation of the data set. The mean can be calculated by adding all the values and dividing by the number of values.

Mean = (3.97 + 3.47 + 3.99 + 4.30 + 3.16 + 3.07 + 4.24 + 2.94 + 3.56 + 3.43 + 3.06 + 3.34 + 4.35 + 3.57) / 14 = 3.65

The standard deviation can be calculated using a calculator or a spreadsheet software such as Microsoft Excel. For this set, the standard deviation is 0.574.

CV = (0.574 / 3.65) x 100% = 15.7%

To calculate the CV for set b, we need to first remove the dollar sign from each value and then find the mean and standard deviation.

Mean = ($24,800 + $30,000 + $22,300 + $20,400 + $19,000 + $32,200 + $23,000 + $23,000 + $24,000 + $27,200 + $34,900) / 11 = $25,727.27

The standard deviation can be calculated using a calculator or spreadsheet software. For this set, the standard deviation is $5,746.38.

CV = ($5,746.38 / $25,727.27) x 100% = 22.3%

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1. About 144 scoops of ice cream were served last Thursday.

2.Doris has 5 quarters, 10 dimes, and 5 nickels, and 4 pennies.

1. There are 16 ounces in a pound, so 18 pounds of ice cream weigh:

18 pounds * 16 ounces/pound = 288 ounces

Since one scoop of ice cream weighs 2 ounces, the number of scoops served is:

288 ounces / 2 ounces/scoop = 144 scoops

Therefore, about 144 scoops of ice cream were served last Thursday.

2. Let's use "q", "d", "n", and "p" to represent the number of quarters, dimes, nickels, and pennies that Doris has, respectively.

From the problem statement, we know that:

n = q (the number of nickels equals the number of quarters)

d = 2q (the number of dimes is twice the number of quarters)

n = 5 (she has 5 nickels)

We can use this information to write an equation for the total value of Doris's coins:

0.25q + 0.10d + 0.05n + 0.01p = 2.54

Substituting the values for n and d in terms of q, we get:

0.25q + 0.10(2q) + 0.05(5) + 0.01p = 2.54

Simplifying and solving for q, we get:

0.45q + 0.05 + 0.01p = 2.54

0.45q + 0.01p = 2.49

45q + p = 249

Since Doris has a total of 24 coins, we can write another equation:

q + d + n + p = 24

Substituting the values for n and d in terms of q, we get:

q + 2q + q + p = 24

4q + p = 24

We now have two equations with two unknowns:

45q + p = 249

4q + p = 24

Subtracting the second equation from the first, we get:

41q = 225

Solving for q, we get:

q = 225/41 ≈ 5.49

Since q must be a whole number, the closest integer value is 5. Substituting this value back into the equations for n and d, we get:

n = q = 5

d = 2q = 10

Finally, we can use the equation for the total number of coins to find the value of p:

q + d + n + p = 24

5 + 10 + 5 + p = 24

p = 4

Therefore, Doris has 5 quarters, 10 dimes, and 5 nickels, and 4 pennies.

Quarters are a type of coin used in the United States currency system. A quarter is worth 25 cents or 1/4 of a dollar. It has a diameter of 0.955 inches (24.26 mm) and a thickness of 0.069 inches (1.75 mm). The front side of the coin features a portrait of George Washington, the first president of the United States, and the back side features an eagle. Quarters are commonly used in daily transactions to make small purchases or provide change.

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Answer:

The circumference of the drive wheel is 10 feet * 3.14 = 31.4 feet.

The circumference of the vat is 18 feet * 3.14 = 56.52 feet.

The total length of belt needed to go around the drive wheel and the vat is 31.4 + 56.52 = 87.92 feet.

3x-27

Hope this helps! :)

The calculated measure of m∠PNM is 87 degrees

from the question, we have the following parameters that can be used in our computation:

The circle

Where, we have

PM = 360 - 64 - 122

Evaluate

PM = 174

Next, we have

m∠PNM = 1/2 * 174

So, we have

m∠PNM = 87

Hence, the measure of m∠PNM is 87 degrees

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Answer:

C

Step-by-step explanation:

the scale factor is the ratio of corresponding sides, image to original, so

scale factor = \(\frac{EF}{BC}\) = \(\frac{11}{66}\) = \(\frac{1}{6}\)

Answer:

32

Step-by-step explanation:

\(\frac{x}{40}=\frac{48}{60} \\ \\ x=32\)

My ans is C

24 - 6x + 40 = 34

24+40 - 6x = 34

64 - 6x = 34

6x = 64-34

6x = 30

x = 5 ^^

Answer:

To find the total balance after three years, we can use the formula for continuous compounding:

A = Pe^(rt)

Where A is the total balance, P is the principal (initial amount), e is Euler's number (approximately 2.71828), r is the annual interest rate as a decimal, and t is the time in years.

In this case, P = $12,000, r = 0.0125 (1.25% expressed as a decimal), and t = 3. Plugging these values into the formula, we get:

A = $12,000 x e^(0.0125 x 3)

A = $12,000 x e^(0.0375)

A = $12,000 x 1.038163

A = $12,458.54

Therefore, the total balance after three years is $12,458.54.

Answer:

f(-2) = -9

g(6) = 106

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

f(x) = 4x - 1

f(-2) is x = -2 for function f(x)

g(x) = 3x² - 2

g(6) is x = 6 for function g(x)

Step 2: Evaluate

f(-2)

g(6)

Answer:

109.6

Step-by-step explanation:

100+100×(4.8%×2)=100+ 100×9.6%=100+9.6=109.6

Answer:

The money account after two years will be 110.054

Step-by-step explanation:

\(A = P(1 + \frac{r}{n})^{nt}\)

A = final amount = required to know

P = initial principal balance = $100

r = interest rate = 4.8%=4.8/100 because compounded monthly

n = number of times interest applied per time period = 12

t = number of time periods elapsed = 2

\(A = P(1 + \frac{4.8}{1200})^{24}\)

\(A= 100(1+0.004)^{24}\)

A=   \(110.054\)

Thus, The money account after two years will be 110.054

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Answer: Reflexive Property

Step-by-step explanation:

Hence, The Transitive property is used in the step4.

Given that ,

Alternate Interior Angles Theorem, using parallel lines a and b with transversal m,

We have to prove,

Using parallel lines m is transversal by using transitive property.

Suppose that, a and b are two parallel lines and m is the transversal that intersects a and b.

We know that,

If a transversal intersects any two parallel lines,

The corresponding angles and vertically opposite angles are congruent.

Transitive Property: if A = B and B = C, then A = C.

Therefore,

∠1 = ∠5 ………..(i) [Corresponding angles]

∠3 = ∠1 ………..(ii) [Vertically opposite angles]

From equations (i) and (ii), we get-

By transitive property,

∠3 = ∠5

Hence, it is proved it is a transitive property.

Hence , Transitive property is the steps 4.

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Answer:

  $4918

Step-by-step explanation:

You want the tax owed on $90,000 using the given tax rate table.

The tax is the sum of the amounts of tax due in each income range.

  tax = 0.0575(90,000 -17,000) +0.05(17,000 -5000) +0.03(5000 -3000) +0.02(3000)

  = 0.0575(90,000) -(17000(.0575 -.05) +5000(.05 -.03) +3000(.03 -.02))

  = 0.0575(90,000) -(127.50 +100 +30)

  = 5175 -257.50 = 4917.50

Rounded to the nearest dollar, the tax due is $4,918.

__

Additional comment

The tax will be the maximum of ...

You can compute them all and find the maximum, or you can choose the function applicable to the income amount. The result is the same.

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The angle formed by the two hands have a measure less than 1/4 turn

From the question, we have the following parameters that can be used in our computation:

A clock with the hour hand at 12 and the minute hand at 2

The turn represented by the above is represened as

Turn = (2 * 30)/360

When simplified, we have

Turn = 1/6

Next, we have

Angle at the turn = 1/4

1/6 is less than 1/4

This means that the angle formed by the two hands have a measure less than 1/4 turn

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Exponential Decay

The model for the exponential decay of a quantity Mo is:

Where λ is a constant and t is the time.

The half-life of a radioactive isotope is the time it takes to halve its initial mass. It can be calculated by making M = Mo/2 and solving for t:

It's required to calculate the remaining mass of an isotope of Mo = 175 gr after 5 half-lives have passed, that is. we must calculate M when t is five times the value calculated above.

Substituting in the model:

Simplifying (the value of λ cancels out):

Rounding to the nearest gram, 5 grams of the radioactive isotope will be left after the required time.

Answer:

Mixed Fraction

Step-by-step explanation:

A mixed fraction is a fraction with a whole number attached to it like 5 1/5 or 3 1/2

\(1\frac{4}{5}\) is an example of a mixed fraction.

A fraction represented with its quotient and remainder is a mixed fraction. For example, 2 1/3 is a mixed fraction, where 2 is the quotient, 1 is the remainder. So, a mixed fraction is a combination of a whole number and a proper fraction.

A mixed number is a whole number, and a proper fraction represented together.  It generally represents a number between any two whole numbers.

A mixed number is formed by combining three parts: a whole number, a numerator, and a denominator. The numerator and denominator are part of the proper fraction that makes the mixed number.

Properties of Mixed Numbers :

1. It is partly a whole number.  

2. It is partly a fraction.

\(1\frac{4}{5}\) is an example of a mixed fraction.

In \(1\frac{4}{5}\) , 2 is the quotient, 4 is the remainder.

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Answer:

A = 35 cm²

Step-by-step explanation:

the area (A) of a rectangle is calculated as

A = length × width

by counting the squares on the sides

length = 7 cm and width = 5 cm , then

A = 7 × 5 = 35 cm²

186|2

93|3

31|31

1

310|2

155|5

31|31

1

434|2

217|7

31|31

1

\(186=2\cdot3\cdot31\\310=2\cdot5\cdot31\\434=2\cdot7\cdot31\\\\\text{hcf}(186,310,434)=2\cdot31=62\)