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Determine if the two triangles are congruent. If they are, state how you know.
#5 and 6

The value of the expression is 5x⁶y² - 3x³y. Option D

Index forms are defined as mathematical forms that are used to represent values or numbers that are too small or large.

These forms are also referred to as scientific notation or standard forms.

Some rules of index forms are;

From the information given, we have that;

20x⁸y³ - 12x⁵y²/(-4x²y)

Divide by the value, we have;

5x⁸y³ - 3x⁵y²/x²y

Subtract the exponents

5x⁶y² - 3x³y

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Answer:

Step-by-step explanation:

You want to know the slope and intercept of the linear equation that results from taking the logarithm of y = 4(1.4^x).

The applicable rules of logarithms are ...

  log(ab) = log(a) +log(b)

  log(a^b) = b·log(a)

The log of the given equation is ...

  y = 4·1.4^x

  log(y) = log(4·1.4^x)

  log(y) = log(4) +log(1.4^x)

  log(y) = log(4) + x·log(1.4)

In slope-intercept form, this is ...

  log(y) = mx +b

  log(y) = log(1.4)·x +log(4)

Comparing equations, we see ...

  m = log(1.4)

  b = log(4)

__

Additional comment

The line representing log(y) is shown in the attachment, along with verification that its slope and intercept are as found above.

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Anna's total profit was $6000 + $16000 - $4000 = $14000.

How did Anna earn profit

Anna bought $4000 of company stock. The value of the stock doubled when she sold 75% of it, which means she sold 0.75 * $4000 = $3000 worth of stock when its value doubled.

Since the value of the stock doubled, Anna sold the $3000 worth of stock for 2 * $3000 = $6000.

Anna then sold the remainder of the stock (25% of the original amount) for four times the purchase price. Since she originally bought the stock for $4000, the remainder was worth 0.25 * $4000 = $1000.

Selling this remainder for four times the purchase price means that Anna sold it for 4 * $4000 = $16000.

The possible outliers in the sample of high school teachers taken to investigate their number of years of teaching experience would be = 1 and 39. That is option C.

An outlier can be defined as the data that appears to be abnormally far away from other data that are displayed from a random sample of a chosen population.

The outlier can be the extremely low data point or extremely high data point.

When the data is represented on a dot plot or a box plot, the dot that is found in an area that is far away from others are the possible outliers.

From the given data, 1 is the least data chosen and is a possible outlier as after 1 the next figure that is seen is 4. As well as 39 which is very far from 33.

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Randy's error is in the first step of the division, where he subtracts 4x² instead of adding it. The correct subtraction should be: x³ + 2x² + 5x - 3

Randy made an error in the step where he subtracted (2x² - 2x + 1) from (2x² - 3x³ - 3x² + 7x - 3).

Instead of getting -x³ + 4x² + 6x - 4 as the result, he got 2x⁴ - 4x³ + 2x². This error occurred because he forgot to change the sign of all the terms in (x² - 2x + 1) when subtracting it from the polynomial.

It should be (3x³ - 2x² + 7x - 3) divided by (x² - 2x + 1).

Let me proceed with this corrected version of the question.

Randy divides (3x³ - 2x² + 7x - 3) by (x² - 2x + 1) as,
2x² + x + 3
____________
x² - 2x + 1) 3x³ - 2x² + 7x - 3
2x³ - 4x² + 2x
_____________
x³ - 2x² + 5x
x³ - 2x² + x
____________
-3x² + 4x - 3
-3x² + 6x - 3
___________
[tex]-2x^2[/tex] + x - 3

3x³ - 2x² + 7x - 3
-(2x³ - 4x² + 2x)
______________
x³ + 2x² + 5x - 3

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Randy made an error while dividing (2x⁴ - 3x³ - 3x² + 7x - 3) by (x² - 2x + 1). He mistakenly subtracted intermediate results from zero instead of the original polynomial, leading to an incorrect division.

Randy made an error in his division of the polynomial (2x⁴ - 3x³ - 3x² + 7x - 3) by (x² - 2x + 1). Let's go through the division process step by step to identify the mistake:

Randy correctly started by dividing 2x⁴ by x², which gives him 2x² as the first term of the quotient.

He then multiplied (x² - 2x + 1) by 2x², which resulted in 2x⁴ - 4x³ + 2x². So far, so good.

Randy should have subtracted this result from the original polynomial (2x⁴ - 3x³ - 3x² + 7x - 3), but he mistakenly subtracted it from 0. The correct step should have been to subtract 2x⁴ - 4x³ + 2x² from (2x⁴ - 3x³ - 3x² + 7x - 3).

Here's the corrected division:

(2x⁴ - 3x³ - 3x² + 7x - 3) - (2x⁴ - 4x³ + 2x²) = -3x³ - 5x² + 7x - 3

Now, Randy should have continued the division by bringing down the next term, which is -3x², and repeated the process. However, he incorrectly moved to the next step without subtracting -3x³ - 5x² + 7x - 3 from (x² - 2x + 1).

So, Randy's error is that he failed to properly subtract the intermediate result from the original polynomial, causing the division process to go awry.

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Answer:

[tex]2.4286 \:cm[/tex]

Step-by-step explanation:

Volume of a sphere is given by the formula
[tex]V = \dfrac{4}{3} \pi r^3\\\\[/tex]

Given V = 60 cm³, we get

[tex]60 = \dfrac{4}{3} \cdot \pi \cdot r^3\\\\60 = \dfrac{4\pi}{3} r^3\\\\\text{Multiply both sides by $\dfrac{3}{4\pi}$}\\60 \cdot \dfrac{3}{4\pi} = r^3\\\\\dfrac{45}{\pi} = r^3\\\\r^3 = \dfrac{45}{\pi}\\\\r^3 = 14.323945[/tex]

[tex]r = \sqrt{3}{14.323945}[/tex][tex]r = \sqrt[3]{14.323945}\\\\r = 2.4285 \; cm[/tex]

The required expressions are:

f(3)  = 16

h(0) =  - 4

h(g(x)) = 3x + 5

g(y) = y + 3

f(x) - h(x)​ = x² - x - 3

The given functions are,

f(x) = x² + 2x + 1

g(x) = x + 3

h(x) = 3x - 4

Now put x = 3 in  function f(x)

⇒ f(3) = 3² + 2x3 + 1

          = 9 + 6 + 1

          = 16

Now put x = 0 in function h(x)

h(0) = 3x0 - 4

       = -4

Now composition of function

h(g(x)) = 3(g(x)) - 4

          = 3(x+3) - 4

          = 3x + 9 - 4

          = 3x + 5

Now put x = y in function y,

g(y) = y + 3

For, f(x) - h(x)​

= x² + 2x + 1 - (3x - 4)

= x² - x - 3

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=7×4+2/7=30/7

7×7+4/7=53/7

Step-by-step explanation:

:=30/7-53/7=-23/7

to write in a mixed form

-23÷7=3 reminder 2

Answer:

The perimeter is decreased by 4.

Step-by-step explanation:

If the width of a rectangle with length of 5 and width of 4 is decreased by half, then the new width is 2. The new perimeter of the rectangle is calculated as follows:

old perimeter = 2*(length + width) = 2*(5+4) = 18

new perimeter = 2*(length + new width) = 2*(5+2) = 14

The difference between the old perimeter and the new perimeter is 18 - 14 = 4. Therefore, the answer is (E) The perimeter is decreased by 4.

The value of the functions, f(x) at the specified x-values are;

26. A. -1

27. C. 8

28. B. 1/2

29. A. -176

A function is a rule or definition that maps the elements of a set of input variables unto a set of output variables, such that each input maps to exactly one of the elements in the set of the output variables.

26. The function is; f(x) = 3·x² + 2·x - 1

Therefore; f(0) = 3 × 0² + 2 × 0 - 1 = -1

The correct option is therefore;

A. -1

27. The function is; g(x) = (1/2)·x³ + 2·x

Therefore; g(2) = (1/2) × 2³ + 2 × 2 = 8

The correct option is therefore;

C. 8

28. The function is; f(x) = (√(9 - x))/4

Therefore; f(5) = (√(9 - 5))/4 = 1/2

f(5) = 1/2

The correct option is therefore;

B. 1/2

29. The function is; f(x) = (11·(x - 24))/2

Therefore; f(-8) = (11 × ((-8) - 24))/2 = -176

The correct option is therefore;

A. -176

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Answer:

f(x)=(x+3)(x+2)(x-3)(x-4)

Step-by-step explanation:

Answer: f(x)=(x+3)(x+2)(x-3)(x-4)

Step-by-step explanation:

The Lateral area of the cylinder 376.99 square inches and Surface area

is 1054.0 square inches.

The given solid is a cylinder.

The radius of the cylinder,

r = diameter / 2

r = 12 / 2

r = 6 inches

Now, Lateral area of the cylinder

= 2πrh

= 2π(6)(10)

= 120π

≈ 376.99 square inches (rounded to the nearest tenth)

and, Surface area of the cylinder

= 2πr^2 + 2πrh

= 2π(6)^2 + 2π(6)(10)

= 216π + 120π

= 336π

≈ 1054.0 square inches (rounded to the nearest tenth)

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Answer:  1 chocolate costs 27.

Step-by-step explanation:

Let x be the cost of 1 chocolate, we get

8x = 216

 x =  27

Answer:

8 chocolate = 217

1 chocolate = X

1 chocolate × 217 ÷ 8

Answer = 27

One chocolate = 27

Step 1 : you do cross multiply

Step 2: you say 8 chocolate is equal to 217

step 3 : You say 1 chocolate equal to X ( how much does it cost )

step 4 : multiply X with 8 and divide by 8 chocolate

step 5 : you multiply 1 chocolate with 217 and divide by 8

The wideness of the river is soled to be

c. 261.3 feet

The wideness of the river is solved Using SOH CAH TOA

Sin = opposite / hypotenuse - SOH

Cos = adjacent / hypotenuse - CAH

Tan = opposite / adjacent - TOA

The direction of movements describes a right angle triangle of and will be used to find the wideness of the river as follows

Using alternate angle theorem we have that

wideness of the river = (550 / tan 50) - (550 / tan 70)

wideness of the river =461.505 - 200.184

wideness of the river = 261.321

wideness of the river = 261.3 feet

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The monthly payment for the loan to purchase the desktop computer system on the given installment plan is $51.91.

The formula for calculating the monthly payment is:

[tex]M = P * (r * (1 + r)^n) / ((1 + r)^n - 1)[/tex]

Where:

Given:

First, we need to calculate the monthly interest rate (r):

Monthly interest rate (r) = APR / 12

= 15% / 12

= 0.15 / 12

= 0.0125

Next, substitute the values into the formula and calculate the monthly payment (M):

[tex]M = $1,500 * (0.0125 * (1 + 0.0125)^3^6) / ((1 + 0.0125)^3^6 - 1)[/tex]

M = $51.91.

Therefore, the monthly payment for the loan to purchase the desktop computer system on the given installment plan is approximately $51.91.

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Answer:

the answer is as follows

Step-by-step explanation:

(a)

Bank A: Omar would pay a flat fee of $40 for the checking account and debit card, regardless of the number of transactions he makes.

Bank B: Omar would pay $20 for the checking account and debit card, plus $0.40 for each transaction. For 40 transactions, he would pay:

$20 + (40 × $0.40) = $20 + $16 = $36

Therefore, Omar would pay $40 at Bank A and $36 at Bank B for the given month.

(b)

For the given month, Bank B is cheaper by:

$40 - $36 = $4

Therefore, Bank B is cheaper by $4 for the given month.

Step-by-step explanation:

the headline says "college".

What ????

this is a simple multiplication. you have no calculator ?

each one performance had 1323 tickets.

so, 6 of them are

6 × 1323 = 7,938 tickets

that's it. that's all there is to it.

The first derivative of [tex]f(x) = (7x + 3)(4 - 3x)[/tex] with respect to x is [tex]-42x + 19[/tex].

To find the first derivative of the function [tex]f(x) = (7x + 3)(4 - 3x)[/tex], we can apply the product rule of differentiation.

According to the product rule, if we have two functions, u(x) and v(x), the derivative of their product is given by:

[tex](fg)'(x) = f'(x)g(x) + f(x)g'(x)[/tex]

In our case, let's designate u(x) = 7x + 3 and v(x) = 4 - 3x. We can now compute the derivatives of u(x) and v(x):

u'(x) = 7 (the derivative of 7x is 7)

v'(x) = -3 (the derivative of -3x is -3)

Now, we can apply the product rule:

[tex]f'(x) = (7x + 3)(-3) + (7)(4 - 3x)[/tex]

        [tex]= -21x - 9 + 28 - 21x[/tex]

        [tex]= -42x + 19[/tex]

Therefore, the first derivative of [tex]f(x) = (7x + 3)(4 - 3x)[/tex] with respect to x is [tex]-42x + 19[/tex].

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There are 144 different cars that can be created from the given options by using combinations

To calculate this, we need to use the multiplication principle of counting, which states that the total number of combinations is equal to the product of the number of choices for each category.

There are 12 choices for the exterior color,

4 choices for the interior color, and

3 choices for the engine type.

To find the total number of combinations, we multiply these numbers together:

12 x 4 x 3 = 144

Therefore, there are 144 different cars that can be created from the given options.

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To determine which two-way table is a possible representation of the data collected, we need to compare the relative frequencies in the given table with the options W, X, Y, and Z.

Let's analyze each option:

Option W:

Turkey Ham Total

Mayonnaise 0.40 0.20 0.60

Mustard 0.18 0.22 0.40

Total 0.58 0.42 1.00

Comparing the relative frequencies in option W with the given table, we can see that the relative frequencies for "Turkey" and "Ham" are different, so option W is not a possible representation.

Option X:

Turkey Ham Total

Mayonnaise 0.34 0.28 0.62

Mustard 0.24 0.14 0.38

Total 0.58 0.42 1.00

Comparing the relative frequencies in option X with the given table, we can see that the relative frequencies for "Turkey" and "Ham" are different, so option X is not a possible representation.

Option Y:

Turkey Ham Total

Mayonnaise 0.38 0.24 0.62

Mustard 0.20 0.18 0.38

Total 0.58 0.42 1.00

Comparing the relative frequencies in option Y with the given table, we can see that the relative frequencies for "Turkey" and "Ham" match exactly, so option Y is a possible representation.

Option Z:

Turkey Ham Total

Mayonnaise 0.30 0.32 0.62

Mustard 0.28 0.10 0.38

Total 0.58 0.42 1.00

Comparing the relative frequencies in option Z with the given table, we can see that the relative frequencies for "Turkey" and "Ham" are different, so option Z is not a possible representation.

Therefore, the two-way table that is a possible representation of the data collected is:

Y.

Turkey Ham Total

Mayonnaise 0.38 0.24 0.62

Mustard 0.20 0.18 0.38

Total 0.58 0.42 1.00[tex][/tex]

The solution is: Thabang should receive R240 if they decide to split the money based on hours worked.

Here, we have,

If Thabang worked for three hours and Ndivhu worked for two hours, then the total number of hours worked is five.

To determine the amount Thabang will receive if they decided to share their money according to hours, we need to calculate the proportion of the total hours that Thabang worked and multiply that by the total amount of money earned.

Thabang worked for three out of five hours, which is 3/5 or 0.6 of the total time.

To find out how much money he should receive, we can multiply this fraction by the total amount earned:

0.6 x R400 = R240

Therefore, Thabang should receive R240 if they decide to split the money based on hours worked.

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The total mass carried by both vehicles combined is 16,000 kg.

We need to find the total mass carried by both the tempo and the van, given that they can carry 472 and 528 boxes of muffins respectively, with each box weighing 16 kg.
Calculate the mass carried by the tempo
To do this, multiply the number of boxes the tempo can carry (472) by the mass of each box (16 kg).
Mass_tempo = 472 boxes × 16 kg/box = 7552 kg
Calculate the mass carried by the van
Similarly, multiply the number of boxes the van can carry (528) by the mass of each box (16 kg).
Mass_van = 528 boxes × 16 kg/box = 8448 kg
Calculate the total mass carried by both vehicles
Add the masses carried by the tempo and the van.
Total_mass = Mass_tempo + Mass_van = 7552 kg + 8448 kg = 16,000 kg
The total mass carried by both the tempo and the van is 16,000 kg.

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(a) The amplitude of the function is 2.

(b) The amplitude of the function is 3.

Amplitude is interval between the resting position and the maximum migration of the wave.

Formula for amplitude of the function is:

y = A sin (ωt + Ф) or y = A cos (ωt + Ф), where A represent the amplitude.

Given:

(a) y = 2 cos [3(Ф + 45)]

Formula for amplitude is:

y = A cos (ωt + Ф)

(b) y = 3 sin [2(Ф - 90)]

Formula for amplitude is

y = A sin (ωt + Ф)

After compare amplitude with equation than we get amplitudes are 2 and 3.

Therefore, the amplitude of the following function are 2 and 3 respectively.

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The solution is: transformations have been performed on the graph of f(x)= 3√x to obtain the graph of g(x) = -2 3√x - 1 are:

translate the graph down

reflect the graph over the x-axis

stretch the graph away from the x-axis

We assume your function is intended to be ...

g(x) = -2 3√x - 1

The coefficient -2 does two things. Because it is negative, it causes the graph to be reflected across the x-axis. Because it is greater than 1, it causes the graph to be stretched away from the x-axis.

The added constant of -1 causes each y-value to be lower than it was, so translates the graph down 1 unit.

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Answer:

x = -7

Step-by-step explanation:

Since f(x) = [tex](x+7)(9x^2+5x+4)[/tex], we can set both equal to 0.

x + 7 = 0 will give us x = -7.

Now, in the second equation, we will plug into the quadratic formula, when we do that, the number inside the discriminator (which is the square root) is -119. A square root of a negative number is imaginary and not real.

Therefore, the only real zero of the polynomial is -7

There are 120 different combinations of 3 programmers that can be chosen to transfer to the new department

From the question, we have

Total number of programmers, n = 10

Numbers to programmers to select, r = 3

The number of ways of selection could be drawn is calculated using the following combination formula

Total = ⁿCᵣ

Where

n = 10 and r = 3

Substitute the known values in the above equation

Total = ¹⁰C₃

Apply the combination formula

ⁿCᵣ = n!/(n - r)!r!

So, we have

Total = 10!/(7! * 3!)

Evaluate

Total = 120

Hence, the number of ways is 120

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The value of x is 9.

According to the segment addition postulate, the sum of the lengths of two segments is equal to the length of the entire segment.

In this case, GH + HI = GI.

GH = 4x - 6

HI = 2x + 2

GI = 50

Using the segment addition postulate, we can write the equation:

GH + HI = GI

Substituting the given values:

4x - 6 + 2x + 2 = 50

Combining like terms:

6x - 4 = 50

Adding 4 to both sides:

6x = 54

Dividing both sides by 6:

x = 9

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There is approximately an 8.33% chance that two boys will pick the same style of watch from a set of 12 different styles.

To calculate the probability that two boys will pick the same style of watch from a set of 12 different styles, we need to know how many watches each boy will pick.

If each boy is picking one watch from the set of 12 styles independently, then we can calculate the probability as follows:

The first boy has 12 options to choose from.

The second boy also has 12 options, but in order to pick the same style as the first boy, he only has 1 option.

Therefore, the probability that both boys will pick the same style of watch is:

1/12

So, the decimal representation of this probability is approximately:

0.0833

Hence, there is approximately an 8.33% chance that two boys will pick the same style of watch from a set of 12 different styles.

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