In the diagram below, if < 2 is congruent to < 8, then lines a and b are parallel. What would the reason be for this statement?

After 5 years, the investment of $6,000 will grow to approximately $15,819.90 with an interest rate of 18% compounded annually.

If Charmaine places $6,000 in an account that pays 18% interest compounded annually, we can calculate the future value of the investment using the compound interest formula.

The formula to calculate the future value (FV) of an investment with compound interest is given by:

FV = P\((1 + r/n)^(n*t)\)

Where:

- FV represents the future value

- P represents the principal amount (initial investment)

- r represents the annual interest rate (in decimal form)

- n represents the number of compounding periods per year

- t represents the number of years

In this case, Charmaine places $6,000 in the account, the interest rate is 18% (0.18 in decimal form), and the interest is compounded annually (n = 1).

Let's calculate the future value of the investment after a certain number of years.

For example, if we want to find the future value after 5 years, we would substitute the values into the formula:

FV = 6000\((1 + 0.18/1)^(1*5)\)

Calculating this expression, we get:

FV = 6000(1 + 0.18)^(5)

  ≈ 6000\((1.18)^(5)\)

  ≈ 6000(2.63665)

  ≈ $15,819.90

Therefore, after 5 years, the investment of $6,000 will grow to approximately $15,819.90 with an interest rate of 18% compounded annually.

It's important to note that the compound interest formula assumes no withdrawals or additional deposits made during the investment period. Additionally, interest rates and compounding frequencies may vary depending on the specific terms and conditions of the account.

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Answer: The time it takes for a sum of money to amount to a certain amount at a certain interest rate can be calculated using the following formula:

Time = (100 x (Amount - Principal)) / (Principal x Rate)

In this case, the principal is Rs. 2000, the amount is Rs. 2240, and the rate is 4%. Therefore, the time is:

Time = (100 x (2240 - 2000)) / (2000 x 4) = 3 years

Therefore, it will take 3 years for Rs. 2000 to amount to Rs. 2240 at 4% simple interest.

Step-by-step explanation:

(i)  The partial fraction decomposition of\(100/(x^7 * (10 - x))\) is\(100/(x^7 * (10 - x)) = 10/x^7 + (1/10^5)/(10 - x).\) (ii) The expression for t in terms of x is t = 10 ± √(100 + 200/x).

(i) To express the rational function 100/(\(x^7\) * (10 - x)) in partial fractions, we need to decompose it into simpler fractions. The general form of partial fractions for a rational function with distinct linear factors in the denominator is:

A/(factor 1) + B/(factor 2) + C/(factor 3) + ...

In this case, we have two factors: \(x^7\) and (10 - x). Therefore, we can express the given rational function as:

100/(\(x^7\) * (10 - x)) = A/\(x^7\) + B/(10 - x)

To determine the values of A and B, we need to find a common denominator for the right-hand side and combine the fractions:

100/(x^7 * (10 - x)) = (A * (10 - x) + B * \(x^7\))/(\(x^7\) * (10 - x))

Now, we can equate the numerators:

100 = (A * (10 - x) + B * \(x^7\))

To solve for A and B, we can substitute appropriate values of x. Let's choose x = 0 and x = 10:

For x = 0:

100 = (A * (10 - 0) + B * \(0^7\))

100 = 10A

A = 10

For x = 10:

100 = (A * (10 - 10) + B *\(10^7\))

100 = B * 10^7

B = 100 / 10^7

B = 1/10^5

Therefore, the partial fraction decomposition of 100/(\(x^7\) * (10 - x)) is:

100/(\(x^7\) * (10 - x)) = 10/\(x^7\) + (1/10^5)/(10 - x)

(ii) Given the differential equation: dx/dt = (1/100) *\(x^2\) * (10 - x)

We are also given x = 1 when t = 0.

To solve this equation and obtain an expression for t in terms of x, we can separate the variables and integrate both sides:

∫(1/\(x^2\)) dx = ∫((1/100) * (10 - x)) dt

Integrating both sides:

-1/x = (1/100) * (10t - (1/2)\(t^2\)) + C

Where C is the constant of integration.

Now, we can substitute the initial condition x = 1 and t = 0 into the equation to find the value of C:

-1/1 = (1/100) * (10*0 - (1/2)*\(0^2\)) + C

-1 = 0 + C

C = -1

Plugging in the value of C, we have:

-1/x = (1/100) * (10t - (1/2)\(t^2\)) - 1

To solve for t in terms of x, we can rearrange the equation:

1/x = -(1/100) * (10t - (1/2)\(t^2\)) + 1

Multiplying both sides by -1, we get:

-1/x = (1/100) * (10t - (1/2)\(t^2\)) - 1

Simplifying further:

1/x = -(1/100) * (10t - (1/2)\(t^2\)) + 1

Now, we can isolate t on one side of the equation:

(1/100) * (10t - (1/2)t^2) = 1 - 1/x

10t - (1/2)t^2 = 100 - 100/x

Simplifying the equation:

(1/2)\(t^2\) - 10t + (100 - 100/x) = 0

At this point, we have a quadratic equation in terms of t. To solve for t, we can use the quadratic formula:

t = (-(-10) ± √((-10)^2 - 4*(1/2)(100 - 100/x))) / (2(1/2))

Simplifying further:

t = (10 ± √(100 + 200/x)) / 1

t = 10 ± √(100 + 200/x)

Therefore, the expression for t in terms of x is t = 10 ± √(100 + 200/x).

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Answer:480$

Step-by-step explanation:

Hope this helps

Answer:

480

Step-by-step explanation:

Answer:

y= -3x+1

Step-by-step explanation:

x1= -2 x2=2 y1=7 y2=-5

using the formula

(y-y1)/(x-x1)=(y2-y1)/(x2-x1)

(y-7)/(x-(-2))=(-5-7)/(2-(-2))

(y-7)/(x+2)=(-5-7)/(2+2)

(y-7)/(x+2)=(-12)/4

(y-7)/(x+2)=-3

cross multiply

y-7=-3(x+2)

y-7=-3x-6

y=-3x-6+7

y=-3x+1

For a given function, y = F(x), the function is known as an increasing function if the value of y increases as the value of x increases, and the function is known as a decreasing function if the value of y decreases as the value of x increases.

If f'(x)>0 or f'(x)0, then f is increasing in that interval; if f'(x)=0, then f is neither increasing nor decreasing in that interval.

You must first take the derivative, then make it equal to 0, and then determine which zero values the function is positive between in order to determine when a function is rising. In order to determine when the function is positive and, thus, rising, test values on all sides of these.

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Answer:

The answer to (m+3)(m-3) is m^2-9.

Step-by-step explanation:

We will use distributive law to solve this question.

m(m-3)+3(m-3)

= m^2-3m+3m-9

= m^2-9 (since, 3m-3m=0)

As an alternative method, we can use the direct rule learned in algebra: (a+b)(a-b)=a^2-b^2.

so, here a=m and b=3.

(m+3)(m-3)

=m^2-3^2

=m^2-9

Answer:

Step-by-step explanation:6 type

5/25=1/5=20%

1-1/5=4/5=80%

The types of candles are 6. And the probability of a small pink candle and NOT a small pink candle will be 0.20 and 0.80, respectively

Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.

Then the probability is given as,

P = (Favorable event) / (Total event)

The table is given below.

                     Small                 Medium              Large               Total

White               9                         3                        5                       17

Pink                 5                         2                         1                        8

Total               14                        5                         6                       25

The types of candles are given as,

⇒ 2 x 3

⇒ 6

The probability of a small pink candle is as,

P = 5/25

P = 0.20

The probability of NOT a small pink candle is as,

Q = 1 - P

Q = 1 - 0.20

Q = 0.80

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5. Area = 63.75 square units

Perimeter = 34 units

Sum of interior angles = 30 degrees

6. Area = 61. 40 square units

7. Length = 58. 2 units

We need to know that formula for calculating the area of a trapezoid is expressed as;

5. Area = a + b/2(h)

Substitute the values, we have;

Area = 6.5 + 10.5/2(7.5)

Add the values

Area = 63.75 square units

Perimeter = a + b+ c + d

Perimeter = 8.5 +6.5 + 10. 5 + 8.5

Add the values

= 34 units

6. Area of a sector is  = (θ/360º) × πr²

= 110/360 × 3.14 × 8²

Find the square and multiply

= 61. 40 square units

7. Length of an Arc = θ × (π/180) × r

Length = 210 × 3.14/180 × 16

Multiply the values

Length = 58. 2 units

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Answer:

0.625 is equal to 5/8 bag,

Step-by-step explanation:

Answer:

Less Than 1 Bag

Step-by-step explanation:

I-Ready

Step-by-step explanation:

option a 5 = 4x

Answer:

ln 5 = 4x

Step-by-step explanation:

Answer:

The price of each book without sales tax

Step-by-step explanation:

Answer:

0.40

Step-by-step explanation:

the constant rate of change is given to you in the problem.

The number of miles driven (n) and the total cost of renting the car (c) are related by a constant (k) as follows -

c - \(\frac{2}{5} n\) = k

We have a rental car company charges an upfront fee to rent a car, and then charges $0.40 per mile driven.

We have to determine the constant rate of change through which number of miles driven (n) and the total cost of renting the car (c) are related.

Initial count = x

Count increasing per second = 5

Assume that the bacteria count after t seconds is y. Then -

y = x + 5t

for t = 30 ↔ y = 150 + x

According to the question, we have -

Charge per mile driven = $0.40

n - represents the varying number of miles that you drive in the car.

c - represent the total cost (in dollars) you will have to pay for the rental car.

Assume that the upfront fee to rent a car is - $k

Total charge for driving 'n' miles after paying the upfront fee - $0.40n

The total cost for driving 'n' miles in a rental car -

c = k + 0.40n

c - \(\frac{2}{5} n\) = k

Where k is a constant and is equal to upfront fee.

Hence, number of miles driven (n) and the total cost of renting the car (c) are related by a constant (k) as follows -

c - \(\frac{2}{5} n\) = k

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Answer:

x + 2y = 6

2y = -x -6

y = - 1/2 x - 3

From the equation, the y intercept is -3

Put y = 0,

-1/2 x -3 = 0

-1/2 x = 3

x = -6

Therefore, x intercept = -6

If he wants an average of 84, he needs to get at least 93 points.

Remember that the average value between 3 values A, B, and C is:

(A + B + C)/3

Here we know that the first two scores are 76 and 83 points, let's say that the third score is x, if we want to have an average of 84 or more, then we need to solve:

(76 + 83 + x)/3 = 84

159 + x = 252

x = 252 - 159

x = 93

So he needs to get at least 93 points in the next exam.

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Answer:

This relation does not represent a function because the domain 1 repeats.

The domain restrictions for (f/g)(x) are (c) x = 0, 6

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

f(x) = x² - 5x - 6

g(x) = x² - 6x

The composite function (f/g)(x) is calculated as

(f/g)(x) = f(x)/g(x)

substitute the known values in the above equation, so, we have the following representation

(f/g)(x) = (x² - 5x - 6 )/(x² - 6x)

For the domain restriction, we have

x² - 6x = 0

When solved, we have

x =  6 or x = 0

Hence, the domain restrictions for (f/g)(x) are (c) x = 0, 6

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Question

Given f(x) = x² - 5x - 6 and g(x) = x² - 6x, what are the domain restrictions

for (f/g)(x)?

A) x = +6

B) x = 0

C) x = 0,6

D) x = -2,6

Answer:

\(2a^2b*(3a^2-5ab-3b^2)\)

Step-by-step explanation:

Attempt factorization by grouping

(((6•(a^4))•b)-((10•(a^3))•(b^2)))-((2•3a^2)•b^3)

(((6•(a^4))•b)-((2•5a^3)•b^2))-(2•3a^2b^3)

(((2•3a^4) • b) -  (2•5a^3b^2)) -  (2•3a^2b^3)

6a^4b - 10a^3b^2 - 6a^2b^3  =  2a^2b • (3a^2 - 5ab - 3b^2)

Pull out the leading term and put it with the original equation

= 2a^2b • (3a^2 - 5ab - 3b^2)

This would be one of the quicker ways to factor this equation.

Hope this helps.

The number that belongs in the green box using sine rule is 13.96.

The rule of sine or the sine rule states that the ratio of the side length of a triangle to the sine of the opposite angle, which is the same for all three sides.

To calculate the number that belongs in the green box, we use the formula below

Formula:

From the diagram,

Given:

Substitute these values into equation 1

Solve for x

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Answer:

Step-by-step explanation:

MEAN - a). Finds the mean of a numerical data set.

MIN - f). Finds the lowest value of a data set.

COUNT - c). Counts the number of values input for a highlighted data set

MEDIAN - d). Finds the middle value of a numerical data set

MAX - e). Finds the greatest value for a data set

SUM - g). Adds all the numbers in a highlighted range together

MODE - b). Finds the number that occurs most often in a highlighted data set.

Answer:

X = 9, -1

Step-by-step explanation:

1, Factor it

(x-9) (x+1) = 0

2. Both of a factor will = 0

x-9 = 0

x+1=0

3. Solve

x=9

x=1

SOLUTION:

Step 1 :

In this question, we are meant to find the interval notations that represents the range of the graph.

Step 2:

From the graph, we can see that the co -coordinates of A, B , C , D and E are as follows:

From the graph, we can estimate the co-ordinates as follows:

Step 3:

Now, we are to get the interval that represents the range of the graph:

From the graph, we can see that:

Now, to get the range, we can see that:

The correct interval notation that represents the range of the notation is :

Reason :

This is because all the values of y- co-ordinates are contained in the interval:

Answer: 26/75

(4/15) ÷ (10/13) (Multiply the reciprocal of 10/13)

= (4/15) · (13/10) (Cancel out the common factor of 2)

= (2/15) · (13/5) (Multiply the numerators together and denominators together)

= 26/75

Answer:

Hcf of this will 4y I m sure because 4y divide that totally and it is greatest

Answer:

x= -2

y= 0

Step-by-step explanation:

check answer

5(-2)-4(0)= -10

-10-0= -10 (TRUE)

-4(-2)+5(0)= 8

8+0= 8 (TRUE)

Answer: 5x−4y=−10;−4x+5y=8

Step-by-step explanation:

Answer:

commutative property of multiplication

Step-by-step explanation:

Answer:

Multiplication Property

The situation Veronica receives $21 for babysitting, and then spends the same amount, $21, on a new shirt quantities combine to make 0.The correct answer is option C.

When we add +21 (the money she receives) and subtract -21 (the money she spends), the result is 0. This means that the net change in Veronica's money is zero, indicating that the quantities combine to make 0.

In situations A, B, and D, the quantities do not combine to make 0. In situation A, the player earns 4 points for getting an answer right and then earns an additional 4 points for making it around the board.

The total points earned in this situation would be 8, which is not equal to 0.

In situation B, the car is initially filled with 10 gallons of gas, but then half of that, which is 5 gallons, is used on a day's drive. The remaining fuel in the car would be 5 gallons, which is also not equal to 0.

In situation D, the bird flies 25 feet up in the air and then 25 feet across to its nest. The total distance traveled by the bird would be 50 feet, which is not equal to 0.

Therefore, only in situation C, where Veronica receives and spends the same amount of money, do the quantities combine to make 0.

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The probable question may be:

In which of these situations do the quantities combine to make 0?

A. A player a game earns 4 points for getting an answer right. She then earns 4 points for making it around the board.

B. A car is filled with 10 gallons of gas. Half of the 10 gallons are then used on a day's drive.

C. Veronica receives $21 for babysitting. She then spends $21 on a new shirt.

D. A bird flies 25 feet up in the air. It then flies 25 feet across to its nest.

Answer:

She will pay $13.9 for 7.56 liters

Step-by-step explanation:7.56 minus 3.78 equals to 3.78. This means we can just simply add another $6.95, so $6.95 plus $6.95 equals to $13.9

Answer:

Between step 4 and final answer, the incorrect square root is used as a multiplier

Step-by-step explanation:

Process should be

-5√11 + 15√(6 • 4)

-5√11 + 15√6 • √4

-5√11 + 15√6 • 2

-5√11 + 30√6