Write an equation of the line that passes through each pair of points (5,-3), (2,5)

Answer:

the answer is C

Step-by-step explanation:

Answer:

a set of four data pairs with a correlation coefficient r = –0.8

Step-by-step explanation:

edg 2022

The error is present in second step when cancelling numerator and denominator and the solution of the expression \((1+1/x)/(1-1/x^{2} )\) is \(x/x-1\).

Given Expression \((1+1/x)/(1-1/x^{2} )\) and incorrect solution. and we need to identify the error and solve the expression correctly.

The expression is \((1+1/x)/(1-1/x^{2} )\)

In the solution given the second step of cancelling 1's in numerator and denominator is wrong.

The solution which is correct is as under:

\((1+1/x)/(1-1/x^{2} )\)

firstly take LCM in numerator and denominator

=\((x+1)/x/(x^{2} -1)/x^{2}\)

Now we can write the expression properly.

=\((x+1)*x^{2} /(x^{2} -1)*x\)

Power of \(x^{2}\) to be deducted from x

=\((x+1)*x/(x^{2} -1)\)

Now \(x^{2} -1\) can be written as (x+1)(x-1)

=\((x+1)*x/(x+1)(x-1)\)

(x+1) will be deducted now from numerator and denominator.

=x/(x-1)

Hence the solution of the given expression is x/(x-1).

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The answer to this question is x/x₋1

Given the expression is 1₊1/x /1₋1/x²

Take the LCM of the denominators

we get, x₊1/x / x²₋1/x²

Now multiply the expression

=x₊1/x × x²/x²₋1

=(x₊1) x²/ x(x²₋1)

(x²₋1) is in the form of (a²₋b²)=(a₊b)(a₋b)

Therefore, (x₊1)x²/x(x₋1)(x₊1)

After cancelling like terms we get the answer as:

x/(x₋1)

Hence we get the simplification answer as x/(x₋1).

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Answer:

Y = - 2

Step-by-step explanation:

Answer:

304

Step-by-step explanation:

8 x 13 = 104

+200

304

Answer:

96feet

Step-by-step explanation:

U want to find displacement

So

Displacement = velocity x time

Velocity = - 8 feet/s ( negative bcuz going down)

Time = 13

Displacement = - 8 x 13

= - 104

Therefore

200 - 104 = 96feet

For the function y = -3sin(4x - π/3), the amplitude is 3, the period is π/2, and the phase shift is -π/12.

To find the amplitude, period, and phase shift of the function y = -3sin(4x - π/3), we'll analyze the given equation:

1. Amplitude: The amplitude is the absolute value of the coefficient of the sine function. In this case, the coefficient is -3, so the amplitude is |-3| = 3.

2. Period: The period of a sine function is given by the formula (2π) / |B|, where B is the coefficient of the angle inside the sine function. Here, B = 4, so the period is (2π) / 4 = π/2.

3. Phase shift: The phase shift is the value that shifts the graph of the function horizontally. It is given by the expression C / B, where C is the constant added to the angle inside the sine function. In this case, C = -π/3, and B = 4. The phase shift is (-π/3) / 4 = -π/12.

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Answer:

8463.36 m^2

Explanation:

Given the length(l) of the rectangle as 82m and the width(w) as 64m, we can go ahead and determine the area of the rectangle as follows;

The two semi-circles are equivalent to one circle with a diameter of 64m, so the radius of the circle will be;

Let's go ahead and determine the area of the circle given pi as 3.14;

Therefore, the area of the training field can be determined by adding the area of the rectangle and that of the two semicircles;

So you will have $4268.12 when you retire at the age of 65.

The principal, or initial balance of your account, is where discussion of interest begins. This may represent an initial investment or the principal of a loan. In its most basic form, interest is computed as a percentage of the principle. As an illustration, if you agreed to borrow $100 from a friend and repay it with 5% interest, the interest you would pay would simply be 5% of $100: $100(0.05) = $5. Your repayment would total $105, which would include the initial principal plus interest.

Given that : At age of 25, you began saving for retirement. the plan: deposit $150 at the end of each month into an ira that pays 8.4% compounded monthly

\(P_{n} = P_{o}(1 + \frac{r}{k})^{nk}\)

The account's balance after N years is represented by \(P_{n}\).

\(P_{o}\) is the account's opening balance (also called initial deposit, or principal)

The annual interest rate is expressed as r.

The number of compounding cycles in a year is k.

\(P_{40} = 150(1+\frac{0.084}{12})^{40.12}\)

= $4268.12

So you will have $4268.12 when you retire at the age of 65.

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The percentage of vacation cost that is charged to the credit card would be 55 %.

To determine the percentage of the vacation cost that is charged on a credit card, we divide the amount charged on the credit card ($1240) by the total cost of the vacation ($2252) and multiply by 100 to express it as a percentage.

Percentage charged on the credit card = (Amount charged on the credit card / Total cost of the vacation) x 100

= ( 1, 240 / 2, 252) x 100

= 0. 550 x 100

= 55 %

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Answer:

y=2(x square)-2x-3

Step-by-step explanation:

Let dy with y varibles in a hand

And dx with x variables on the other hand

dy=(4x-2)dx

Then by integration

y=2(square x)-2x+constant

Then substitute by x=-1 and y=1 to find the value of the constant

1=2(1)-2(-1)+ constant

Then constant=-3

Then the equation is

y=2(x square)-2x-3

Answer:

Metric

"Metric" means a unit, or measurement.

Hope this helps, have an awesome day! ♣

Can I have brainliest?

Answer:

s=W/F 2800J/700N=4m so the answer is 4m

Since the length of the string is not specified, we cannot find the Y value (fret position) exactly.

Given in this word problem:

Length of the string: Not specified

Number of notes higher than the root note: 3 (G note is 3 notes higher than the E string's root note)

Scale: Not specified

The equation for the fret position can be represented as follows:

fret position = length of string * 2^(-12 * n)

where n is the number of notes higher than the root note.

To find the X value, we need to know the length of the string, which is not specified in the problem.

To find the Y value, we need to calculate the fret position using the equation:

fret position = length of string * 2^(-12 * n)

fret position = length of string * 2^(-12 * 3)

fret position = length of string * 2^-36

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50,400 different anagrams can be made from the letters in the word statistics.

Given word : STATISTICS

Anagrams are words formed by jumbling the positions of the letters given in the word.

For such problems we do factorial of number of words and divide by the repeated letters factorials.

Total number of letters = 10

They can be permutated among themselves in 10! ways.

Some letters are repeated in word STATISTICS

Since, there are 3 S's and 3 T's and 2 I's

So, Number of anagrams = \(\frac{10!}{3!.3!.2!}\)

= \(\frac{10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3!}{3! \times 3 \times 2 \times 1 \times 2 \times 1}\)

= \(\frac{10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4}{3 \times 2 \times 2}\)

= 10 × 9 × 8 × 7 × 2 × 5

= 50,400

50,400 different anagrams can be made from the letters in the word statistics.

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Answer:

angleC = 35°

Step-by-step explanation:

Because AC is the diameter of the circle, angle B = 90°

Then we can use the idea that there are 180° in a triangle to find angle C.

55 + 90 + c = 180

145 + c = 180

c = 35

The measure of angleC = 35°

Answer:

a. \(\dfrac{dx}{dt} = 6\frac{2}{3} \cdot c\)

b. \(x(t) = 6\frac{2}{3} \cdot c \cdot t\)

c. \(c = \dfrac{3}{8} \ g/L\)

Step-by-step explanation:

a. The volume of water initially in the fish tank = 15 liters

The volume of brine added per minute = 5 liters per minute

The rate at which the mixture is drained = 5 liters per minute

The amount of salt in the fish tank after t minutes = x

Where the volume of water with x grams of salt = 15 liters

dx =  (5·c - 5·c/3)×dt = 20/3·c = \(6\frac{2}{3} \cdot c \cdot dt\)

\(\dfrac{dx}{dt} = 6\frac{2}{3} \cdot c\)

b. The amount of salt, x after t minutes is given by the relation

\(\dfrac{dx}{dt} = 6\frac{2}{3} \cdot c\)

\(dx = 6\frac{2}{3} \cdot c \cdot dt\)

\(x(t) = \int\limits \, dx = \int\limits \left ( 6\frac{2}{3} \cdot c \right) \cdot dt\)

\(x(t) = 6\frac{2}{3} \cdot c \cdot t\)

c. Given that in 10 minutes, the amount of salt in the tank = 25 grams, and the volume is 15 liters, we have;

\(x(10) = 25 \ grams(15 \ in \ liters) = 6\frac{2}{3} \times c \times 10\)

\(6\frac{2}{3} \times c =\dfrac{25 \ grams }{10}\)

\(c =\dfrac{25 \ g/L }{10 \times 6\frac{2}{3} } = \dfrac{25 \ g/L}{10 \times \dfrac{20}{3} } =\dfrac{3}{200} \times 25 \ g/L= \dfrac{75}{200} \ g/L = \dfrac{3}{8} \ g/L\)

\(c = \dfrac{3}{8} \ g/L\)

Answer:

11 hours

Step-by-step explanation:

270/18=15 per hour

so 165/15 = 11

Answer:

11 hours

Step-by-step explanation:

270:18 simplified is 15:1

165/15 = 11

Hope this helps!

Answer:

12

Step-by-step explanation:

In an equation left side = right side.

Answer:

x=16

Step-by-step explanation:

if the lines were parallel then that means that (7x+2) = (8x-14) because they are corresponding angles. just isolate the varible so subtract 7x from both sides and add 14 to both sides. and they you get x=16

Answer:

Solution :

{x,y} = {0/14261512,4}

Step-by-step explanation:

Solve by Substitution :

// Solve equation [2] for the variable y

[2] y = x + 4

// Plug this in for variable y in equation [1]

[1] 12x - 5•(x +4) = -20

[1] 7x = 0

// Solve equation [1] for the variable x

[1] 7x = 0

[1] x = 0

// By now we know this much :

x = 0

y = x+4

// Use the x value to solve for y

y = (-0/14261512)+4 = 4

Generally, the angles with their sines equal to 1/2 is 30 degree angles.

In a right-angled triangle, the side opposite to the 30 degree angle is equal to half of the hypotenuse's length.

We see that JK = JM/2, therefore the angle opposite to JK (KMJ) is 30 degrees.

Similarly, KM = LM/2, so the angle opposite to KM (KLM) is 30 degrees.

If we look at the big right-angled triangle, JM = JL/2 so that also proves that KLM equals 30 degrees.

The solution is that, KLM equals 30 degrees, so this angle in the figure is the sine equal to 1/2.

Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles

here, we have,

The six trigonometric functions are sin , cos , tan , cosec , sec and cot

Let the angle be θ , such that

sin θ = opposite / hypotenuse

cos θ = adjacent / hypotenuse

tan θ = opposite / adjacent

here, we have,

we know that,

Generally, the angles with their sines equal to 1/2 is 30 degree angles.

In a right-angled triangle, the side opposite to the 30 degree angle is equal to half of the hypotenuse's length.

We see that

JK = JM/2,

therefore the angle opposite to JK (KMJ) is 30 degrees.

Similarly, KM = LM/2,

so the angle opposite to KM (KLM) is 30 degrees.

If we look at the big right-angled triangle,

JM = JL/2

so that also proves that KLM equals 30 degrees.

Hence, The solution is that, KLM equals 30 degrees, so this angle in the figure is the sine equal to 1/2.

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The expression for the power delivered to a resistance in terms of csc^2 2 pi ft is P = I^2_0 R (csc^2 2 pi ft).

According to the given information, the power delivered to a resistance R when an alternating current of frequency f and peak current I_0 passes through it is represented by the equation P = I^2_0 R sin^2 2 pi ft.

To express this equation in terms of csc^2 2 pi ft, we can use the trigonometric identity csc^2 x = 1/sin^2 x. Substituting this identity into the equation, we get P = I^2_0 R (1/sin^2 2 pi ft).

Since csc^2 x is the reciprocal of sin^2 x, we can rewrite the equation as P = I^2_0 R (csc^2 2 pi ft). This expression represents the power delivered to the resistance in terms of csc^2 2 pi ft.

Therefore, the correct expression for the power delivered to the resistance in terms of csc^2 2 pi ft is P = I^2_0 R (csc^2 2 pi ft).

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Nina originally had more than 105 songs on her MP3 player

Information about the problem:

To solve this problem, we have to state the equation using the information of the problem:

Initial song + songs added > Total songs

x + 15 > 120

x > 120 - 15

x > 105 song

We can say that they are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.

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$7.50

Step-by-step explanation:

$2.50 x 3 = $7.50

We multiplied it by 3, because 20 x 3 is 60, and Mr. Dennis bought 60 ounces.

Janet can simplify and solve the resulting equation to find the Value(s) of y.(y^2 - 1)(y + 1) * (y + y^2 - 5) = (y^2 - 1)(y + 1) * (y^2 + y + 2)

To solve the equation y + y^2 - 5 / (y^2 - 1) = y^2 + y + 2 / (y + 1), Janet needs to get rid of the denominators in order to simplify the equation and solve for y. One way to do this is by multiplying both sides of the equation by the common denominator of all the fractions involved.

In this case, the common denominator is (y^2 - 1)(y + 1). So, Janet should multiply both sides of the equation by (y^2 - 1)(y + 1) to eliminate the denominators.

Multiplying both sides by (y^2 - 1)(y + 1) yields:

(y^2 - 1)(y + 1) * (y + y^2 - 5) / (y^2 - 1) = (y^2 - 1)(y + 1) * (y^2 + y + 2) / (y + 1)

By multiplying, we cancel out the denominators:

(y^2 - 1)(y + 1) * (y + y^2 - 5) = (y^2 - 1)(y + 1) * (y^2 + y + 2)

Now, Janet can simplify and solve the resulting equation to find the value(s) of y.

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Step-by-step explanation:

There is ONE at the beginning then one every 16 yards to the end

2 km = 2000 m  = 2187.2266 yards

2187.2266 yds / (16 yds /marker) = 136.7 = ~137     PLUS the one at the start = 138  markers

The probability that the Austin orphaned pet is a dog is 32.34%.

The probability that the Austin orphaned dog is a Chihuahua is 29.38%.

Probability determines the chances that an event would happen in a random event. The probability the event occurs is 1 and the probability that the event does not occur is 0.

The probability that an orphaned pet in an animal shelter in Austin is a dog = total number of dogs in Austin / total number of pets

(2.76 + 2.86 + 3.44 + 2.65) / (2.76 + 2.86 + 3.44 + 2.65 + 24.50) =

11.71/36.21 = 32.34%

The probability that an orphaned dog in the same animal shelter in Austin is a Chihuahua = total number of Chihuahua in Austin /  total number of dogs in Austin

3.44 / 11.71 = 29.38%

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Answer:

true

Step-by-step explanation:

Answer:

A or D

Step-by-step explanation:

Answer: x1  = 5

               x2 = 1

Step-by-step explanation:

1. Identify the coefficients

2. Move the constant to the right side of the equation and combine

3.  Complete the square

4. Solve for x

Answer:

x = 5 and 1

Step-by-step explanation:

\(x^2-6x+5=0\\x_{1,\:2}=\frac{-\left(-6\right)\pm \sqrt{\left(-6\right)^2-4\cdot \:1\cdot \:5}}{2\cdot \:1}\\x_{1,\:2}=\frac{-\left(-6\right)\pm \:4}{2\cdot \:1}\\\rightarrow x_1=\frac{-\left(-6\right)+4}{2\cdot \:1},\:x_2=\frac{-\left(-6\right)-4}{2\cdot \:1}\\\\\frac{-\left(-6\right)+4}{2\cdot \:1}\\\\=\frac{6+4}{2\cdot \:1}\\\\=\frac{10}{2\cdot \:1}\\\\=\frac{10}{2}\\\\=5\\\\\\\frac{-\left(-6\right)-4}{2\cdot \:1}\\\\=\frac{6-4}{2\cdot \:1}\\\\=\frac{2}{2\cdot \:1}\\\\=\frac{2}{2}\\\\=1\)

====================================================

Work Shown:

r = 3 is the radius of the circular base

h = 12 is the height of the cylinder

pi = 3.14 approximately

SA = surface area of the cylinder

SA = 2pi*r^2 + 2pi*r*h

SA = 2*3.14*3^2 + 2*3.14*3*12

SA = 282.6