8+10p=12+10p-4
Help me please

Answer:

distance = 7.07 units

Step-by-step explanation:

x difference = 7

y difference = -1

using the Pythagorean theorem:

7² + -1² = d²

d² = 49 + 1 = 50

d = 7.07

Answer:

7.1

Step-by-step explanation:

distance between the x is 7 and y is 1

And to find the hypotenuse, you use the quadratic formula, 7^2 + 1^2 = c^2

c=50

and take the square root, which is 7.071, rounds to 7.1

The bicycle is moving at a speed of 14,356 meters per hour.

Here, we are given that the wheel of a bicycle is spinning at the rate of 150 revolutions per minute.

The diameter of the wheel is 20 inches

⇒ radius = 10 inches

⇒ circumference of the wheel = 2 × π × 10

= 20π

Thus, the wheel will cover a distance of (20π × 150) inches in a minute

= 300π

now, we know that 1 inch = 0.254 meters

⇒ 300π inches = 300π × 0.254

= 76.2π

Thus, the bicycle covers 76.2π meters in a minute

⇒ it'll cover 76.2π × 60 meters in an hour

= 4572π

= 4572 × 3.14

= 14,356.08

Thus, the bicycle is moving at a speed of 14,356 meters per hour.

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Answer:

6.4 - 0.4y

Step-by-step explanation:

Answer:

6.4-0.4y

Step-by-step explanation:

First you subtract 2.5 from 8.9. Then you subtract 4 from 3.6. Hope that is the correct answer.

Answer:

a) 7/4 b) 5 c) 2

Step-by-step explanation:

Logrithmic Rule for a and b

Let a, M, N be positive real numbers.

a)  

logaM - logaN = loga(M/N)

log9(7) - log9(4) = log9 (7/4)

b)

logaM + logaN = logaMN

log2 (x) + log2(9) = log2(45)

x9=45

(x9)/9 = 45/9

x = 5

c)

Change of base formula.

logb​(x)=logd​(b)/logd​(x)​

x log6(5) = log6(25) divide each term by log6(5)

x log6(5) / log6(5) = log6(25) / log6(5)   Cancel common factor log6(5)

x = log6(25) / log6(5)

x = log6(5^2) / log6(5)

Expand log6(5^2) by moving 2 outside the logarithm.

x = 2log6(5) / log6(5) cancel the like term log6(5)

x = 2

Answer:

x=-3

Step-by-step explanation:

2 x - 3 y = -12.

4 x + y =  -10.

Answer:

X=3

Step-by-step explanation:

Trust me ;))

A part of a line that has 1 endpoint and extends indefinitely in only one direction is called a ray.

A ray is named using its endpoint first, and then any other point on the ray

Properties of ray:

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Answer:1

14

Step-by-step explanation:

substitue 60 into 1.6

y = 1.6(60) + 48

96 + 48

144

2

The first term of the infinite geometric series is 625.Let's dive deeper into the explanation.

We are given that the sum of the infinite geometric series is \(\( \frac{15625}{24} \)\)and the common ratio is\(\( \frac{1}{25} \).\)The formula for the sum of an infinite geometric series is \(\( S = \frac{a}{1 - r} \)\), where \( a \) is the first term and \( r \) is the common ratio.
Substituting the given values into the formula, we have \(\( \frac{15625}{24} = \frac{a}{1 - \frac{1}{25}} \).\)To find the value of \( a \), we need to isolate it on one side of the equation.
To do this, we can simplify the denominator on the right-hand side.\(\( 1 - \frac{1}{25} = \frac{25}{25} - \frac{1}{25} = \frac{24}{25} \).\)
Now, we have \(\( \frac{15625}{24} = \frac{a}{\frac{24}{25}} \).\) To divide by a fraction, we multiply by its reciprocal. So, we can rewrite the equation as \( \frac{15625}{24} \times\(\frac{25}{24} = a \).\)
Simplifying the right-hand side of the equation, we get \(\( \frac{625}{1} = a \).\)Therefore, the first term of the infinite geometric series is 625.
In conclusion, the first term of the given infinite geometric series is 625, which corresponds to option (a).



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Answer:

x=-13, y=-4

Step-by-step explanation:

Answer: x=-7    y=-2

Step-by-step explanation:

x+2y=-11

3y=x+1

x=-2y-11    (1)

3y=x+1      (2)

Substitute the value of x of equation (1) into equation (2):

3y=-2y-11+1

3y=-2y-10

3y+2y=-2y-10+2y

5y=-10

Divide both parts of the equation by 5:

y=-2

Substitute the value of y=-2 into equation (1):

x=-2(-2)-11

x=4-11

x=-7

Thus, (-7,-2)

Answer:

P = 12x should be the answer.

Hope this helps!

From V

The cosine function that describes the graph is given as follows:

y = 4cos(0.5πx) - 2.

The function is at it's maximum value at the origin, hence it is a cosine function.

The function is defined as follows:

y = Acos(Bx) + C.

In which the parameters are given as follows:

The function has a maximum value of 2 and a minimum value of -6, for a difference of 8, hence the amplitude is given as follows:

2A = 8

A = 4.

The shortest distance between repetitions is of 4 units, hence the period is of 4 and the coefficient B is given as follows:

2π/B = 4

4B = 2π

B = 0.5π.

The function oscillates between -6 and 2, while with no vertical shift it would oscillate between -A = -4 and A = 4, hence the coefficient C is given as follows:

C = -2.

Hence the function is:

y = 4cos(0.5πx) - 2.

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Answer:

-2

Step-by-step explanation:

For the given expression to be undefined, this means that the denominator must be zero.

From the given expression, the denominator is x + 2

Equating this to zero;

x+2 = 0

Subtract 2 from both sides

x+2-2 = 0 -2

x = -2

Hence the value of x that makes it undefined is -2

The solution set of a homogeneous system of 18 linear equations in 20 variables lies in the null space of the coefficient matrix.

To know that every associated nonhomogeneous equation has a solution, we need to ensure that the homogeneous system has a nontrivial solution.

This means that we need to know whether the rank of the coefficient matrix of the homogeneous system is less than the number of variables, i.e., whether there exist free variables.

If the rank is less than the number of variables, then there are infinitely many solutions to the homogeneous system, and thus every associated nonhomogeneous equation has a solution.

However,

We also need to ensure that the particular solution to the nonhomogeneous equation does not lie in the null space of the coefficient matrix.

This is equivalent to checking whether the null space of the coefficient matrix is orthogonal to the vector on the right-hand side of the nonhomogeneous equation.

If it is, then the nonhomogeneous equation has a solution.

So, in summary, to know that every associated nonhomogeneous equation has a solution.

We need to know whether the rank of the coefficient matrix of the homogeneous system is less than the number of variables, and we need to check whether the particular solution lies in the null space of the coefficient matrix.

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The outcomes of five students' quizzes in both science and English had a 0.23 correlation coefficient, or r.

By calculating the square root of the total squared variances, one may calculate the standard deviation. On that normal distribution curve, a line drawn one standard deviation (or one sigma) above or below the average value would represent a zone having 68 percent of the data points.

given

6.4 = average score for English

is the standard deviation

number of observations = 5

standard deviation  = 1.6

Correlation (r) coefficient

\(r = 1/(n - 1) (n - 1) [((X-m1)/s1) * ((Y-m2-m2/s2)]\)

\((-0. 2 * 0.625) + (-0.7 * - 1.25) + (1.3 * - 0.625) + (-1.2 * 0) + (0.8 * 1.25) = 0.9375\)

\(r = 0.9375/(5-1)\s= 0.234\s= 0.23\)

The outcomes of five students' quizzes in both science and English had a 0.23 correlation coefficient, or r.

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Vertically compressing the exponential parent function f(x) = 2^x by a factor of 3 means multiplying every function value by 1/3, resulting in a steeper and narrower curve closer to the x-axis.

If we vertically compress the exponential parent function f(x) = 2^x by a factor of 3, it means that every point on the graph of the function will be compressed closer to the x-axis. In other words, the function values will be multiplied by 1/3.

Let's consider a point on the original exponential function, (x, f(x)). After the vertical compression, this point will have the coordinates (x, (1/3)f(x)). For example, if f(x) = 8 for some x, after compression, the corresponding point will be (x, (1/3)(8)) = (x, 8/3).

This vertical compression affects all points on the graph uniformly, resulting in a steeper and narrower curve compared to the original exponential function.

The y-values of the compressed function will be one-third of the y-values of the original function for each x-value. Therefore, the graph will be squeezed vertically, with the y-values closer to the x-axis.

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The required Matlab code to find the greatest common divisor of a number using the Euclidean algorithm is shown.

To find the greatest common divisor (GCD) of two numbers using the Euclidean algorithm in MATLAB, you can use the following code:

% Replace '12345678' with your actual student number

studentNumber = '12345678';

% Extract the first 4 digits as the first number

firstNumber = str2double(studentNumber(1:4));

% Extract the last 3 digits as the second number

secondNumber = str2double(studentNumber(end-2:end));

% Find the GCD using the Euclidean algorithm

gcdValue = gcd(firstNumber, secondNumber);

% Display the result

disp(['The GCD of ' num2str(firstNumber) ' and ' num2str(secondNumber) ' is ' num2str(gcdValue) '.']);

Make sure to replace '12345678' with your actual student number. The code extracts the first 4 digits as the first number and the last 3 digits as the second number using string indexing. Then, the gcd function in MATLAB is used to calculate the GCD of the two numbers. Finally, the result is displayed using the disp function.

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Given data:

The principal is

The time is

The interest is

Concept:

The formula to calculate interest rate (R) is given below as

By substituting the values in the formula above, we will have

Hence,

The final answer is 5%

Answer: 5n+30

( The problem was incomplete on my end )

( Hope this helps )

the probability that the coin will lie entirely within one of the target squares is 1/32.

To find the probability that the coin will lie entirely within one of the target squares, we need to consider the ratio of the area of the target squares to the total area of the chessboard.

The total area of the chessboard is given by the sum of the areas of all the squares. Since each square measures 2" x 2", the total area is:

Total Area = (2" x 2") x (number of squares)

The number of squares on a chessboard is 64, so the total area is:

Total Area = (2" x 2") x 64 = 256"

Now, let's consider the area of one target square. Since it measures 2" x 2", the area is 4".

To calculate the probability, we divide the area of the target squares by the total area:

Probability = (Area of target squares) / (Total Area)

Probability = (4" x 2) / 256"

Probability = 8 / 256

Simplifying the fraction, we get:

Probability = 1 / 32

Therefore, the probability that the coin will lie entirely within one of the target squares is 1/32.

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Answer:

B

Step-by-step explanation:

The solutions of the system of equations are option (A) (3, 7) and (-3, -5)

To solve the system of equations, use the concept of substitution, which involves solving one equation for one variable and then substituting that expression into the other equation to eliminate one variable and solve for the other variable.

In this case, solve equation (1) for y in terms of x and substitute that expression into equation (2), which allowed us to solve for x. Then we used the values of x to find the corresponding values of y.

Here we have

y = 2x + 1 --- (1)

y = x²+ 2x -8 --- (2)

From (1) and (2)

=>  x²+ 2x - 8 = 2x + 1

Subtract 2x + 1 from both sides

=>  x²+ 2x - 8 - 2x - 1 =  2x + 1 - 2x - 1  

=> x² - 9 = 0

Now add 9 on both sides

=> x² - 9 = 0 + 9

=> x² = 9

=> x = √9  

=> x = ± 3

From (1)

At x = 3

=> y = 2(3) + 1 = 7

At x = - 3

=> y = 2(-3) + 1 = - 5

Therefore,

The solutions of the system of equations are option (A) (3, 7) and (-3, -5)

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Answer:

6 servings

Step-by-step explanation:

Let's say there are x 2/3 cup servings in a 4 cup container.

We multiply 2/3 by x to get the amount of cups that will produce and set that equal to 4 (because we want 4 cups):

(2/3) * x = 4

Divide both sides by 2/3, or multiply both sides by the reciprocal 3/2:

x = 4 * (3/2) = 12/2 = 6

The answer is 6 servings.

Answer:

9. 89

Step-by-step explanation:

A squared + B squared = C squared

7 squared + 7 squared = 98 squared

Find the square root of 98 (I recommend using a calculator)

You should get 9.89 as an answer.

The equation for the circle with a diameter whose endpoints are (2, -5) and (-3, 1) is (x - 1)^2 + (y - 1)^2 = 13.

The endpoints are (2, -5) and (-3,1).

The standard form equation for a circle is known as

\((x-a)^2+(y-b)^2=r^2\)

where (a, b) are the center's coordinates and (r) is the radius.

Taking into account the stated endpoints of the diameter. The center will then be at the midpoint, and the radius will be the distance between the center and either of the two endpoints.

Calculating the midpoint is as follows:

\(\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)\)

where, \((x_{1},y_{1})\) and \((x_{2},y_{2})\) are two points.

Now putting the values

\(\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)=\left(\frac{-2+4}{2}, \frac{3-1}{2}\right)\)

\(\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)=\left(\frac{2}{2}, \frac{2}{2}\right)\)

\(\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)=\left(2, 1)\)

Now we determine the equation of circle.

The center (2, 1) and the terminal are the two points (-2, 3).

r = \(\sqrt{(-2-1)^2+(3-1)^2}\)

r =\(\sqrt{(-3)^2+(2)^2}\)

r = \(\sqrt{9+4}\)

r = √13

Now we can write the equation of circle as:

(x - 1)^2 + (y - 1)^2 = (√13)^2

(x - 1)^2 + (y - 1)^2 = 13

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The complete question is:

Find the equation for the circle with a diameter whose endpoints are (2, -5) and (-3, 1).

Write the standard equation for the circle.

Step-by-step explanation:

11dvccvgtgcgt5cjuuhh

The estimated current price of the stock is $57.83.

To calculate the stock's current price, we can use the dividend discount model (DDM). The DDM states that the price of a stock is equal to the present value of its future dividends.

In this case, the dividend is expected to grow at a rate of 24% per year for the next 2 years and then at a constant rate of 5% thereafter. We can calculate the dividends for the next two years as follows:

D1 = D0 * (1 + growth rate) = $2.2 * (1 + 0.24) = $2.728

D2 = D1 * (1 + growth rate) = $2.728 * (1 + 0.24) = $3.386

To find the price of the stock at the end of year 2 (P2), we can use the Gordon growth model:

P2 = D2 / (r - g) = $3.386 / (0.09 - 0.05) = $84.65

Next, we need to discount the future price of the stock at the end of year 2 to its present value using the required rate of return. The required rate of return is the risk-free rate plus the product of the stock's beta and the market risk premium:

r = risk-free rate + (beta * market risk premium) = 0.09 + (1.3 * 0.045) = 0.1565

Now, we can calculate the present value of the future price:

P0 = P2 / (1 + r)^2 = $84.65 / (1 + 0.1565)^2 = $57.83

Therefore, based on the given information and calculations, the estimated current price of the stock is $57.83.

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Answer:

\(\frac{1}{3}\)

Step-by-step explanation:

Step 1: Simplify

\(\frac{12}{12} =1\)

Step 2: Multiply by \(\frac{1}{3}\)

\(1*\frac{1}{3}=\frac{1}{3}\)

Hope this helps! :)

Answer:

the markup is 8%

Step-by-step explanation:

Taylor series for \(f(x) = 6 \cos(x)\) centered at \(a = 3\) is: \(f(x) = 6 \cos(3) - 6 \sin(3)(x-3) - 3 \cos(3)(x-3)^2 + 2 \sin(3)(x-3)^3 + \cos(3)(x-3)^4 + \cdots\). To find the Taylor series for \(f(x) = 6 \cos(x)\) centered at \(a = 3\), we need to find the derivatives of \(f\) at \(x = a\) and evaluate them.

The derivatives of \(\cos(x)\) are:

\(\frac{d}{dx} \cos(x) = -\sin(x)\)

\(\frac{d^2}{dx^2} \cos(x) = -\cos(x)\)

\(\frac{d^3}{dx^3} \cos(x) = \sin(x)\)

\(\frac{d^4}{dx^4} \cos(x) = \cos(x)\)

and so on...

To find the Taylor series, we evaluate these derivatives at \(x = a = 3\):

\(f(a) = f(3) = 6 \cos(3) = 6 \cos(3)\)

\(f'(a) = f'(3) = -6 \sin(3)\)

\(f''(a) = f''(3) = -6 \cos(3)\)

\(f'''(a) = f'''(3) = 6 \sin(3)\)

\(f''''(a) = f''''(3) = 6 \cos(3)\)

The general form of the Taylor series is:

\(f(x) = f(a) + f'(a)(x-a) + \frac{f''(a)}{2!}(x-a)^2 + \frac{f'''(a)}{3!}(x-a)^3 + \frac{f''''(a)}{4!}(x-a)^4 + \cdots\)

Plugging in the values we found, the Taylor series for \(f(x) = 6 \cos(x)\) centered at \(a = 3\) is:

\(f(x) = 6 \cos(3) - 6 \sin(3)(x-3) - 3 \cos(3)(x-3)^2 + 2 \sin(3)(x-3)^3 + \cos(3)(x-3)^4 + \cdots\)

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f(x) = 6cos(3) - 6sin(3)(x - 3) + 6cos(3)(x - 3)²/2 - 6sin(3)(x - 3)³/6 + 6cos(3)(x - 3\()^4\) /24 + ... is the Taylor series expansion for f(x) = 6cos(x) centered at a = 3.

We have,

To find the Taylor series for the function f(x) = 6cos(x) centered at a = 3, we can use the general formula for the Taylor series expansion:

f(x) = f(a) + f'(a)(x - a)/1! + f''(a)(x - a)^2/2! + f'''(a)(x - a)^3/3! + ...

First, let's find the derivatives of f(x) = 6cos(x):

f'(x) = -6sin(x)

f''(x) = -6cos(x)

f'''(x) = 6sin(x)

f''''(x) = 6cos(x)

Now, we can evaluate these derivatives at x = a = 3:

f(3) = 6cos(3)

f'(3) = -6sin(3)

f''(3) = -6cos(3)

f'''(3) = 6sin(3)

f''''(3) = 6cos(3)

Substituting these values into the Taylor series formula, we have:

f(x) = f(3) + f'(3)(x - 3)/1! + f''(3)(x - 3)^2/2! + f'''(3)(x - 3)^3/3! + f''''(3)(x - 3)^4/4! + ...

Thus,

f(x) = 6cos(3) - 6sin(3)(x - 3) + 6cos(3)(x - 3)²/2 - 6sin(3)(x - 3)³/6 + 6cos(3)(x - 3\()^4\) /24 + ... is the Taylor series expansion for f(x) = 6cos(x) centered at a = 3.

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Answer:

x2-14x+52 is the answer in my calculation.