In the diagram, a circle centered at the origin, a right triangle, and the Pythagorean theorem are used to derive the equation of a circle, x2 + y2 = r2. If the center of the circle were moved from the origin to the point (h, k) and point P at (x, y) remains on the edge of the circle, which could represent the equation of the new circle? (h + x)2 + (k + y)2 = r2 (x – h)2 + (y – k)2 = r2 (k + x)2 + (h + y)2 = r2 (x – k)2 + (y – h)2 = r2

Answer:

B is le answer

Step-by-step explanation:

To find the values of the variables in each equation, isolate the variable on one side by performing operations. The solutions for the variables are 4, -1, 2, 6, no solution, and 10.8 for the respective equations.

To find the value of the variable in each equation, we need to isolate the variable on one side of the equation. Let's solve each equation step by step:

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Answer:

C 40

Step-by-step explanation:

The sum of the angles of a triangle add to 180 degrees

y+10 + 2y + 50 = 180

Combine like terms

3y + 60 =180

Subtract 60 from each side

3y+60-60 = 180-60

3y = 120

Divide by 3

3y/3 = 120/3

y = 40

The sum of all the angles of a triangle is 180 degrees. To solve for y you can make a formula of the sum of the angles equal to 180 like so...

y + 10 + 2y + 50 = 180

Now you must combine like terms. This means that first numbers with the same variables (y) must be combined...

(y + 2y) + 10 + 50 = 180

3y + 10 + 50 = 180

Combine like terms 10 and 50...

3y + 60 = 180

Now bring 60 to the left side by subtracting 60 to both sides (what you do on one side you must do to the other). Since 60 is being added on the left side, subtraction (the opposite of addition) will cancel it out (make it zero) from the left side and bring it over to the right side.

3y + 60 - 60 = 180 - 60

3y + 0 = 120

3y = 120

Next divide 3 to both sides to finish isolating x. Since 3 is being multiplied by x, division (the opposite of multiplication) will cancel 3 out (in this case it will make 3 one) from the left side and bring it over to the right side.

3y / 3 = 120 / 3

y = 40

C. 40

Hope this helped!

~Just a girl in love with Shawn Mendes

To convert feet per minute into miles per hour, use the conversion factor of 5280 feet in 1 mile and 60 minutes in 1 hour. Divide the given value by 5280 to get the number of miles, then divide the result by 60 to convert minutes to hours.

To convert feet per minute into miles per hour, you need to use the conversion factor of 5280 feet in 1 mile and 60 minutes in 1 hour. Here's the step-by-step calculation:

For example, if you have a speed of 300 feet per minute:

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Answer:

2x-10

Step-by-step explanation:

original equation: 2(×-5)

distributive property: 2(x) 2(-5) =2x-10

Answer:

2x-10

2(x-5)

2*x=2x

2*5=10

Answer:

f(3) = 9

Step-by-step explanation:

Wherever you see an x on the right, put a 3 in for that x

f(x) = 2x^2 + x - 12

f(3) = 2*(3)^2 + 3 - 12

f(3) = 2*9 + 3 - 12

f(3) = 18 + 3 - 12

f(3) = 9

Answer:

f(x) = x + 13

Step-by-step explanation:

Given f(x) then f(x) + c represents a vertical translation

• If c > 0 then vertical shift up ↑ of c units

• If c < 0 then vertical shift down ↓ of c units

here c = + 13, hence

f(x) = x + 13

Let the base = x

Then the height would be 2x ( twice the length of the base.

Now using the given formula you get:

25 = 1/2 * 2x *x

Multiply 2x by 1/2:

1/2 * 2x = 2x/2

25 = 2x/2 * x

2x/2 = 1x, now you have:

25 = x *x

Multiply x by x:

25 = x^2

Take the square root of both sides:

x = √25

x = 5

Answer:

14/3

Step-by-step explanation:

Simplify the following:

48/6 - 10/3

Hint: | Reduce 48/6 to lowest terms. Start by finding the GCD of 48 and 6.

The gcd of 48 and 6 is 6, so 48/6 = (6×8)/(6×1) = 6/6×8 = 8:

8 - 10/3

Hint: | Put the fractions in 8 - 10/3 over a common denominator.

Put 8 - 10/3 over the common denominator 3. 8 - 10/3 = (3×8)/3 - 10/3:

(3×8)/3 - 10/3

Hint: | Multiply 3 and 8 together.

3×8 = 24:

24/3 - 10/3

Hint: | Subtract the fractions over a common denominator to a single fraction.

24/3 - 10/3 = (24 - 10)/3:

(24 - 10)/3

Hint: | Subtract 10 from 24.

| 2 | 4

- | 1 | 0

| 1 | 4:

Answer:  14/3

Answer:

Your answer is 4 and 2/3

Step-by-step explanation:

Hope this helps have a good day!

Answer:

The correct answer is first option

512 cubic mm

Step-by-step explanation:

Points to remember

Volume of hexagonal pyramid = Base area * height

To find the volume of hexagonal pyramid

It is given that, base area = 64 square mm and

height = 8 mm

Volume = Base area * Height

 = 64 * 8

 = 512 cubic mm

Therefore the correct answer is first option

512 cubic mm

Answer:

Solution (-2, 7)

Step-by-step explanation:

2x + 3y = 17      (1)

5x + 6y = 32    (2)

Using elimination method

Multiply (-2) to the equation (1)

-4x - 6y = -34  

Now you have 2 new equations

-4x - 6y = -34

5x + 6y = 32

----------------------------Add

x = -2

Substitute x = -2 into 2x + 3y = 17

2(-2) + 3y = 17

- 4 + 3y = 17

3y = 21

 y = 7

Solution (-2, 7)

Final answer:

The solution to the system of equations 2x + 3y = 17 and 5x + 6y = 32 using the elimination method is x = -2 and y = 7.

Explanation:

To solve the system of equations using the method of elimination, we manipulate the equations to make the coefficients of either x or y the same, and then subtract one equation from the other to eliminate that variable. Let's consider the given equations:

2x + 3y = 17 (Equation 1)

5x + 6y = 32 (Equation 2)

We can see that the coefficients of y are in the ratio of 3:6 or 1:2. To use elimination, we want the coefficients to match, so we can multiply Equation 1 by 2:

(2)(2x) + (2)(3y) = (2)(17)

4x + 6y = 34 (New Equation 1)

Now we can subtract the new Equation 1 from Equation 2:

(5x + 6y) - (4x + 6y) = 32 - 34

5x - 4x + 6y - 6y = -2

x = -2

Now that we have a value for x, we can substitute it back into one of the original equations to solve for y. Let's substitute x into Equation 1:

2(-2) + 3y = 17

-4 + 3y = 17

3y = 17 + 4

3y = 21

y = 7

The solution to the system of equations is x = -2 and y = 7.

Answer:

17/13

Step-by-step explanation:

Answer:

Step-by-step explanation:

" / " indicates "division" and should not be used in this context.

If you meant:  -2 square root 13 plus 19 square root 13, the simplest result would be 17 square root 13.

Note that if you click on the "omega" symbol (below), a menu of symbols will appear, including the square root symbol √.

Then:  -2√13 + 19√13 = 17√13.

Answer:

c

Step-by-step explanation:

The best first step to solve the equation -2(x+3)=-10 is to distribute the -2 across the parentheses, simplify the equation, and then solve for x.

Checking the answer by substituting the value of x back into the original equation ensures the solution is correct.

When solving the equation -2(x+3)=-10, the best first step to simplify the equation is to distribute the multiplication of -2 across the parentheses.

This is done to eliminate the parentheses and simplify the equation into its simplest form. After distribution, you would then have the simplified equation -2x - 6 = -10.

From there, you can proceed to solve for x by adding 6 to both sides of the equation to isolate the term with x, then dividing both sides by -2 to find the value of x.

Here are the basic problem-solving steps:

Once you've calculated the value of x, it's important to check the answer to ensure it is reasonable.

You can do this by substituting the value of x back into the original equation.

Answer:

y- intercept = 4

Step-by-step explanation:

The y- intercept is the value of the y- coordinate where the line crosses the y- axis.

Here the y- intercept = 4 or (0, 4) ← coordinates of point

Answer:

( 0 , 4 )

Step-by-step explanation:

The y - intercept of the line is where the line hit's or crosses the y - axis and in the case since the line goes through 4 on the y - axis

ANSWER

[tex]p(x) = 6x - 15[/tex]

EXPLANATION

The revenue from selling x necklaces is

[tex]r(x) = 10x[/tex]

The cost of buying x necklaces is

[tex]c(x) = 4x + 15[/tex]

The profit from selling x necklaces is

[tex]p(x) = r(x) - c(x)[/tex]

We substitute the functions to get;

[tex]p(x) = 10x- (4x + 15)[/tex]

[tex]p(x) = 10x- 4x - 15[/tex]

[tex]p(x) = 6x - 15[/tex]

Therefore the function for the profit is

[tex]p(x) = 6x - 15[/tex]

Answer:

x = 5

Step-by-step explanation:

Using the rule of logarithms

[tex]log_{b}[/tex] x = n ⇔ x = [tex]b^{n}[/tex]

Given

[tex]log_{2}[/tex](3x - 7) = 3, then

3x - 7 = 2³ = 8 ( add 7 to both sides )

3x = 15 ( divide both sides by 3 )

x = 5

The required solution of logarithmic expression  log2 (3x - 7) = 3 is x = 5. Option B is correct.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
To solve for x in the equation log2 (3x - 7) = 3, we first use the definition of a logarithm to change the logarithmic form to the exponential form.

log2 (3x - 7) = 3

2³ = 3x - 7

Next, we solve for x by adding 7 to both sides of the equation:

8  + 7= 3x - 7 + 7

15 = 3x

Finally, we divide both sides of the equation by 3:

x = 5

So, the solution of log2 (3x - 7) = 3 is x = 5.

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The answer is:

The fourth graph.

We are given the following equation:

[tex]f(x)=x[/tex]

Then, we need to find the graph of f(x+2) that will be equal to:

[tex]f(x+2)=x+2[/tex]

[tex]y=x+2[/tex]

Now, finding the x-axis interception, making "y" equal to 0, we have:

[tex]0=x+2[/tex]

[tex]-2=x[/tex]

Therefore, the x-axis interception point is located at (-2,0), it matches with the fourth graph.

Now, finding the y-axis interception, making "x" equal to 0, we have:

[tex]y=x+2[/tex]

[tex]y=0+2=2[/tex]

Therefore, the y-axis interception point is located at (0,2), it matches with the fourth graph.

Hence, we have that the graph of f(x+2) is the fourth graph since the second graph function cuts the x-axis at -2 and the y-axis at 2.

Have a nice day!

Answer: 717,000

Step-by-step explanation:

716,773 rounded to the nearest thousand is 717000 because the 7 is closer to 10 than it is to 0

Hello There!

716,772 rounded to the nearest thousand would be 717,000

772 is closer to 717,000 than 716,000

Answer:

Step-by-step explanation:

The question does say at most 10. That includes 10. So the circle on 10 should indicate it is closed or fully filled in.

The shading should go left. It should indicate less than 10.

When eggs are delivered, if one notices that B. The shells of the eggs have cracks in them, the eggs should be rejected.

Eggs that have cracks in them can be potentially dangerous to people because microorganisms like bacteria can enter through those cracks and either spoil the egg or make it harmful for consumption.

It is therefore best that an egg that has a crack, be rejected upon delivery.

Other options are incorrect because:

In conclusion, if an egg has a crack in it upon delivery, it should be rejected.

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Answer:

The Building's tall and wide ratio is 90 : 45 = 2 : 1

now the wide is 3, let's say that tall is a.

2 / 1 = a / 3

a = 2 x 3

a = 6

So the picture will be 6 feet tall.

[tex]12\dfrac{1}{3}-6\dfrac{9}{10}=12\dfrac{10}{30}-6\dfrac{27}{30}=6+\left(-\dfrac{17}{30}\right)=5\dfrac{13}{30}[/tex]

Answer:

it is the second one because 1/2 divided by 3 equals 1/6 3 times

Answer: If [tex]a=b[/tex] and [tex]b=c[/tex], then [tex]a=c[/tex]

Step-by-step explanation:

Let be "a", "b", and "c" all real numbers, the Transitive property of equalities states that :

If [tex]a=b[/tex] and [tex]b=c[/tex], then [tex]a=c[/tex]

You can observe that if two numbers are equal to the same number, then all this numbers are equal to each other.

For example, applying the Transitive property of equalities to:

[tex]x+3=5[/tex] and [tex]2x+1=5[/tex]

You can equate them:

[tex]x+3=2x+1[/tex]

And solve for "x":

[tex]3-1=2x-x\\\\x=2[/tex]

Answer:

The correct answer option is: If a = b and b = c, then a = c.  

Step-by-step explanation:

The Transitive Property of Equality states that if one value, lets say [tex] a [/tex] is equal to another value, call it [tex] b [/tex], which is equal to another value, call it [tex] c [/tex], then the very first value [tex] a [/tex] would be equal to the third value [tex] c [/tex].

So from the given answer options, the correct option is: If a = b and b = c, then a = c.  

ANSWER

Relative minimum occurs at x=0

Relative maximum occurs at x=-2

EXPLANATION

The given function is;

[tex]f(x) = 3 {x}^{3} + 9 {x}^{2} - 1[/tex]

We take the first derivative to get:

[tex]f'(x) = 9 {x}^{2} + 18x[/tex]

At turning point f'(x)=0

[tex] 9 {x}^{2} + 18x = 0[/tex]

[tex] 9x(x + 2) = 0[/tex]

[tex]x = 0 \: or \: x = - 2[/tex]

We take the second derivative to get

[tex]f''(x) = 18x + 18

[/tex]

[tex]f''(0) = 18(0) + 18 = 18 \: > \: 0[/tex]

Relative minimum occurs at x=0

[tex]f''( - 2) = 18( - 2)+ 18 = - 18 \: < \: 0[/tex]

Relative maximum occurs at x=-2

Answer:

Relative minimum occurs at x=0

Relative maximum occurs at x=-2

Step-by-step explanation:

Answer:

Option D is correct.

Step-by-step explanation:

We need to find the pattern in the values as the exponents increase.

First value is 1/3

if we multiply 3 with 1/3 i.e. 1/3*3 we get 1

The next value is 1 in the table.

Now, if we multiply 1 with 3 i.e. 1*3 we get 3

The next value is 3 in the table.

Now, if we multiply 3 with 3 i.e 3*3 we get 9

So, the next value is 9 in the table.

So, if we multiply 3 with the previous value we get the next value in the table.

Hence Option D multiply the previous value by 3 is correct.

Answer:

Approximately 68%

Step-by-step explanation:

The number of potato chips in a bag is normally distributed with a mean of 71 and a standard deviation of 2, that is to say:

X ∼ N(µ, σ2) ⇒ X ∼ N(71, 4).

Now, to find the percentage of bags that contain between 69 and 73 potatos we need the help of a calculator.

Pluging the data into a calculator we get that the percentage of bags that contain between 69 and 73 potatos is 68.27% ≈ 68%.

The solution is: Approximately 68%

Answer:

Approximately 68% percent of bags contain between 69 and 73 potato chips.

Step-by-step explanation:

Number of chips in a bag is normally distributed.

Mean = 71

Standard deviation = 2

We know that in normal distribution, 34.1% of bags will fall with in one standard deviation on one side. On both sides within the range of 1 standard deviation, 34.1 + 34.1 = 68.2 % of bags will fall.

A table of normal distribution about mean is attached for better understanding.

Our range is:

69 to 73

71 - 2 to 71 + 2

71 ± 2

mean ± standard deviation

Our range is within 1 standard deviation. Hence, Approximately 68% of bags contain between 69 and 73 potato chips.

Answer:

8

Step-by-step explanation:

–16 • 1/8 • 4 + 32 ÷ 2

Using PEMDAS, we multiply and divide from left to right since there are no parentheses or exponents.

-2 • 4 + 32 ÷ 2

-8 +32 ÷ 2

-8 + 16

Now we add and subtract from left to right

8