Which equation can be used to find the measure of angle BAC?

Answer:

(x-3)² + (y-2)² = 25

Step-by-step explanation:

A circle's equation is (x-h)² + (y-k)² = r². When centered at the origin, h and k equal 0. If you shift the circle, say, one unit up, then k equals 1, and the equation is x² + (y-1)² = r².

So for your circle, the equation would be (x-3)² + (y-2)² = 5² or (x-3)² + (y-2)² = 25.

Answer:

b and d

Step-by-step explanation:

b. 1/x^-1

=(1/x)^-1

=x

d. x^1/3 * x^1/3 * x^1/3

=x^1/3+1/3+1/3

=x^3/3

=x^1

=x....

Answer:

Circle A and circle B are similar

Step-by-step explanation:

* Lets explain similarity of circles

- Figures can be proven similar if one, or more, similarity transformations

 reflections, translations, rotations, dilations can be found that map one

 figure onto another

- To prove all circles are similar, a translation and a scale factor from a

  dilation will be found to map one circle onto another

* Lets solve the problem

∵ Circle A has center (-1 , 1) and radius 1

∵ The standard form of the equation of the circle is:

   (x - h)² + (y - k)² = r² , where (h , k) are the coordinates the center

   and r is the radius

∴ Equation circle A is (x - -1)² + (y - 1)² = (1)²

∴ Equation circle A is (x + 1)² + (y - 1)² = 1

∵ Circle B has center (-3 , 2) and radius 2

∴ Equation circle B is (x - -3)² + (y - 2)² = (2)²

∴ Equation circle B is (x + 3)² + (y - 2)² = 4

- By comparing between the equations of circle A and circle B

# Remember:

- If the function f(x) translated horizontally to the right  

 by h units, then the new function g(x) = f(x - h)

- If the function f(x) translated horizontally to the left  

 by h units, then the new function g(x) = f(x + h)

- If the function f(x) translated vertically up  

 by k units, then the new function g(x) = f(x) + k

- If the function f(x) translated vertically down  

 by k units, then the new function g(x) = f(x) – k

∵ -3 - -1 = -2 and 2 - 1 = 1

∴ The center of circle A moves 2 units to the left and 1 unit up to

  have the same center of circle B

∴ Circle A translate 2 units to the left and 1 unit up

∵ The radius of circle A = 1 and the radius of circle B = 2

∴ Circle A dilated by scale factor 2/1 to be circle B

∴ Circle B is the image of circle A after translation 2 units to the left

  and 1 unit up followed by dilation with scale factor 2

- By using the 2nd fact above

∴ Circle A and circle B are similar

Answer:

I believe it would be B

Step-by-step explanation:

take x and y values and figure it out what it is by itself

Answer:

r equals 4- this is the value of r

hope this helps

Step-by-step explanation:

Answer:

[tex]\large\boxed{r=4}[/tex]

Step-by-step explanation:

In this question, we're going to need to solve the equation for r.

This means that we need to get the r by itself to see what it equals to.

Lets solve:

[tex]15r- 6r=36\\\\\text{Subtract 15r and -6r}\\\\9r=36\\\\\text{Now you will divide}\\\\r=4[/tex]

When you're done solving, you should get r = 4

This means that the value of r is 4 (or r = 4)

Answer:

[tex]\frac{1}{36}[/tex]

Step-by-step explanation:

All die rolls have a 1 in 6 chance of landing on any specific number (because they have 6 equal sides). In probability, two independent events with probabilities a and b will occur concurrently [tex]a*b[/tex] of the time. In this case, [tex]a=b=\frac{1}{6} \to p=a*b=\frac{1}{6}*\frac{1}{6}=\frac{1}{36}[/tex]

Answer:

Required probability = 1/36

Step-by-step explanation:

It is given that,single die is rolled twice

The outcomes of rolling a die are

1, 2, 3, 4, 5, and 6

Total = 6

To find the probability

Probability of getting 2 = 1/6

Probability of getting 5 = 1/6

Therefore probability of rolling a 2 the first time and a 5 the second time. = 1/6 * 1/6 = 1/36

Answer:

False

Step-by-step explanation:

I think this is a true or false question.

The statement is false.

Here is an example of it being false:

Choose the irrational number to be [tex]\sqrt{2}[/tex] and the rational to be 1.

The product of these numbers is [tex]\sqrt{2}[/tex] which is irrational, not rational.

Answer:

False

Step-by-step explanation:

Ight so any irrational number times a rational number is irrational. But keep in mind that If its 0 times an irrational number, its going to be 0, which is a rational number. So irrational x rational = irrational. Irrational x 0=rational 0.

Hope this helped

[tex]f(x) = x^2(x^2 + 9)(x^3 + 2x)\\\\f(-x) = (-x)^2((-x)^2 + 9)((-x)^3 + 2\cdot(-x))\\f(-x)=x^2(x^2+9)(-x^3-2x)\\f(-x)=-x^2(x^2+9)(x^3+2x)\\\Large f(-x)\not =f(x)\implies\text{not even}\\\\-f(x)=-x^2(x^2+9)(x^3+2x)\\ -f(x)=f(-x)\implies \text{odd}[/tex]

Detailed solution to math problems involving functions and mappings.

1. The function represented by the table:

Identify the pattern in the table to determine the function.

The cost increases by $1.95 for every 3 apples, so the function is C(a) = 0.65a (A).

2. Translating a function:

To shift f(x) = x^4 five units right and seven units down, the correct function is g(x) = (x+5)^4 - 7 (D).

3. Mapping the function:

Using the mapping provided, the correct values are: f(5) = 1, f(3) = 0, f(11) = 2, f(21) = 3 (A).

Answer:

D x=15

Step-by-step explanation:

3(2x+5)=3x+4x

Distribute the 3

6x +15 = 3x+4x

Combine like terms

6x+15 = 7x

Subtract 6x from each side

6x+15 -6x = 7x-6x

15 =x

Answer:

The answer is

B. x =>z

They all equal the same.

Answer:

Volume of Cylinder = 981.75 cubic inches

Step-by-step explanation:

There is no answer choice shown, but i will answer this using formula for volume of cylinder and round the answer to 2 decimal places.

You match it with the choices that u have.

The volume of a cylinder is given by the formula  [tex]V=\pi r^2 h[/tex]

Where

V is the volume

r is the radius (half of diameter)

h is the height

We know diameter is 5, so radius is 2.5

also, the height is 50

We simply plug it in the formula and solve:

[tex]V=\pi r^2 h\\V=\pi (2.5)^2 (50)\\V=981.75[/tex]

Answer:

12 miles

Step-by-step explanation:

Jay walks 0.75 miles in 15 minutes, or 1/4 hour, so his speed is:

0.75 mi / 0.25 hr = 3 mi/hr

Paul walks 2.5 miles in 30 minutes, or 1/2 hour, so his speed is:

2.5 mi / 0.50 hr = 5 mi/hr

After 1.5 hours, Jay has walked a distance of:

3 mi/hr × 1.5 hr = 4.5 mi

And Paul has walked a distance of:

5 mi/hr × 1.5 hr = 7.5 mi

So the total distance between them is:

4.5 mi + 7.5 mi = 12 mi

Answer:

G'(0,5)

H'(4,-5)

F'(-2,-2)

Step-by-step explanation:

We need to identify the three vertices from the figure on the graph:

G(-3,5)

H(1,-5)

F(-5,-2).

If we translate these points 3 units to right, then that effects the x-coordinates.

So 3 more than -3, is 0.

3 more than 1 is 4.

3 more than -5 is -2.

So the new points are:

G'(0,5)

H'(4,-5)

F'(-2,-2).

Answer:

[tex]\large\boxed{\dfrac{4^{-\frac{11}{3}}}{4^{-\frac{2}{3}}}=\dfrac{1}{64}}[/tex]

Step-by-step explanation:

[tex]\dfrac{4^{-\frac{11}{3}}}{4^{-\frac{2}{3}}}\qquad\text{use}\ \dfrac{a^n}{a^m}=a^{n-m}\\\\=4^{-\frac{11}{3}-\left(-\frac{2}{3}\right)}=4^{-\frac{11}{3}+\frac{2}{3}}=4^{-\frac{9}{3}}=4^{-3}\qquad\text{use}\ a^{-n}=\dfrac{1}{a^n}\\\\=\dfrac{1}{4^3}=\dfrac{1}{64}[/tex]

The simplification of the expression is [tex]\dfrac{1}{64}[/tex].

Exponentiation(the process of raising some number to some power) have some basic rules as:

[tex]a^{-b} = \dfrac{1}{a^b}\\\\a^0 = 1 (a \neq 0)\\\\a^1 = a\\\\(a^b)^c = a^{b \times c}\\\\ a^b \times a^c = a^{b+c} \\\\[/tex]

Given ;

[tex]\dfrac{(4^{-11/3})}{(4^{-2/3})}[/tex]

We know that

[tex]\dfrac{a^m}{a^n} = a^{m-n}[/tex]

[tex]\dfrac{(4^{-11/3})}{(4^{-2/3})} = 4^({-11/3 + 2/3})\\\\\\= 4 ^{-9/3}\\\\= 4^{-3}\\\\[/tex]

Hence, [tex]\dfrac{1}{4^3} = \dfrac{1}{64}[/tex]

Learn more about exponentiation here:

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Answer:

D

Step-by-step explanation:

Plug in and see.

Check A: Lets plug in (0,3) into y<2/3 x+2.

3<2/3 (0)+2

3<2 is not true so not A

Check C: Lets plug in (3,5) into y<2/3 x+2.

5<2/3 (3)+2

5<2+2

5<4 is not true so not C

Check B: Lets plug in (-3,1) into y<2/3 x+2.

1<2/3 (-3)+2

1<0 is not true so not B

Check D: Lets plug in (1,2) into y<2/3 x+2.

2<2/3 (1)+2

2<2/3+2 is true so D

Answer:

15 is your answer.

Step-by-step explanation:

Let "a number" = x

"Three times a number increase(d) by 4" = 3x + 4

"...is the same as" = "="

"four times that number decreased by 11" = 4x - 11

Set the equation:

3x + 4 = 4x - 11

Isolate the variable, x. Subtract 4x and 4 from both sides:

3x (-4x) + 4 (-4) = 4x (-4x) - 11 (-4)

3x - 4x = -11 - 4

Simplify. Combine like terms:

-x = -15

Isolate the variable, x. Divide -1 from both sides:

(-x)/-1 = (-15)/-1

x = (-15)/(-1)

x = 15

15 is your answer.

~

For this case we must construct a function of the form [tex]y = f (x)[/tex] taking as reference the values of the table.

It is observed that if we evaluate the following function we have:

[tex]f (x) = x + 4[/tex]

Different signs are subtracted and the sign of the major is placed.

[tex]f (-3) = - 3 + 4 = 1\\f (-2) = - 2 + 4 = 2\\f (-1) = - 1 + 4 = 3\\f (0) = 0 + 4 = 4[/tex]

So, the function is:[tex]f (x) = x + 4[/tex]

Answer:

[tex]f (x) = x + 4[/tex]

Answer:

Step-by-step explanation:

Lets assume that a sphere with greater radius = R = 5cm

And a sphere with smaller radius = r = 4cm

Volume of a sphere = 4/3 π * r³

To find the volume of a sphere with radius 5.

Put the value in the formula.

=4/3π * r³

=4/3π *(5)³

5³ = 5*5*5=125

=4/3π * 125

=4/3 *3.14 *125

=1570/3

=523.3 cm³

Now find the volume of sphere with radius= 4

4/3π*r³

=4/3π * 4³

4³= 4*4*4=64

=4/3*3.14*64

=803.84/3

=267.9cm³

Now to find the space between the spheres subtract the volume of smaller sphere from the volume of larger sphere.

We can write it as:

Space between the spheres = Volume of larger sphere - Volume of smaller sphere

= 523.3 cm³ - 267.9cm³

= 255.4cm³ ....

Answer:

m < A = 101 degrees.

Step-by-step explanation:

The transverse line crosses 2 parallel lines (opposite angles of a rectangle are parallel) ,  so the same side angles add up to 180 degrees.

m < A + 79 = 180

m < A = 101 degrees.

Answer:

A=101°

Step-by-step explanation:

The two lengths of the rectangle are parallel and therefore the sides of the path form two parallel transversals.

The angle marked 79° and the angle marked A are supplementary ( they add up to 180°)

A+79=180°

A=180-79

=101°

In the physics context of free fall, it would take an object approximately 7.67 seconds to fall from a 944-foot tower, neglecting air resistance. This is calculated using the formula for distance of a freely falling object s(t)=16t^2.

The question deals with the physics concept of free fall, specifically directed to the time it would take an object to fall from a certain height. Given that the distance s(t) of a freely falling object is given by the equation s(t)=16t^2, we can find the time t for an object to fall from a height of 944 feet, which is the height of the specific tower.

Setting s(t) equal to the height of the tower, we get: 944=16t^2. Solving this equation for t, we'll get the square root of 944/16 which is approximately 7.67 seconds. Therefore, it would take an object about 7.67 seconds to fall to the ground from the top of the 944-foot tower, neglecting air resistance.

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To determine how long it takes for an object to fall from a 944-foot tower, we use the formula s(t) = 16t^2. Solving for t, we find that it takes approximately 7.68 seconds. Thus, the object hits the ground after 7.68 seconds.

Neglecting air resistance, the distance s(t) in feet traveled by a freely falling object is given by the function s(t)=16t^2, where t is time in seconds. The height of a certain tower is 944 feet. How long would it take an object to fall on the ground from the top of the building?

To solve this problem, we need to determine the time t it takes for the object to hit the ground. Given the height h = 944 feet, we'll use the formula for the distance fallen:

s(t) = 16t^2

We set s(t) equal to the height of the tower:

944 = 16t^2

Next, solve for t:

Divide both sides by 16:

944 / 16 = t^2

t^2 = 59

Take the square root of both sides:

t = √59

t ≈ 7.68 seconds

Therefore, it would take approximately 7.68 seconds for an object to fall to the ground from the top of the building.

Induction is the correct answer; when you use induction form general ideas and rules based on your experiences and observations. I hope this will help you! Have a wonderful day!

Answer:

d. induction

Step-by-step explanation:

When you use induction you form general ideas and rules based on your experiences and observations.

Answer:

37

Step-by-step explanation:

So this is probably not the correct mathematical way to do it, but it is really easy so you'll probably understand quicker. So a median is the middle number, so how do you find it. First, I counted how many numbers there were (17). Then I subtracted by one to get an even number (if you already have an even number skip this step, and just divide by 2). So now we have 16, so I divided it by 2 to get 8 and just added that 1 that we took out and got 9. So i counted from 24 and the 9th number was 37. To double check I did the same from 56 and got 37.

Answer:

[tex]\large\boxed{(f-g)(x)=-x^2+3x+7}[/tex]

Step-by-step explanation:

[tex](f-g)(x)=f(x)-g(x)\\\\f(x)=3x+1,\ g(x)=x^2-6\\\\(f-g)(x)=(3x+1)-(x^2-6)=3x+1-x^2+6=-x^2+3x+7[/tex]

Answer:

The length is 9 and the width is 6.

Step-by-step explanation:

6*9 = 54 and 9 is 3 greater than 6.

Answer:

The original price of a skateboard is $64

Step-by-step explanation:

Let

x ----> the original price of a skateboard

y ----> the new price of a skateboard

we know that

The linear equation that represent this problem is equal to

y=x-15 ----> equation A

y=49 ---> equation B

substitute equation B in equation A and solve for x

49=x-15

Adds 15 both sides

49+15=x

64=x

Rewrite

x=$64

Answer:

I hope this helps! <3

Step-by-step explanation:

To solve the equation 3x - 2 = 37, you add 2 to both sides to get 3x = 39. Then, you divide by 3 to solve for x, obtaining x = 13.

To solve the equation

3x − 2 = 37

for x, you start by moving the -2 to the other side of the equation by adding 2 to both sides. This gives you

3x = 39

. Then, you isolate x by dividing every term by 3. After dividing, you find that

x = 13

. So the solution to the equation 3x - 2 = 37 is x = 13.

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To solve the equation, add 2 to both sides and then divide by 3 to isolate the variable x. The solution is x = 13.

To solve the equation 3x - 2 = 37, we need to isolate the variable x. Here are the steps:

Therefore, the solution to the equation is x = 13.

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