What are the solutions to the system of equations?

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

[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]

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 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:

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:

g(3)=11 I think

Step-by-step explanation:

Since x is 3, you substitute it in for the x. So it would be 3 squared +2.

I'm not sure if this is right but I tried helping.

Answer:

g(3) =11

Step-by-step explanation:

g(x) = x^2 +2

Let x =3

g(3) = 3^2 +2

      = 9+2

      = 11

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:

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:

D is correct option

Step-by-step explanation:

The correct option is D.

The standard quadratic equation is ax²+bx+c=0

Where a and b are coefficients and c is constant.

It means that constant are on the L.H.S and there is 0 on the right hand side.

Therefore to make it a quadratic equation first of all you have to add 11 at both sides so that the R.H.S becomes 0.

The given equation is:

2x2-x+ 2 = -11

If we add 11 on both sides the equation will be:

2x2-x+ 2 +11= -11+11

2x^2-x+13=0

Thus the correct option is D

You can further solve it by applying quadratic formula....

Final answer:

The most logical first step to solve the quadratic equation 2x² - x + 2 = -11 is to set up smaller equations using the zero product rule and then applthe quadratic formula. The correct option is c.

Explanation:

The most logical first step to solve the quadratic equation 2x² - x + 2 = -11 is to:

C. Set up smaller equations using the zero product rule.

Once the equation is rearranged, apply the quadratic formula to determine the values of x.

Using the quadratic formula yields the solutions by substituting the values of a, b, and c correctly.

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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Answer:

$65720

Step-by-step explanation:

The job pays a starting salary of $62000, and raises $3720 per year. In one year, Carlos will be earning $62000 + $3720 =  $65720

Final answer:

Carlos's salary in one year will be $65720, which is the sum of his starting salary, $62000, and the promised annual raise of $3720.

Explanation:

After graduating from college, Carlos has received two different job offers, both offering a starting salary of $62000, and one includes a promise of a $3720 raise per year. To calculate his salary in one year, we need to add this annual raise to his starting salary.

Starting salary: $62000

Raise after one year: $3720

Carlos's salary in one year: $62000 + $3720 = $65720

This computation shows that with the promised annual raise, Carlos's salary for the next year would be $65720.

Answer:

125

Step-by-step explanation:

500 ÷ 4 = 125

I think this is the right answer. sorry if I'm wrong.

Answer:

x=5 assuming that x is the radius.

x is the radius?

Step-by-step explanation:

[tex]V=\frac{4}{3} \pi r^3[/tex] is the volume of a sphere.

We are given [tex]V=\frac{500}{3} \pi[/tex] cubic units.

We are asked to find the value of x.  If x is not the radius, please correct me:

[tex]V=\frac{4}{3}\pi r^3[/tex] with  [tex]V=\frac{500}{3} \pi[/tex]  and the assumption that x is r.

[tex]\frac{500}{3}\pi=\frac{4}{3}\pi x^3[/tex]

If you multiply both sides by 3, then you would have:

[tex]500 \pi=4 \pi x^3[/tex]

If you divide both sides by [tex]\pi[/tex] you will have:

[tex]500=4x^3[/tex]

If you divide both sides by 4, you will have:

[tex]125=x^3[/tex]

The last step would be to take the cube root of both sides:

[tex]\sqrt[3]{125}=x[/tex]

[tex]5=x[/tex]

[tex]x=5[/tex]

Answer:

x =96 degree.

Step-by-step explanation:

Given : Triangle .

To find : The value of x is

Solution : We have given triangle

Exterior Angle sum property of triangle : Sum of all exterior angle of triangle is 360.

130 + 134 + x = 360 .

264 + x = 360.

On subtracting both sides by 264 .

x = 360 - 264 .

x = 96.

Therefore, x =96 degree.

Using Exterior Angle sum property of the triangle, The value of x will be 96 degree.

Exterior Angle sum property of the triangle states that the Sum of all exterior angles of the triangle is 360.

Given: Two exterior angles measure of 130 and 134 degrees.

To find: The value of x is

So,

130 + 134 + x = 360 .

264 + x = 360.

x = 360 - 264 .

x = 96.

Using Exterior Angle sum property of the triangle, The value of x will be 96 degrees.

Learn more about angles here;

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Answer:

x = -2, x = 0, and x = 3

Step-by-step explanation:

it was right lol

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:

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:

Option D y=3

Step-by-step explanation:

The question in English is

Which of the following functions is a constant function?

we know that

A constant function is a function whose output value is the same for every input value

so

Verify each case

case A) y=x+1

This is not a constant function, this is a linear equation

Is a function whose output value is different for every input value

case B) y=x+2

This is not a constant function, this is a linear equation

Is a function whose output value is different for every input value

case C) x=y+3

This is not a constant function, this is a linear equation

Is a function whose output value is different for every input value

case D) y=3

This is a constant function

Is a function whose output value is the same for every input value

[tex]\bf 4csc(x)+6=-2\implies 4csc(x)=-8\implies csc(x)=\cfrac{-8}{4}\implies csc(x)=-2 \\\\\\ \cfrac{1}{sin(x)}=-2\implies \cfrac{1}{-2}=sin(x)\implies sin^{-1}\left( -\cfrac{1}{2} \right)=x\implies x= \begin{cases} \frac{7\pi }{6}\\\\ \frac{11\pi }{6} \end{cases}[/tex]

Answer:

73°

Step-by-step explanation:

Since WX = WZ then ΔWXZ is isosceles and WY is perpendicular to XZ

Hence ∠XYW = 90°

YW bisects XWZ, hence ⇒ ∠ YWX = ∠YWZ = 17°

The sum of the 3 angles in ΔWXY = 180°, hence

∠WXY = 180° - (90 + 17)° = 180° - 107° = 73°

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°

Answer:

I hope this helps! <3

Step-by-step explanation:

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:

sum of angles of triamgle is 180 degree

the half base× hight ue1/2×b×h

use the formula for all qusetions

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:

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:

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

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:

[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]

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