How can you determine whether two circles are congruent?

The required equation of the hyperbola is expressed as

[tex]\frac{x^2}{10}- \frac{y^2}{15}=1 \\[/tex]

The standard form for calculating the equation of a parabola along the x-axis is expressed as:

[tex]\frac{(x-k)^2}{a^2}-\frac{(y-h)^2}{b^2} = 1 \ ............. 1[/tex] where:

(h, k) is the center

(k±c, h) are the foci

[tex]x=h\pm\frac{a^2}{c}[/tex] is the directrix

From the question given, we can see that foci = (±5, 0)

k±c, h = ±5, 0

k = 0

h = 0

c = 5

From the directrix,

[tex]x=h\pm\frac{a^2}{c}\\x =0\pm\frac{a^2}{5}\\\pm2 = \pm\frac{a^2}{5}\\a^2 = 10\\[/tex]

Also, we need to know that;

a²+b² = c²

10 + b² = 5²

b² = 25 - 10

b² = 15

Substituting the gotten values into the equation of a hyperbola;

[tex]\frac{(x-0)^2}{10}- \frac{(y-0)^2}{15} =1\\\frac{x^2}{10}- \frac{y^2}{15} =1\\[/tex]

This gives the required equation of the hyperbola

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Answer:

The answers are between C and D

Step-by-step explanation:

It can't be A or B because they create a horizontal hyperbola, when the directrices are vertical.

Answer:

67% (rounded)

Step-by-step explanation:

Since there is 1-6,

There is 3,4,5,6 which is 4/6 chance being above 2.

2/3 = 66.6%  

Answer:1/36

Step-by-step explanation:

Answer:

Im sorry i dont understand what you mean by sentence but there are 6 boys

Step-by-step explanation:

Answer:

i dont understand thisssssssss im sorrrryy what is c(5)?????? huhhhhhhhhh

Step-by-step explanation:

Answer:

A. the control group in an experiment

Step-by-step explanation:

Researchers give one group a new cold medicine and compare them with to a group that takes no medicine. The group that is not given any medicine is the control group in an experiment.

Researchers are those who do research on something i.e. systematics and deep investigation into something.

Control Group is that group in research which does not take any medication or untreated group.

During the research while a new type of medicine is to be tested, the group that receives the medication or being tested is called the experimented group and the group that does not receive the treatment  is called the control group.

Hence, we can say that the group that is not given any medicine is the control group in an experiment.

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Answer:

[tex]11^2 *11^10 \\13^6 *13^4\\14^9 * 14^10\\2^4*2^4\\7^8*7^6\\3^3*3^9[/tex]

Step-by-step explanation:

Please Mark Brainliest for helping

Answer:

3/7

Step-by-step explanation:

There are 7 letters in ALABAMA. And there are 4 A's in ALABAMA. So if you're trying to not get an A then you would subtract 4 from 7. Which you would get 3/7 of the letters in ALABAMA are not A.

Answer:

15 + 0.05x ≤ 50

Step-by-step explanation:

The cost needs to be less than or equal to 50. Thus, the equation would be

15 + 0.05x ≤ 50

Answer:

113.1 in

Step-by-step explanation:

C = πd

d = 36

C = 36π = 113.1 in

Answer:

65 degrees

Step-by-step explanation:

90 + 90 + 115 + x = 360

x= 65

Answer:

True

Step-by-step explanation:

Answer:

i think its true but u can also copy and paste some of it like this: Is the energy transferred from a firepit to my cold hands transferred through the process called radiation?

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Using the tangent ratio in the right triangle

tanθ = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{7}{4}[/tex] , then

θ = [tex]tan^{-1}[/tex] ([tex]\frac{7}{4}[/tex] ) ≈ 60° ( to the nearest degree )

Answer:

see below

Step-by-step explanation:

w = x+y/z

Subtract x from each side

w-x = x+y/z -x

w-x = y/z

Multiply each side by z

(w-x) *z = y/z*z

(w-x) *z = y

You can distribute the z if desired

wz -xz = y

Answer:

y = z(w - x)

Step-by-step explanation:

w = x + y/z

Subtract x from both sides

w - x = y/z

Multiply both sides by z

z(w - x) = y

Flip

y = z(w - x)

Answer:

Option. A

Step-by-step explanation:

Have a great day!

Answer: A

Step-by-step explanation: there's 8 spaces on the spinner

Answer:

A maximum of 4 days

Step-by-step explanation:

Inequality: 95 + 11.50x ≤ 150

Okay so the 95 is his fee. Then for everyday, it's 11.50 and we don't know how many days yet, so 11.50x. The 95 dollars and the 11.50x has to equal to or less than 150 since that is how much he has to spend on vaca.

95 + 11.50x ≤ 150

-95                   -95

11.50x ≤  55

/11.50       /11.50

X=4.78260869565

You would round down since he has a budget.

Answer:

Yes, they would get different values

Step-by-step explanation:

Given

[tex](4 * 35) + (36 * 8)[/tex]

Required

Would there be different value for the expression?

From the question, we understand that both students made no computational errors. This doesn't mean that the students cannot make other errors.

For instance, the expression can be solved (wrongly) in the following ways;

[tex](4 * 35) + (36 * 8) \to 4 * 35 + 36 * 8 \to 140 + 36 * 8 \to 176 * 8 = 1408[/tex]

[tex](4 * 35) + (36 * 8) \to 4 * 35 + 36 * 8 \to 4 * 71 * 8 \to = 2272[/tex]

While the correct solution is:

[tex](4 * 35) + (36 * 8) \to 140 + 288 =428[/tex]

Hence, it is possible for two students to get different values

Answer:

AB = 7

Step-by-step explanation:

The polygon pictured is a hexagon, which means that it has 6 equal side lengths. The perimeter is 42. AB is the length of one side.

Perimeter = 6 x length of one side

If you plug everything you know in the equation, you would get...

42 = 6 x length of one side

42 ÷ 6 = 7

So, 7 is the length of AB, since in a hexagon, all sides are the same length.

The length of side AB  is 7.

A regular polygon is a closed shape that has straight sides of equal length and interior angles of equal measure.

This means that all of the sides and angles of a regular polygon are congruent (i.e., have the same size).

We have,

The given polygon is a hexagon since it has 6 faces.

Now,

The six faces are equal in length.

So,

6 faces length = 42

Now,

Each face = x

And,

6x = 42

x = 42/6

x = 7

Thus,

The length of AB  is 7.

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9514 1404 393

Answer:

  see attached

Step-by-step explanation:

When rotation is 180° or 360°, the direction is immaterial. The result is the same no matter which direction you go.

Answer:

= 5^-8 . 5^-10

= 5^(-8 ) + (-10)

=5^-18

Answer:

5^-18

Step-by-step explanation:

[tex](5^{-8})(5^{-10}) = 5^{-8-10} = 5^{-18}[/tex]

answer:

=y^(-4+3)

=y^ (-1)

Answer:

1920

Step-by-step explanation:

Volume of larger rectangular prism: 10 * 8 * 14 = 1120

Volume of smaller rectangular prism: 10 * 10 * 8 = 800

Volume of whole prism: 1120 + 800 = 1920

Hence, your answer is 1920

Answer:

there are seven variable terms

Step-by-step explanation:

variables are letters (a, b, c, etc.)

i hope this helps :)

Answer:

The answer is 4 because are all separate variables (also  combines into one variable)

Step-by-step explanation:

Answer:

B) 63 ft.

Step-by-step explanation:

To find how long it takes for a rotation, we need to find the circumference.

To do so, we use the formula 2(pi)r

To find the radius, we divide the diameter in half :

d = 20

r = d/2

r = 20 / 2

r = 10

Then, we plug that into the formula :

2(pi)10

Insert that into your calculator :

2(pi)10 = 62.83

Simplify :

62.83 = 63 ft.

Exact Answer:     x = 16/3

Approximate Answer:      x = 5.333

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

Work Shown:

base = 3x-1

height = x

area of triangle = (base*height)/2

40 = x*(3x-1)/2

40*2 = 3x^2 - x

80 = 3x^2 - x

0 = 3x^2 - x - 80

3x^2 - x - 80 = 0

Now apply the quadratic formula

[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(-1)\pm\sqrt{(-1)^2-4(3)(-80)}}{2(3)}\\\\x = \frac{1\pm\sqrt{961}}{6}\\\\x = \frac{1\pm31}{6}\\\\x = \frac{1+31}{6} \ \text{ or } \ x = \frac{1-31}{6}\\\\x = \frac{32}{6} \ \text{ or } \ x = \frac{-30}{6}\\\\x = \frac{16}{3} \ \text{ or } \ x = -5\\\\x \approx 5.333 \ \text{ or } \ x = -5\\\\[/tex]

A negative height doesn't make sense, so we ignore x = -5

The only solution is x = 16/3 which approximates to x = 5.333

Answer:

c=-18 d=2

Step-by-step explanation:

[ 6 8 -11 15 ]-[c+2 3 -5 d-4 ]=[ 22 5 -6 17]

The equation tells that when the two matrices are subtracted we get the resultant matrix.

Each element of the first matrix corresponds to each element of the second matrix

From above

6- (c+2)= 22

6- c-2= 22

4-c= 22

-c= 22-4

-c= 18

c= -18

And

15-( d-4)= 17

15- d+4= 17

19-d= 17

-d= 17-19

-d= -2

d= 2

Answer:

D

Step-by-step explanation:

c= -18

d= 2

Answer:

Let the three consecutive numbers be x,x+1,x+2 . The numbers are: 23,24,and25 and the smallest one is 23

Step-by-step explanation:

Answer: (x-1) + (x) + (x+1) = 72; smallest number is 23.

Step-by-step explanation:

The numbers are consecutive, meaning they sit next to each other on a number line. For example 4, 5, 6.

Because they are three consecutive numbers, their average will be the value of the middle one. For example the average of 4, 5, 6 is 5.

Knowing this, we can divide 72 by three to get the value of the middle number.

72/3 = 24, so the middle number is 24.

The numbers that fall either side of 24 on the number line are 23 and 25, so the three consecutive numbers are 23, 24, 25.

You can also set up and solve the equation: (x-1) + (x) + (x+1) = 72 because the numbers are consecutive.

To solve, combine like terms. The (-1) and (+1) cancel out and the equation becomes 3x = 72.

72/3 = 24, so x = 24, and the smallest term, (x-1) = 23.