Friction creates heat and lowers the _______

The vertices of the hyperbola are the x-intercepts of the hyperbola

The equation of the hyperbola is [tex]\frac{y^2}{400} -\frac{x^2}{81} = 1[/tex]

The equation of a hyperbola is represented as:

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

The vertices are (20,0) and (-20,0).

So, the center of the hyperbola is:

(h,k) = (0,0).

Also, we have:

a = 20

This gives

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

Evaluate

[tex]\frac{y^2}{a^2} -\frac{x^2}{b^2} = 1[/tex]

Substitute 20 for a

[tex]\frac{y^2}{20^2} -\frac{x^2}{b^2} = 1[/tex]

[tex]\frac{y^2}{400} -\frac{x^2}{b^2} = 1[/tex]

The length of the conjugate axis is:

l = 18 units

So, we have:

[tex]b = \frac{18}2 = 9[/tex]

The equation becomes:

[tex]\frac{y^2}{400} -\frac{x^2}{9^2} = 1[/tex]

[tex]\frac{y^2}{400} -\frac{x^2}{81} = 1[/tex]

Hence, the equation of the hyperbola is [tex]\frac{y^2}{400} -\frac{x^2}{81} = 1[/tex]

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Answer:

27 children

Step-by-step explanation:

For every 9 children, there are 4 adults. Those numbers added together equal 13. Now, if we divide the total number of adults and children by 13, we will get the number of how many groups there are of 9 kids and 4 adults.

39 / 13 = 3

There are 3 groups of 9 kids and 4 adults, which means to find the total number of children, we have to multiply 3 by 9.

3 * 9 = 27

Therefore, there are 27 children total. I know this was probably really confusing, but I hope it helped in some way! Have a lovely day!! :)

Answer: c-3

Step-by-step explanation:

it is wanting you to take c minus 3

Answer:

The day that Angelique and Bentley will be at the gym on the same day is; the 42nd day.

Angelique's days:
6, 12, 18, 24, 30, 36, 42

Bentley's days:
7, 14, 21, 28, 35, 42

In conclusion, the earliest day that Angelique and Bentley will be at the gym on the same day will be, the 42nd day.

Step-by-step explanation:

Have a great rest of your day
#TheWizzer

Answer:

They felt it gave the commissioners too much power and was unfair to slaves by giving them a trail without injury

Answer:

14 weeks

Step-by-step explanation:

First, write as an equation with x the number of weeks Ayan and Gemma's money:

-> Ayan's money: 48+10x because every week he wins 10 more dollars

-> Gemma's money 300-8x

Finally just solve the equation for x where ayan's money = gemma's money so :

48+10x=300-8x

add 8x on both side: 48+18x=300

substract 48 on both side to isolate x : 18x =252

devide by 18 on both side : x=14

So that is how it goes hope this helps

Answer: I think the answer is 25 nickels? Im sorry if I get it wrong

Step-by-step explanation:

Answer:

35cm

120cm^2

Step-by-step explanation:

Answer:

1. The perimeter of figure a is 36 cm.

2. The area of figure a is 60 cm².

3. The perimeter of figure b is 14.25 in.

4. The area of figure b is 7.031 in².

If it's wrong tell me

Answer:

1. Z-24 < 12

2. A-12.65 ≤ 26,000

3. Z-999 < 500

4. -10x ≥ 25

5. f - -1 < 0 or f+1 < 0

6. y/14 ≥ 0.5

Answer:

8.60 inches

Step-by-step explanation:

The equation for circumference is 2πr. So we can solve for r (radius).

27inches=2πr

divide both sides by 2π :

r=4.299

The equation for diameter is 2*r so we just multiply

4.299 *2 = 8.598

since we have to round to the hundredth place the answer would be

8.60

The approximate diameter of the circular clock is 8.60 inches.

Circumference of a circle is defined as the total length of the boundary of the circle.

The concept is same as the perimeter for straight sided figures.

Given that,

Circumference of the clock = 27 inches

The formula to find the circumference is,

C = 2πr

where r is the radius.

2r is the diameter.

2πr = 27

2r = 27 / 3.14

2r = 8.5987 ≈ 8.60

Hence the diameter of the clock is 8.60 inches.

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#SPJ2

Answer:

Ali played on his PSP longer

Step-by-step explanation:

3/4 of an hour is long than 2/3 because 3/4 of an hour is 45 minutes and 2/3 of an hour is 40 minutes and 45 > 40

Answer:

Step-by-step explanation:

[tex]\qquad\qquad\huge\underline{\boxed{\sf Answer}}[/tex]

Let's solve ~

[tex]\qquad \sf  \dashrightarrow \: log(2x - 3) = - 1[/tex]

[tex]\qquad \sf  \dashrightarrow \:2x - 3 = {10}^{ - 1} [/tex]

[tex]\qquad \sf  \dashrightarrow \:2x = 0.1 + 3[/tex]

[tex]\qquad \sf  \dashrightarrow \:x = 3.1 \div 2[/tex]

[tex]\qquad \sf  \dashrightarrow \:x = 1.55[/tex]

Answer:

7.5 minutes

Step-by-step explanation:

90 seconds is equivalent to 1.5 minutes

1.5×5=7.5

Answer:

f^12

Step-by-step explanation:

f^4  * f^8

We that a^b * a^c = a^(b+c)

f^(4+8)

f^12

Hello!

We have the following expression:

[tex]\bf{f^4*f^8}[/tex]

Recall the Properties of Exponents:

[tex]\bold{a^ma^n=a^{m+n}}[/tex]

According to the property, if we have the same bases multiplied together, then we just add their exponents:

[tex]\bf{f^4f^8=f^{4+8}}[/tex]

Simplify:

[tex]\bf{f^{12}}[/tex]

Hope everything is clear.

Let me know if you have any questions!

[tex]\rule{2}{2}[/tex]Knowledge is Power!

Answer:

2:4

Step-by-step explanation: Subtract 1 from total amount then find the number of girls I think sorry

Answer:

x=2

Step-by-step explanation:

2(x)+5 =9
2(2)+5=9

Answer: The number is 2

Creating an Equation:

     The underlined portion of the sentence becomes a part of our mathematical equation in the next line.

           2 times some number plus 5 equals 9

           2 times n plus 5 equals 9

           2n plus 5 equals 9

           2n + 5 equals 9

           2n + 5 = 9

Solving our Equation:

     I will take the equation we created, and isolate variable n to solve.

           2n + 5 = 9

           2n + 5 - 5 = 9 - 5

           2n = 4

           (2n ) / 2 = (4) / 2

           n = 2

The sin ratio will be helpful in finding the missing side length and the missing side length is 29.50 units.

The trigonometric ratio is defined as the ratio of the pair of a right-angled triangle.

We have a right-angle triangle in the figure in which:

Length of the hypotenuse = x unit

Length of the side opposite to the angle = 12

And the angle is given between sides adjacent to the angle to the hypotenuse = 24°

We know the:

[tex]\rm sin\theta = \frac{Side \ opposite \ to \ the \ angle}{hypotenuse }[/tex]

[tex]\rm sin24 = \frac{12}{x}[/tex]

[tex]\rm x = \frac{12}{sin24}[/tex]

x = 29.50 units

Thus, the sin ratio will be helpful in finding the missing side length and the missing side length is 29.50 units.

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Answer:

  B.  (15, 19)

Step-by-step explanation:

To check to see if a particular ordered pair is a solution to an equation, use the values for the variables and see if the equation is true.

A. 4/5(0) +7 = 7 ≠ 1

B. 4/5(15) +7 = 19 . . . . . . is a solution

C. 4/5(-5) +7 = 3 ≠ 11

D. 4/5(-2) +7 = 27/5 ≠ 1

__

A calculator can help with this.

Answer:

86 cm

Step-by-step explanation:

parameter of the Pentagon

= the parameter of the square + the parameter of the

triangle

= 48 + 38

= 86

Answer:

Fraction form: 1/8

Decimal form: 0.125

Step-by-step explanation:

Slope of line = [-6 - (-8)]/[8 - ( -8)]

= [-6 + 8]/[8 + 8]

= 2/16

= 1/8

= 0.125

0.625

Explanation:
We know that 0.125 is equal to 1/8, so you can then multiply 0.125 by 5.

Dividing 5/8, It's Equal To 0.625

Step-by-step explanation:

5/8 = O.625

Answer:

less than

Step-by-step explanation:

Answer:

B) less than

Step-by-step explanation:

We can start by looking at the number infront of the fractions. We know that 2 is less than 3 which also means that 2 and 7/8 is less than 3 and 1/4.

I hope this helps!!

Please mark brainliest!

Answer:

2.5

Step-by-step explanation:

Let M and P stand for the money that Mike(M) and Pete(P) have.

We discover that M + P = $84.00

We also find that M = $24.00

This means that :

M + P = $84.00

$24.00 + P = $84.00

P = $60.00

The ratio of P to M is ($60.00/$24.00) or 2.5   (P/M - 2.5)

in the II Quadrant, let's recall that the adjacent side or cosine is negative whilst the opposite side or sine is positive, thus

[tex]tan(\theta )=-\sqrt{\cfrac{19}{17}}\implies tan(\theta )=\cfrac{\stackrel{opposite}{\sqrt{19}}}{\underset{adjacent}{-\sqrt{17}}}\impliedby \qquad \textit{let's find the \underline{hypotenuse}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c=\sqrt{a^2+b^2} \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases}[/tex]

[tex]c=\sqrt{(-\sqrt{17})^2~~ + ~~(\sqrt{19})^2}\implies c=\sqrt{17+19}\implies c=\sqrt{36}\implies c=6 \\\\[-0.35em] ~\dotfill\\\\ ~\hfill cos(\theta )=\cfrac{\stackrel{adjacent}{-\sqrt{17}}}{\underset{hypotenuse}{6}}~\hfill[/tex]

Answer:

$864

Step-by-step explanation:

The solution to the system of equations is (-3, -5) because the point satisfies both equations

A linear function is in the form:

y = mx + b

Where m is the slope (rate of change) and b is the y intercept

Line A:

y = x − 2  (1)

Line B:

y = 3x + 4   (2)

Solving both equations simultaneously gives:

x = -3, y = -5

The solution to the system of equations is (-3, -5) because the point satisfies both equations

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Answer:

13) Squares, Rectangles. 14) Rhombus, Square.

15) Parallelogram, rectangle, rhombus, square

Step-by-step explanation:

Answer:

1/3x+1/2

Step-by-step explanation: