Solve the following equations. Show your work. Submit to your teacher when you have completed the sheet.

Given :

The temperature of a pot of water is 62 F .

The temperature increases  by 20 F per minute when being heated .

To Find :

Write an equation to represent  the linear relationship.

Solution :

Here , the temperature is increasing directly with the time .

Therefore , it is a linear equation .

Let temperature varies with as :

T = at+b   .... equation 1 .

( Here , a and b are constants )

Now , at t= 0 min .

[tex]T = 62 =a\times 0 + b[/tex]

[tex]b=62[/tex]    

Now , after 1 min temperature will be , T = 62 +20 =82 F

[tex]T = 82 = a\times 1+62\\a=20[/tex]

Putting value of a ans b in equation 1 , we get :

[tex]T=20t+62\ F[/tex]

Hence , this is the required relation .

Answer:y=10x-1

Step-by-step explanation:

9x+7y

x=8 and y=3

9(8)+7(3)

72+7(3)

72+21

=93

Answer:

since you are trying to get the scaled copy smaller you need to instead of multiply by 7 multiply by 1/7

Step-by-step explanation:

Answer:8

Step-by-step explanation:

Answer:

Since its due quickly ill just write the answer. Let me know if you want the work as well though.

3*(1.06)=3.18

so,

24/(3.18)=7.57

You can't have half an ice cream cone ( i wish we could though :( ) , you can only get 7

7 ice cream cones

Answer:

7 x 21

Step-by-step explanation:

We can say that the dimensions are a and b. Since this is a rectangle, we know that the perimeter will be 2a + 2b. So our first equation is:

2a + 2b = 56.

They also tell us that the length is 3 times its width. So we can say this:

a = 3b.

Now we can substitute, and we can do the full problem with the given info:

2a + 2b = 56

a = 3b

2a = 6b

6b + 2b = 56

8b = 56

b = 7

Now that we know b, we can multiply it by 3 to get a:

b = 7

a = 3b

a = 21.

So our answer is:

a = 21

b = 7

Answer:

Dimensions:

7 x 21

Answer:

Width=7

Length=21

Step-by-step explanation:

p=56 feet

L=3W

P=2L + 2W

56=2(3W)+2W

56=6W+2W

56=8W

W=56/8 = 7 ⇒ Width=7

L=3W

L=3*7

L=21 feet ( length=21 feet)

check : p=2l+2w

P=2(21)+2(7)

p=42+14=56

In mathematics, the reciprocal, or multiplicative inverse, of a number x is the number which, when multiplied by x, yields 1. It is denoted 1/x or x-1.

Answer:

RUn on sentence

Step-by-step explanation:

3/4 + 1/8 + 1/10 = 39/40

............................................

Answer:

39/40 Please mark my answer the brainliest. It will get me to the next level!

Step-by-step explanation:

4=4, 8, 12, 16, 20, 24, 28, 32, 36, 40

8=8, 16, 24, 32, 40.

10=10, 20, 30, 40.

GCF=40

3/4=30/40

1/8=5/40

1/10=4/40

30+5+4=39

Answer:

3.125

Step-by-step explanation:

-14÷(-4.48)

14÷(4.48)

divide that you will get 3.125

25/8, 3 1/8

is its alternative form.

Answer:

2y-6

Step-by-step explanation:

Six less = Subracted by 6.

Answer:

4 to 3

Step-by-step explanation:

Since in the question it is mentioned that the ratio is written by comparing the number of video games with respect to sports to the number of video games with respect to the driving is 4: 3

Also the ratio defines a relationship between the two variables

So, the ratio that is equal to cotton ratio is 4 to 3 and the same is to be considered

Answer:

Your answer is 4 to 3

Step-by-step explanation:

Answer:

2) 24

3) 13

4) 27

Step-by-step explanation:

2) 3(2)^4-1=3(2)^3=24

3) 3(5)-2=15=2=13

4) 4(6-1)+7=4(5)+7=20+7=27

(a+b+c)^3=a^3 +b^3+c^3-2(ab+ac+bc)

216=a^3+b^3+c^3-2(11)

a^3+b^3+c^3=238

but ıdk how can ı find -3abc :/

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Work Shown:

a+b+c = 6

(a+b+c)^2 = 6^2

(a+b+c)(a+b+c) = 36

a(a+b+c)+b(a+b+c)+c(a+b+c) = 36

a^2+ab+ca+ab+b^2+ca+bc+c^2 = 36

a^2+b^2+c^2+2ab+2bc+2ca = 36

a^2+b^2+c^2+2(ab+bc+ca) = 36

a^2+b^2+c^2+2*11 = 36

a^2+b^2+c^2+22 = 36

a^2+b^2+c^2 = 36-22

a^2+b^2+c^2 = 14

-----------------------

a^3+b^3+c^3-3abc = (a+b+c)*(a^2+b^2+c^2 - (ab+bc+ca) )

a^3+b^3+c^3-3abc = 6*(14 - 11)

a^3+b^3+c^3-3abc = 18

Answer:

is A

Step-by-step explanation:

Answer:

17

Step-by-step explanation:

Answer: She bought 17 books

Step-by-step explanation:

Add $6 to the amount that she paid to find out how much money she would have paid.

45 + 6 = 51  so she would have paid $51  

Now divide 51 by 3 to find out how many books she bought.

51 / 3 = 17  

So because of the discount, she paid $45 for 17 books.

Answer:

Step-by-step explanation:

If Point P is the interior of ∠OZQ, then ∠ O Z P +∠ P Z Q = ∠ O Z Q

Given  O Z Q = 125 and m ∠ O Z P =62, to get  ∠ P Z Q, substitute the given angles into the formula above as shown;

∠ O Z P +∠ P Z Q = ∠ O Z Q

62 +∠ P Z Q = 125

subtract 62 from both sides

62 +∠ P Z Q - 62= 125 - 62

∠ P Z Q  = 63°

Hence the angle ∠ P Z Q  is 63°

Answer:

w > -2

Step-by-step explanation:

9 + w > 7

Subtract 9 from both sides to end up with w alone on the left side.

w > -2

Answer:

∠ CAD = 32°

Step-by-step explanation:

The sum of the angles in Δ ABD = 180°, thus

∠ BAD + 100° + 48° = 180°

∠ BAD + 148° = 180° ( subtract 148° from both sides )

∠ BAD = 32°

Since AD bisects ∠ CAB , then

∠ CAD = ∠ BAD = 32°

Answer:

3x^3 + x^2 -7x - 5

Step-by-step explanation:

SOOOOOOO you use the distributive property and multiply by each term.

Answer:

3x^3 + x^2 -7x -5

Step-by-step explanation:

(3x-5)(x^2+2x+1) you multiply and then add to get to 3x^3 + x^2 -7x -5.

*For example (x+2)(x+3) will be x^2+5x+6 The same logic is applied.

Answer:

y=2x-58

Explanation:

In order to write our point-slope formula (y=mx+C format), we first need to figure out the slope (m). To figure out the slope, we divide the change in y by the change in x between the two points (rise/run). The rise is 30 (2-(-28)) and the run is 15 (30-15). Therefore the slope is 2 (30/15)

This gives us:

y=2x + c

Now to figure out C (which will be the y-intercept of the graph) we substitute in the values from one of the points. So our x=30 and our y=2:

2=2(30) + c

2=60+c

2-60=c

-58=c

So now we know that our C (constant) is - 58.

Hence our point-slope formula is:

y=2x-58

Which you can test with the other point:

-28=2(15) - 58

Hope this helped!

Answer:

y-2=2

Step-by-step explanation:

Answer: 89m+45=c

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

-12 x -2 = 24. 24-16=8

Answer:

x = 9π

x = 1620°

x ≈ 28.27433

Step-by-step explanation:

Move constant to the right-hand side and change its sign which it'll look like

x = π + 8π

Then collect like terms which youll end up with

x = 9π

Answer:

Step-by-step explanation:

In an arithmetic sequence the common difference is always the difference between the next term and the previous term:

[tex]d= a_2-a_1=a_3-a_2=...=a_{150}-a_{149}=....[/tex]

we have:   [tex]a_1=2\quad and\quad a_2=5[/tex]  

so:

     [tex]d=5-2 =3[/tex]

Answer:

Domain : 0° < x <90°

Range: 90° < y < 180°.

Step-by-step explanation:

When we have a function:

f(x) = y

the domain is the set of the possible values of x, and the range is the set of the possible values of y.

In this case we have:

x + y = 180°

such that x < y

Let's analyze the possible values of x.

The smallest possible value of x must be larger than 0°, as we are workin with suplementary angles.

Knowing this, we can find the maximum value for y:

0° + y = 180°

y = 180° is the maximum of the range.

Then we have:

0° < x

y < 180°

To find the other extreme, we can use the other relation:

x < y.

Then, we can impose that x = y (this value will not be either in the range nor the domain)

if x = y then:

x + y = x + x = 180

2*x = 180

x = 90°

This will be the maximum of the domain and the minimum of the range.

Then we have that the domain is:

0° < x <90°

And the range is:

90° < y < 180°.

Answer:

Digits that should be written when doing calculations

-by-step explanation:

Answer:

A

Step-by-step explanation: