20. The temperature of a pot of water is 62*F. The temperature increases
by 20*F per minute when being heated. Write an equation to represent
the linear relationship. *
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 .
Use properties of operations to find the quotient. -14 ÷ (-4.48)
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.
a rectangluar rug has a length that is 3 times its width. The perimieter is 56 feet. what are the dimensions?
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
9+w>7 what is the inequality?
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
What is the value of the expression below
x = 8 and y = 3
9x + 7y
9x+7y
x=8 and y=3
9(8)+7(3)
72+7(3)
72+21
=93
2•14+ 3•7
————-
71 - 15
what scale factor would you use on the 14-inch by 21-inch rectangle to return it to its original 2-inch by 3-inch size
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:
where should the decimal point be placed in the example shown
Answer:
A
Step-by-step explanation:
If a+b+c=6,ab+bc+ca=11,then what is a3+b3+c3-3abc
(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 :/
===============================================
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
Find the point-slope equation for the line that passes through the points (30,2) and (15,-28) use the first point in your equation
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:
The local cable TV provider charges $89.00 per month for basic service, and has a $45.00 one-time "Activation Fee" for new accounts. Write (choose) the model for the Total Cost (C) of having cable TV as a function of the number of months (m) that you have service.
Answer: 89m+45=c
Step-by-step explanation:
kaitlin bought some books. she spent a total of 45 after a discount of $6 off her total purchase. Each book cost $3. How many books did she buy
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.
Help needed ASAP will give brainliest please I NEED HELP ITS TIME LIMIT :(
Answer:
RUn on sentence
Step-by-step explanation:
if your last period started on Augest 6 and stopped on Augest 11. when will you have your next period?
The formula x + y = 180 can be used to find the degrees of supplementary angles, where x is the smaller angle. Find the domain and range of this solution
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°.
16 less than the product of - 2 and -12
Answer:
8
Step-by-step explanation:
-12 x -2 = 24. 24-16=8
Super simple question could you explain it and write it out WILL MARK BRAINLEST
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
a car tire has a radius of 10.4 inches what distance will the tire travel after 20 rotations
Answer:
is A
Step-by-step explanation:
I don’t know what to do here someone please help
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
Graph this function: y–3= – (x+10)
Click to select points on the graph.
Answer:
See below
Step-by-step explanation:
We can simply use a graphing calculator to graph the function
[tex]\boxed{y-3 = -(x+10)}[/tex]
See in the attached file!
PLEASE HELP FAST..ASSIGNMENT IS DUE IN MINUTES!!
An ice cream cone costs $3
plus 6% sales tax. How many
Icecream cones can be purchased
for $24?
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
pls ignore the numbers that was another problem :)
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
Point P is the interior of LaTeX: \angle OZQ.\: ∠ O Z Q . If LaTeX: m\:\angle\:OZQ\: m ∠ O Z Q = 125 and LaTeX: m\angle OZP\: m ∠ O Z P =62, what is LaTeX: m\angle PZQ m ∠ P Z Q ?
Answer:
63°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°
Colton wrote a ratio comparing the number of sports video games that he owns to the number of driving video games that he owns as 4:3. Which ratio is equivalent to Colton's ratio?
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:
Which equation represents the data shown in the table below? Fence Length (y) 100 150 180 240 Number of Posts (x) 11 16 19 25 A y 10x 1 B y 10(x 1) C y 10x 1 D y 10(x 1)
Answer:y=10x-1
Step-by-step explanation:
3x-5)(x2+2x+1) Please show working
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.
In an arithmetic sequence, the first term is 2 and the second term is 5. Find the common difference.
Answer:
d = 3Step-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]
“six less than twice y”
Answer:
2y-6
Step-by-step explanation:
Six less = Subracted by 6.
What is the definition of significant digits?
Answer:
Digits that should be written when doing calculations
-by-step explanation:
Please please please help! D:
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°