Answers
Answer:
Y=[tex]\frac{2}{3}[/tex]x+4
Step-by-step explanation:
Slope formula is y=mx+b
This is because the slope is 2 over 3: “rise over run”
Slope = m so: y=[tex]\frac{2}{3}[/tex]X+b
We need to find be, that easy because to find b, we have to look at the y axis. Were does the line intercept the y axis?
It is at (0,4) or just simply “4”
Now plug in b=4 into the equation:
y=[tex]\frac{2}{3}[/tex]X+4
Related Questions
As a bowl of soup cools, the temperature of the soup is given by the twice-differentiable function H for 0[tex]\leq[/tex]t[tex]\leq[/tex]12, where H(t) is measured in degrees Celsius (C), and time t is measured in minutes. Values of H(t) at selected values of time t are shown in the table above.
a) Use the data in the table to approximate H'(5). Show the computations that led to your answer. Using correct units, explain the meaning of H'(5) in the context of the problem.
b) Is there a time t for 0[tex]\leq[/tex]t[tex]\leq[/tex]12 at which the temperature of the soup is 60C? Justify your answer.
c) The temperature of the soup is also modeled by the twice-differentiable function C for 0[tex]\leq[/tex]t[tex]\leq[/tex]12, where C(t) is measured in degrees Celsius (C), and time tis measured in minutes. It is known C(3)= 80 and the derivative of C is given by C'(t)= -3.6e-0.05t. Write an equation for the line tangent to the graph at t=3 and use it to approximate C(5).
d) Based on the model given in part c, at what rate, in degrees Celsius per minute minute, is the rate of change of the temperature of the soup changing at t=3 minutes?
Answers
The rate of change of temperature with time at a point in time is given by
the derivative of the function for the temperature of the soup.
The correct responses are;
a) H'(5) is approximately -2.6 degrees Celsius per minute.b) Yesc) The equation for the line tangent is y = -3.6·t + 90.8The approximate value of C(5) is 72.8 °Cd) The rate of change of the temperature of the soup at t = 3 minutes is -3.6 degrees Celsius per minute.Reasons:
a) From the data in the table, we have;
The approximate value of H'(5) is given by the average value of the rate of
change of the temperature with time between points, t = 3, and t = 8
Therefore;
[tex]\displaystyle H'(5) = \mathbf{\frac{H(8) - H(3)}{8 - 3}}[/tex]
Which gives;
[tex]\displaystyle H'(5) = \frac{80 - 67}{8 - 3} = \mathbf{2.6}[/tex]
Therefore, H'(5) = -2.6°C per minute
b) Given that the function is twice differentiable over the interval, 0 ≤ t ≤ 12, the function for the change in temperature is continuous in the interval 0 ≤ t ≤ 12
At t = 0, H(0) = 90 °C
At t = 12, H(12) = 58 °C
58 °C < 60 < 90 °CTherefore, there exist a temperature, of 60 °C between 90° C and 58 °C
c) The given derivative of C is, [tex]C'(t) = \mathbf{-3.6 \cdot e^{-0.05 \cdot t}}[/tex]
At t = 3, we have;
[tex]The \ slope \ at \ t = 3 \ is \ C'(3) = -3.6 \cdot e^{-0.05 \times 3} \approx -3.1[/tex]
Therefore, we have;
y - 80 ≈ -3.1 × (x - 3)
The equation for the tangent is; y = -3.6 × (x - 3) + 80
y = -3.6·x + 10.8 + 80 = -3.6·x + 90.8
The equation for the tangent is; y = -3.6·x + 90.8The value of C(5) is approximately, C(5) ≈ -3.6 × 5 + 90.8 = 72.8
C(5) ≈ 72.8°d) Based on the the model above, the rate at which the temperature of the
soup is changing at t = 3 minutes is -3.6 degrees per minute.
Learn more about calculus and concepts here:
https://brainly.com/question/20336420
PLEASE HELP!!!!! I WILL REWARD
Answers
Answer:
the fourth bubble or d
Step-by-step explanation:
x has to equal to or less than 6
need help solving this
Answers
Answer:
x = (√21)/2
Step-by-step explanation:
The sides of a 30°-60°-90° triangle have the ratios 1 : √3 : 2. That means the middle-length side is (√3)/2 times the length of the longest side.
x = (√3)/2·√7
[tex]\boxed{x=\dfrac{\sqrt{21}}{2}}[/tex]
can some1 please help:(
Answers
A) -2/5hope it helps ....❤
im stuck step bro #im a guy
Answers
Answer:
Well then...
Step-by-step explanation:
HELP!!
is {(-3,-6),(-2,-1),(-1,-0),(0,3),(1,15)} a function??
Answers
It's a function because we don't have any repeated x coordinates. Any given x input value leads to exactly one y output value.
The domain is {-3,-2,-1,0,1} which is the set of all x inputs.
The range is {-6, -1, 0, 3, 15} which is the set of y outputs.
Desmond has 169 square bricks that he is arranging in a row to make a patio. Every row must have to have the same number of bricks. How many bricks are in each row? Describe the shape of the patio
Answers
The second side of a triangular deck is 4 feet longer than the shortest side, and the third side is 4 feet shorter than twice the length of the shortest side. If the perimeter of the deck is 52 feet, what are the lengths of the three sides?
Answers
Answer:
13 ft, 17 ft, 22 ft
Step-by-step explanation:
let x be the shortest side, then second side is x + 4 and the third side is
2x - 4
sum the 3 sides and equate to 52
x + x + 4 + 2x - 4 = 52 , simplify
4x = 52 ( divide both sides by 4 )
x = 13
x + 4 = 13 + 4 = 17
2x - 4 = 2(13) - 4 = 26 - 4 = 22
lengths of 3 sides are 13 ft, 17 ft and 22 ft
What is the value
of m when p= 32
3p + 2 = m
m =
O
11
00
8
O
5
3
Answers
3(32)+2=m
96+2=m
M=98
The data set below shows a relationship between the number of hours tara works and her paycheck:{ 1, 25), (2, 40), (3, 55), (4, 70), (5, 85), (6, 100) what is Tara's hourly pay rate?
Answers
Step-by-step explanation:
Need to find out total hours and total pay and simplify the answer.
Total Hours = 1+2+3+4+5+6 = 21
Total Pay = 25+40+55+70+85+100 = 375
Pay ÷ Hours = 375 ÷ 21 = 17.86
Not convinced with this answer tbh but it's what I got.
I NEED HELP! The surface area of a triangle is base times height. True or False?
Answers
Answer:
true
Step-by-step explanation:
i learned this in like 7th grade
Which of the following is the graph of y = |x - 3|
Answers
Answer:
y = | x - 3 | is graphed on the attachment below ↓
Step-by-step explanation:
If you ever need an equation graphed, here's a useful site called Desmos that can do that really well and for free.
Choose all the numbers that make the comparison true.
42 > __
A, 22
B, 64
C, 41
D,40
E, 40
Answers
Answer:
22, 40, 40, and 41
Step-by-step explanation:
happy to help have a nice day
A recipe requires 1/3 cup of water for every 2/5 cups of sugar. How much
sugar would you need for a full cup of water?
Answers
Answer:
1 1/5
Step-by-step explanation:
Listen
ol
Figure B is a scale image of Figure A, as shown.
2.5
Figure A
Figure B
Enter the scale factor applied to Figure A to produce Figure B.
Enter your answer as a fraction, like this. 42/53
Answers
Answer:
scale factor = [tex]\frac{14}{5}[/tex]
Step-by-step explanation:
The scale factor is the ratio of corresponding sides, image to original.
scale factor = [tex]\frac{7}{2.5}[/tex] = [tex]\frac{7(2)}{2.5(2)}[/tex] = [tex]\frac{14}{5}[/tex]
Given ABCD, solve for x.
A. 11
B. 13
C. 14
D. 12
Answers
Answer:
Step-by-step explanation:
Because you have a parallelogram, the two angles shown are "same side interior angles" which means they add up to 180°.
We would say that they are supplementary (they add up to 180°)
So add them together and set them equal to 180°
(4x+18) + (8x+30) = 180°
This is all adding, so we dont really need any of these parenthesis.
4x+18+8x+30=180
Add the x terms together and add the constants (plain numbers) together.
12x + 48 = 180
Subtract 48 from both sides of the equation.
12x = 132
Divide both sides by 12
x = 11
Ivanna drove 420 miles using 18 gallons of gas. At this rate, how many gallons of gas would she need to drive 357 miles?
Answers
Answer:
15.3 GAL.
Step-by-step explanation:
The game starts as follows. You pick one medal without unwrapping it, and then the game host unwraps one of the remaining medals and reveals that it is a silver medal. (Assume here that the host unwraps a medal with equal probability, but knowing where the gold medal was and avoiding unwrapping the gold medal if still on the table, to keep the game interesting to watch until the end.) You have now three medals left to unwrap (one in your hand, two on the table). At this point, the host gives you the option to change your mind and swap your medal for one of the two left on the table. What would you do at this point? Would you keep your medal, or swap it with one of the two medals left on the table? If so, which one?
Answers
Answer:
I'd swap with one on the table (the left one) but with my luck it would be a sword made of rubber
Given that in ABC, angle C is 12 less than 4 times x, angle A is 11 more than twice x, and angle B is 8 less than 3 times x. Find the m of angle
C
Answers
Answer:
m∠C = 72°
Step-by-step explanation:
The sum of the angles in the triangle is 180°.
A +B +C = 180°
(2x +11)° +(3x -8)° +(4x -12)° = 180°
9x = 189 . . . . . . . . divide by °, add 9
x = 21 . . . . . . . . . divide by 9
Angle C is ...
(4x -12)° = (4(21) -12)° = 72° . . . . angle C
_____
Additional comment
Angle A is 53°; angle B is 55°.
you walk 3/4 miles to a grocery store. Then you walk another 1/5 miles to a shoe store. How many miles have you walked in all?
Answers
Answer:
19/20 miles
Step-by-step explanation:
3/4 + 1/5
3/4 = 0.75
1/5 = 0.2
3/4 + 1/5
= 0.75 + 0.2
= 0.95
= 95/100
= 19/20
Therefore,
the miles you have walked in all is 19/20.
HELP ANSWER PART A AND B
Answers
Answer:
part A: median is 12
part B: interquartile rage is 10
Step-by-step explanation:
Part A: to find your median on a box and whisker plot, you just need to look at your middle line in your box. In this case it's 12.
Part B: to find your interquartile range on a box and whisker plot, you subtract your Q1 and Q3. Your Q1 and Q3 will be the two outside lines that make up the rest of your box, in this case would be 6 and 16. To find your Q1 if you don't already have your plot set up, you separate the numbers that are given to you in half and find the median of each side. The first half will be your Q1 and the second half your Q3.
Ben made some apple pies. For every 4 cups of butter, he added 3 cups of water. The ratio of butter to water in Ben's apple pies is ____. (5 points)
Question 1 options:
1)
2)
3)
3
4)
4
Answers
Answer:
4 Trust me
Step-by-step explanation:
3 2/3 + 2 3/5 + x = 8
Answers
Answer: x= [tex]-\frac {109}{15}[/tex]
When using a ruler, where is the unit?
- The tick marks on the ruler.
- The space between the tick marks on the ruler.
-The numbers on the ruler.
Answers
Answer:
Is it The numbers on the ruler?
Step-by-step explanation:
Company A makes 20 notebooks in 4 hours. Company B make 28 notebooks in
3 hours. Write a statement comparing the number of notebooks made per
hour.
Answers
Help please , need answer ASAP
Answers
Answer:
(fg)(9) = 948
Step-by-step explanation:
(fg)(9) = f(9)×g(9) = (9 +3)(9^2 -2) = (12)(79)
(fg)(9) = 948
Use the long division method to find the result when 12x3 - 27x2 + 13x + 30 is
divided by 4x + 3.

Answers
Answer:
your answer will become 69.
find the greatest common factor GCF and the least common multiple LCM of these Numbers. 8and 9
Answers
Answer:
LCM is [tex]72[/tex]
GCF is [tex]1[/tex]
Step-by-step explanation:
LCM is least common multiplier
LCM of
[tex]8,9=8\times 9\\\\=72[/tex]
GCF is greatest common factor
Factors of [tex]8=1,2,4,8[/tex]
Factors of [tex]9=1,3,9[/tex]
Greatest common factor is [tex]1[/tex]
GCF is [tex]1[/tex]
Melissa has 120 kilograms of rice. Her mother sold 105 kilograms. What percent of the rice was sold? with solution :D please
Answers
Answer:
225
Step-by-step explanation:
po ang answer ko
please comment if I'm wrong
Jillian is making accessories for the soccer team. She uses 677.46 inches of fabric on headbands for 38 players and 4 coaches. She also uses 366.32 inches of fabric on wristbands for just the players. How much fabric was used on a headband and wristband for each player?
Answers
The amount of fabric used to make the headband is 16.13 inches. The amount of fabric used to make the wristband is 9.64 inches.
In order to determine the amount of fabric used to make the accessories, the total inches used would be divided by the total number of people the accessory was made for.
The amount of fabric used to make headband for a player = total quantity of fabrics used / total number of people
677.46 / (38 + 4)
677.46 / 42
= 16.13 inches
The amount of fabric used to make wristband for a player = total quantity of fabrics used / total number of players
366.32 / 38 = 9.64 inches
To learn more about division, please check: https://brainly.com/question/194007