Answers
Answer:
A) 30 minutes after the air conditioner started to cool the house, the temperature inside the house has dropped to 76°F
B) [tex]f(x)=-0.4x+88[/tex]
Step-by-step explanation:
A)
In this problem, f(x) represents temperature, in degrees Fahrenheit, of Sam’s house x minutes after the air conditioner started to cool the house.
So we have:
x = minutes after the air conditioner started to cool the house
f(x) = temperature
Here we want to find what is the meaning of
[tex]f(30)=76[/tex]
Which implies that:
[tex]x=30[/tex], which means that 30 minutes have passed after the conditioner has started to cool the house
[tex]f(x)=76[/tex], which means that the temperature of the room at that time is 76°F
So, the interpretation of f(30) =76 is that:
"30 minutes after the air conditioner started to cool the house, the temperature inside the house has dropped to 76°F"
B)
Here we want to write explicitly a function that tells us how the temperature inside the house varies as a function of x, the number of minutes passed after the air conditioner has turned on.
We know the following information:
- At time x = 0, the temperature inside the house is 88°F
- At time x = 30 min, the temperature inside the house is 76°F
We can assume that the temperature inside the house changes linearly with time; so, we can describe the temperature function with the equation of a line:
[tex]f(x)=mx+q[/tex]
where
[tex]q[/tex] is the value of the temperature at x = 0, so q = 88
m is the rate of change of the temperature
The rate of change can be found by calculating the rate of change of the temperature with respect to the change in time; so we find:
[tex]m=\frac{76-88}{30-0} =-0.4[/tex]
which means that the temperature decreases by 0.4°F every minute. So, the function can be written as
[tex]f(x)=-0.4x+88[/tex]
Related Questions
EXPAND AND SIMPLIFY
2(5x + 3) - 2(2x-3)
Answers
Hey there!
2(5x + 3) - 2(2x-3)
DISTRIBUTE
= 2(5x) + 2(3) - 2(2x) - 2(-3)
= 10x + 6 - 4x + 6
COMBINE the LIKE TERMS
= 6x + 12
Therefore, your answer should be:
6x + 12
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
10x + 6 - 4x - 6
14x
Sergei buys a rectangular rug for his living room. He measures the diagonal of the rug to be 18 feet. The length of the rug is 3 feet longer than the width. What are the approximate dimensions of the rug? Round each dimension to the nearest tenth of a foot. 10. 4 feet by 7. 4 feet 11. 1 feet by 8. 1 feet 13. 4 feet by 10. 4 feet 14. 1 feet by 11. 1 feet.
Answers
A rectangular rug divided by its diagonal becomes a right angle triangle
The length and width of the rug is 14.1 feet by 11.1 feet
A right angle triangle has the longest side as the hypotenus which is also the diagonal.Diagonal = 18 feet
width = x
length = x + 3
diagonal ² = length ² + width ²
18² = x² + (x + 3)²
18² = x² + x² + 6x + 9
324 = 2x² + 6x + 9
2x² + 6x + 9 - 324 = 0
2x² + 6x - 315 = 0
solve using quadratic formula
x = - b ± √b² - 4ac / 2a
= - 6 ± √6² - 4×2×-315 / 2×2
= -6 ± √36 - (-2520) / 4
= -6 ± √36 + 2520/4
= -6 ± √2556 / 4
= - 6 ± 6√71 / 4
= -6/4 ± 6√71 / 4
= -3/2 ± 3√71/2
x = 11.1392 or -14.1392
The value of x can't be negative
So,
x = 11.1 to the nearest tenth
Therefore, the value of width and length is
width = x
= 11.1 feet
length = x + 3
= 11.1 + 3
= 14.1 feet
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A student is making a model of the famous Giza pyramid,
which has four triangular sides and a square base. The
scale of the model is 1:1,000.
How many sides should the model pyramid have?
A. 6
B. 4.
C. 3
D. 12
Answers
Answer:
Choose the option D
Hi, please help again lol
Answers
Answer:
?? No questions asked here
The minute hand of a clock turns 6 degrees per minute. In ten minutes the minute hand turns what fraction of a full 360 turn?
Answers
Answer:
25%
Step-by-step explanation:
15 times 6 is 90
90 is 25 % of 360
Solve. 10−2x=3x+7
x=3/5
x=17/5
x = 17
Answers
Answer: x = (3/5)
Step-by-step explanation:
10−2x=3x+7
3 = 5x [Consolidate terms]
x = (3/5)
How to solve the Expected value
Answers
Answer:
The expected value is 50 degrees.
Step-by-step explanation:
This circle has a perfect section of 50 degrees marked, then another unknown sector, and since they are marked with a congruent marker, that means they are the same! The unknown sector is 50 degrees in length.
Madelyn is 1.85 meters tall. At 12 noon, she measures the length of a tree's shadow to be 39.75 meters. She stands 34.9 meters away from the tree, so that the tip of her shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest hundredth of a meter.
Answers
The relationship between her height and the tree's is an illustration of ratios and proportions
The height of the tree is approximately 2.11 meters
Her height is represented as:
[tex]\mathbf{h =1.85}[/tex]
At 12 noon, the length of the tree's shadow and her distance from the shadow are given as:
[tex]\mathbf{D =39.75}[/tex]
[tex]\mathbf{d =34.9}[/tex]
To calculate the height (H) of the tree, we make use of the following equivalent ratios
[tex]\mathbf{H : h =D : d}[/tex]
So, we have:
[tex]\mathbf{H : 1.85 =39.75 : 34.9}[/tex]
Express ratio as fraction
[tex]\mathbf{\frac{H }{ 1.85 }=\frac{39.75 }{ 34.9}}[/tex]
Multiply both sides by 1.85
[tex]\mathbf{H=1.85 \times \frac{39.75 }{ 34.9}}[/tex]
[tex]\mathbf{H=2.11}[/tex]
Hence, the height of the tree is approximately 2.11 meters
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Which answer is an equation in point-slope form for the given point and slope? point: (7, 4); slope: 6.
Answers
Answer: the answer is
y-4=6*(x-7)
Step-by-step explanation:
help meeeeeee.....!!!!
I WILL MARK BRAINIEST!!!
Answers
8x=35
X= 35/8
-7y=35
Y=-5
X-intercept: 35/8
Y intercept: -5
Answer:
X = 35/8
Y = -5
Admission to a science museum is $22 for an adult. The cost for a child is five dollars less than the cost for an adult. What would be the total cost of admission for 12 adults and 15 children? Explain.
Answers
Children: $22 - $5 = $17
22a + 17c = t
22(12) + 17(15) = t
264 + 255 = $519
The total cost of admission is $519.
Hope this helped!
What is the slope of the line that passes through (0, 7) and (3, 10)?
Answers
Answer:
slope = 1
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 7 ) and (x₂, y₂ ) = (3, 10 )
m = [tex]\frac{10-7}{3-0}[/tex] = [tex]\frac{3}{3}[/tex] = 1
Name
Lily Daku November 17, 2021 pec
Common Core Standards Practi
Selected Response
co
1. Find the slope of the line that
passes through the points (-1,9)
and (3, 17).
Answers
Substitute
(9 - 17/-1 - 3) = 2
28% of what number is 21.
Answers
Answer:
i think it´s 75..
Step-by-step explanation:
HELP PLZZ!!!!!
Find x.
Answers
Answer:
6.1
Step-by-step explanation:
So you would use tan as u are looking for the opposite and already have the adjacent.
tan(22) x 15 = 6.06 or 6.1
Answer:
x = 6.06
Step-by-step explanation:
tan (22°) = x/15
0.404 = x/15
x = 6.06
(ASAP) i need help plsssssszzz
Answers
Answer:
the first one is right....
in a certain game, a fair die is rolled and a player gains 20 points if the die shows a 6. if the die does not show a 6, the player loses 3 points. if the die were to be rolled 100 times, what would be the expected total gain or loss for the player?
Answers
The expected gain or loss is an illustration of mean and expected values.
The expected total gain is 83 points
The given parameters are:
Addition of 20 points for rolling a 6Removal of 3 points for not rolling a 6The probability of rolling a 6 in a fair die is 1/6.
The probability of not rolling a 6 in a fair die is 5/6.
So, the expected gain in each game is:
[tex]\mathbf{E(x) = 20 \times \frac 16 - 3 \times \frac 56}[/tex]
[tex]\mathbf{E(x) = \frac{20}6 - \frac{15}6}[/tex]
Take LCM
[tex]\mathbf{E(x) = \frac{5}6}[/tex]
[tex]\mathbf{E(x) = 0.83}[/tex]
The number of games is 100.
So, the expected gain is:
[tex]\mathbf{Gain = 100 \times 0.83}[/tex]
[tex]\mathbf{Gain = 83}[/tex]
Hence, the expected total gain is 83 points
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Anyone know what this truly means?
Answers
Answer:
The person is saying that everyone has their own view of God.
A example is...
"I believe God isn't real"That is someones view on God.
Need help with this one too plzzz
Answers
Answer:
0.83
Step-by-step explanation:
volume = length*height*width
1500=L*30*60
1500=1800L
1500/1800 = 0.83
length = 0.83
Which of the binomials below is a factor of this trinomial?
x² + x -20
O A. X+ 2
O B. X+4
O C. X-4
O D. X-2
Answers
Answer:
C. X-4
Step-by-step explanation:
x^2+x-20
=(x-4)(x+5)
Answer:
C.
Step-by-step explanation:
Sorry I Can't explain because I'm busy right now
The supermarket has 10 aisles. 1 of the aisles is empty. What percentage of the aisles are empty?
Write your answer using a percent sign (%).
Answers
Answer:
10%
Step-by-step explanation:
1 out of 10 isles is the same as doing 1 divided by 10, which gets 0.1. To make this a percentage you would multiply it by 100 to get 10%
The product of −2 and a number x is greater than 30. Whats the solution of the inequality.
Answers
Answer: x < -15
Step-by-step explanation:
(-2)*(x) > 30
x < -15 The inequality reverses direction when a negative number is used in the manipulation (we divided by -2).
I need help this goes towards my grade so please be correct
Answers
Answer:
0 us the answer for this question
Two mechanics worked on a car. The first mechanic charged $55 per hour, and the second mechanic charged $60 per hour. The mechanics worked for a combined total of 20 hours, and together they charged a total of $1125. How long did each mechanic work?
Answers
Answer:
15 and 5 hours.
Step-by-step explanation:
Call x the time taken by the first chap, and y the second.
[tex]\left \{ {{x+y = 20 \atop {55x+60y=1125}} \right.[/tex]
Let's divide by 5 and play with the LHS of the first equation a bit:
[tex]11x+ 11y +y = 225\\11(x+y)+y= 225[/tex] we know how much x+y is ( first equation!) let's solve.
[tex]11(20) +y = 225 \rightarrow y=5[/tex] At this point it's easy to check that [tex]x=15[/tex]
PLSSSSS I REALLY NEED HELP IT IS DUE VERY SOON AND THIS IS MY LAST QUESTION I AM BEGGING EXTRA POINTS WILL BE INCLUDED FOR WHOEVER ANSWERS! GRAPH AND TABLE INCLUDED! the graph shows the relationship between the distance that a snail crawls and the time that it crawls. a. Use the points on the graph to make a table. b. Write the equation for the relationship and tell what each variable represents.
Answers
Answer: y=10x
Step-by-step explanation:
Answer:
Step-by-step explanation:
the answer is y=1x+2
Find the perimeter. Simplify your answer.
Answers
7y+10+7y+10+y-4
14y+20+y-4
15y+20-4
15y+16
answer= 15y+16
Answer:
7y+10+7y+10+y-4=
(7y+7y+y)+(10+10-4)=
15y+16=
The number of trees and the number of apples are given in the table above. Determine which statement below is correct.
1. The table is proportional and the unit rate is 1/13
2. The table is proportional and the unit rate is 13.
3. The table is not proportional.
Answers
Answer:
2.
Step-by-step explanation:
The number of trees times 13
A sno-cone machine priced at $140 is on sale for 20% off. The sales tax rate is 6%. What is the price of the sno-cone machine after the discount and sales tax?
A) $112.00
B) $118.72
C) $28.00
D) none of the above
Answers
Answer:
118.72
Step-by-step explanation:
I just used my calculator 0-0 hope this helped :)
Which equations are true and can be used to find the factors of 32? Check all that apply. A. 32 divided by 1 = 32 B. 32 divided by 2 = 16 C. 32 divided by 3 = 12 Or D. 32 divided by 8 =4
Answers
Answer:
A, B, D are correct
Step-by-step explanation:
A. 32 divided by 1 = 32
Works, it is correct
B. 32 divided by 2 = 16
Works, it is correct
C. 32 divided by 3 = 12
Incorrect, 12 x 3 = 36, not 32
D. 32 divided by 8 = 4
Works, it is correct
-Chetan K
On what interval is the function increasing.