Using linear function concepts, it is found that:
a) The function is y = 88 - 6x.
b) The tank has been draining it for 9 minutes.
What is a linear function?
A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.Item a:
The full volume of the tank is of 88 gallons, hence the y-intercept is of b = 88.The volume can be drained at a rate of 6 gallons per minute, hence the slope is of m = -6.Thus, the equation is given by:
y = 88 - 6x.
Item b:
This is x for which y = 34, hence:
y = 88 - 6x
34 = 88 - 6x
6x = 54
x = 9.
The tank has been draining it for 9 minutes.
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The amount of water in the tank is given by y = -6x + 88, it would take 9 minutes for the water to remain 34 gallons.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Let y represent the amount of water after x minutes.
The Rock has an 88-gallon fish tank which can be drained at a rate of 6 gallons per minute. Hence:
m = -6, b = 88
y = -6x + 88
For 34 gallons:
34 = -6x + 88
x = 9
The amount of water in the tank is given by y = -6x + 88, it would take 9 minutes for the water to remain 34 gallons.
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Which number best represents the slope of the graphed line?
Y410
-10
10
10
Answer:
1/2
Step-by-step explanation:
I took the test and rise/run is being asked
Easy math help picture below problem 4
Answer: is 126 degrees
Step-by-step explanation:
908636549723 times 47647647 divided bye 98
Answer:
4.4177953e17
Step-by-step explanation:
i think that's the answer im not sure i worked it out in my notebook sorry if it's wrong
the radius r of a sphere is 4cm and is increasing at the rate of 0.5cm . At what rate is the volume?
Answer:
32π or 100.53 cm^3 to the nearest hundredth.
Step-by-step explanation:
dr/dt = 0.5
V = (4/3)π r^3
So dV/dr = (4/3)* 3 π r^(3-1)
= 4πr^2
Rate of increase in volume:
dV/dt = dV/dr * dr/dt
At r = 4:
Rate of increase in Volume
dV/dt = 4π(4)^2 * 0.5
= 64π * 0.5
= 32π.
Help asap no links pls
……….
Step-by-step explanation:
I will take long to answer this so i will give you the key to answering it.
Basically, since you know the sum of all the angles of a triangle equal 180, all you have to do is use 180 and subtract the numbers alredy there together to get the missing amount.
For example, to find out the answer to A, you already know two of the degree measurements which are 72 and 68. Now, subtract them with 180.
72+68=140
180-140=40
So, therefore, A equals 40 degrees.
I will give you one more example.
If you want to find the measurements of the angles B and C, the same process will happen. The only thing that is different is that only one known measurement is provided which is 36.5 but not so fast, they gave you a hint. That square above B. That means B is a right angle. So we got one measurement in the triangle, B is 90 degrees. Alright now continue like before.
90+36.5=126.5
180-126.5=53.5
Hope this helps.
please help fast ......
Answer:
1/625
Step-by-step explanation:
You can reduce it to:
5^-8/5^-4
which becomes
1/5^4
which is 1/625
What is the absolute deviation of 30 in this data set?
{26, 35, 27, 30, 22}
2
3
5
8
Using it's concept, it is found that the absolute deviation of 30 in the data set is of 2.
What is the absolute deviation of a measure?The absolute deviation of a measure is given by the absolute value of the differente between the measure and the mean.
The mean is the sum of all observations divided by the number of observations. In this data-set, it is given by:
M = (26 + 35 + 27 + 30 + 22)/5 = 28
30 - 28 = 2, hence, the absolute deviation of 30 in the data set is of 2.
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Answer:
The answer is 2
Step-by-step explanation:
I took the test
You have 5/10 of a pizza left over from your pool party. If you sent 7/11 of the leftover pizza home with your friends, how much of the pizza do you have left in the box?
Answer:
Step-by-step explanation:
[tex]\frac{5}{10} * \frac{7}{11} = \frac{35}{110}\\ \frac{35}{110} = \frac{7}{55}[/tex]
Answer:
2/11.
Step-by-step explanation:
5/10 is 1/2, and you sen 7/11 of this away, meaning you have 4/11 for yourself. Multiplying 4/11 by 1/2, we get 2/11.
bob has 12 red cards and 20 green cards. what is the ratio of bobs red cards to his green card
Answer:
3:5
If Bob has 12 red cards and 20 green cards, all we have to do is write the two numbers seperated by a colon.[tex]12~to~20 -- > 12:20[/tex]
How did we get 3:5 then, you may be asking? It is just a few simple steps. All you need to do is find the divisor. How do we find the divisor? Find the lowest or highest number that both parameters are divisible by.[tex]\frac{12 / 4}{20 / 4} = \frac{3}{5} -- > 3:5[/tex]
________________________________________________________
The problem is now complete, time to go over what we just learned while reading this.
________________________________________________________
What did we learn?We learned how to find and simplify ratios in a story problem.
Related questions? Ask me in the comments box.
Help please :(
Kelly's mother is 35. Kelly is 13. How old will Kelly be when her mom is 50?
Kelly's mother is 35. Kelly is 13. How old will Kelly's mom be when Kelly is 50?
REAL CAREFULLY PLEASE HELP
[tex]Thank you![/tex]
________________________________________________________
If Kelly's mom is 35, it will take her 15 more years to become 50. Make an equation to represent this.[tex]35 + 15 = 50[/tex]
Next, you want to add 15 to Kelly's age because for each year her mom ages, she ages for that same number of years.[tex]13 + 15 = 28[/tex]
________________________________________________________
For the second problem, we just do an inverse of the problem. If Kelly is 13 and her mom is 35, how long will it take Kelly to become 50? How old will her mom be?It would take Kelly 37 more years to become 50, because 37 + 13 = 50
Now that we have found the number of years remaining, add her mother's age by the remaining years left, r
[tex]35 + r(37) = 72[/tex]
Mr. Mares' class has 28 students. If five people can work together on a group project, estimate the number of groups that there will be by rounding the larger number.
28/5 = 5.6
then round it up so it would be 6
Nathan and some friends are going to the movies. At the theater, they sell a bag of
popcorn for $4.50 and a drink for $4.25. How much would it cost if they bought 7
bags of popcorn and 3 drinks? How much would it cost if they bought p bags of
popcorn and d drinks?
Answer:
$44.25
Step-by-step explanation:
($4.50×7)+(4.25×3)
=$31.50+$12.75
=$44.25
$44.25 is the cost if they bought 7 bags of popcorn and 3 drinks and 4.50p+4.25d is for p bags of popcorn and d drinks.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given that
popcorn for $4.50
drink for $4.25.
There are 7 bags of popcorn and 3 drinks.
So let us find the total cost.
7(4.50)+3(4.25)
31.5+12.75
44.25
So $44.25 is the cost if they bought 7 bags of popcorn and 3 drinks
Now we need to find cost for p bags of popcorn and d drinks.
4.50p+4.25d
Hence $44.25 is the cost if they bought 7 bags of popcorn and 3 drinks and 4.50p+4.25d is for p bags of popcorn and d drinks.
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NEED HELP WITH THIS QUESTION QUICK!!!
Answer:
204 degrees is the answer
Step-by-step explanation:
.l
The first term of an arithmetic progression is 18 and the 18th is 60. Determine the common difference of the A.P
Answer:
42/17
Step-by-step explanation:
First term, a = 18
T18 = 60
Common difference, d = ?
[tex]T_{18} = 18 + (18 - 1)d \\ 60 = 18 + 17d \\ 17d = 42 \\ d = \frac{42}{17} [/tex]
Solve for x. Round to the nearest tenth, if necessary.
Answer:
since the adjacent is given which is 6.3 and we are to solve for the hypotenuse, it's best to use Cos
since Cos(27°)=adjacent/hypotenuse
we can substitute in the values
therefore we have Cos(27°)=6.3/x
x=6.3/Cos(27°)
x=7.06...
rounding this to the nearest tenth will be 7.1
therefore x=7.1
Vivian is trying to save money for her summer vacation. She puts $40 in her lucky money jar on week 1. She will put an additional $15 in the lucky jar each week.
a. Write an explicit formula for this scenario?
b. How much money will she have saved for her vacation by week 20.
Answer:
she saved $340 in total
Step-by-step explanation:
(15 x 20) + 40 = s
s = savings
Can you guys answer b
Answer:
2⁶-1
Step-by-step explanation:
[tex] ({2}^{0} + {2}^{1} + {2}^{2} + {2}^{3}) + {2}^{4} + {2}^{5} \\ = ({2}^{4} - 1) + {2}^{4} + {2}^{5} \\ = 2( {2}^{4} ) + {2}^{5} - 1 \\ = {2}^{5} + {2}^{5} - 1 \\ = 2( {2}^{5} ) - 1 \\ = {2}^{6} - 1[/tex]
Solve for x.
Enter the solutions from least to greatest.
—4x2 – 7 = -11
lesser x =
greater x =
Answer:
lesser x = - 1 , greater x = 1
Step-by-step explanation:
- 4x² - 7 = - 11 ( add 7 to both sides )
- 4x² = - 4 ( divide both sides by - 4 )
x² = 1 ( take square root of both sides )
x = ± [tex]\sqrt{1}[/tex] = ± 1
then
lesser x = - 1
greater x = 1
Linda is baking a pumpkin pie for her family and friends at Thanksgiving.
She is baking the pie in a 10 inch pie plate. What is the area of her pie?
Answer:
about 78in^2
Step-by-step explanation:
A = [tex]\pi r^{2}[/tex]
A = [tex]\pi 5^{2}[/tex]
A = [tex]\pi * 25[/tex]
A = 3.14 * 25
A ≈ 78[tex]in^{2}[/tex]
Can someone please help me with this? Thank you. No links!
Answer: 2(mJKL)=mJL
Step-by-step explanation: The arc angle is double the inscribed angle
4. Find the surface area of the triangular prism:
5 ft
5 ft
3 ft
14 ft
8 ft
Shows work please
Answer:
276ft^2
Step-by-step explanation:
A triangular prism is made up of multiple faces, just like any three-dimensional shape. Let's do the calculations for this shape together.
Top two faces: 5ft × 14ft × 2 = 140ft^2 (we multiply by two b/c there are two rectangles, so we save a step)
Front and back face: 8ft × 3ft = 24ft^2 (we do not divide by two b/c there are two triangles, so we save a step)
Bottom face*: 8ft × 14ft = 112ft^2
*Note: Don't solve for this face when calculating latent surface area, or when calculating the SA of a compound shape.
Now, we just add up the areas of all the shapes.
140 + 112 + 24 = 276
Final answer: 276ft^2
Find the radius and the diameter to the nearest hundredth when C = 8π yd. Use 3.14 for π.
Answer:
Diameter=8
Radius=4
Step-by-step explanation:
The equation for circumference is dπ where "d" is the diameter.
C = 8π
d=8
The equation for radius is d/2
r=8/2
r=4
If n is at least 7, which inequality best represents the values of n?
On>7
On<7
On 27
Ons 7
Answer:
n ≥ 7
Step-by-step explanation:
The English descriptor "is at least" corresponds to the math relation "is greater than or equal to." In symbols, we have ...
"n is at least 7" ⇔ n ≥ 7
Answer:
n ≥ 7
Step-by-step explanation:
If the question states "at least 7", it means the inequality should include 7 and the rest of the values lying in the set of the inequality are greater than 7 as 7 is the least value.
Inequality
n ≥ 7Which of the lines is a line of symmetry for the triangle?
A. FG and HI
B. DE only
C. none of the lines
D. FG only
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
The Correct choice is :
A. FG and HIAs we know, line of symmetry divides a figure into two equal halves, where the two resultant figures are congruent to each other.
which equation below would best represent how to find the area of the square ?
Answer:
Step-by-step explanation:
well the area of a square is equal to the Width x Height. For example each side being 4 would be 4x4x4x4 or 4 to the second power.
Deb recorded the number of cups of water she drank for 7 days.The median number of cups of water she drank was 6.The range of the number of cups of water she drank was 4. Which statement can be made from the given information?
Answer:
lol, that is true she should stop drinking too much water.
But all jokes aside, the answer is A. At least one day she drank exactly 6 cups of water.
Please help now
Pic below
Help picture below problem 15
Payton bought a couple new dog toys for her puppy. The bone she bought cost $5.25and the frisbee cost $6.75. About how much did the toys cost? ESTIMATE UR ANSWER AND SHOW UR WORK PLS!
6. Roger bought a hamburger and french fries for $4.84. He paid with a $10 bill. Abouthow much change should he have gotten back? ESTIMATE UR ANSWER AND SHOW UR WORK PLS!
Answer:
The toys cost about $12.
Roger should have gotten back about $5.15 in change.
Step-by-step explanation:
Dog Toys Question:
Bone cost $5.25, so you can estimate it to be about $5.
Frisbee cost $6.75, so you can estimate it to be about &7.
To get estimated total, add $5 + $7 = about $12 total.
Roger's Change Question:
The hamburger and fries cost $4.84, so you can round that out to $4.85.
$10 - estimated $4.85 = about $5.15 in change.
You could also round the $4.84 cost of the hamburger and fries to $5 even. In this case, $10 - estimated $5 = about $5 in change.
Angle ABC and angle CBD are complementary. What is the value of X?
Answer:
26
Step-by-step explanation:
complementary means two angles that add up to 90 degrees
90-38=52
52÷2=26
to check work you can do 26×2 (since there's 2x) = 52
52+38=90