The function f(t) that describes this scenario will be A = -42.57t + 1399.28
Let the amount of oil remaining after time t be ALet the time taken be "t"
This required linear expression will be given as A= mt + b
Writing the gallons of oil and the time taken as a coordinate point (A, t), these are given as (11, 931) and (18, 633)
m is the rate of change = 633-931/18-11
m = -298/7
m = -42.57
Get the intercept;
633 = -42.57(18) + b
633 = -766.29 + b
b = 1,399.28
Heence the function f(t) that describes this scenario will be A = -42.57t + 1399.28
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can anyone give definition of liner expression
need it ASAP
Answer:
The definition of a linear equation is an algebraic equation in which each term has an exponent of one and the graphing of the equation results in a straight line
Step-by-step explanation:
u single?
solve the given problem
Step-by-step explanation:
the first step in my opinion would be find the norm(s) in this scenario.
100 pounds is a good norming weight.
the speed of these 100 pounds with a 10 HP motor is
50ft/30sec = 5/3 ft/s
so, then let's ask next what size of motor is needed to lift the same 100 pounds 40 ft in 40 seconds
40ft/40sec = 1 ft/s
to get the same speed as in the first case the motor need to be weaker (to move slower). and that goes by the same factor as the ratio between the 2 speeds :
5/3×f = 1
f = 3/5
10 HP × f = 10 × 3/5 = 30/5 = 6 HP
so, it takes a 6 HP motor to lift these same 100 pounds 40 ft in 40 seconds.
and now, how strong must the motor be to lift 800 pounds (= 8 times the original 100 pounds) with the same speed ?
well, 8 times
8×6 = 48 HP
so, it would take a 48 horsepower motor to lift 800 pounds 40 ft in 40 seconds.
the equation would then be
HP = p/100 × 6 = 6p/100 = 3p/50
HP = horsepower
p = pounds
the rest I cannot really answer, as I don't know your class and it's contents.
I hope I covered the topics of your class with that solution.
A school allots £3000 to spend on a trip to the theatre.
Theatre tickets have a regular cost of £45 each and are on offer for off.
A train ticket for the day will cost £20 each
If 3 teachers and the maximum number of students attend, how many students go on the trip?
Answer:
32
Step-by-step explanation:
V (1) = 65t+280, where time , in minutes,.the pump has been on .
how many gallons of water were.in the tank when the pumps were turned on
Is the figure shown in the xy- plane a parallelogram? Why or why not. use the coordinates to history your answer.
Please help!!! Due in 15 mins !!
Answer:
Step-by-step explanation:
It is a parrallelogram, the two lines are Parallel to each other meaning they will never cross each other
The given xy- plane is a parallelogram.
When a plane figure is called a parallelogram?
A plane figure is called a parallelogram when it have four sides, in which opposite sides are parallel to each other and each side is equal in length to its opposite side.
How to find the distance between two points?If [tex](x_{1},y_{1} })[/tex] and [tex](x_{2},y_{2})[/tex] are the two points then the distance between these points is given by
[tex]d=\sqrt{(x_{2}-x_{1}) ^{2} +(y_{2}-y_{1} ) ^{2} }[/tex]
Where, d is the distance between two points.
According to the given question
We have a plane figure PSTO
And the coordinates of points P, S, T, and O are (a, b), (a + c, b), (c, 0) and (0,0) respectively.
Now, the length of the sides by distance formula
PS = [tex]\sqrt{(a-a-c)^{2}+(b-b)^{2} }[/tex]
PS = [tex]\sqrt{c^{2}+0 }[/tex]
PS = c
Similarly,
ST =[tex]\sqrt{(a+c-c)^{2}+(b-0)^{2} }[/tex]
ST = [tex]\sqrt{a^{2} +b^{2} }[/tex]
TO = [tex]\sqrt{(c-0)^{2}+(0-0)^{2} }[/tex]
TO = [tex]\sqrt{c^{2} }[/tex]
TO = c
And, PO = [tex]\sqrt{(a-0)^{2}+(b-0)^{2} }[/tex]
PO = [tex]\sqrt{a^{2} +b^{2} }[/tex]
From the above calculation we found that
PS = TO
PO = ST
⇒ Length of the opposite sides of the plane figure are equals.
And from the given figure we can see that the opposite sides are also parallel to each other.
Therefore, the given xy- plane is a parallelogram.
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What is the ninth term of the arithmetic sequence defined by the rule below?
A(n) = -15 + 2(n – 1).
A. 1
B. -1
C. 31
D. -31
Answer:
A
Step-by-step explanation:
Substitute n = 9 into the nth term rule
A(9) = - 15 + 2(9 - 1) = - 15 + 2(8) = - 15 + 16 = 1 → A
Eight times a number increased by 4 times the number is less than 36. What is the number? . logo thon 13 then find the
Answer:
36
Step-by-step explanation:
First, you subtract 4 by 36 which is 32. Then, divide 32 by 8 which equals 4 therefore the answer is 36.
Can some one help? This is sooooooo hard
Answer:
median is a hight of a triangle
What point located in quadrant IV has an x-value that is 3 units from the origin and a y-value that is 4 units from the origin?
John has quarters, nickels, and dimes. He has 4 more nickels than quarters and twice as many dimes than nickels. If he had $6.00, how many quarters does he have?
Show your work in the are below.
Make sure you define the variable. Start with "Let x be..."
Answer:
Let the no of quarters be x
According to given,
x + (x+4) + (x+4)/2 = 6
x + (x+4) + (x + 8)/2 = 6
x + x + 4 + (x + 8)/2 = 6
[2 (2x + 4) + (x + 2)]/2 = 6
4x + 8 + x + 2 = 6 × 2
5x + 10 = 12
5x = 12 - 10
5x = 2
x = 2/5
•°• x = 0.4
1 doller = 4 quarter
0.4 doller = p
p = 0.4 × 4 = 1.6
•°• There are 1.6 quarter.
ATQ
[tex]\\ \sf\longmapsto x+x+4+2(x+4)=6[/tex]
[tex]\\ \sf\longmapsto 2x+4+2x+8=6[/tex]
[tex]\\ \sf\longmapsto 4x+12=6[/tex]
[tex]\\ \sf\longmapsto 4x=-6[/tex]
[tex]\\ \sf\longmapsto x=-3/2[/tex]
[tex]\\ \sf\longmapsto x=|-1.5|[/tex]
[tex]\\ \sf\longmapsto x=1.5[/tex]
What kind of slope does the graph have?
It has a positive slope.
when it starts at the bottom left like that and goes up it is positive. :)
In the first week of July, a record people went to the local swimming pool. In the second week, fewer people went to the pool than in the first week. In the third week, more people went to the pool than in the second week. In the fourth week, fewer people went to the pool than in the third week. What is the percent decrease in the number of people who went to the pool over these four weeks?
Answer:
10%
Step-by-step explanation:
What is the solution for -10 < x - 9?
x > -19
x < -1
x < -19
x > -1
Answer:
x > -1
Step-by-step explanation:
-10 < x - 9
Add 9 to each side
-10+9 < x - 9+9
-1 < x
x > -1
Answer:
x > - 1Step-by-step explanation:
- 10 < x - 9
- 10 + 9 < x - 9 + 9
- 1 < x
x > - 1
Hope it helps!!***WILL GIVE BRAINLIEST***
A triangular garden is to be split so that the angle at vertex B is bisected. This diagram was supplied by the landscape architect, but you do not have a way to measure the angles at B. You do have the given side lengths, so what is the length of side AD that will allow the angle at B to be bisected?
A.
5 m
B.
4 m
C.
2 m
D.
3 m
The length of side AD that will allow the angle at B to be bisected is 3m, the correct option is D.
What is Angle Bisector Theorem?According to the angle bisector theorem, the angle bisector of an angle of a triangle bisects the opposite side into two parts that are proportional to the other two sides.
The sides of the triangle are 5,7 and (x+4) m.
The BD will be the angle bisector of angle B only if
x/4 = 5/7
x = 5 *4 / 7
x = 20/7 = 2.85 ≈ 3m
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What is the equation on the graph?
Please help!!!
Answer:
y = -1/4x + 2
Step-by-step explanation:
using the slope-intercept form (y=mx+b) m is the slope of the line which is -1/4 because it is decreasing and b is the y-intercept of the line which is 2
HELP- I NEED LOTS OF HELP
Answer:
|279|
Step-by-step explanation:
so when ur doing absolute value you js need distance so lets work with the problem, if ur 279 feet below water u would need to get to zero feet below sea level (ground lvl) to do so how many feet towards ground lvl would u go? (279 clearly) so the distance from how many feet under u are to the ground lvl is ur absolute value.
Tbh in school they over complicate it if u need an absolute number from a negative number like -279 (as it is in the problem) you would js make it a positive (if its positive 279 u js say the absolute value is 279)
(also the absolute value is the distance between the number and zero so yh u can put that)
Find the value of x. 130 Х
Answer:
60
Step-by-step explanation:
edge
At the gym, Hillary swims every 6 days and runs every 4 days. If she did both activities today, in how many days will she do both activities again on the same day?"
Answer:
we know that
Hillary
swims every 6 days---> Multiples of 6---> 6-12-18-24-30-36-42-48-54
runs every 4 days-----> Multiples of 4----> 4-8-12-16-20-24-28-32-36-40-44-48
cycles every 16 days---> Multiples of 16---> 16-32-48-64
therefore
In 48 days she will do all three on the same day.
the answer is
48 days
Step-by-step explanation:
The 3 in 75,341 is ______ the value of the 3 in 293,467
Answer:
3 in 75,341 = the hundreth place. 3 in 293,467 = the thousandth place.
Step-by-step explanation:
[tex]\sf 3(5x+4)[/tex]
[tex]\boxed{\sf Have \: a \: nice\: day!}[/tex]
Answer:
[tex]3(5x + 4) = 3 \times 5x + 3 \times 4 \\ = 15x + 12 [/tex]
Answer:
15x+12
Step-by-step explanation:multiply 5x + 4 by 3 hence answer is 15x +12
Alice bought 4 apples and 8 bananas for $4. Betty bought 6 apples and 10 bananas for $5.50
each fruit cost?
Answer:
Apples cost 50 cents and bananas 25 cents.
please mark brainliest if this helped
Step-by-step explanation:
1) Assign variable (x,y) to apples and bananas.
x=apples
y=bananas
2) Write system of equations for Alice and Betty.
Alice: 4x+8y=4
Betty: 6x+10y=5.5
3) Use substitution, elimination, or graphing to solve for x and y.
x=0.5
y=0.25
7/8 minus1/4 minus 1/2
7/8 minus1/4 minus 1/2
7/8 - 1/4 - 1/2 =
(1 × 7)/(1 × 8) - (2 × 1)/(2 × 4) - (4 × 1)/(4 × 2) =
7/8 - 2/8 - 4/8 =
(7 - 2 - 4)/8 =
1/8
the answer is 1/8
3/4 in simplest form WILL GIVE BRANLYEST!!!
Answer:
3/4 is in it's simplest form
Step-by-step explanation:
3/4 cannot be simplified any more, so it is at it's simplest form
Raven was a writing a story. She was trying to figure out how long it would take for her to write it. If she can ride 2 2/3 pages in one hour, how many pages will she have written after 2 1/2 hours? who is correct?
Answer:
She would have written 6 2/3 pages.
Step-by-step explanation:
2 2/3 pages = 1 hour
6 2/3 pages = 2 1/2 hours
List the angles of the triangle in order from least to greatest.
Answer:
3rd option
Step-by-step explanation:
The angle opposite the shortest side is the smallest
The angle opposite the longest side is the largest
Shortest side is AC with ∠ B opposite , thus smallest
Longest side is AB with ∠ C opposite, thus largest
Then order of angles from least to greatest is
∠ B , ∠ A , ∠ C
Which two lines are parallel?
1. 5y=-3x-5
2. 5y = -1-3x
3. 3y - 2x = -1
A. 1 and 3
B. 2 and 3
C. None of the lines are parallel.
D. 1 and 2
A recipe for apple crisp uses 4 parts oats,8 parts brown sugar,and 10 parts flour. In simplest form,how many parts of brown sugar are there for every part of flour?
Answer:
8:10
Step-by-step explanation:
8 parts for brown sugar and 10 parts flour.
In simplest, 4:5 (divide 8 and 10 by 2)
Functions f (solid) and g (dashed) are graphed.
What is the equation of g in terms of f?
A. G(x)=f(x)
B. g(x)=-f(x)
C. g(x)=f(-x)
D. g(x)=-f(-x)
PLZ HELP DUE TODAY 100 POINTS AND BRAINLIEST
Write each expression using an exponent
1. 8 × 8 × 8 × 8 × 8 × 8 × 8
2. 4
Evaluate each expression
4. 9² 5. 99^1
6. 3,105^0 7. 22²
8. 2^7 9. 3^4
Answer:
1. 8^7
2. 2^2
Step-by-step explanation:
I am not sure about these
4. 6.32066568875585e+24
5. 1.0853858230617127e+182
6. Infinity
#1
8×8×8×8×8×8×8=8^7#2
4=2^2#3
9^5.99^19^5.99#4
3105^0.7.22^2278.2(484)134648.8#5
2^7.9.3^42^7.3^6$14,038 is invested, part at 14% and the rest at 12%. If the interest earned from the amount invested at 14% exceeds the interest earned from the amount invested at 12% by $984.34, how much is invested at each rate? (Round to two decimal places if necessary.)
Answer:
492.99
Step-by-step explanation: x = amount invested at 12%
y = amount invested at 9%
---
x + y = 20287
0.12x = 0.09y + 492.99
---
put the system of linear equations into standard form
---
x + y = 20287
0.12x - 0.09y = 492.99
The amount invested at 14% is $4144 and the amount invested at 12% is $9894.
What is simple interest?Simple interest is a method of calculating the interest charge. Simple interest can be calculated as the product of principal amount, rate and time period.
Simple Interest = (Principal × Rate × Time) / 100
We are given that;
Investment at 14%= $14,038
Investment at 12%= $984.34
Now,
Let x be the amount invested at 14% and y be the amount invested at 12%. Then we have:
x + y = 14038 (total amount invested)
0.14x - 0.12y = 984.34 (difference in interest)
We can solve this system of equations by substitution or elimination. For example, by elimination, we can multiply the first equation by 0.12 and subtract it from the second equation to get:
0.02x = 82.88
x = 4144
Then we can plug x into the first equation and get:
y = 14038 - 4144
y = 9894
Therefore, the simple interest will be $4144 and $9894.
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