Step-by-step explanation:
the function is
ride cost c = mile rate r × miles m + flat rate f
c = r×m + f
now let's put the values in we know and solve for r and f :
9 = r×3 + f
17 = r×7 + f
now, since one term is the same in both equations, we use a simple trick for speed, and we subtract the whole first equation from the second :
17 = r×7 + f
- 9 = r×3 + f
-------------------
8 = r×4 + 0
r = 8/4 = $2
9 = 2×3 + f = 6 + f
f = $3
the first rate is $3, and it costs $2 per mile.
A pool with a square bottom is to have a volume of 2000 cubic feet. The owners plan to use a fancy tile to complete the pool. The sides of the pool will cost $80 per square foot and the bottom of the pool will cost $40 per square foot. Find the pool dimensions that will minimize the cost of construction.
The pool dimensions that will minimize the cost of construction are length of square bottom = 20 ft and height of pool = 5 ft
Let l be the length of side of the square bottom of the pool and h be the height of the pool.
Its volume V = l²h
Now, the total surface area of the pool equal the area of its sides plus the area of its base.
The area of its 4 sides is 4lh.
Since the cost of the side of the pool is $80 per square foot, the total cost for the sides of the pool is C = $80 × 4lh = $ 320lh
Also, The area of its square bottom is l².
Since the cost of the side of the pool is $40 per square foot, the total cost for the square bottom of the pool is C' = $40 × l² = $ 40l²
So, the total cost of the pool is C" = C + C' = 320lh + 40l²
C" = 320lh + 40l²
Since the volume equals 2000 ft³, V = l²h
2000 = l²h
h = 2000/l²
Substituting h into C", we have
C" = 320lh + 40l²
C" = 320l × 2000/l² + 40l²
C" = 640000/l + 40l²
To find the value of l which makes C" minimum, we differentiate C" with respect to l and equate it to zero.
So, dC"/dl = d(640000/l + 40l²)/dl
dC"/dl = d(640000/l)/dl + d(40l²)/dl
dC"/dl = -640000/l² + 80l
Equating dC"/dl to zero, we have
-640000/l² + 80l = 0
-640000/l² = -80l
Cross-multiplying, we have
640000 = 80l³
Dividing through by 80, we have
l³ = 640000/80
l³ = 8000
Taking cube root of both sides, we have
l = ∛8000
l = 20 ft
We differentiate C" twice to determine if this value of l gives a minimum for C".
So, d²C"/dl² = d(-640000/l² + 80l)/dl
d²C"/dl² = d(-640000/l²)/dl + d(80l)/dl
d²C"/dl² = 640000/l³ + 80
Substituting l = 20, we have
d²C"/dl² = 640000/l³ + 80
d²C"/dl² = 640000/20³ + 80
d²C"/dl² = 640000/8000 + 80
d²C"/dl² = 80 + 80
d²C"/dl² = 160 > 0
Since d²C"/dl² = 160 > 0. So, l = 20 ft gives a minimum for C".
Since h = 2000/l²
Substituting l = 20 into the equation, we have
h = 2000/l²
h = 2000/20²
h = 2000/400
h = 5 ft
So, the pool dimensions that will minimize the cost of construction are length of square bottom = 20 ft and height of pool = 5 ft
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The graph of f(x) = 2x is shown on the grid.
On a coordinate plane, an exponential function approaches y = 0 in quadrant 2 and increases into quadrant 1. It goes through points (0, 1), (1, 2), (2, 4).
The graph of g(x) = (One-half)x is the graph of f(x) = 2x reflected over the y-axis. Which graph represents g(x)?
On a coordinate plane, an exponential function approaches x = 0 in quadrant 4 and increases into quadrant 1.
On a coordinate plane, an exponential function decreases from quadrant 2 into quadrant 1 and approaches y = 0.
On a coordinate plane, an exponential function approaches y = 0 in quadrant 3 and curves down into quadrant 4.
On a coordinate plane, an exponential function approaches x = 0 in quadrant 1 and curves down and to the right into quadrant 4.
Answer:
Your answer would be the second option.
Explanation:
As it is looking for an exponential decay function, you must find one. As an exponential function has to be sloping negatively, you must find the graph that does just this. The only graph that does is graph number two. Henceforth your answer is graph number two, or B. (I also did this quiz, and got a 100%)
Hope This Helps!
The graph represents g(x) is B) On a coordinate plane, an exponential function decreases from quadrant 2 into quadrant 1 and approaches y = 0.
What is exponential growth or decay function?Consider the function:
[tex]y = a(1\pm r)^m[/tex]
where m is the number of times this growth/decay occurs, a = initial amount, and r = fraction by which this growth/decay occurs.
If there is negative sign, then there is exponential decay happening by r fraction or 100r %
The graph of f(x) = 2x is shown.
it is looking for an exponential decay function, As an exponential function has to be sloping negatively.
Draw the graph of the equation by using the table shown below:
x f(x)
-2 -4
-1 -2
0 0
The graph the exponential function approaches y = 0 in quadrant 1.
The function increases into quadrant 2 and It crosses the y-axis at (0, 1).
Hence, the correct option is B) On a coordinate plane, an exponential function decreases from quadrant 2 into quadrant 1 and approaches y = 0.
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Consider the equation 12x - 15y = 70
Solve for x (in terms of y)
Solve for y (in terms of x)
PLEASE HELP MEEEE IM IN A TEST!
In a right triangle one angle is 55° and the hypotenuse is 20 mm which expression will give you the correct length in millimeters of the leg adjacent to the 55° angle?
Answer:
D 20cos55º
Step-by-step explanation:
cos = adj/hyp
cos55 = adj/20
20cos55 = adj
-5x+3-2x-4+4x-5= −
x+8m2x+8m2 =
(x+6)(x+6)(x+6)(x+6)
Answer:
is this even a real question?
Step-by-step explanation:
NEED HELP ON THIS QUICKLY!!!!!!!
1. Write an exponential function to represent the spread of Carter's social media post.
2. Graph each function using at least three points for each curve. All graphs should be placed together on the same coordinate plane, so be sure to label each curve. You may graph your equation by hand on a piece of paper and scan your work, or you may use graphing technology.
3. Using the functions for each student, predict how many shares each student's post will be received on Day 3 and then on Day 10. Justify your answers.
4. If Amber decides to mail copies of her photo to the 45 residents of her grandmother's assisted living facility, the new function representing her photo shares is f(x) = 3(4)x + 45. How does this graph compare with the original graph of Amber's photo share?
5. Based on your results, which students' post travels the fastest? How is this shown in the equation form of the functions?
6. If you had to choose, would you prefer a post with fewer friends initially but more shares, like Amber, or more friends initially but fewer shares? Justify your answer with your calculations from previous questions.
BELOW IS A SCREENSHOT OF THE GRAPH OF THEIR RESULTS
Answer:
Step-by-step explanation:
1. f(x)=10*(2)^x
2. Attached
3. Attached
4. Use DESMOS to make this change in Amber's graph, using f(x) = 3(4)x + 45.
5. Amber grows the quickest. The starting base, 4, is greater than the others (f(x)=3*(4)^x).
6. I'd prefer more friends initially, even with fewer shares.
what is the answer help
Answer:
1
Step-by-step explanation:
y=-x-1
when it is perpendicular, it is the opposite then flip the fractions so 1 and if you flip 1 it is still 1
If two figures are similar, what can you say about them? Be specific and give at least 3 details.
Answer:
im confused as to if these terms are supposed to be specific or if you are looking for certain ones
Step-by-step explanation:
but i would say congruent, corresponding angles, and equal
Find the value of each expression.
A) 3√9-16
B) -7√0.36+5.4
[tex]3 \sqrt{9} - 16 = ... \\ = 3(3) - 16 = 9 - 16 \\ = \bold{ - 5}[/tex]
[tex] \: [/tex]
B.)[tex] - 7 \sqrt{0.36} + 5.4 = ... \\ = - 7(0.6) + 5.4 = - 4.2 + 5.4 \\ = 5.4 - 4.2 = \bold{1.2}[/tex]
x+y=3
2x-y=0
substituition method
Answer:
(1, 2 )
Step-by-step explanation:
x + y = 3 (subtract x from both sides )
y = 3 - x → (1)
2x - y = 0 → (2)
Substitute y = 3 - x into (2)
2x - (3 - x) = 0
2x - 3 + x = 0
3x - 3 = 0 ( add 3 to both sides )
3x = 3 ( divide both sides by 3 )
x = 1
Substitute x = 1 into (1)
y = 3 - 1 = 2
solution is (1, 2 )
What is the greatest perfect square that is a factor of 4725
Answer:
225 is a greatest perfect square that is a factor of 4725 .54 views
a 10 meter piece of wire is cut into two pieces . one piece is 2 meters longer than the other. how long are the pieces
Write in the form a to the power of n where n < 01/ 9x9x9x9x9x9x9x9x9x9
The answer is
31381059609
Melissa makes necklaces and sells them online. She charges $88 per necklace. Her monthly expenses are $3745. How many necklaces must she sell if she wants to make a profit of at least $1,650?
Answer:
She must sell at least 18 necklaces to have a profit of at least 1,650 . In order to pay for her monthly expenses she needs to sell at least 43 necklaces. If she wants to have 1,650 remaining after paying for her monthly expenses she'll have to sell around 61 necklaces.
Which is not a way to write the answer to this problem?
Answer:
D. 887 ÷ 43 ≈ 21
Step-by-step explanation:
Dan rolls 2 fair dice and adds the results from each.
Work out the probability of getting a total that is a factor of 15.
Answer:
[tex]\frac{1}{18}[/tex]
Step-by-step explanation:
If there are six sides on a die then there are 36 different rolls
The factors of 15 are (3×5) and (5×3) so you would get 2/36
When you simplify that you get 1/18
I hope this helps!!
Step-by-step explanation:
there are six squares in each dice so 3×5=15 and 5×3=15answer is 1/836 x 1/9, show work please !
Answer:
4 [tex]\frac{1}{3}[/tex]
Step-by-step explanation:
39 × [tex]\frac{1}{9}[/tex]
39 times 1 is 39
39/9 is 4.33333333 Which is also, 4 [tex]\frac{1}{3}[/tex]
pls i only have 1 minute left hurry
Answer:
look at the picture i have sent
Slope is -4 and (6,1) is on the like the equation of the line is
Answer:
y=-4x+25
Step-by-step explanation:
If this is Point-Slope then:
y-y1=m(x-x1) m=slope
m= -4 Coordinates=(6,1)
y-1=-4(x-6)
y-1= -4x +24
y=-4x+25
helpppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppp i will put brailny
Answer:
fraction 1/4. decimal 0.25 percent 25%
Step-by-step explanation:
5:20=5/20=1/4
1/4 is 0.25
the percentage is 25% aftr multiplying the decimal by 100%
Kate had 50 thousands-blocks in her package of base-ten blocks. How many ten thousands-blocks does that equal?
5
50
500
5000
Step-by-step explanation:
50000÷10
=5000
MARK ME BRAINLIEST
Ricardo borrows $1,850 for 10 months at an interest rate of 12.25%. What amount will
he have paid back at the end of the loan period?
9514 1404 393
Answer:
$2038.85
Step-by-step explanation:
The value of the loan at that point is given by ...
A = P(1 +rt) . . . . . Principal P, rate r, time t (years)
A = $1850(1 + 0.1225·(10/12)) = $2038.85
Ricardo will have paid back $2038.85 at the end of the loan period.
_____
Additional comment
We assume that the loan accrues simple interest and that the amount due is the sum of principal and interest at the end of the loan period.
The question is not specific as to whether interest compounds, or whether intermediate (monthly) payments are made. There are many possible ways the loan could be repaid, generally involving different amounts for the different terms.
The area of the surface of a ball is equal to the area of the curved surface of a right circular cylinder. If both the height and diameter of the cylinder are 12cm , find the diameter of the ball
Answer:
D=12 cm
Step-by-step explanation:
please check the image for the answer. Thank you .
a, b, c and d are positive integers, such that a+b+ab = 20, c+d+cd = 34. Find (a+b+c+d)·a·b·c·d
please help mee
i’ve been on this for so long
Please Help Im Doing A Test And Really Need The Answer!
Please no fake answer for points
Answer:
The last one (16+20+3+8)
Step-by-step explanation:
add up all the sides not including the 3 inside
Answer:
(16+20+3+8)
Step-by-step explanation:
The perimeter is the measurement on the outside of the shape.
so (3+16+20+8) = 47
Ya'll how do I graph this? I haven't graphed anything in 3 years
Use a coordinate plane to plot these points and connect them to make a quadrilateral. Then construct a similar quadrilateral (A’B’C’D’) on the same coordinate plane. You may use a ruler and protractor if necessary.
A (-2,3), B (1, 5), C (3, -1), (-1, 3)
There you go! Hope this helps! :)
Write the equation of the line in fully simplified slope-intercept form
Answer:
y = - x + 6
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 6) and (x₂, y₂ ) = (6, 0) ← 2 points on the line
m = [tex]\frac{0-6}{6-0}[/tex] = [tex]\frac{-6}{6}[/tex] = - 1
The line crosses the y- axis at (0, 6 ) ⇒ c = 6
y = - x + 6 ← equation of line
Plzzz help meeee plzzzzzz
Answer:
a) $560
b) 80%
c) $1134
Step-by-step explanation:
a)The profit is the difference between selling price and cost price:
profit = $1260 -700 = $560
__
b)As a fraction of the cost price, the profit is ...
$560/$700 × 100% = 80% . . . . of the cost price
__
c)A 10% discount from the selling price makes it ...
$1260 × (1 -10%) = 0.90×$1260 = $1134
A student will pay $1134 for a calculator.
Red At Santa's workshop, Jingles
the Elf sampled candy canes. He found
that 18 candy canes were broken. This
number represented 15% of the total
number of candy canes he inspected.
What was the total number of candy
canes Jingles sampled?
Based on the total number of candy canes damaged and the proportion of the total it was, the total inspected was 120 candy canes.
Assuming the total number of candy canes inspected is x, the relevant formula would be:
18 = x × 15%
Solving for x would give us:
18 = 0.15x
x = 18 / 0.15
= 120 candy canes
In conclusion, 120 canes were sampled.
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