Juan alquiló un auto por un día. La tarifa mínima es $490.00, con un cargo adicional de $9.70 por cada kilómetro que maneje. Juan pagó $2847.10 cuando entregó el auto. ¿Qué cantidad de kilómetros manejó? kilómetros Х $ ? ​

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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Evaluate

[tex] \sf \longmapsto \: y + h[/tex]

When

Let's start.

[tex] \sf \longmapsto \: y + h[/tex]

[tex] \sf \longmapsto6 +0[/tex]

[tex] \sf \longmapsto6[/tex]

Answer:

7:4 is the new ratio.

Step-by-step explanation:

set a proportion; (8+4 = 12)

7 x

-- = --

4 12

12/4 = 3

3 x 7 = 21

x = 21

new ratio: 21:12

simplifies: 7:4 (division of 3)

The new ratio of blue to green dye in its simplest form is 7/6.

Blue and green dye are mixed in a 7:4 ratio to make 44 litres of a teal-coloured dye. A further 8 litres of green dye are added to the mixture. What is the new ratio of blue to green dye in its simplest form to be determined.

The ratio can be defined as the comparison of the fraction of one quantity towards others. e.g.- water in milk.

Calculating the fraction of blue and green in the teal dye,
Blue dye = 7/(4+7) * 44
Blue dye = 7/11 * 44
Blue dye = 28 liters
Similarly,
Green dye = 7/12*44
Green dye = 16
Now
Blue dye = green dye = 28+16 = 44
Now gree dye is increase by 8 liters
new volume fraction of green dye = 16+8
                                                  = 24
a fraction of blue dye remains the same,
the ratio of blue dye to new green dye in teal colored.
= 28/24
=7/6

Thus, the new ratio of blue to green dye in its simplest form is 7/6.

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Answer:

502

Step-by-step explanation

108 has the numbers 0, 1, and 8 which added together totals 9

603 has the numbers 0, 3, and 6 which added together totals 9

360 has the numbers 0, 3, and 6 which added together totals 9

502 has the numbers 0, 2, and 5 which equal 7

502 is the odd one out

Answer:

Step-by-step explanation:

Given:

Required equations:

Solve by elimination, multiply the first equation by 10 and subtract from the second equation:

Find p:

Let's take the given as,

→ q = quarters (25)

→ d = dimes (10)

→ 1320 will be the amount

→ q + d = 72

→ 25q + 10d = 1320

Now we can solve for q,

→ (25q - 10q) + (10d - 10d) = 1320 - (10 × 72)

→ 15q = 1320 - 720

→ 15q = 600

→ q = 600/15

→ [ q = 40 ]

From this equation,

→ q + d = 72

We can solve for the d,

→ 40 + d = 72

→ d = 72 - 40

→ [ d = 32 ]

There are 40 quarters & 32 dimes.

Answer:

271.433606 (in, cm, or whichever unit)

Step-by-step explanation:

To find the areas of the ends of the cylinder, the circles, you would use the formula:

2(π * r²)

The diameter is twice the length of the radius so to find the radius, you would divide the length of the diameter in half. So with a diameter of 10.8 units, it would become 5.4 units.

2(π * 5.4²) = 183.217684

To find the surface area of the rectangle of the cylinder, you would multiply the circumference of the base of the cylinder by the height. The formula to find the circumference is 2πr. The circumference would be 33.9292007 units. 33.9292007 * 2.6 = 88.2159218.

Then add the areas to find the total.

183.217684 + 88.2159218 = 271.433606

Answer:

8000

Step-by-step explanation:

Answer:

397

Step-by-step explanation:

1. To evaluate this expression, we plug in the value of x and simplify.

Therefore, the answer is 397.

Answer:

The answer is 2.70

Step-by-step explanation:

18+2.70= 20.70

20.70-2.70=18

Answer:

x is -3

Step-by-step explanation:

Answer:

i dont know sry....i ned points..

15% of $18 is $2.70...........

I can't give a very good answer as I don't know what resources are available to you, but this is what I managed to find with a ti-84 calculator.

[tex]y=-31.24+1.34x[/tex]

If you want a better step-by-step, tell me what's in that 'open statistics calculator' option and I'll see what I can figure out.

edit: missed that second part of the question

Using this equation to calculate a test grade with a homework grade of 90:

[tex]y=-31.24+1.34(90)=89[/tex]

Answer:

6°

Step-by-step explanation:

The angles in a triangle always add up to 180°. Let’s call the third angle x. That means that:

154 + 20 + x = 180 ->

174 + x = 180 ->

x = 180 - 174 ->

x = 6°

Hope that help! :)

Answer:

-1/2

Step-by-step explanation:

Answer:

The code is 8415

Step-by-step explanation:

Multiply the original dimensions by the scale:

8 x 3.5 = 28

6 x 3.5 = 21

New dimensions:  length = 28, width = 21

Answer:

1

Step-by-step explanation:

/14-15/

/-1/

1(because absolute value of any real number is always positive and for zero itself zero)

Step-by-step explanation:

as you can see, the distance between 2 points can always be seen as the Hypotenuse or baseline of a right-angled triangle created by the differences of the x and y coordinates of both points.

the drawn triangle is nothing else than that.

to calculate the length of a side in such a triangle we need to use Pythagoras :

c² = a² + b²

c is the Hypotenuse of baseline of the triangle and is opposite of the 90 degree angle.

a and b are the legs of the triangle "enclosing" the 90 degree angle.

so, we have

AB² = AC² + BC²

AC and BC we know : the coordinate differences in x and y directions.

AC = (4, 5) to (4, 2). as the x coordinates are the same, the difference is just the difference in the y coordinates : 5-2 = 3.

BC = (1, 2) to (4, 2). as the y coordinates are the same, the difference is just the difference in the x coordinates : 5-1 = 3.

AB² = 3² + 3² = 9 + 9 = 18

AB = sqrt(18)

FYI : sqrt(18) = sqrt(9×2) = 3×sqrt(2)

Answer:

I only know the second one sooorrry

if you say its classification so that type of traingle is obtuse triangle

Step-by-step explanation:

Answer:

-10n

Step-by-step explanation:

To simplify, you add like terms so by looking at the problem you can see the 8 and the 2 both have an n after, so you can combine them.

so negative 8 minus 2 = -10 and since there are like terms you add the n making the answer -10n

If it was -8n -2 you could not simplify it since the 2 is single and without the same letter

Same with -8n - 2p because it is not the same letter

Answer:

[tex]y=\frac{4}{3}x-.333[/tex]

Step-by-step explanation:

Answer- 15.8 Miles

Explanation photo was given above.

Answer:

2,400

Step-by-step explanation:

Can I please have brainliest?? thanks!! have an awesome day and good luck with your math :)

Answer:

2,400

Step-by-step explanation:

Answer:

It is congruent doe to the angle side angle congruence thereom AKA ASA

Step-by-step explanation:

That means there are two angles and one side in between. A pair of triangles  that follow this rule has an angle that is congruent to one angle. Then a side that has a tick mark after the angle must match another. Then the last angle has to match another angle ( and it can't be the same angle as before).  Usually the first pair angles have 1 semicircle and the second pair has 2 semicircles.

Answer:

-10

Step-by-step explanation:

The rate of change is also known as the slope of the function thus the slope will be -600.

A slope is a tangent or angle at a point and a slope is the intensity of inclination of any geometrical lines.

Slope = Tanx where x will be the angle from the positive x-axis at that point.

The slope is also calculated by differentiation for example slope of y = sinx will be y' = cosx.

As per the given,

Bacteria are dying at a constant rate of $600$ an hour.

The rate of change = -600/hour

Slope = y/x = number of bacteria change/time taken

If the graph is a straight line then it will remain constant.

Slope = -600

Hence "The rate of change is also known as the slope of the function thus the slope will be -600".

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Answer:

y=4

Step-by-step explanation:

84=30y-9y, first you collect like terms.

84=21y, swap the sides

21y=84, devide both sides and you get y =4

Answer:

[tex]T(2,4) and U(11,13)[/tex]

Step-by-step explanation:

[tex]\left \{ {{-6y = -12} \atop {3x + 2y = -2}} \right. <=> \left \{ {{y = 2} \atop {3x + 2y = -2}} \right. <=> \left \{ {{y=2} \atop {3x + 2*2 = -2}} \right. <=> \left \{ {{y=2} \atop {3x = -6}} \right. <=> \left \{ {{y=2} \atop {x=-2}} \right.\\ => \left \{ {{y=2} \atop {x=-2}} \right.[/tex]