Find slope intercept form

The dimensions of the tank with minimum weight are 24*24*12 ft

What is rectangular tank?

There is a benefit to employing vertical cylindrical stores that are put behind the double glass as in the Trombe wall system because a rectangular tank that extends from floor to ceiling is relatively expensive to construct and must be constructed to withstand quite high hydraulic pressures.

The tank with minimum weight is the one with minimum surface area.

Let x= base width and base height

     h= height of the tank

The volume of tank is :

  v=hx²

substitute v=6912 ft³

 6912=hx²

  h= 6912/x²............(1)

Formula for the tank surface area is:

A=x²+4xh

On substituting h value and simplifying,

A=x²+(27.648/x)

Differentiate with respect to x and equate to zero

2x-(27.648/x²)=0

On simplifying,

x³=27648/2 = [tex]\sqrt[^3]{13824}[/tex]

x= 24

substitute x=24 into the equation 1

h= 6912/(24)²= 12 ft

So, the dimensions of the tank with minimum weight are 24*24*12 ft

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The composite figure has an area of 205 square feet

In this question we find the composite figure formed by two right triangles and two rectangles, whose total area is the sum of the areas of the two right right triangles and two rectangles. Then, the area formula is shown below:

A = Σ A' + Σ A''

Where:

The area formulas for right triangles and rectangles:

Right triangles

A = 0.5 · b · h

Where:

Rectangles

A = b · h

Now we proceed to calculate the area of the composite figure:

A = 0.5 · (13 ft) · (20 ft) + 0.5 · (11 ft) · (4 ft) + (4 ft) · (8 ft) + (7 ft) · (3 ft)

A = 130 ft² + 22 ft² + 32 ft² + 21 ft²

A = 130 ft² + 75 ft²

A = 205 ft²

The area of the composite figure is equal to 205 square feet.

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keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

[tex]y=1+2x\implies y=\stackrel{\stackrel{m}{\downarrow }}{2}x+1\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{2\implies \cfrac{2}{1}} ~\hfill \stackrel{reciprocal}{\cfrac{1}{2}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{1}{2}}}[/tex]

so we're really looking for the equation of a line whose slope is -1/2 and that it passes through (4 , -4)

[tex](\stackrel{x_1}{4}~,~\stackrel{y_1}{-4})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{1}{2} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-4)}=\stackrel{m}{- \cfrac{1}{2}}(x-\stackrel{x_1}{4}) \implies y +4= -\cfrac{1}{2} (x -4) \\\\\\ y+4=-\cfrac{1}{2}x+2\implies {\Large \begin{array}{llll} y=-\cfrac{1}{2}x-2 \end{array}}[/tex]

Answer:

  (d)  (x, y) ⇒ (x -6, y -6)

Step-by-step explanation:

You want to know the transformation rule that translates A(2, -6) to A'(-4, -12).

The amount of translation is the difference between the image coordinates and the original coordinates:

  A' -A = (-4, -12) -(2, -6) = (-4 -2, -12 -(-6)) = (-6, -6)

The amount is added to the original coordinates to give the translated coordinates:

  (x, y) ⇒ (x -6, y -6)

⇒The given function is a linear function as we know the general equation of a straight line is y=mx+c

Option d is the answer.

Answer:under

Step-by-step explanation:

so if you do 54times 2 it is 108so then you do 16 times 108 and you get 1728

Answer:

flight is under the limit

Step-by-step explanation:

1 suitcase=16kg

2 suitcases=16kgx2=32kg

1 passenger has 32kg

54x32=1728kg

54 passengers have 1728kg

1728kg is less than 2250kg which means flight is under the limit

Answer:

First choice since the maximum amount of hot dogs sold is 125 and domain is found by the x-axis (x) not the y-axis (y)

The fourth integer is 16.

Key skills needed: Casework, Mean, Median, and Mode

1) We start with 4 numbers _ _ _ _

2) We can determine two of the numbers by using the fact that the median is 14 and the mode is 14.

3) The numbers would have to be:

   _ 14 14 _

   _ 14 14 14

The 2nd one does not work because the last number would have to be a 6 to have a mean of 14, but the range would not be 14.

4) So, our numbers are _ 14 14 _

5) The two numbers add up to 20 (in order to have a mean of 14. If you subtract the bigger one by the smaller one, it will be 14.

6) We can make a system: saying x is the bigger number and y is the smaller number.

x + y = 20

x - y = 14

Add both and you will get 2x = 32 (since the y values cancel out).

7) divide by on both sides, and x = 16.

8) To find y, we can plug x back in to one equation:

16 + y = 20

y = 4

Our smaller number is 4 and our bigger number is 16.

9) Therefore the numbers are: 4, 14, 14, 16

Hence the answers is, the fourth integer is 16.

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Option (C) is the correct one and the sum of all four-digit positive integers greater than 2019 that can be formed in the given way is 476,661.

Given, the integer 2019 can be formed by placing two consecutive two-digit positive integers, 19 and 20, in decreasing order.

We have to find the sum of all four-digit positive integers greater than 2019 that can be formed in this way.

First number that can be formed in the given way is,

2120

and the last number that can be formed in the given way is,

9998

As, we can observe that the last two digits of all the numbers will make an A.P and in similar way the first two digits also make an A.P

So, first finding the sum of last two digits which is forming an A.P

first term be, 20 and last term be, 98

also, the number of terms be, 79

Sum = 79/2(20 + 98)

Sum = 79×59

Sum = 4661

So, the last two digits of the final answer will be 61 and 46 will add as carry.

Now, similarly finding the sum of first two digit numbers be

Sum = 79/2(21 + 99)

Sum = 79×60

Sum = 4740

on adding the carry of 46, we get

4740 + 46 = 4786

So, the sum of all four-digit positive integers greater than 2019 that can be formed in the given way is 476,661

Hence, option (C) is the correct one and the sum of all four-digit positive integers greater than 2019 that can be formed in the given way is 476,661.

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Answer:

It is about $0.07 per pair for the expense report.

Step-by-step explanation:

You have to divide 89.28 by 6 to get the unit price. 89.28/6=0.06720430107 or about $0.07. Hope this helps! I am up doing math too -_-. Please don't mark me brainliest, I just love to help.

Answer:

Step-by-step explanation:

1) (x-6)

2) (x-3)

3) x(x-3)(x-6)

Answer:

468.11

Step-by-step explanation:

k = 294.57 + 173.54 = 468.11

Answer:

k = 468.11

Step-by-step explanation:

Given equation,

→ k - 173.54 = 294.57

Now the value of k will be,

→ k - 173.54 = 294.57

→ k = 294.57 + 173.54

→ [ k = 468.11 ]

Hence, value of k is 468.11.

Answer: 20 PURPLE marbels

Step-by-step explanation:

no explanation

Answer:

the is 200 purple marbles 70 red marbles

1. $5

2. $2 for each mile

3.equation, in slope-intercept form, that relates the cost compared to the miles traveled for a Green Caby=x+5

What is an explanation of the slope-intercept form?

Simply put, the slope-intercept form is the way to write a line's equation so that the y-intercept (where the line crosses the vertical y-axis) and slope (steepness) are instantly visible. This form is frequently known as the y = mx + b form.

1. The graph shows that the Green Cab will cost you $5 for a distance of 0 miles.

2. According to the graph, $1 is spent for every mile traveled.

3. Because y increases by the same amount for every 1 increase in x, the slope is 1.

The slope intercept form is y=mx+b.

m=slope

intercept b=y

Since we are aware that the slope is 1, we can enter it.

y=1x+b

=y=x+b

By looking at the graph and calculating what y equals when x is 0, we may get the y intercept.

It is the y intercept (0,5)

So that the equation is in slope intercept form, we may enter that.

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Answer:

Slope: -2

Step-by-step explanation:

(This answer is if you meant to write 6y = 3x - 9)

First, change the standard equation form into a linear equation form, y=mx+b. To do this, divide both sides by 6 to get:

[tex]y=\frac{3}{6} x-\frac{9}{6}[/tex]

This can then simplify to:

[tex]y=\frac{1}{2} x-\frac{3}{2}[/tex]

In order to find the equation of a perpendicular line, you need to find the opposite reciprocal of the current slope:

[tex]y=-2x-\frac{3}{2}[/tex]

The slope is m, meaning that the slope of the perpendicular equation is -2.

Hope this helps!

The amount of money that he will make for 2 hours of baby sitting work is $18

The function is

f(x) = 4x + 10

The function f(x) is the amount of money Francis makes when babysitting for x hours

The function is the mathematical statement that shows the relationship between one variable and another variable. If one variable is dependent variable then the other variable will independent variable

The function

f(x) = 4x + 10

The number of hours x = 2 hours

Substitute the values of x in the function

f(2) = 4(2) + 10

f(2) = 8 +10

f(2) = $18

Hence, the amount of money that he will make for 2 hours of baby sitting work is $18

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Answer:

940,000.00

Step-by-step explanation:

The 8 goes into the 3 and since 8 is bigger than 5 or 4 it rounds it up to the next umber, which is 4

Cyclones are cyclic rotating air masses around a low atmospheric pressure center which when viewed from above looks like a circle. It causes heavy rainfall and thunderstorm. The speed of a cyclone often varies between 30 to 50 km which is enough to destroy anything behind its path. It moves clockwise in the southern hemisphere and anticlockwise in the northern hemisphere.

There are two types of cyclones Tropical cyclones and Extratropical cyclones:

There are different names for cyclones in different countries such as:

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Answer:

Sp=cp+p

sp=590+75

sp=625

The inequality in the slope-intercept form is y≥(3x/7)+3 when the graph is in of a linear inequality.

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction. The letter m is frequently used to represent slope; the reason for this usage is unclear, but it can be found in O'Brien's (1844)[2] and Todhunter's formulations of the equation for a straight line as y = mx + b and y = mx + c, respectively.

Let the linear equation be

y=m x +c

From the graph the lines are passing through the points (-7,0), (0,3)

Slope m =(3-0)/(0+7)

m=3/7

c=y-intercept

Therefore, c=3

Substitute the values in the above equation.

y=(-3/7)x+3

7y=3x+21

But, here we need to use the inequality which satisfies the shaded region.

Let us consider the point (1,2)

7(2)=3(1)+21

14=24 (But 14≠24)

Therefore, 14≥24

So, we have to use ≥ sign

7y≥3x+21

y≥(3x/7)+3

The inequality in the slope-intercept form is,

y≥(3x/7)+3

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The required position of the -2.25 lies above the -2.25 on the vertical number line.

Given that,
If -2.5 < -2.25, how are the positions of the two numbers related on the vertical number line is to be determined.

A number line is defined as the number marked on the line calibrated into an equal number of units. For example -1, 0, 1, and so on.

Here,
Since -2.5 is 0.25 lower than -2.25, and also the -2.25 is greater than -2.5.
So on the vertical number line, -2.25 lies 0.25 units above the number -2.5.

Thus, the required position of the -2.25 lies above the -2.25 on the vertical number line.

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Answer:

On the vertical number line, -2.5 is located below -2.25.

Step-by-step explanation:

edmentum answer. have a good day

Answer:5

Step-by-step explanation:

19 + 14 = 33

27 + 11 = 38

38 - 33 = 5

The Equation of the graph in slope-intercept form is 3y = 1350 - 100x

Misty will travel 150 miles after 9 hours

It will take misty 12 hours to cover 50 miles

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant. The standard form of a linear equation in two variables is of the form Ax + By = C. Here, x and y are variables, A and B are coefficients and C is a constant.

Equation of line in slope-intercept form is y = mx + c

let y be the distance in miles and x be the time in hours.

from the graph when x = 0, y = 450

substituting into the equation,

450 = 0(m) + c

c = 450 which is the intercept

Also from the graph, taking the point (3, 350)

when x = 3, y = 350

350 = 3m + 450

3m = 350 - 450

3m = -100

m = -100/3

SO the equation of straight line becomes

y = -100x/3 + 450

multiply through by 3

3y = -100x + 1350

if misty travel 9 hours that is x = 9, then y =

3y = -100(9) + 1350

3y = 450

y = 450/3

y = 150 miles

If there are 5o miles remaining,

y = 50, x =

3(50) = -100x +1350

100x = 1350 -150

100x = 1200

x = 1200/100

x = 12 hours.

The Equation of the graph is 3y = 1350 - 100x

Misty will travelled 150 miles after 9 hours

It will take misty 12 hours to cover 50 miles

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Answer:

In algebra class, we are learning about the commutative property. We are also learning about coefficients and how to evaluate expressions. Another thing we are learning about is the order of operations where you have to simplify at the end, and in each problem there are terms and variables.

Answer:

8+3x=-8

x=-5 1/3

Step-by-step explanation:

triple a number means to multiply by 3

More than is to add

8+3x=-8

-8.      -8

3x=-16

x=-5 1/3

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If an athlete runs at a rate of 309 yd. /min. If one lap is 315 yard athlete then athlete covers 18.63 laps in 19 minutes

What is a conversion factor?

A fraction that is equal to "1" is a conversion factor. The numerator and denominator are the same amount, but they are expressed in different units. It is used to change a number's unit of measurement. In order to do that, multiply the initial number by the fraction equal to "1"; this maintains the original number's value but modifies the units.

An athlete run at a rate of 309 yds. /min.

If one lap is 315 yard

Then total number of yards covered by the athlete is 5871.

I.e. 309 x 19 = 5871.

So total laps covered by the athlete in 19 minutes is

     [tex]\frac{5871}{315}=18.63[/tex]

Hence, athlete covers 18.63 laps in 19 minutes

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Answer:

0

Step-by-step explanation:

f(x) is basically y (or in this case k(x))

to find the k(6) we find the y value when x is 6

we look and the graph and see that it is 0

that is your answer