Write the slope-intercept form of the equation of the line through the given point with the given slope.
Through: (4,-3), slope= -1/6

Given :

A cylindrical tank with radius 3m is being filled with water at a rate 4m³/min.

To Find :

How fast is the height of the water increasing.

Solution :

We know, volume of cylinder is given by :

[tex]V = \pi r^2h[/tex]       ....1)

Also, we have given that, [tex]\dfrac{dV}{dt} = 4 \ m^3/min[/tex] .

Differentiating equation 1) w.r.t  t we get :

[tex]\dfrac{dV}{dt} =3^2 \pi \dfrac{ dh }{dt}\\\\\dfrac{dh}{dt} = \dfrac{4}{3^2 \times \pi}\\\\\dfrac{dh}{dt} = 0.141 \ m/min[/tex]

Therefore, the height of water is increasing at a rate of 0.141 m/min.

Answer:

3 months

Step-by-step explanation: Let after m months they saved same amount of money.

Given,

Saving of Jaclyn = $ 120,

Amount earned by him/her per month = $ 40,

So, the total amount contained by him/her in m months = Saving + earning for m months

= 120 + 40m,

Similarly, saving of Pedro = $ 180,

Amount earned by him/her per month = $ 20,

So, the total amount contained by him/her in m months = 180 + 20m

Thus, we can write,

120 + 40m = 180 + 20m

40m = 180 + 20m - 120

40m - 20m = 60

20m = 60

⇒ m =  = 3.

Hence, it will take 3 months before which Jaclyn and Pedro have saved the same amount of money.

Answer:

100-51=49

49/100 x 58

= $28.42

Answer:

28.42

Step-by-step explanation:

the equation would be 58 times .49

58 times .49 is 28.42

Answer:

bncjk make sure bgfdf hi olb f see him be see vg hhzch

Answer: You got 57 points out of 60.

Step-by-step explanation: Hope this helps :)

Answer:

C) The third option. To find the y intercept move vertically, to find the slope, y2-y1/x2-x1

Step-by-step explanation:

Answer:

-2?

Step-by-step explanation:

Multiply -1 by -4 to get 4

subtract 20 from 12 to get -8

[tex]\frac{-8}{4}[/tex] simplify to get -2

Answer:

804−803+702−1

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

Identity property/ Associative Property

Answer:

-11...................

Answer:

-11

Step-by-step explanation:

22/2=11

its negative so make it negative

Answer:

Step-by-step explanation:

[tex]given \\ f(x) = x ^{2} + 10x + 21 \: and \: g(x) = x + 7[/tex]

[tex]as \: we \: know \: (f.g)x \: is \: same \: as[/tex]

[tex]f(g(x))[/tex]

[tex]so \: [/tex]

[tex]f(x + 7) = ( x + 7) ^{2} + 10(x + 7) + 21[/tex]

[tex]f(x + 7) = {x}^{2} + 14x + 49 + 10x + 70 + 21[/tex]

[tex]f(x + 7) = x^{2} + 24x + 140[/tex]

[tex]therefore [/tex]

[tex](f.g)x = {x}^{2} + 24x + 140[/tex]

Answer:

3,161

Step-by-step explanation:

Khan

Step-by-step explanation:

you have to divide first then you round

Answer:

-8

Step-by-step explanation:

Answer:

4th one is the right answer.

| x | -2 | 1 | 2 | 3 |

| y | -6 | 3| 6 | 9 |

Step-by-step explanation:

The x and y relationship is in the form y=kx and the graph starts from the origin.

Therefore the graph represents a proportional relationship which holds a equation y=x/3, where k=1/3.

Answer:

6

Step-by-step explanation:

Answer:

The range of the function is:

Range R = {14, 17, 20}

Step-by-step explanation:

Given the function

[tex]f(x) = 3x + 2[/tex]

We also know that range is the set of values of the dependent variable for which a function is defined.  

In other words,  

We are given that the domain of the function is:

Domain D = {4, 5, 6}

Now,

substituting x = 4 in the function

f(4) = 3(4) + 2

f(4) = 12 + 2

f(4) = 14

substituting x = 5 in the function

f(5) = 3(5) + 2

f(5) = 15 + 2

f(5) = 17

substituting x = 6 in the function

f(6) = 3(6) + 2

f(6) = 18 + 2

f(6) = 20

Thus, we conclude that:

at x = 4, y = 14

at x = 5, y = 17

at x = 6, y = 20

Thus, the range of the function is:

Range R = {14, 17, 20}

Answer:

yes

Step-by-step explanation:

you would multiply 2 and 3 then you would add whatever you got from that to 3 which would be 6+3

hope this helps!

Answer:

-0.6283

Step-by-step explanation:

-36° × π/180 = -0.6283rad

aswer

Answer:

-36π/180 or -.6283

Step-by-step explanation:

To convert from degrees to radians you multiply it by π/180

So you have -36π/180 which gets you around -.6283

Answer:

48

Step-by-step explanation:

Answer:  48

Step-by-step explanation:

Since 5 x 4 = 20 and you have to do the same with the numerator and denominator, 12 x 4 = 48

Answer: 17/25 pizza per each family member.

Answer:

The equation of the line in slope intercept form that passes through the point (-3, 5) and is parallel to y= - 2/3x is [tex]\mathbf{y=-\frac{2}{3}x+3 }[/tex]

Step-by-step explanation:

We need to Write the equation of the line in slope intercept form that passes through the point (-3, 5) and is parallel to y= - 2/3x

The general equation in slope-intercept form is: [tex]y=mx+b[/tex] where m is slope and b is y-intercept.

Finding Slope:

Both the equations given are parallel. So, they will be having same slope.

Slope of given equation y= - 2/3x is m = -2/3

This equation is in slope-intercept form, comparing with general equation  [tex]y=mx+b[/tex] where m is slope , we get the value of m= -2/3

So, slope of required line is: m = -2/3

Finding y-intercept:

Using slope m = -2/3 and point (-3,5) we can find y-intercept

[tex]y=mx+b\\5=-\frac{2}{3}(-3)+b\\5=2+b\\ b=5-2\\b=3[/tex]

So, we get b = 3

Now, the equation of required line having slope m = -2/3 and y-intercept b =3

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

The equation of the line in slope intercept form that passes through the point (-3, 5) and is parallel to y= - 2/3x is [tex]\mathbf{y=-\frac{2}{3}x+3 }[/tex]

Answer:

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

Step-by-step explanation:

5 = –⅔[–3] + b

2

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

Parallel equations have SIMILAR RATE OF CHANGES [SLOPES], so –⅔ remains as is.

I am joyous to assist you at any time.

Answer:

850.

You just multiply the 8.5 by 100.

Answer:

850

Step-by-step explanation:

50 dkms(dekameters) in 0.5 km(kilometer)

8.5/0.5 =17

17*50 = 850

Answer:

A number plus seven times itself equals 1200.

Step-by-step explanation:

The number is "x", and 7 times itself is 7 "x". When one adds the two, they get 1200. Hence it models the situation;

x + 7x = 1200.

Answer:

Step-by-step explanation:

marc has x amount of money. His mom offers to give him seven times his money as a Christmas gift. when he combined,  his starting money and what his mom gives him, it added up to $1200. What was marc’s starting money (x)

The original value of A is greater than original value of B.

The given parameters:

The original value of A is calculated as follows;

[tex]\frac{125}{100} \times A = 120\\\\1.25A = 120\\\\A =\frac{120}{1.25} \\\\A = \$ 96[/tex]

The original value of B is calculated as follows;

[tex]\frac{135}{100} \times B = 90\\\\1.35 B = 90\\\\B = \frac{90}{1.35} \\\\B = \$ 66.67[/tex]

Thus, the original value of A is greater than original value of B.

Learn more about percentages here: https://brainly.com/question/24304697

Answer:

1 = c

2 = b

3 = d

4 = d

5 = a

Step-by-step explanation:

1) 3x-4>17

2) 3x-4<17

3) 3x-4<=17

4) 3x-4<=17

5) 3x-4>=17

Answer:

Step-by-step explanation:

Answer:

$12

Step-by-step explanation:

Juan borrowed $10

His mother loaned him $3 more

= $10 + $3

= $13

He sold $25 worth of lemonade in the first week

If the pays his mother then the amount that will be left with him can be calculated as follows

= $25 - $13

= $12

Answer:

$12

Step-by-step explanation:

got it on edge

Answer:

$12

Step-by-step explanation:

30% of 40 = 12

Answer:

its 28.00

Step-by-step explanation:

trust me

Answer:

Step-by-step explanation:

From the question we are told that

Edges of 8 feet, 4 feet, and 1/2 foot

Generally the volume V_p of the right rectangular prism is mathematically represented as

[tex]V_p=8*4*0.5[/tex]

[tex]V_p=16[/tex]

Generally volume of the cube V_c is mathematically given as

[tex]V_c =(\frac{1}{2})^3[/tex]

[tex]V_c =\frac{1}{6}[/tex]

Therefore total number of cubes is given as

[tex]V=\frac{V_p}{V_c}[/tex]

[tex]V=\frac{16}{\frac{1}{6}}[/tex]

[tex]V=96[/tex]