i need help with this

30 is the area of the rectangle changing at the instant when the other side is 12 cm and increasing at 3cm per minute

The area of Rectangle is length times of width.

Given,

A rectangle has one side of 10cm

We need to find how fast is the area of the rectangle changing at the instant when the other side is 12 cm  and increasing at 3cm per minute

This can be written as A=10x

Now differentiate with respect to t.

dA/dt=10 dx/dt

increasing at 3cm per minute

dx/dt=3

dA/dt=10 (3)

dA/dt=30

Hence 30 is the area of the rectangle changing at the instant when the other side is 12 cm and increasing at 3cm per minute

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Answer:

2

Step-by-step explanation:

8b - 27 = -11

8b = 16

b = 2

The variable b will equal 2

Let's check

Answer:

i. 2040  ii.1632

Step-by-step explanation:

I think i did this right..

Answer:

  C.  19.50 lbs

Step-by-step explanation:

3 feet 3 inches is nearly 4 feet, but is a little shorter. That means the weight of the bar will be nearly 24 pounds, but a little less.

It cannot be 29 or 78 pounds, because those weights are more than 24 pounds. It cannot be 3 pounds, because that weight is significantly less. The only viable answer choice is 19.50 pounds.

__

We assume the weight is proportional to the length. Then the weight (w) of the shorter bar will be ...

  w/39 = 24/48 . . . . . weight in pounds/length in inches

  w = 39(24/48) = 39/2 = 19.5

The weight of the shorter bar is 19.5 pounds.

Answer:

Ok

Step-by-step explanation:

Ok

Answer:

solution is (3,-1/2)

Step-by-step explanation:

Answer:

14

Step-by-step explanation:

The number of elements in M is 31, so let's make set M the set of the first 31 natural numbers.

M = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31}

Set N has 18 elements. We need to choose 18 elements to place in set N.

The union of sets M and N has 35 elements. That means that since set M contributes 31 elements to the union, set N only contribute 4 new elements to the union. That means that 14 of the 18 elements in N are in common with set M.

Set N can be:

N = {18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35}

Answer: 14

Based on the weight of the old box of crackers, we can infer that the weight of the new box is 14.4 ounces.

The old box weighed 12 ounces and the new box has 20% more than the old box had.

The new box should therefore weigh 20% more than the old box which means that it weighs:

= Weight of old box x ( 1 + increase in new box)

= 12 x (1 + 20%)

= 14.4 ounces

In conclusion, the new box weighs 14.4 ounces.

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Answer:

n

Step-by-step explanation:

Answer:

[tex]x=14[/tex]

Step-by-step explanation:

Multiply both sides by -5:

[tex]-\frac{1}{5} (x-4)=-2[/tex]:

[tex]-\frac{1}{5} (x-4)*-5=-2*-5[/tex]

[tex]1(x-4)=10[/tex]

[tex]x-4=10[/tex]

Add 4 to both sides:

[tex]x-4+4=10+4[/tex]

[tex]x=14[/tex]

Answer:

-3 ≤ x ≤ 0

Step-by-step explanation:

2x + 3 ≤ 3

2x ≤ 0

x ≤ 0

-2x - 3 ≤ 3

-2x ≤ 6

x ≥ -3

Answer:

After substituting We multiply 5 with 9.

Step-by-step explanation:

Given Expression 5 + ( 9x - 3 ) ÷ 2

5 + ( 9 × 5 - 3 ) ÷ 2

5 + ( 45 - 3 ) ÷ 2

5 + ( 42 ) ÷ 2

5 + 21

26

Answer:

yea it is

Step-by-step explanation:

Answer:

[tex] \frac{4}{(g + 4) ^{2} }[/tex]

Step-by-step explanation:

[tex] \frac{g}{g(g + 4)} - \frac{g}{(g + 4) ^{2} } [/tex]

[tex] \frac{1}{g + 4} - \frac{g}{(g + 4) ^{2} } [/tex]

[tex] \frac{g + 4}{(g + 4) ^{2} } - \frac{g}{(g + 4) ^{2} } [/tex]

[tex] \frac{g + 4 - g}{(g + 4) ^{2} } [/tex]

[tex] \frac{4}{(g + 4) ^{2} } [/tex]

[tex] \frac{4}{g^{2} + 8g + 16 } [/tex]

Hope It's Help

Answer:

x = -6

y = 8

Step-by-step explanation:

Using substitution method.

2x + y = -4 -----------(I)

      y = - 4 - 2x -----------(II)

5x + 3y = -6 -------------------(III)

Substitute y = -4 -2x in equation (III)

5x + 3(-4-2x) = - 6

5x - 12  - 6x = -6

5x - 6x - 12 = -6

Combine like terms

    -x - 12     = -6   {Add 12 to both sides}

              -x = -6 + 12

              -x = 6              {Multiply by (-1)}

               x = -6

Substitute x = -6 in equation (II)

y = - 4 - 2*(-6)

  = -4 + 12

y = 8

Answer:

A.

y = 3(x + 3)^2 + 3

Step-by-step explanation:

The vertex form of the equation is y=a(x-h)2 + k  

You know that the vertex (h,k)  is (-3,3) and a point on the parabola is (4,150). So what you’re needed ing to find is a bc all of the other letters can be replaced into the equation.  

First I would put the equation into vertex form using the vertex given in the problem. : y= (x - (-3))2 + (3). Then I would use the ordered pair (4,150) and replace the x and y with those values

150 = a(4 + 3)2 + 3  

Now simplify

150 = a (7)2 + 3  

150 = 49a + 3      Important: please be sure to square.

147 = 49a

3= a  

Next replace a into the formula now leaving x and y alone.

y = 3 (x+3)2 + 3   [Vertex form]

I hope this helps. Have a great day!

Answer:

A.  [tex]y = 3(x + 3)^2 +3[/tex]

Step-by-step explanation:

The vertex form is:

[tex]y = a(x - h)^2 + k[/tex]

Where [tex]a[/tex] is the variable that determinate if the parabola is facing up or facing down and [tex]h[/tex] is the [tex]x[/tex] coordinate of the vertex and [tex]k[/tex] is the [tex]y[/tex] coordinate of the vertex.

So with the given values we have:

[tex]150 = a(4 + 3)^2 + 3[/tex]

Then isolate [tex]a[/tex] for find the missing value.

[tex]147 = a49\\\frac{147}{49} = a\\3 = a[/tex]

Then the final answer is [tex]y = 3(x + 3)^2 +3[/tex]

Answer:

B) The amount of service fee, in dollars

Step-by-step explanation:

Look for words relating to "one time," as that indicates the constant

Answer:

-4,1 -3,0 -2,1 -1,2 0,3 1,4 2,5 3,6 4,7

Step-by-step explanation:

when x increases by one, so does y. The slope of the line is 1 btw.

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

ok done. thank to me :>

Answer:

7/12

Step-by-step explanation:

Answer:

4 = a

5 = a

hope this answer helps you dear!

Answer:

39

Step-by-step explanation:

15^2 +36^2 = c^2

225 + 1296 = 1,551

√1551 = 39

[tex]9^x = \dfrac 1{27}\\\\\implies (3^2)^x = \dfrac{1}{3^3}\\\\\implies 3^{2x} = 3^{-3}\\\\\implies 2x = -3 \\\\ \implies x = -\dfrac 32[/tex]

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

Step-by-step explanation:

the break down probabilities are for the same given day ? one day ?

if that is so, then the expected value for a break down day for tractor 1 will be 34 days (rounded up 100%/3%), and for tractor 2 20 days (100%/5%).

that would be horrible. a tractor would only work for about a month without major repair.

because normally such probabilities are given for a warranty period like 1 or 3 or 5 years.

but the description does not say anything about that. so, we have to go with the primary assumption.

so, the question is about the probability that both things happen at the same time (the same day).

this is like asking for the probability of rolling a double 6 with two dice - both events (a 6 on a die) have to happen "together". so it is the probability of one event multiplied by the probability of the second event : 1/6 × 1/6 = 1/36

5% = 0.05 (5% is 5 hundredths) = 5/100

3% = 0.03 (3% is 3 hundredths) = 3/100

now both events (break-down of both tractors) happen together means 5/100 × 3/100 = 15/10000 = 0.0015

that means the probability in % is 0.15%

that means in other words, this event (both tractors breaking down on the save day) is expected to happen 15 times in 10000 days, or once every 667 days (or roughly every 2 years).

Answer:

no

Step-by-step explanation:

to be perpendicular the second equation would have to be -x (the opposite of x)

these lines are parallel

Answer:

No, not perpendicular

Step-by-step explanation:

Compare the slopes of the two lines.  In each case the slope is 1.  Therefore the slopes are not negative reciprocals of one another, and the lines are NOT perpendicular.

Answer:

£ 305.4

Step-by-step explanation:

[tex]549*\frac{1}{3}*1+164*0.5+(549*\frac{2}{3}-164)*0.2\\\\=183+82+40.4\\\\=305.4[/tex]

Answer:3/8

Step-by-step explanation: 3/4 x 1/2 = 3/8