Solve each system by elimination
7x + 8y = -29
-3x -8y = 17

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:

-3 ≤ x ≤ 0

Step-by-step explanation:

2x + 3 ≤ 3

2x ≤ 0

x ≤ 0

-2x - 3 ≤ 3

-2x ≤ 6

x ≥ -3

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:

Step-by-step explanation:

1. 2x + 3y = 1,470

–2x –2x

3y = –2x + 1,470

3y/ 3 = –2x/3 + 1,470/3

y = –2x/3 + 490

The y-intercept of this equation is 490 and the slope is -2x/3.

2. I would graph this line by finding the y-intercept 490 first.

Then, you would move down twice from 490 to 488.

Finally, you would move to the right 3 times.

3. F(x) = –2x/3 + 490

The graph would represent the profit of Sal’s Sandwich Shop on every sandwich and wrap from the lunch specials last month.

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:

The prime factors of 492 are 2, 3, 41.

Step-by-step explanation:

→ 492 = 2 × 2 × ? × ?

→ 492 = 2 × 2 × 3 × 41

Let's check,

→ 492 = (2 × 2) × (3 × 41)

→ 492 = 4 × 123

→ 492 = 492

→ LHS = RHS

Hence, prime factors of 492 are 2, 3, 41.

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:

[tex]x=\frac{27+\sqrt143i}{8}{} ,\frac{27-\sqrt{143i} }{8}[/tex]

[tex]y=-9+\frac{27+\sqrt{143} i}{4} ,-9+\frac{27-\sqrt{143} i}{4}[/tex]

Step-by-step explanation:

1) Solve for 2x - y = 9

A. Solve for y.

2x - y = 9

B. Subtract 2x from both sides.

-y = 9 - 2x

C. Multiply both sides by -1.

y = -9 + 2x

D. Regroup terms.

y = 2x - 9

2) Substitute y = 2x- 9 into 4x² + 3y² - 2x + y = 16

A. Start with the original equation.

4x² + 3y² - 2x + y = 16

B. Let y = 2x - 9.

4x² + 3(2x - 9)² - 2x + 2x - 9 = 16

C. Simplify.

16x² - 108x + 234 = 16

3) Solve for x in 16x² - 108x + 234 = 16

A. Solve for x.

16x² - 108x + 234 -= 16

B. Move all terms to one side.

16x² - 108x + 234 - 16 = 0

C. Simplify 16x² - 108x + 234 - 16 to 16 x² - 108x + 218

16 x² - 108x + 218 = 0

D. Use the Quadratic Formula.

[tex]x=\frac{108+4\sqrt{143}i }{32}[/tex], [tex]\frac{108-4\sqrt{143} i}{32}[/tex]

E. Simplify solutions.

[tex]x=\frac{27+\sqrt{143} i}{8} ,\frac{27-\sqrt{143} i}{8}[/tex]

4) Substitute [tex]x=\frac{27+\sqrt{143}i }{8} ,\frac{27-\sqrt{143}i }{8}[/tex] into y = 2x - 9.

1) Start with the original equation.

y = 2x - 9

2) Let x = [tex]\frac{27+\sqrt{143} i}{8} ,\frac{27-\sqrt{143}i }{8} .[/tex]

[tex]y=2*\frac{27+\sqrt{143} i}{8} -9,2*\frac{27-\sqrt{143}i }{8} -9[/tex]

3) Simplify

[tex]y=-9+\frac{27+\sqrt{143}i }{4} ,-9+\frac{27-\sqrt{143i} }{4}[/tex]

Answer:

If he climbed 80 mountains in the span of 10 months then you should divide the 80 by 10 which makes it 8.. so I believe the correct answer is 8 mountains per month

Answer:

Jim climbed 8 mountains per month and 10 mountains in 1.

Step-by-step explanation:

This means that he can climb 8 times as many mountains in one year, whether that is within the next 9 months or not depends on how much time he has available to do it.

============================================================

Explanation:

Draw a straight line from home plate to second base. Two right triangles form. Each triangle has both legs equal to 90 ft. The hypotenuse is what we're after. We'll use the pythagorean theorem to find it.

[tex]a^2 + b^2 = c^2\\\\c = \sqrt{a^2 + b^2}\\\\c = \sqrt{90^2 + 90^2}\\\\c = \sqrt{16200}\\\\c \approx 127.27922\\\\c \approx \boldsymbol{127.3}\\\\[/tex]

It's approximately 127.3 feet from home plate to second base. This is a straight line distance. Any curved path the ball takes will travel a slightly longer distance; however, we only consider the straight line distance for the sake of simplicity.

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.

Answer:

x = 10

Step-by-step explanation:

Perimeter of a triangle = the sum of the three sided of the triangle.

In an isosceles triangle, there are two equal sides and  a base.

Perimeter = ( 3x - 6) + (3x - 6) + x

            58 = 7x - 12

            58 + 12 = 7x

                   70  = 7x

                    [tex]\frac{70}{7} = \frac{7x}{7}[/tex]

                    10 = x

Answer:

7/12

Step-by-step explanation:

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:

100:60

Step-by-step explanation:

$1 is equal to 100 cents

So we can compare it as 100:60

Hope this helps!

Answer:

5:3.

Step-by-step explanation:

That would be 1:0.60

= 100:60

= 5:3.

[tex]2x = \frac{x+2}{2} => 4x = x + 2 => 3x = 2 => x = 2/3[/tex]

ok done. Thank to me :>

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:

[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:

2

Step-by-step explanation:

8b - 27 = -11

8b = 16

b = 2

The variable b will equal 2

Let's check

Answer:

$9.68 per Hour, $11.72 per Hour.

Step-by-step explanation:

What you thought of..

10% of original pay wage = $0.80

Sofia's Pay Wage will be incremented by 10% of $8 every 6 Months.

Function:

Sofia's Pay Wage = e

Original Pay Wage = o

Increment = i

6 Months = t

e = o + ti

1 Year = 12 Months

$8 + ($0.80 x 2) = $9.60

In 1 Year, Sofia's Pay Wage will be $9.60 per Hour

$8 + ($0.80 x 4) = $11.20

In 2 Years, Sofia's Pay Wage will be $11.20 per Hour

What I Thought Of..

Sofia's Pay Wage will be incremented by 10% every 6 Months.

Function:

Sofia's Pay Wage = e

Original Pay Wage = o

Increment = i

6 Months = t

e = o + t(ei)

1 Year = 12 Months

($8 + {10% of Sofia's Pay Wage}) = $8.80

($8.80 + {10% of Sofia's Pay Wage}) = $9.68

In 1 Year, Sofia's Pay Wage will be $9.68 per Hour

($9.68 + {10% of Sofia's Pay Wage}) = $10.65

($10.65 + {10% of Sofia's Pay Wage}) = $11.72

In 2 Years, Sofia's Pay Wage will be $11.72 per Hour

Brainly? (I spent a while on this)

50

If 10 is 20% of a number, we can multiply it by 5 to get the original number.

So 10 * 5 = 50, and 20% of 50 is 10.

I hope this helps! :)

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

Answer:

Step-by-step explanation:

251 divided by something has to equal to a number it will divide by...

2 3 = 2x 2 x 2 = 8

x

p 2 = pxp

251 divided by 25 x8

/49 x8

/100x8

/4x 8

so I would say  5

Answer:

Simplify 1√26inindexform

Simplify √26.

Checking square roots, we see that 52 = 25 and 62 = 36.

Our answer is not an integer, so we try simplify it into the product of an integer and a radical.

Answer:

x = 8 and y = 21

Step-by-step explanation:

3y + 27 = 90 so 3y = 90 -27 which is 63 and to get y you divide 63 by 3 to get 21

Angles on a straight line add up to 180 so 180 = x + 90 + 8x + 18

Then you minus 90 from 180 to get 90 = x + 8x + 18 which simplifies to 90 = 9x + 18

Then you minus 18 from 90to get 72 = 9x

Then divide 72 by 9 to get x = 8

Answer:3/8

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

Answer:

39

Step-by-step explanation:

15^2 +36^2 = c^2

225 + 1296 = 1,551

√1551 = 39