Work out m and c for the line: 2 y + 6 x = − 4

Answer:

Its is the second one

Step-by-step explanation:

Remember: rise over run

The b of the equation is -2 because that is how far it goes down on the y axis.

The slope is 3x.

Put the slope like this 3/1= rise/run

Sorry for the delayed response!  

Answer:

if you remember the bell curve 32 32 13.5 13.5 2.35 2.35 and .15 put the mean in the middle of the bell curve we find that 13.5 + 2.35 + .15 so

16% is your probablility

Answer:

It's decreasing quickest  between 3:23 and 3:24 (where the steepest drop on the graph is)

Answer:

3:23-3:24

…………………..

9.56 m of the wire should be used for the square, to maximize the total area of the wire

Let x be the side length of the square.

So, the perimeter of the square is:

[tex]\mathbf{P_s=4x}[/tex]

Let y represent the side length of the equilateral triangle.

So, the perimeter of the triangle is:

[tex]\mathbf{P_t=3y}[/tex]

The length of the wire is given as:

[tex]\mathbf{P=22}[/tex]

This implies that:

[tex]\mathbf{P_s + P_t=22}[/tex]

Substitute values for Ps and Pt

[tex]\mathbf{4x + 3y=22}[/tex]

Make y the subject

[tex]\mathbf{y=\frac{22 -4x}3}[/tex]

For an equilateral triangle of side length y, the height (h) of the triangle is:

[tex]\mathbf{h =\frac y2\sqrt 3}[/tex]

The area of the triangle is then calculated as:

[tex]\mathbf{A_t = \frac 12 yh}[/tex]

This gives

[tex]\mathbf{A_t = \frac 12 y\times \frac y2\sqrt 3}[/tex]

[tex]\mathbf{A_t = \frac{y^2}{4}\sqrt 3}[/tex]

The area of the square is:

[tex]\mathbf{A_s = x^2}[/tex]

So, the total area is:

[tex]\mathbf{A = A_s + A_t}[/tex]

[tex]\mathbf{A = x^2 + \frac{y^2}{4}\sqrt 3}[/tex]

Substitute [tex]\mathbf{y=\frac{22 -4x}3}[/tex]

[tex]\mathbf{A = x^2 + (\frac{22 - 4x}{3})^2 \times \frac{\sqrt 3}{4}}[/tex]

Differentiate

[tex]\mathbf{A' = 2x + \frac{\sqrt 3}{4} \times \frac 19 \times 2(22 - 4x) \times (-4)}[/tex]

[tex]\mathbf{A' = 2x - \sqrt 3 \times \frac 19 \times 2(22 - 4x) }[/tex]

[tex]\mathbf{A' = 2x - \frac{2\sqrt 3}9 (22 - 4x) }[/tex]

Set to 0

[tex]\mathbf{2x - \frac{2\sqrt 3}9 (22 - 4x) = 0}[/tex]

Rewrite as:

[tex]\mathbf{2x = \frac{2\sqrt 3}9 (22 - 4x) }[/tex]

Divide through by 2

[tex]\mathbf{x = \frac{\sqrt 3}9 (22 - 4x) }[/tex]

Multiply through by 9

[tex]\mathbf{9x = \sqrt 3 (22 - 4x) }[/tex]

Open bracket

[tex]\mathbf{9x = 22\sqrt 3 - 4x\sqrt 3 }[/tex]

Collect like terms

[tex]\mathbf{9x +4x\sqrt 3= 22\sqrt 3 }[/tex]

Factor out x

[tex]\mathbf{x(9 +4\sqrt 3)= 22\sqrt 3 }[/tex]

Solve for x

[tex]\mathbf{x= \frac{22\sqrt 3}{9 +4\sqrt 3} }[/tex]

Simplify

[tex]\mathbf{x= \frac{38.11}{9 +6.93} }[/tex]

[tex]\mathbf{x= \frac{38.11}{15.93} }[/tex]

[tex]\mathbf{x= 2.39 }[/tex]

Recall that, the perimeter of the square is:

[tex]\mathbf{P_s=4x}[/tex]

So, we have:

[tex]\mathbf{P_s=4 \times 2.39}[/tex]

[tex]\mathbf{P_s=9.56}[/tex]

Hence, 9.56 m of the wire should be used for the square

Read more about maximizing lengths at:

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Answer:

0.036%

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

-1/2m=-18

m=36

answer is D

Answer:

m = 36

Step-by-step explanation:

[tex]\frac{1}{3} m+3-\frac{5}{6}m=-15[/tex]

Combine like terms:

[tex](\frac{1}{3} m+(-\frac{5}{6}m)[/tex]

[tex](\frac{2}{6} m+(-\frac{5}{6}m)[/tex]

[tex]-\frac{3}{6}m = -\frac{1}{2} m[/tex]

[tex]-\frac{1}{2}m+3=-15[/tex]

Subtract 3 from each side:

[tex]-\frac{1}{2}m=-18[/tex]

Multiply each side by -2:

[tex]m = 36[/tex]

Answer:

55/63

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

5 percent * 60 =

(5:100)* 60 =

(5* 60):100 =

300:100 = 3

Answer: 57

Step-by-step explanation:

5% of 60 is 3 and 60-3 is 57

Answer:

D

Step-by-step explanation:

Answer:

$740.86

Step-by-step explanation:

Let me know if you need the steps.

9514 1404 393

Answer:

  40%

Step-by-step explanation:

15 -9 = 6 gallons remain.  The fraction remaining can be expressed as a percentage by multiplying it by 100%.

  fraction remaining = (remaining gallons)/(capacity) = 6/15 = 2/5

  percent remaining = 2/5 × 100% = 40%

Answer:

Step-by-step explanation:

[tex]x^4+7x^2-144=0\\x^4+16x^{2} -9x^{2} -144=0\\x^{2} (x^{2} +16)-9(x^{2} +16)=0\\(x^{2} +16)(x^{2} -9)=0\\(x^{2} -(-16))(x^{2} -3^2)=0\\(x^{2} -16 \iota^2)(x+3)(x-3)=0\\(x^{2} -(4\iota)^2)(x+3)(x-3)=0\\(x+4\iota)(x-4\iota)(x+3)(x-3)=0\\x=\pm4 \iota,\pm3[/tex]

1. Each if them would get 20 fruits

[tex]23 + 37 = 60[/tex]

[tex]60 \div 3 = 20[/tex]

2. There should be 5 rows of tables needed to sit all the invited guests

On every row there would be 26 people, so then we need to divide 130 by 26 and we get 5. Then if we check, 26 times 5 equals 130.

Hope that helped:)

Step-by-step explanation:

the answer is in the image above

Answer:

Step-by-step explanation:

Convert improper fraction to mixed fraction.

[tex]\dfrac{5}{3}=1\dfrac{2}{3}[/tex]

1 2/3 is between 1 and 2. denominator is three. Divide into 3 parts.

Answer:  Choice C

(x, y) → (x – 3, y + 5)

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

Explanation:

The "5 units up" portion means that each y value increases by 5. Therefore, we go from y to y+5. Going from x to x-3 means that we shift each point 3 units to the right.

For example, if the starting point is (1,7), then we have the following steps:

[tex](x,y) \to (x-3,y+5)\\\\(1,7) \to (1-3,7+5)\\\\(1,7) \to (-2,12)\\\\[/tex]

The point (1,7) moves 5 units up and 3 units to the left to arrive at (-2,12).

Note that the order doesn't matter. We could start moving 5 units up, then go 3 units left. Or we could start going 3 units left, then 5 units up. We'll arrive at the same destination.

We want to find the absolute difference between the greatest and the least of 3 consecutive terms of an arithmetic sequence that meet some given criteria. We will get that the difference is 3.88 or 12.88.

We know that the difference between any pair of two consecutive terms in an arithmetic sequence is a constant.

So if that difference is D, we can write 3 consecutive terms as:

A, A + D, A + 2*D

The sum must be equal to 27, then we have:

A + (A + D) + (A + 2*D) = 27

And the sum of their squares is equal to 293, then we have:

A^2 + (A + D)^2 + (A + 2*D)^2 = 293

If we simplify these two equations we get:

3*A + 2*D = 27

3*A^2 + 6*D*A + 5*D^2 = 293

To solve this, we just need to isolate one of the variables in the first equation and then replace that in the other one.

3*A = 27 - 2*D

A = (27 - 2*D)/3 = 9 - (2/3)*D

Replacing that on the other equation we get:

3*(9 - (2/3)*D)^2 + 6*(9 - (2/3)*D)*D + 5*D^2 = 293

Now we can solve this for D:

3*(81 - 2*9*(2/3)*D + D^2) + 54*D - 4*D^2 + 5*D^2 = 293

(243 - 293) + 18*D + 4*D^2 = 0

-50 + 18*D + 4*D^2 = 0

That is just a quadratic equation, the solutions are given by:

[tex]D = \frac{-18 \pm \sqrt{18^2 - 4*4*(-50)} }{2*4} \\\\D = \frac{-18 \pm 33.53}{8}[/tex]

Then we have two possible values for D, we take the positive one to get:

D = (-18 + 33.53)/8 = 1.94

And the difference between the greatest and least of these 3 numbers is twice the common difference, so is equal to 2*D = 2*1.94 = 3.88

If instead we take the other solution, we get:

D = (-18 - 33.53)/8 = -6.44

Then the absolute difference is -2*D = -2*-6.44 = 12.88

If you want to learn more, you can read:

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Answer:

104. Explanation: There are 4 10 s to multiply.

Step-by-step explanation:

Step-by-step explanation:

Given -

x

2

=

8

y

It is a parabola opening up.

The general form of the equation of a parabola opening up is -

x

2

=

4

a

y

9514 1404 393

Answer:

  A) (0, 0)

  B) (1, −25)

  D) (−1, 25)

Step-by-step explanation:

For the point to lie on the line, the y-value must be -25 times the x-value. That is the case for points A, B, D.

Answer:

2

Step-by-step explanation:

Answer:

I think you may have written it down wrong because no solution for that is possible.

Answer:

how is traffic to + 54 degree + 42 degree then that 96 degree - by 180 degree you get you will get 84 degree

Answer:

3 hours and 45 minutes

Step-by-step explanation:

let's assume the tank has a volume of x liters.

let's assume the speed of filling it is x/6 liters per hour for A and x/10 liters per hour for B.

the formula to calculate the time is:

time = volume / speed

If the pumps work together, the total speed is x/6 + x/10, which is 16/60 x

So the time this takes is:

time = x / (16/60 x) = 60/16 hours = 3.75 hours = 3 hours and 45 minutes.

Answer:

.40

Step-by-step explanation:

move the decimal over 2 times

Answer:

40%=0.4

Step-by-step explanation:

Answer:

$0.55 for one can

Step-by-step explanation:

16 cans of lemonade = $8.80

1 can of lemonade = $8.80 / 16 = $0.55

Answer:

Step-by-step explanation:

For the shown triangle we use the tangent of 60° angle to find the value of x:

Angle A and 60° are complementary.

The measure of angle A:

Step-by-step explanation:

[tex] \tan(60) = \frac{x}{14} \\ \\ \sqrt{3} = \frac{x}{14} \\ \\ x = \sqrt[14]{3} [/tex]

the measure of angel A

m < a = 90-60 = 30

nani .-. why tho?

why need followers?

must reason why

Answer:

JUPITER SATURN MARS

Step-by-step explanation:

Answer:

D.    Graph c

Step-by-step explanation:

I got this answer correct on Gradpoint

Answer:

8/3

Step-by-step explanation:

1 foot = 12 inches, so it would be 32/12. After simplifying and dividing 4 on both sides, you would get 8/3.