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icang [17]
3 years ago
7

Question 1

Mathematics
1 answer:
timofeeve [1]3 years ago
6 0

Answer:

4(xy + w + z)

Step-by-step explanation:

The expression to be factored is:

          4xy + 12w + 12z

Factoring an equation involves taking out common terms from the expression that will then make it more simpler and simplified.

To solve this problem, we need to find the factors of the given terms:

            4xy

            12w

            12z

The numbers given as coefficients of the variables are;

                       4            12               12

A factor is any integer that divides a number evenly;

             Factors of 4 are 1, 2 and 4

                              12 are 1, 2,3,4,6 and 12

The common factors between 4 and 12 are those numbers that can divide both digits:

      These are  1, 2, and 4, they are common to both

Now, the greatest common factor is the highest of this factors which is 4

 Therefore, the greatest common factor of 12 and 4 is 4

Also, xy, w and z has no common factors

Factoring

                 4xy + 12w + 12z  = 4(xy + w + z)

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What amount of a 40% acid solution must be mixed with 200 mL 10% solution to produce a 20% solution?
vaieri [72.5K]

Answer:

Step-by-step explanation:

(x + 200)20 = 200(10) + x(40)

20x + 4000 = 2000 + 40x

2000 = 20x

X = 100 mL

8 0
2 years ago
HELP PLEASE! Can you please explain so I can understand how it was completed?
nlexa [21]

Answer:

(3 square root of 2 , 135°), (-3 square root of 2 , 315°)

Step-by-step explanation:

Hello!

We need to determine two pairs of polar coordinates for the point (3, -3) with 0°≤ θ < 360°.

We know that the polar coordinate system is a two-dimensional coordinate. The two dimensions are:

  • The radial coordinate which is often denoted by r.
  • The angular coordinate by θ.

So we need to find r and θ. So we know that:

r=\sqrt{x^{2}+y^{2}}       (1)

x = rcos(θ)                                   (2)

x = rsin(θ)                                    (3)

From the statement we know that (x, y) = (3, -3).

Using the equation (1) we find that:

r=\sqrt{x^{2}+y^{2}}=\sqrt{3^{2}+(-3)^{2}} = 3\sqrt{2}

Using the equations (2) and (3) we find that:

3 = rcos(θ)

-3 = rsin(θ)

Solving the system of equations:

θ= -45

Then:

r = 3\sqrt{2}[/tex]

θ= -45 or 315

Notice that  there are two feasible angles, they both have a tangent of -1. The X will take the positive value, and Y the negative one.

So, the solution is:

(3 square root of 2 , 135°), (-3 square root of 2 , 315°)

4 0
3 years ago
Priya is hosting a poetry club meeting this week and plans to have fruit punch and cheese for the meeting. She is preparing 8 ou
Sveta_85 [38]

Answer:

b= $3.99×2 + $2.50= $10.48

Step-by-step explanation:

We have the following unknowns:

p: number of people in the club

f: ounces of fruit punch

c: ounces of cheese

b: budget in dollars

We know that

p=12

Priya is preparing 8 ounces of fruit punch per person, so:

f= 8×p = 8×12 = 96

We need 96 ounces of fruit punch

Priya is preparing 2 ounces of cheese per person, so:

c= 2×p = 2×12 = 24

We need 24 ounces of cheese

A package of cheese contains 16 ounces and costs $3.99. In order to get all the cheese we need, Priya have to buy 2 packages of cheese.

2×16=32

32>24

A one-gallon jug of fruit punch contains 128 ounces and costs $2.50. Then, Priya have to buy only one gallon jug.

128>96

The budget would be:

b= $3.99×2 + $2.50×1

3 0
3 years ago
493,295. <br><br> And the first nine is the number of rounding
evablogger [386]

Answer:

490,000

Step-by-step explanation:

since 9 is the number we are rounding we look at the next number to the right and either we round up or down depending upon that number. since it is a 3 we round down but if it was a 5 or higher that number would be 500,000

8 0
3 years ago
Read 2 more answers
Hiiii!
fenix001 [56]

Answer:

100,000,000

Step-by-step explanation:

You can just add up the zeros, if that makes sense.

5 0
3 years ago
Read 2 more answers
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