Kerr is going to pack 9 baby carrots, 12 crackers and 18 grapes into lunch boxes . How many of each food item will there be in a lunch box if she packs the items into the greatest number of indentical lunch boxes

Answer:

When raising an expression of that format to any power, after grouping like terms, you'll always find that the odd numbered terms are positive, and the even numbered terms are negative.

For example:

(x - y)² = x² − 2xy + y²

(x - y)³ = x³ − 3x²y + 3xy² − y³

(x - y)⁴ =x⁴ − 4x³y + 6x²y² − 4xy³ + y⁴

etc.

9514 1404 393

Answer:

  (x, y) = (1, 1)

Step-by-step explanation:

About Algebra

All of Algebra is based on a few simple rules:

When we solve equations by substitution, we make use of these facts.

__

About Substitution

Generally, substitution in equation solving is done for the purpose of eliminating a variable from the equation. That usually means you want to write an expression for one variable in terms of other variables.

Finding the Expression to Substitute

In this set of equations, the variables are x and y. We can substitute for y an expression involving x, or we can substitute for x an expression involving y. These equations are written in such a way that either method works as well as the other.

Let's choose to substitute for y. This means we need an equation of the form ...

  y = <some expression involving x>

The first equation makes it easy to get that. If we add y (to both sides, see rule 3 above), we get ...

  5x -y +y = 4 +y

  5x = 4 + y . . . . . . . . . simplified

Subtracting 4 (from both sides) gets us the form we want.

  5x -4 = 4 -4 + y

  5x -4 = y . . . . . . by rule 4 above, we can use (5x-4) anyplace you see y

Using the Expression to Substitute

Now, we have an expression for y that we can use in the second equation. There, y is multiplied by 4, so we need to be sure to multiply the whole expression by 4:

  -x + 4(5x -4) = 3 . . . . . . substituted for y in the second equation

  -x +20x -16 = 3 . . . . . use the distributive property to eliminate parentheses

  19x -16 = 3 . . . .  . . collect terms

This has a constant (-16) where we don't want it, so we can add 16 (to both sides) to get rid of it.

  19x -16 +16 = 3 +16

  19x = 19 . . . . simplify

Now, we can divide by 19 (to both sides) to get x by itself.

  (19x)/19 = 19/19

  x = 1 . . . . almost done; we still need to find y

Finishing Up

Using the equation for y that we used for substitution, we can find y from our value of x.

  y = 5x -4 = 5×1 -4 = 5-4

  y = 1

So, the solution is x = 1, y = 1, or (x, y) = (1, 1).

_____

Additional comment

In this set of equations, both variables (x and y) appear with coefficients of 1 (actually, -1). This makes it easy to solve for an expression that can be substituted for the variable. In systems of equations that you want to solve by substitution, it usually works well to start by looking for a variable with a coefficient of 1 (or -1). Use that to write the substitution expression as we did here.

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Alternate Solution

If you use a variable with a coefficient other than 1 to write the substitution expression, you end up with fractions. That's OK if you're comfortable with arithmetic using fractions. It generally requires more care.

For example, we could solve the first equation for x:

  x = (4 +y)/5

Substituting that into the second equation gives ...

  -(4 +y)/5 +4y = 3

  -4/5 -y/5 +4y = 3

  (3 4/5)y = 3 4/5 . . . . . add 4/5 (to both sides), collect terms

Now, you get to divide by 3 4/5 to get ...

  y = (3 4/5)/(3 4/5) = 1

Fortunately, in this case, we can see the numerator and denominator are identical, so the division result is 1. If it weren't you'd be faced with dividing mixed numbers--not always a student's first choice of fun math operations.

  x = (4 +1)/5 = 1 . . . . finishing up

Answer:

[tex]m(\widehat{WXZ})[/tex] = 160°

Step-by-step explanation:

By angle sum postulate,

m∠WYX + m∠XYZ = m∠WYZ

m∠WYZ = 50° + 30°

              = 80°

Since, inscribes angle (∠WYZ) = [tex]\frac{1}{2}\times (\text{Intercepted arc WXZ})[/tex]

80° = [tex]\frac{1}{2}(\widehat{WXZ})[/tex]

[tex]m(\widehat{WXZ})[/tex] = 160°

Answer:

10x+12 is the answer in my calculation.

Answer:

i       edgggg   g t   g        h tr  fe erfg bh  hnhy r hrh r    r t hth

Step-by-step explanation:

125 cm ans

may be it is helpful

Answer:

it will be 3/4

Answer:

54.039 in word form is: fifty-four and thirty-nine thousandths.

Step-by-step explanation:

The word "thousandth" represents the order of an element in a set that occupies the position equivalent to the number thousand. In this case, the symbol "." Between the numbers shows us that there is a number in the position equivalent to the number thousand, so we must add the word "thousandth" when the number shown in the question needs to be written in word form. Thus, we can conclude that the correct way to write 54,039 in word form is "Fifty-four and thirty-nine thousandths."

Answer:

Step-by-step explanation:

hblhhbbhbbhubulvt

Equation: 43.22 = 24x + 1.94

43.22 = 24x + 1.94

-1.94                -1.94

41.28 = 24x

/24       /24

1.72 =    x

Answer: $1.72 per bottle of juice

Answer:

3,120,000

there are 52 weeks in a year:

52 x 15 = 780

Now multiply the salary to it:

780 x 4,000 = 3,120,000

I think this is correct

Answer:

d

Step-by-step explanation:

I got it correct so it must be correct

Answer:

b=-4

Step-by-step explanation:

basically divide both sides by 14 which equal -4

The solution to the equation 14b = -56 is b = -4.

To solve the equation 14b = -56 for b, we can divide both sides of the equation by 14 to isolate the variable b.

14b ÷ 14 = -56 ÷ 14

Simplifying:

b = -56 ÷ 14

b = -4

Therefore, the solution to the equation 14b = -56 is b = -4.

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Answer:

i thnk its a...but i could be wrong..

Step-by-step explanation:

Answer:

The answer should be B cuz it's different relationship

Step-by-step explanation:

Answer: 1/2

Step-by-step explanation:

Just remove the negative

Answer:

1. 144 : 16 = 9

2. 13.5 x 17 = 229.5

Answer:

you're correct! the answer is c

Step-by-step explanation:

the factors would be (x+2)(x-3) and when you solve that you get c

Answer:

6

Step-by-step explanation:

-2/100 x x/3

Answer:

The second one is rectangle.

It is because it have the following properties;

1) Opposite side are equal.

2) Opposite angles are equal.

3) Diagonals bisect each other.

4) Diagonals are equal.

5) Each angle is a right angle (90⁰).

I hope this will help you

Answer:

$3701.45. I hope this helps :)

Step-by-step explanation:

Answer:

5.4h-2.7d-15

Step-by-step explanation:

8h minus 6.7d minus 15 plus 4d minus 2.6h

using the knowledge or principle of algebra

5.4h minus 2.7d minus 15

Answer:

Step-by-step explanation:

Answer:

you have to do 52 divided by cos of 38 to get the answer of 65.99ft

Answer:14.37500

Step-by-step explanation:

Answer:

14.375

Step-by-step explanation:

Answer:

Step-by-step explanation:

2.5:3.5 = 1:1.4

1 3/4 : 2 11/12 = 1:5/3

5/3 > 1.4 so megan gets more cookies

so kaitlyn uses more

Answer:

(-2,4)

Step-by-step explanation:

Since this is a system of equations, just look where the two lines intersect.

In this case, the intersecting pair is: (-2, 4)

Answer:

necesito más información

Answer:

(-1,-2)

Step-by-step explanation:

Answer:

it all depends on the length of the adjoining leg

Step-by-step explanation:

Answer:

8. 95

Step-by-step explanation:

The last equation 37 + 58 can be best solved by solving it vertically.  Put 37 and 58 side to side vertically to add easier on a piece of paper.  The first digit answer is 15, carry the 1 to the second digit and add it with 3 and 5.  Your final answer should be 95.

The property that you should use is the Associative Property where you can switch the numbers to put the larger number on top and the smaller number on the bottom.  No matter how it is changed, you should get the right answer.

Answer:

8. 95

Step-by-step explanation:

The point will be inverted when (6,-2) is rotated 90° counterclockwise i.e., the new point will be (-2,6).

It is given that a point (6,-2) is rotated 90° counterclockwise about origin.

We have to find the new point after rotation.

What do you mean by rotation counterclockwise ?

If something is moving counterclockwise that meant it is moving in the opposite direction to the direction in which the hands of a clock move.

As per the question ;

A point (6,-2) is rotated 90° counterclockwise about origin.

Let's assume (6,-2) = (x , y)

If we rotate it 90°counterclockwise ; then the point will be inverted ; i.e.,

(x , y ) ⇒ ( y , x)

So ;

(6 , -2) = (-2,6)

So ;

The new point will be ;

= (-2 , 6)

Thus , the point will be inverted when (6,-2) is rotated 90° counterclockwise i.e., the new point will be (-2,6).

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