During the summer, you had an ice cream cone with
your friends almost every day. Your parents bought
a half gallon of ice cream for $4.75. It was on
Sale for 15% off. What was the sale price?

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:

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:

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:

sinθ = [tex]\frac{8}{10}[/tex]

Step-by-step explanation:

sinθ = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{8}{10}[/tex]

Answer:

sin theta=p/h

=BC/AC

=8cm/10cm

=4cm/5cm

Hope it helps you.

Answer:

1. 144 : 16 = 9

2. 13.5 x 17 = 229.5

Answer:

it will be 3/4

Answer:

10x+12 is the answer in my calculation.

Answer: B. 2y3 + 5y2 – 5y

Step-by-step explanation: From the expression 2y3 + 5y2 – 5y, the highest degree of the polynomial is 3. Hence, 2y3 + 5y2 – 5y is a polynomial with a degree of 3.

Answer:

the person on top is right its B

Step-by-step explanation:

but i got it because the assignment on edge said it's right

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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Answer:

81

Step-by-step explanation:

8^2 + 2 * 8 + 1

= 64 + 16 + 1

= 80 + 1

= 81

Answer:

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

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.

Answer:

$3701.45. I hope this helps :)

Step-by-step explanation:

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:

necesito más información

Answer:

(-1,-2)

Step-by-step explanation:

Answer:

a) [tex]5\sqrt{3} + 3\sqrt{5}[/tex]

b) [tex]4(\sqrt{2} + \sqrt{7})[/tex]

Step-by-step explanation:

a) [tex]9\sqrt{3} - 4\sqrt{3} +\sqrt{5} + 2\sqrt{5}[/tex]

Taking √3 & √5 common respectively,

[tex]=> \sqrt{3} (9 - 4) + \sqrt{5} (1 + 2)[/tex]

[tex]=> 5\sqrt{3} + 3\sqrt{5}[/tex]

b) [tex]10\sqrt{2} + 4\sqrt{7} - 6\sqrt{2}[/tex]

Taking √2 common ,

[tex]=> \sqrt{2} (10-6) + 4\sqrt{7}[/tex]

[tex]=> 4\sqrt{2} + 4\sqrt{7}[/tex]

Taking 4 common ,

[tex]=> 4(\sqrt{2} + \sqrt{7})[/tex]

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: 1/2

Step-by-step explanation:

Just remove the negative

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 :

Sum = 2x-7 + (-2x) and equivalent expression = -7

Step-by-step explanation:

First number is (2x-7) and other number is opposite of 2x i.e. (-2x).

We need to write the sum of 2x - 7 and the opposite of 2x

Opposite of 2x is (-2x)

Sum means to add the number :

2x-7 + (-2x)

Removing parentheses,

2x-7 - 2x

Taking like terms together,

2x-2x-7= 0-7

= -7

Hence, the answer is -7.

Answer:

[tex]5 \sqrt{5} - 2 \sqrt{5} = 3 \sqrt{5} \\ 8 \sqrt{7} + 3 \sqrt{7} = 11 \sqrt{7} [/tex]

hope this helps.

Answer:

[tex]11 \sqrt{7} [/tex]

Step-by-step explanation:

[tex]8 \sqrt{7} + 3 \sqrt{7} [/tex]

[tex] \sqrt{7} (8 + 3) [/tex]

[tex]11 \sqrt{7} [/tex]

Answer:

5

Step-by-step explanation:

Hence, the average speed to the cyclist is 16mph.

Speed is defined as the rate of change of position of an object in any direction. Speed is measured as the ratio of distance to the time in which the distance was covered. Speed is a scalar quantity as it has only direction and no magnitude.

We know,

distance covered = 4 miles

time taken = 15 minutes = [tex]\frac{1}{4}[/tex]hours

speed = [tex]\frac{4}{\frac{1}{4} }[/tex] = 16

Hence, speed is 16.

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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:

Answer:14.37500

Step-by-step explanation:

Answer:

14.375

Step-by-step explanation:

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."