Use the substitution method to solve the given system of equations. -6y+18=12x and y=3-2x

7% = 0.07

14.50 *1.07 =  15.52 new price

Based on the information given, Pat has 4 more cards than Frank.

The number of cards that Pat has = 9 cards

Number of cards that Steve has = 3 cards

Since Frank has two more cards than Steve, the total number of cards that Frank has will be: = 3 + 2 = 5

In order to know the number of cards that Pat has more than Frank, we will have to calculate the difference between the cards that they've. This will be:

= Pat's card - Frank's card

= 9 - 5

= 4

Therefore, Pat has 4 more cards than Frank.

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Your answer would be, 133.92 my good friend!

Answer: Explanation is given below.

Step-by-step explanation: Given that Patti is using mental mathematics to evaluate the expression (70+12.8+30)+6.1 and recognises that it will be easier to simplify if she can combined 70 and 30 in the beginning. We are to explain the way in which the properties of operation allow Patti to take that approach.

We will be using the following associative property of real numbers:

[tex](a+b+c)+d=(a+c)+(b+d).[/tex]

Therefore, the simplification is as follows:

[tex](70+12.8+30)+6.1\\\\=(70+30)+(12.8+6.1)\\\\=100+18.9\\\\=118.9.[/tex]

Hence explained.

Answer:

She can use the commutative property to rewrite the expression as (70 + 30 + 12.8) + 6.1

( D )

The answer is d

i hope this helps

After the second bounce, the ball will rise to a height of 0.36 meter.

To find the height the ball will rise after the second bounce, we can use the given information that the ball always bounces to 3/5 of the height from which it falls. In this case, the ball falls from a height of 1 meter.

For the first bounce, the ball rises to 3/5 of 1 meter, which is 0.6 meter. For the second bounce, the ball will rise to 3/5 of 0.6 meter. To calculate this, we multiply 3/5 by 0.6 meter, which gives us 0.36 meter.

Therefore, after the second bounce, the ball will rise to a height of 0.36 meter.

The greater than symbol, ">," accurately compares the two fractions because 2/4 > 3/8. They are 2/4 and 3/8, respectively.

something that represents another item. especially: something tangible that denotes or implies something else that is not itself imaginable or demonstrable. The lion is a representation of bravery. an alternative to a word or combination of words, such as a letter, character, or sign.

given

= 2/4 = 0.5

= 3/8 = roughly 0.37

The greater than symbol, ">," accurately compares the two fractions because 2/4 > 3/8.

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Final answer:

To compare 2/4 and 3/8, simplify 2/4 to 1/2, then convert to eighths, resulting in 4/8. Since 4/8 is greater than 3/8, 2/4 is greater than 3/8.

Explanation:

To compare the fractions 2/4 and 3/8, we need to find a common denominator or convert them to a common form such as decimals.

The simplest way is to notice that 2/4 can be simplified to 1/2.

Now, if we convert 1/2 to eighths, we get 4/8 because we multiply both the numerator and denominator by 4 to get the common denominator of 8 (1 x 4)/(2 x 4) = 4/8.

Comparing 4/8 with 3/8, we can see that 4/8 is larger than 3/8, as 4 is greater than 3.

Hence, the correct inequality symbol to compare 2/4 and 3/8 is ">".

According to the transitive property of inequality which states that if a > b and b > c then a > c, if 4/8 > 3/8 and 2/4 is equal to 4/8, then 2/4 > 3/8.

Matt needs to sell approximately 28 books to make $30 for the week.

To find the number of books Matt needs to sell to make $30 for the week, we need to use the given information that Matt gets $6 for selling 9 books and $9 for selling 11 books.

Let's first find the amount of money Matt makes for each book:

For 9 books, Matt makes $6, so he makes $\frac{6}{9} = \frac{2}{3}$ dollars per book.

For 11 books, Matt makes $9, so he makes $\frac{9}{11}$ dollars per book.

Now, we can set up an equation to find the number of books Matt needs to sell to make $30:

2/3 x + 9/11 x=30

where (x) is the number of books Matt needs to sell.

Simplifying the equation, we get:

x = 28

Therefore, Matt needs to sell approximately 28 books to make $30 for the week. Since he cannot sell a fraction of a book, he would need to sell either 28 or 29 books to make $30.

Set the following: Length = L    Width = W

The length is twice the width:    L = 2*W     or:  W = L/2

Perimeter: P = 60ft = 2*L + 2*W

Substituting L for W in the perimeter equation gives:

P = 60ft = 2*L + 2*(L/2) = 2*L + L = 3L

L = 60ft/3 = 20ft    W=L/2=20ft/2=10ft

Verify result:  Perimeter= P = 60ft = 2L + 2W = 2*20ft +2*10ft = 40ft+20ft = 60ft

The area of the rectangular is: Area = A = Length*Width = L*W = 20ft*10ft = 200 (ft)^2

Hopefully This Helps!!

Final answer:

To find the area of a rectangle when the perimeter is given, determine the dimensions using the relationship between length and width and then calculate the area. In this case, the area of the garden is 200 square units.

Explanation:

The length of a rectangle is twice the width. If the perimeter of the rectangle is 60 units, find the area of the garden.

Let the width of the rectangle be x. Therefore, the length is 2x.

The perimeter of a rectangle is given by 2(length + width), which in this case is 2(2x + x) = 60 units.

Solving for x, we get x = 10. Therefore, the width is 10 units and the length is 20 units. The area of the garden is length x width = 20 x 10 = 200 square units.