An isosceles triangle in which the two equal sides, labeled a, are longer than the base, labeled b.

Question

This isosceles triangle has two sides of equal length, a, that are longer than the length of the base, b. The perimeter of the triangle is 15.7 centimeters. The equation 2a + b = 15.7 models this information.

If one of the longer sides is 6.3 centimeters, which equation can be used to find the length of the base

Answer 1

To find the length of the base \( b \) of the isosceles triangle when one of the longer sides \( a \) is given to be 6.3 centimeters, you can use the perimeter equation provided:

\[ 2a + b = 15.7 \]

Given that \( a = 6.3 \) centimeters, you can substitute this value into the equation:

\[ 2(6.3) + b = 15.7 \]

Now, calculate \( 2(6.3) \):

\[ 12.6 + b = 15.7 \]

Next, to solve for \( b \), subtract 12.6 from both sides:

\[ b = 15.7 - 12.6 \]

Calculating that gives:

\[ b = 3.1 \]

Thus, the equation you can use to find \( b \) after substituting \( a = 6.3 \) is:

\[ b = 15.7 - 2a \]

In this specific case, it becomes:

\[ b = 15.7 - 12.6 \]

Resulting in \( b = 3.1 \) centimeters.

Answer 2

This isosceles triangle has two sides of equal length, a, that are longer than the length of the base, b. The perimeter of the triangle is 15.7 centimeters. The equation 2a + b = 15.7 models this information.

If one of the longer sides is 6.3 centimeters, which equation can be used to find the length of the base?

12.6 + b = 15.7 <------

An isosceles triangle in which the two equal sides, labeled a, are longer than the base, labeled b.
This isosceles triangle has two sides of equal length, a, that are longer than the length of the base, b. The perimeter of the triangle is 15.7 centimeters. The equation 2a+b=15.7 can be used to find the side lengths.

If one of the longer sides is 6.3 centimeters, what is the length of the base?

cm

Answer 3

To find the length of the base \( b \) of the isosceles triangle when one of the equal sides \( a \) is given as 6.3 centimeters, we can start with the perimeter equation:

\[ 2a + b = 15.7 \]

Substituting \( a = 6.3 \) cm into this equation:

1. Calculate \( 2a \): \[ 2(6.3) = 12.6 \]

2. Substitute this back into the equation: \[ 12.6 + b = 15.7 \]

3. To isolate \( b \), subtract 12.6 from both sides: \[ b = 15.7 - 12.6 \]

4. Calculate the value of \( b \): \[ b = 3.1 \]

So, the length of the base \( b \) is 3.1 centimeters.

Answer 4

Hugh bought some magazines that cost $3.95 each and some books that cost $8.95 each. He spent a total of $47.65. Let m represent the number of magazines and b represent the number of books. Which equation models the situation?
m+b=47.95
m+b=60.55
3.95m+8.95b=47.65
8.95m+3.95b=47.65

Answer 5

To model the situation where Hugh bought magazines and books with the respective costs and total expenditure, we need to represent it with an equation that encompasses both types of items he purchased.

Let:

• \( m \) = the number of magazines
• \( b \) = the number of books

The cost for each magazine is $3.95, and the cost for each book is $8.95. Therefore, the total cost for the magazines and books can be expressed with the equation:

\[ 3.95m + 8.95b = 47.65 \]

This equation shows the total amount spent on magazines and books, which is equal to $47.65.

Hence, the correct equation that models the situation is:

\( 3.95m + 8.95b = 47.65 \).

Answer 6

Hugh bought some magazines that cost $3.95 each and some books that cost $8.95 each. He spent a total of $47.65. If Hugh bought 3 magazines, how many books did he buy?

The equation that models the problem is 3.95m + 8.95b = 47.65, where m is the number of magazines and b is the number of books.

books

Answer 7

Given the equation that models the problem:

\[ 3.95m + 8.95b = 47.65 \]

You mentioned that Hugh bought 3 magazines, so we can substitute \( m = 3 \) into the equation:

\[ 3.95(3) + 8.95b = 47.65 \]

Now, calculate \( 3.95(3) \):

\[ 3.95 \times 3 = 11.85 \]

Now the equation will look like this:

\[ 11.85 + 8.95b = 47.65 \]

Next, subtract \( 11.85 \) from both sides to isolate the term with \( b \):

\[ 8.95b = 47.65 - 11.85 \]

Calculating the right side gives:

\[ 8.95b = 35.80 \]

Now, divide both sides by \( 8.95 \) to solve for \( b \):

\[ b = \frac{35.80}{8.95} \]

Calculating that gives:

\[ b \approx 4 \]

Therefore, Hugh bought 4 books.

Answer 8

A 2 column table with 5 rows. The first column, yards of red fabric, x, has the entries 1, 2, 3, 4. The second column, yards of blue fabric, y, has the entries 27, 26, 25, 24.
Sophie is buying fabric to make items for a craft fair. The table shows some combinations of how much of each color fabric she might buy. Which equations model the total yards of fabric Sophie will buy? Check all that apply.

x+y=28
28+x=y
x-y=28
28-x=y
28-y=x

Answer 9

To determine which equations model the total yards of fabric Sophie will buy, let's analyze the provided data from the table. The first column represents yards of red fabric (denoted as \( x \)), and the second column represents yards of blue fabric (denoted as \( y \)).

The table entries are as follows:

| Yards of Red Fabric (x) | Yards of Blue Fabric (y) | |--------------------------|--------------------------| | 1 | 27 | | 2 | 26 | | 3 | 25 | | 4 | 24 |

From this data, we can observe that the total quantity of fabric Sophie is buying seems to be \( 28 \) yards for each combination of \( x \) and \( y \):

\[ x + y = 28 \]

Now let's examine the other equations provided:

1. \( x + y = 28 \):

   • This equation is correct as it directly reflects that the total yards of red and blue fabric combined is 28 yards.

2. \( 28 + x = y \):

   • This equation is incorrect. It suggests that the yards of blue fabric are 28 plus the yards of red fabric, which does not match the table.

3. \( x - y = 28 \):

   • This equation is also incorrect, as it suggests that the yards of red fabric exceed the yards of blue fabric by 28, which is not represented in the table.

4. \( 28 - x = y \):

   • This equation is correct because it implies that the yards of blue fabric equals 28 minus the yards of red fabric, which fits with the combinations presented in the table.

5. \( 28 - y = x \):

   • This equation is also correct, as it implies that the yards of red fabric equals 28 minus the yards of blue fabric, consistent with the data provided.

Summary of Correct Equations:

• \( x + y = 28 \)
• \( 28 - x = y \)
• \( 28 - y = x \)

Thus, the equations that correctly model the total yards of fabric Sophie will buy are:

1. \( x + y = 28 \)
2. \( 28 - x = y \)
3. \( 28 - y = x \)