The tables show the cat population on two islands over several years. Describe

Philip made a total of 9 bracelets and necklaces from 120 inches of cord. He used 8 inches of cord for each bracelet and 20 inch

Viktor [21]

Answer:

So Philip made 5 bracelets and 4 necklaces.

Step-by-step explanation:

Let x = number of bracelets and y = number of necklaces.

Since we have a total of 9 bracelets and necklaces,

x + y = 9 (1)

Also, we have 8 inches of cord for each bracelet and 20 inches of cord for each necklace, then the total length for the bracelet is 8x and that for the necklace is 20y.

So, the total length for both is 8x + 20y. Since the total length of cord used is 120 inches,

8x + 20y = 120 (2)

Simplifying it we have

2x + 5y = 30 (3).

Writing equations (1) and (3) in matrix form, we have

$\left[\begin{array}{ccc}1&1\\2&5\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}9\\30\end{array}\right]$

Using Cramer's rule to solve for x and y,

$x = det \left[\begin{array}{ccc}9&1\\30&5\end{array}\right] /det \left[\begin{array}{ccc}1&1\\2&5\end{array}\right] \\$

x = (9 × 5 - 30 × 1) ÷ (1 × 5 - 1 × 2)

x = (45 - 30) ÷ (5 - 2)

x = 15 ÷ 3

x = 5

$y = det \left[\begin{array}{ccc}1&9\\2&30\end{array}\right] /det \left[\begin{array}{ccc}1&1\\2&5\end{array}\right] \\$

y = (30 × 1 - 9 × 2) ÷ (1 × 5 - 1 × 2)

y = (30 - 18) ÷ (5 - 2)

y = 12 ÷ 3

y = 4

So Philip made 5 bracelets and 4 necklaces.

3 0

3 years ago

What is i^84? a) -i b) i c) -1 d) 1

mariarad [96]

Answer:

D) 1

Step-by-step explanation:

When you start raising i to certain powers, you begin to notice a pattern.

$i^1=i \\\\i^2=-1 \\\\i^3=-i \\\\i^4=1 \\\\i^5=i \\\\ i^6=-1 \\\\ i^7=-i \\\\i^8= 1$

This cycle repeats forever. Since 84 is a multiple of 4, i^84 must be 1. Hope this helps!

7 0

4 years ago

What is w-4>9 written on a number line?

Aleksandr-060686 [28]

There would be an open circle on positive 12 with the arrow moving to the right.

7 0

3 years ago

Rahul solved the equation 2(x – ) – 2 left-parenthesis x minus StartFraction 1 Over 8 EndFraction right-parenthesis minus StartF

Ghella [55]

Rahul use addition property of equality in step 2.

Solution:

The image of the question is attached below.

Step 1:

$$2 x-\frac{1}{4}-\frac{3}{5} x=\frac{55}{4}$

combine like terms together.

$$2 x-\frac{3}{5} x-\frac{1}{4}=\frac{55}{4}$

To make the denominator same multiply and divide 2x by 5.

$$\frac{10}{5} x-\frac{3}{5} x-\frac{1}{4}=\frac{55}{4}$

Step 2:

$$\frac{7}{5} x-\frac{1}{4}=\frac{55}{4}$

By addition property of equality, add $\frac{1}{4}$ on both side of the equation.

$$\frac{7}{5} x-\frac{1}{4}+\frac{1}{4}=\frac{55}{4}+\frac{1}{4}$

Step 3:

$$ \frac{7}{5} x=\frac{56}{4}$

Step 4:

Multiply by $\frac{5}{7}$ on both side of the equation.

$x=10$

Hence Rahul use addition property of equality in step 2.

3 0

3 years ago

Read 2 more answers

The volume of a cylinder with base radius 3 cm in height 6 cm is what cubic centimeters

Sindrei [870]

Answer:

22/7 * 3 * 3 * 6 ~ 169.65 cubic centimeters

5 0

3 years ago