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audreymarie2940
03.11.2020 •
Mathematics
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 inches of cord for each necklace. Use matrices to find the number of bracelets and the number of necklaces that Philip made.
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Ответ:
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
Using Cramer's rule to solve for x and y,
x = (9 × 5 - 30 × 1) ÷ (1 × 5 - 1 × 2)
x = (45 - 30) ÷ (5 - 2)
x = 15 ÷ 3
x = 5
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.
Ответ:
Answer
The answer is 49 degrees
Explanation
The exterior angle, the angle outside the triangle, it going to equal the angles inside the triangles.
w-19+w=w+30 Combine like term so combine the w's to be 2w
2w-19=w+30 Add 19 to both sides 30+19=49
2w=w+49 Subtract w from both sides 2w-w=w
w=49
To check your work you can plug 49 into w and you get that the angles inside the triangle is 79 and the exterior angle is 79 when you plug back in 79 and 79=79