X² + y² = 225
x - 7y = -75
x = 7y - 75
x² + y² = 225
(7y-75)² + y² = 225
(7y - 75)(7y - 75) + y² = 225
49y² - 525y - 525y + 5625 + y² = 225
50y² - 1050y + 5400 = 0
50(y² - 21y + 108) = 0
y² - 21y + 108 ⇒ (y - 12)(y - 9)
x = 7(12) - 75
x = 84 - 75
x = 9 ⇒ (9,12)
x = 7(9) - 75
x = 63 - 75
x = -12 ⇒ (-12,9)
Answer:
The final cost is 1.07($17.15) = $18.35
Step-by-step explanation:
If the discount is 30%, we can find the discounted price by taking 70% of the original price (since 100% - 30% = 70%). Substitute the equivalent 0.70 to calculate the discount price: 0.70($24.50) = $17.15. This is the discounted price.
The final cost is $17.15 times 1.07, which includes the discounted price plus the 7% tax. That final cost is 1.07($17.15) = $18.35.
Answer:
79 books
Step-by-step explanation:
45% books not returned = 55% books will be returned
145 books currently checked out
55% of 145 = 79.75
since you can't return 3/4 of a book, i would round down to 79.
9514 1404 393
Answer:
a) The new triangle is a reflection of the original across the origin. All angles, segment lengths, and line slopes have been preserved: the transformed triangle is congruent with the original.
b) The new triangle is a reflection of the original across the origin and a dilation by a factor of 2. Angles have been preserved: the transformed triangle is similar to the original. The transformation is NOT rigid.
Step-by-step explanation:
1. The transformed triangle is blue in the attachment. It is congruent with the original. The transformation is "rigid," a reflection across the origin. All angles and lengths have been preserved, as well as line slopes.
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2. The transformed triangle is orange in the attachment. It is similar to the original, in that angles have been preserved and lengths are proportional. It is a reflection across the origin and a dilation by a factor of 2. Line slopes have also been preserved. A dilation is NOT a "rigid" transformation.
In a 30°-60°-90° triangle, the longer leg is √3 times the shorter leg. In your triangle, ...
the shorter leg is 10.