#1) A gold bracelet that sells for $320 is on sale for 40% off. One way to find the amount by which the regular price is reduced is to multiply $320 by
a) 3/10
b) 2/5
c) 3/5
d) 5/8
#2) A triangle can have sides whose lengths are 9 cm, 16 cm, and
a) 7 cm
b) 8 cm
c) 25 cm
d) 26 cm
1. 40%/100% = 40/100 = 2/5.
2. The largest side should be less than the sum of the two smaller sides:
9cm, 16cm, and 8cm.
16 < 9 + 8.
#1) To find the amount by which the regular price is reduced, we need to calculate 40% of the regular price.
The regular price of the gold bracelet is $320.
To find 40% of $320, multiply $320 by 40/100 (which is the same as 0.40).
This can be done by multiplying $320 by 0.40:
$320 * 0.40 = $128
So, the amount by which the regular price is reduced is $128.
Therefore, the correct answer is (a) 3/10, since 40% is equivalent to 3/10.
#2) To determine if a triangle can have sides whose lengths are 9 cm, 16 cm, and x cm, we can apply the triangle inequality theorem.
According to the triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the remaining side.
In this case, the triangle has sides of 9 cm and 16 cm. Let's see if we can find a value for x that satisfies the triangle inequality.
9 + 16 > x
25 > x
Therefore, the length of the third side (x) must be less than 25 cm.
Among the given options, the only value that satisfies this condition is (a) 7 cm.
So, the correct answer is (a) 7 cm.