These triangles are congruent by AAS condition hence the statement is true
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SR = 450
<span>S = 450/R </span>
<span>(S - 3)(R + 5) = 450 </span>
<span>(450/R - 3)(R + 5) = 450 </span>
<span>(450 - 3R)(R + 5) = 450R </span>
<span>450R + 2250 - 3R^2 - 15R = 450R </span>
<span>3R^2 + 15R - 2250 = 0 </span>
<span>R^2 + 5R - 750 = 0 </span>
<span>R^2 + 30R - 25R - 750 = 0 </span>
<span>R(R + 30) - 25(R + 30) = 0 </span>
<span>(R + 30)(R - 25) = 0 </span>
<span>R ∈ {-30,25}
</span>
<span>Only positive numbers make sense in this context, therefore R = 25.</span>
Answer: 30 baskets.
<u>Step-by-step explanation:</u>
You need to find the Greatest Common Factor (GCF).
240 (apples) = 2 x 2 x 2 x 2 x 3 x 5
150 (pears) = 2 x 3 x 5 x 5
GCF (240, 150) = 2 x 3 x 5
= 30
You can make 30 baskets containing 240/30 = 8 apples and 150/30 = 5 pears.
Answer: a) 278382 oz
b) 43 oz
c) 64.1 oz
Step-by-step explanation:
a) 8 T. 1,398 lb. 14 oz. × 6
First we need to change it in 'oz'.
As we know that
so, it becomes,
8 T. 1,398 lb. 14 oz. × 6 becomes
b) 349 lb. 6 oz. ÷ 130
It becomes,
c) 6 T. 294 lb. ÷ 3,071
First it becomes,
At last it becomes,
Hence, a) 278382 oz
b) 43 oz
c) 64.1 oz
The volume of the removed portion is 35 cm³.
Step-by-step explanation:
Given,
The length× width× height (L×B×H) of the outer part = 3 cm×3 cm×7 cm
The length× width× height (l×b×h) of the inner part = 2 cm×2 cm×7 cm
To find the volume of the removed portion.
Formula
The volume of the removed portion = volume of outer part - volume of inner part
Volume of rectangular prism = l×b×h
Now,
Volume of outer part = 3×3×7 cm³ = 63 cm³
Volume of inner part = 2×2×7 cm³ = 28 cm³
Hence,
The volume of the removed portion = 63-28 cm³ = 35 cm³
