An expression has numbers, variables, and mathematical operations. The equation that must be true so that x²+mx+m is a perfect square trinomial is x²+mx+m=(x+2)².
<h3>What is an Expression?</h3>
In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
A perfect square trinomial is in the form (a+b)²=a²+b²+2ab. If we compare the perfect square trinomial x²+mx+m, we will get that the value of m should be such that it satisfies the equation 
. Since there is only one value that can satisfy this equation that is 2.
Therefore, the equation that must be true so that x²+mx+m is a perfect square trinomial is x²+mx+m=(x+2)².
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Answer:
Step(iii)
The value of 'f' = 3
Step-by-step explanation:
<u><em>Step(i):-</em></u>
Given - 12 = 4(f-6)
Multiply
- 12 = 4 f - 24
<u><em>Step(ii):-</em></u>
- 12 = 4 f - 24
Adding '12' on both sides, we get
- 12 + 12 = 4 f - 24 + 12
0 = 4 f - 12
4f - 12 =0
4 f = 12
<u><em>Step(iii):</em></u>-
Dividing '4' on both sides, we get
f = 3
Answer:
The dishwasher will use 80 gallons of water to wash 10 loads of dishes.
Step-by-step explanation:
Given,
Water used for 4 loads of dishes = 32 gallons
Ratio of water used to load of dishes = 32:4
Let,
x represents the gallons of water required for 10 loads of dishes.
Ratio of water used to load of dishes = x:10
Using proportion
Ratio of water used to load of dishes :: Ratio of water used to load of dishes
Product of mean = Product of extreme
Dividing both sides by 4
The dishwasher will use 80 gallons of water to wash 10 loads of dishes.
Answer:
r = 12.89
Step-by-step explanation:
18(2) + 15(3) = 81 = C
C = 2πr
81 = 2πr
81/2 = πr
r = 81/2π ≈ 12.89
