Answer:
Step-by-step explanation:
Side A is the longest side
Side B is half of A = A/2
Side C is 8m less than A = A-8
Perimeter of traingle = A+B+C
52 = A + A/2 + A-8
Collect like terms
52+8= A+A/2+A
60 = 5/2 A
Divide 60 by the coefficient of A
60÷5/2 = A
60×2/5= A
A=24m
Substitute the value of A into the expressions for sides B and C
Side B =A/2=24/2=12m
Side C =A-8=24-8=16m
The sides of the triangle are 24m, 12m and 16m
Answer:
Therefore the solution is = k{-7,5,1} where k ∈R
Step-by-step explanation:
Given that,
f₁(x) =x
f₂(x)= x²
f₃(x)= 7x - 5x²
Also,
g(x) = c₁f₁(x)+c₂f₂(x)+c₃f₃(x)
Putting the values of f₁(x), f₂(x) and f₃(x).
g(x) = c₁.x+c₂x²+c₃(7x-5x²)
Given condition that g(x)= 0
∴ c₁.x+c₂x²+c₃(7x-5x²)=0
⇒(c₁+7c₃)x +(c₂-5c₃)x² = 0
Comparing the coefficients of x and x²
∴c₁+7c₃=0 and c₂-5c₃ =0
Let c₃= k [k∈R]
Then c₁ = -7k and c₂=5k
Therefore the solution is = { c₁,c₂,c₃}
= {-7k, 5k, k}
=k{-7,5,1}
Answer:
1a) t = 0.17b
1b) $36.03
2) 51,167.50
Step-by-step explanation:
1a) 17% converted to a decimal (divide by 100) = 0.17. Multiply that by the amount of the bill (before tipping) to get the amount of the tip
1b) The bill of $248 represents the entire bill (100%) plus the tip amount (17%) which makes 117%. As a decimal, this is 1.17.
To find what the cost was without the tip, divide the bill total by 1.17
248/1.17 = 211.97. That was the bill before the tip was added.
248-211.97 = 36.03 was the tip added.
2) 5.5% converted to a decimal is 0.055
0.55 x 48,500 = 2667.50
$2,667.50 + $48,500 = 51,167.50
Or, you can use what we did in 1b, and his new salary is 1.055 times 48,500
1.055 x 48,500 = 51,167.50
Answer:
The temperature changed by 
overnight.
The temperature changed by 
overnight each hour.
Step-by-step explanation:
Given that:
Temperature at 7 PM last night = 
Temperature at 7 AM the next morning = 
a. The change in temperature from 7 PM to 8 AM = Temperature at 7 AM - Temperature at 7 PM
Negative sign indicates that the temperature has decreased.
b. Change in temperature each hour:
Divide the Change in temperature with the number of hours.
Negative sign indicates that the temperature has decreased.
