Answer:
x = 2 ±i
Step-by-step explanation:
x^2 = 4x-5
Subtract 4x from each side
x^2 - 4x = 4x-5 -4x
x^2 - 4x= -5
Complete the square
Take the coefficient of the x term, divide by 2 and square it
-4/2 =2 2^2 =4
Add 4 to each side
x^2 -4x+4 = -5 +4
The left side is (x-coefficient of the x term/2)^2
(x-2)^2 = -1
Take the square root of each side
sqrt((x-2)^2) = sqrt(-1)
x-2 = ±i
Add 2 to each side
x-2+2 = 2 ±i
x = 2 ±i
Answer:
a. f(-1)=12
b. f(2t)=16t²-6t+5
c. f(t-2)=4t²-19t+27
Step-by-step explanation:
For a, b, c, we are given an input. We plug that into f(x) to find our answers.
a. f(-1)=12
f(-1)=4(-1)²-3(-1)+5
f(-1)=4+3+5
f(-1)=12
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b. f(2t)=16t²-6t+5
f(2t)=4(2t)²-3(2t)+5
f(2t)=4(4t²)-6t+5
f(2t)=16t²-6t+5
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c. f(t-2)=4t²-19t+27
f(t-2)=4(t-2)²-3(t-2)+5
f(t-2)=4(t²-4t+4)-3t+6+5
f(t-2)=4t²-16t+16-3t+6+5
f(t-2)=4t²-19t+27
Answer:
1. $686.94
2. $735.03
3. $10707.55
4. $17631.94
5. $19635.72
Step-by-step explanation:
1st Question:
The interest rate is 7% for each year. This means that each year the person has to pay 7% more than the previous amount. So we need to multiply the initial amount by (0.07+1=1.07) in order to get the interest for the first year. if we want to find the second year's interests then we will have to multiply 2 (1.07)'s and so on.
in this case our function is: 600*(1.07)^t=P(t)
when t=2 P(2)=600*(1.07)^2=$686.94
2nd Question:
Function: 600*(1.07)^t=P(t)
when t=3 P(3)=600*(1.07)^3=$735.03
3rd Question:
initial value=$8500
1+0.08=1.08
Function: 8500*(1.08)^t=P(t)
t=3
P(3)=8500*(1.08)^3=$10707.55
4th Question:
initial value=$12000
1+1.08=1.08
t=5
Function: P(t)=12000*(1.08)^t
P(5)=12000*(1.08)^5=$17631.94
5th Question:
Function: 14000*(1.07)^t=P(t)
P(5)=14000*(1.07)^5
P(5)=$19635.72
Angles in straight line add to 180 degrees
180-142=38
180-133=47
180-38-47=95
180-95=85 degrees
B
