Work shown above! Answer would be 2x^2 -16x + 30
Answer:
A.
Step-by-step explanation:
If
AND
y = x + 7, then by the transitive property of equality:
We can solve for the values of x by getting everything on one side of the equals sign and then solving for x:
We can factor out the common x to get:
x(x + 1) = 0
which tells us by the Zero Product Property that either
x = 0 and/or x + 1 = 0 and x = -1
We are expecting 2 solutions for x since this is a second degree polynomial. We will sub both -1 and 0 into y = x + 7 to solve for the corresponding values of y
y = 0 + 7 so
y = 7 and the coordinate is (0, 7)
y = -1 + 7 so
y = 6 and the coordinate is (-1, 6)
It is asking you to find the sum of k^2 - 1 from k=1 to k=4. Since that is only 4 numbers, calculating the sum by hand wouldn’t be that bad.
(1^2 - 1) + (2^2 - 1) + (3^2 - 1) + (4^2 - 1) = 26
The easier way to find the sum is to use a few simple formulas.
When we have a term that is just a constant c, the formula is c*n.
When we have a variable k, the formula is k*n*(n+1)/2.
When we have a squared variable, the formula is k*n*(n+1)*(2n+1)/6.
In this case, we have a squared variable k^2 and a constant of -1.
So plug in n=4 to the formulas:
4*5*9/6 - 1*4 = 26
The answer is 26
Answer: E = 56
Step-by-step explanation:
E is proportional to √C
To remove proportionality, introduce a constant (k).
E = k × √C
From question,
E = 40 and C = 25
So,
40 = k ×√25
40 = k × 5
k = 8
Now,
C = 49
k = 8
E = ?
E = k√C
E = 8 × √49
E = 8 × 7
E = 56
Answer:
Investment A = 3650
Investment B = 1350
Step-by-step explanation:
Given that:
Total interest earned = 332.50
Total Principal invested = 5000
Investment A:
Rate = 8%
Time = 1 year
Principal = a
Interest earned = 0.08a
Investment B:
Rate = 3%
Time = 1 year
Principal = b
Interest earned = 0.03b
a + b = 5000 ____(1)
0.08a + 0.03b = 332.50 - - - (2)
From (1)
a = 5000 - b
Into (2)
0.08(5000 - b) + 0.03b = 332.50
400 - 0.08b + 0.03b = 332.50
400 - 0.05b = 332.50
-0.05b = - 67.5
b = $1350
a = 5000 - b
a = 5000 - 1350
a = $3650
