yeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeetStep-by-step explanation:
.
<u>Part 1</u>
The gradient of the line is , so the equation is .
This means the system is
<u>Part 2</u>
Substituting in the coordinates (-3,11) and (2,1) into the equation of the parabola,
Subtracting the equations, we get 10=5a, and thus a = 2
Substituting a = 2 back into the system, we get b = -7
<u>Part 3</u>
The equation of the parabola is , and the turning point is at . Therefore, the value of y is -7
Answer:
16 months faster
Step-by-step explanation:
Answer:
σ =2√2 .....
Step-by-step explanation:
Lets find the mean first
mean = 2+4+6+8+10/5
m = 30/5
m = 6
σ =√1/5[(2-6)²+(4-6)²+(6-6)²+(8-6)²+(10-6)²]
σ = √1/5[(-4)²+(-2)²+(0)²+(2)²+(4)²]
σ=√1/5[(16+4+0+4+16)]
σ = √1/5(40)
σ = √8
Take the square root of 8.
σ =2√2 .....
Answer:
Step-by-step explanation:
<h3>Given</h3>
<u>Inequality</u>: (x-1)(x+2)(2x-7)≤0
<h3>Solution: </h3>
<u>If we solve the corresponding equation (x-1)(x+2)(2x-7)²= 0, we get roots </u>
<u>We need to consider the following 4 intervals: </u>
- (−∞; −2), [−2; 1], (1; 3.5), (3.5; ∞)
<u>1st interval</u> (−∞; −2)
- The expression (x-1)(x+2)(2x-7)² is positive as two of the multiples are negative and one is always positive (square number), and therefore does not satisfy the inequality.
<u>2nd interval</u> [−2; 1]
- The expression is negative as only one of the multiples is negative, and therefore the interval (−1; 2) satisfies the inequality.
<u>3rd interval</u> (1; 3.5)
- The expression is positive as all the multiples are positive. Therefore, the interval (1; 3.5) also does not satisfy the inequality.
<u>4th interval</u>
- The expression is positive as above, and therefore also does not satisfy the inequality.
<u>So, the answer to the inequality is:
</u>