Answer:
Step-by-step explanation:
1. Find two numbers that add to make the coefficient of x (in this case, -5) and that multiply to make the constant term multiplied by the coefficient of x^2 (in this case, -2 x 3 = -6)
Two numbers that work are -6 and +1
-6 x +1 = -6
-6 + -1 = -5
2. Split the middle term into the two numbers that you found.
3x^2 -6x +x -2 = 0
I've put the -6 on the left side because in our next step, when we factorise, it will be easier than having the numbers the other way around.
3. Factorise the left side by taking out common factors from each pair. The pairs I'm talking about here are '3x^2 and -6x', and 'x and -2'
3x (x-2) +1 (x-2) = 0
4. You now have two numbers both being multiplied by the term x-2. We can rearrange this equation to give us two brackets being multiplied by each other.
(3x + 1) (x-2) = 0
5. According to the Null Factor Law, if two terms are multiplied together and the result is 0, then one of those terms must be 0. Make both terms equal to 0 and solve each for x.
3x + 1 = 0 x-2 = 0
3x = -1 x = 2
x = -1/3
6. The solutions to this equation are x = 2 and x = -1/3
Subtract 7a from both sides giving you 10=-5a and divide everything by 5. This gives you a=-2
Answer:
Yes it is a right angled triangle
Step-by-step explanation:
If its a right triangle it would satisfy the Pythagoras theorem.
29.3^2 = 858.49
28.5^2 = 812.25
6.8^2 = 46.24
Adding the last 2 values:
812.25 + 46.24
= 858.49
So YES.
Answer:
Kindly check explanation
Step-by-step explanation:
Given the following :
Population mean (μ) = 2.55
Population standard deviation (σ) = 0.5
Sample size (n) = 30
Sample mean (x) = 2.76
α = 0.05
STEP 1:
Stress score in general executive (s1)
Stress score in exercising executive (s2)
Null : s1 = s2
Alternative : s1 < s2
STEP 2:
Shape of distribution = normal
Population mean (μ) = 2.55
Population standard deviation (σ) = 0.5
Sample size (n) = 30
Sample mean (x) = 2.76
α = 0.05
Decision rule :
α = 0.05 which corresponds to a t score (t0) ;
df = n - 1 = 30 - 1= 30 at 0.05 = 1.699
If :
(Test statistic (t) > t0) ; reject the Null
(right tailed test)
Test statistic (t) :
(x - μ) / (σ/√n)
(2.76 - 2.55) / (0.5/√30)
0.21 / 0.0913
= 2.30
t > t0
2.30 > 1.699
t is more extreme than t0
Hence, reject the null at α = 0.05
Answer:
8.66 meters
Step-by-step explanation:
Assuming that the building is completely straight, a right angle is formed and therefore a right triangle.
Thanks to this we can calculate the height at which the ladder reaches the wall using the Pythagorean theorem, this height being one of the legs.
We have to:
c ^ 2 = a ^ 2 + b ^ 2
c = 10
a = 5
replacing
b ^ 2 = 10 ^ 2 - 5 ^ 2
b ^ 2 = 75
b = 8.66
that is to say that the height at which the ladder reaches the wall is 8.66 meters
