Answer:
9. 6k + 5 and 2k - 1.
10. 5√2 .
Step-by-step explanation:
9. Area = 12k^2 + 4k - 5
Factoring:
12k^2 - 6k + 10k - 5
= 6k(2k - 1) + 5(2k - 1)
= (6k + 5)(2k - 1)
So the required lengths are 6k + 5 and 2k - 1.
10. The ratio of a leg to the hypotenuse is 1: √2 so if the hypotenus = 10 the length of a leg is 10 / √2
= 10 √2 / 2
= 5√2 .
The area is equal to 230 CM.
area for rectangle :
area = width times length
area = 7 x 20 = 140CM
area for triangle:
area = 1/2 times base times height
area = 1/2 x 20 x 9 = 90CM
ADD:
140+90 = 230 CM
Answer:
x = 7
Step-by-step explanation:
y = (x – 7)^2 – 3
This equation is in vertex form
y = a(x-h)^2 +k
where (h,k) is the vertex
For a vertical parabola, the line of symmetry is x=h
x = 7
Answer:
Step-by-step explanation:
You are to make 5 assemblies.
Each assembly requires the use of 1 Type A bolt.
To make the 5 assemblies, you need 5 Type A bolts.
The container of bolts has a total of 60 bolts.
The focus - Type A bolts - is 20 out of this 60.
The probability of obtaining a Type A bolt at all, is 20/60, which is = 1/3
(A) What is the probability of taking the exact number of Type A bolts you need for your 5 assemblies, if you randomly take 10 bolts from the container?
- The exact number of Type A bolts you need for the 5 assemblies is 5
1/3 × 5/10 = 5/30 = 1/6 = 0.167
(B) What is the probability of taking/having less than 5 Type A bolts out of the randomly selected 10 bolts? The solution is to sum up the following:
1/3 × 4/10 = 0.133
1/3 × 3/10 = 0.1
1/3 × 2/10 = 0.067
1/3 × 1/10 = 0.033
1/3 × 0/10 = 0
TOTAL = 0.333
