Answer:
The value of c that will result in a perfect square trinomial is (3)^2 or 9
The perfect square trinomial is: 
Step-by-step explanation:
We need to determine the value of c that will result in a perfect square trinomial.
Perfect square trinomial are of form: 
Now, the equation given is:
Looking at the term 6w, we can write it as 2(w)(3)
We are given: a = w, 2ab = 2(w)(3) so, b will be: (3)^2
So, we will be adding (3)^2 on both sides
So, The value of c that will result in a perfect square trinomial is (3)^2 or 9
The perfect square trinomial is:
We have 3 people: Paul, Daniel and Patricia. Let each name denote that person’s current age in years. Remember that % is the symbol for 1/100.
PAUL: (#A) Paul = Patricia – 2
DANIEL:
(#B) Daniel = 125% * Patricia = 125 * (1/100) * Patricia = 1.25 * Patricia
(#C) Ten years ago, Daniel’s age at that time would have been Daniel’s current age – 10. IE “Daniel – 10”.
Ten years ago, Patricia’s age at that time would have been Patricia’s current age – 10. IE “Patricia – 10”.
Ten years ago, Daniel’s age at that time (IE Daniel – 10) was 50% greater than Patricia’s age at the time (Patricia – 10).
IE
Daniel – 10 = 150% * (Patricia – 10)
Daniel – 10 = 1.50 * (Patricia – 10)
Daniel – 10 = 1.50 * Patricia – 1.50 * 10
Daniel – 10 = 1.50 * Patricia – 15
Daniel = 1.50 * Patricia – 15 + 10
Daniel = 1.50 * Patricia – 5
So now we have 3 equations in 3 unknowns:
(A) Paul = Patricia – 2
(B) Daniel = 1.25 * Patricia
(C) Daniel = 1.50 * Patricia – 5
Solve equations B & C simultaneously
1.25 * Patricia = 1.50 * Patricia – 5
1.25 * Patricia – 1.50 * Patricia = – 5
– 0.25 * Patricia = – 5
Patricia = (– 5) / (– 0.25)
Patricia = + 20
So now we can write the 3 people’s ages:
(a) Patricia = 20
(b) Paul = Patricia – 2 = 20 – 2 = 18
(c) Daniel = 1.25 * Patricia = 1.25 * 20 = 25
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<span>Finally, we check our solution against the original question. </span>
Paul is two years younger than Patricia. ……… 20 – 2 = 18 ✔
Daniel is 25% older than Patricia. ……… 25 = 125% * 20 ✔
Ten years ago, Daniel was 50% older than Patricia. 25 – 10 = 150% (20– 10) ✔
Hope that helped :)
Answer:
46.3
Step-by-step explanation:
Mean is the average of all values. You add all the values on the table and divide them by the amount of values (here there are 10 land animals so you would divide by 10).
Answer:
x ≥ -0.75
Step-by-step explanation:
3.75 - 3x ≤ 6
Subtract 3.75 on both sides.
- 3x ≤ 6 - 3.75
- 3x ≤ 2.25
Divide both sides with -3.
x ≥ 2.25/-3
x ≥ -0.75
