Answer:
<u><em>The Father is currently 47 and the Son is 7</em></u>
Step-by-step explanation:
Let F and S be the present ages of Father and Son, respectively.
We are told that <u>(F-2) = 9(S-2)</u> [2 years ago, father age was nine times the son age]
We also learn that <u>(F+3) = 5(S+3)</u> [3 years later it will be 5 times only]
Take the first expression and isolate one of the variables (S or F). I'll isolate F:
(F-2) = 9(S-2)
F = 9S - 16
Now use this in the second expression:
(F+3) = 5(S+3)
((9S-16)+3) = 5(S+3)
9S-13 = 5S+15
4S = 28
S = 7
Since F = 9S-16,
F = 9*(7)-16
F = 47
<u><em>Father is 47 and Son is 7</em></u>
CHECK:
Was the father 9 times the age of his son 2 years ago?
Father would have been 45 and son 5. Yes, 9*5 = 45
In 3 years will he be 5 times older than his son? Yes, Father would be 50 and son would be 10. 5*(10) = 50
There is only one requirement for three sides in order to be considered possible in constructing a triangle. That requirement is
<em>The sum of any of the two sides must be greater than the third side</em>
11 + 15 = 26 > 21
11+ 21 = 33 > 15
15 + 21 = 16 > 11
Since all of the combination fulfill the requirement, yes we could create the triangle with those sides.
Answer:
5.50x + 2y ≤ 18
Step-by-step explanation:
Romona has a total of $18 and she has to spend it on dog food.
Dry god food cost $5.50 per bag and wet dog food cost $2.00 per can.
We have to write an inequality to show the above condition.
Let the number of dry and wet dog food she buys be x and y.
The total cost of dog food must be less than $18.
Then,
5.50x + 2y ≤ 18
This is the required linear inequality.
First we note symmetry in the expression's coefficients.
We also note that 7*3=21, and 7+3=10.
From the rational roots theorem, we are tempted to try with 3 and 7 as coefficients of the factors.
Try
(7b+3)(3b+7)=21b^2+(49+9)b+21
By switching the sign of 3b+7 to 3b-7, we get the signs right, to check:
(7b+3)(3b-7)=21b^2+(9-49)b-21=21b^2-40b-21 ....right!
So
(7b+3)(3b-7)=21b^2-40b-21
