consec numbers are right after each other like 2, 3, 4
now if
2 is x
3 is x+1
4 is x+2
same for all consec numbers
=x +x+1 +x+2
Now this one says, 2 times the second and 3 times the third so its
=x +2(x+1) +3(x+2)
now the second part
x +2(x+1) +3(x+2) = 170
x + 2x + 2 + 3x + 6 = 170
6x + 8 = 170
6x = 170 -8
6x = 162
x = 27
so the numbers are 27, 28 and 29
Answer:
Step-by-step explanation:
0 = 5x + 7
-7 = 5x
x = - 7/5 = -1.4
There is a typo in the quadratic term.
I am goint to solve this question assuming that the correct expression is 162x + 731 = - y - 9x^2
Now, you should know that the vertex form is y = a(x - h)^2 + k, where the vertex is (h,k).
So, we just must transform the quadratic function into that form. To do that you must complete squares. I will do it step by step
start: 162 x + 731 = - y - 9x^2
1) Transpose terms:
y = - 9x^2 - 162x + 731
2) extract common factor ot the two terms with x^2 and x.
y = - 9 (x^2 + 18x) + 731
3) complete squares for x^2 + 18x, which is (x + 9)^2 - 81
=> y = - 9 [ ( x + 9)^2 - 81 ] + 731
4) solve the square brackets
=> y = - 9 (x + 9)^2 - 9*81 + 731
=> y = - 9(x + 9)^2 -729 + 731
=> y = - 9 (x + 9)^2 + 2
Answer: y = - 9 (x + 9)^2 + 2
Answer:
6a) 1
6b) 11
7a) 4
7b) 10
8a) 6
8b) 14
9a) 11
9b) 13
Step-by-step explanation:
In order to make a triangle, we need to follow this property:
a <= b + c
(Known as "triangle inequality")
Where 'a' is the bigger side and 'b' and 'c' are the other two sides.
So, using this property, we can solve the following problems:
6a) Maximum side will be 6:
6 <= 5 + c
c = 1
6b) Minimum sides will be 5 and 6:
a <= 5 + 6
a = 11
7a) Maximum side will be 7:
7 <= 3 + c
c = 4
7b) Minimum sides will be 3 and 7:
a <= 3 + 7
a = 10
8a) Maximum side will be 10:
10 <= 4 + c
c = 6
8b) Minimum sides will be 4 and 10:
a <= 4 + 10
a = 14
9a) Maximum side will be 12:
12 <= 1 + c
c = 11
9b) Minimum sides will be 1 and 12:
a <= 1 + 12
a = 13
(7.20 * 4) - 10 = 28.80 - 10 = 18.80
12(18.80) + 0.25*12(18.80) = 225.60 + 56.40 = $282