Answer:
one gadget costs $15.80
Step-by-step explanation:
Let w = cost of one widget
Let g = cost of one gadget
Given:
- Five widgets and three gadgets cost $109. 90
⇒ 5w + 3g = 109.9
Given:
- One widget and four gadgets cost $75. 70
⇒ w + 4g = 75.7
Rewrite w + 4g = 75.7 to make w the subject:
⇒ w = 75.7 - 4g
Substitute into 5w + 3g = 109.9 and solve for g:
⇒ 5(75.7 - 4g) + 3g = 109.9
⇒ 378.5 - 20g + 3g = 109.9
⇒ 378.5 - 109.9 = 20g - 3g
⇒ 268.6 = 17g
⇒ g = 15.8
Therefore, one gadget costs $15.80
To find the cost of one widget, substitute the found value for g into
w = 75.7 - 4g and solve for w:
⇒ w = 75.7 - 4(15.8)
⇒ w = 75.7 - 63.2
⇒ w = 12.5
Therefore, one widget costs $12.50
Answer:
2(3x + 7)(2x - 1)
Step-by-step explanation:
You can see it a little easier if you take out a common factor of 2
2(6x^2 + 11x - 7)
The 6 leaves you with a lot of factors, the 7 does not. It only has 2 factors.
Let 6 factor into 2 and 3 and the 7 into 7 and 1
2(3x - 1 )(2x + 7)
Now remove the brackets.
2(6x^2 + 21x - 2x - 7) This obviously does not work but we'll combine like terms anyway.
2(6x^2 + 19x - 7)
So we'll try it again
2(3x + 7)(2x - 1)
2(6x^2 + 14x - 3x - 7) Looks like we have it.
2(6x^2 + 11x - 7)
So the right factors are
2(3x + 7)(2x - 1)
Answer:
Well it will be 7+5=12 and 6+6=12
Step-by-step explanation:
Answer:
AB = 4
BC = 4
AC = 8
Step-by-step explanation:
Given, B is the midpoint of AC which means it divided the AC into two equal parts. Using this information we can write the following equation:
5x - 6 = 2x add 6 to both sides
5x = 2x + 6 subtract 2x from both sides
3x = 6 divide both sides by 3
x = 2 to find the length of AB, AC, and BC replace x with 2
AB = 5*2 - 6
BC = 2*2
AC = 8 (sum of AB and BC)
