As before – all are similar so I will pick the harder one.
AB = CD
AB = 9(x-2)
CD = x + 3(x+5)
9(x-2) = x + 3(x+5)
Now multiply out and solve
9x – 18 = x + 3x + 15
9x – x – 3x = 15 + 18
5x = 33
x = 6.6
Now go back and find the lengths
AB = 9(x-2) = 9(6.6 – 2) = 41.4
CD = AB = 41.4
CE = x = 6.6
ED = 3(x+5) = 3(6.6+5) = 34.8
Now let’s look at Ch 5.6 #14.
Parts a-c are similar – so will do part c since the harder.
Area = x + 20 = (x-1)4 > I am just stating all things that are equal based on the given.
x+20 = (x-1)4
x+20 = 4x -4 > multiplied out
20 + 4 = 4x – x > moved similar items to same side
24 = 3x
x = 8
Now we know x, we have to find the sides (ALWAYS GO BACK AND MAKE SURE YOU KNOW WHAT WAS ASKED)
x -1 = 8 – 1 = 7
4 = 4
For problem 5.6, parts a-d are all pretty much the same. Here I will do part d) since a hair more complex. The steps the same for the others.
Since AB = CD, we can substitute the following
AB is x + 6(x+2)
CD is 2(x+10)
x + 6(x+2) = 2(x+10)
So to find the length of AB and CD, I need to figure out x. So solve the equation.
x + 6(x+2) = 2(x+10)
x + 6x + 12 = 2x + 20 – I just multiplied everything out
x + 6x – 2x = 20 – 12 > I moved all the x terms to the left and all the constants (numbers) to the right
5x = 8 > did the math
x = 8/5 = 1.6
Now I have x, but the problem asked for the lengths.
So now we can find the parts
AB = x + 6(x+2) = 1.6 + 6(1.6 + 2) = 1.6 + 6(3.6) = 23.2
AE = x = 1.6
EB = 6(x+2) = 21.6
CD = AB = 23.2
To do the others – follow the same process
This is an error in the Algebra Solutions Manual
In Algebra 1, chapter 5 lesson 1 problem 10x, the answer key says the answer is true for all positive integers. But isn’t it true for all integers? 1 to the power of x =1. If it is a negative power, it is still one, right?
Dr. Callahan Answer:
You are correct. Should be for all real numbers – not just integers. I tend to test these in a calculator to make sure though 😉
So that is incorrect in the Solutions manual.
Just for completeness sake – my goto math tool is Wolfram – so here is there answer.