Solve by substitution
Just plug in y=-x-1 into y+x=3
So we get:
Simplify that:
And since that is not true, that means this system of equations has no solutions!
Answer:
arc AC = 111°
Step-by-step explanation:
∠APC is a central angle, so arc AC is equal to the measure of ∠APC.
∠APC and ∠BPC are supplementary. So, m∠APC + m∠BPC = 180
m∠APC + 69 = 180
m∠APC = 111
arc AC = 111°
Answer: −18x+4
Step-by-step explanation:
=(−6)(3x+ −2/3)
=(−6)(3x)+(−6)(
−2/3)
Answer:
x > 1/5
Step-by-step explanation:
All of these three triangle inequalities must be satisfied:
AB +BC > AC
BC +CA > BA
CA +AB > CB
___
Taking these one at a time, we have ...
AB +BC > AC
3x +4 + 2x +5 > 4x
x +9 > 0 . . . . . subtract 4x
x > -9
__
BC +CA > BA
2x +5 + 4x > 3x +4
3x > -1 . . . . . . subtract 3x+5
x > -1/3 . . . . . divide by 3
__
CA + AB > CB
4x + 3x +4 > 2x +5
5x > 1 . . . . . . subtract 2x+4
x > 1/5
___
The only values of x that satisfy all of these inequalities are those such that ...
x > 1/5
There's a really easy way to convert any units to other units.
Right now, we have the fraction (4 miles) / (2 hours).
We want to find a fraction that's exactly equal to that one,
but has the units of (miles/minute) or maybe (feet/minute).
Just take the original fraction, and multiply it by some other
fractions.
Each fraction you multiply it by must have the value of ' 1 ' so
you don't change the value of the original fraction. But it can
have different units, that cancel with other units to eventually
give you the units you want.
(4 miles / 2 hours) times (1 hour / 60 minutes)
The second fraction is equal to ' 1 ', because the top and the bottom
have the same value ... 1 hour is the same thing as 60 minutes.
Multiply the fractions: (4 miles x 1 hour) / (2 hour x 60 minutes)
Now you can cancel 'hour' from the top and the bottom, and you have
(4 miles x 1) / (2 x 60 minutes)
= (4 miles) / (120 minutes)
= (4 / 120) mile/minute = 0.0333... mile / minute .
Let's do it again, go a little farther, and get an answer that
might mean more and feel more like an answer.
(4 miles) / (2 hours) x (5280 feet / mile) x (1 hour / 60 minutes)
The 2nd and 3rd fractions both have the value of ' 1 ', because
the top is equal to the bottom.
Multiply all three fractions:
(4 miles x 5280 feet x 1 hour) / (2 hours x 1 mile x 60 minutes)
You can cancel both 'mile' and 'hour' out of the top and bottom,
and look what you have left:
(4 x 5280 feet x 1) / (2 x 1 x 60 minutes)
= (4 x 5280) / (2 x 60) feet / minutes
= (21,120 / 120) feet/minute = 176 feet per minute
