<span>0 = x² + 10x + 16
Subtract </span><span>x^2+10x+16 from each side
</span><span>0−<span>(<span><span>x^2+10x</span>+16</span>) </span></span>= x^2+10x+16−(<span>x^2+10x+16</span>)
<span><span>−x^2−10x</span>−16</span>=<span>0
</span>
Factor left side
<span><span>(<span>−x−2</span>)</span><span>(x+8)</span></span>=<span>0
</span>
Set all factors to equal 0
<span><span><span>−x</span>−2</span>=<span><span><span>0<span> or </span></span>x</span>+8</span></span>=<span>0
</span>
The solutions are x = -2 and x = -8
0.6 is the decimal for 9/15
Step 1:
First, let's order the number from least to greatest.
A. -0.31
B. -0.33
C. -0.38
D. -0.29
We could see that A, B, and C's numbers are already from least to greatest, so all we have to do is to move -0.29 (D) up to the top, since -0.29 is the number with the lowest value.
C. -0.38
B. -0.33
A. -0.31
D. -0.29
Step 2:
Let's look at the four number lines. Remember that we already organized the numbers from least to greatest, so the order they go in on the number line is: C, B, A, and D. Since Line C and D Don't follow that rule, we know those are not our answers. Also on line B, C is on the left of -0.4, but C's value is less than -0.4, so B is wrong. We are left with line A.
Line A: C. -0.38, B. -0.33, A. -0.31, D. -0.29
Our answer: Line A
Typically if it is a linear function then it doesn't matter. However if it is a quadratic, cubic, and so on and so forth....(
![x^{2},x^{3},x^{4}](https://tex.z-dn.net/?f=%20x%5E%7B2%7D%2Cx%5E%7B3%7D%2Cx%5E%7B4%7D%20)
) you may want to used the distance formula if you are not given any other points (with the exception of the vertex, asymptote or roots... etc).
Answer: 5 hours
Step-by-step explanation:
Given: The distance between the cities Atlanta and Indianapolis=540 miles
The speed of motorcycle= 48 mph
Since, ![Time=\frac{Distance}{speed}](https://tex.z-dn.net/?f=Time%3D%5Cfrac%7BDistance%7D%7Bspeed%7D)
![\\\Rightarrow\text{Time taken by motorcycle to travel}=\frac{540}{48}=11.25\ hours](https://tex.z-dn.net/?f=%5C%5C%5CRightarrow%5Ctext%7BTime%20taken%20by%20motorcycle%20to%20travel%7D%3D%5Cfrac%7B540%7D%7B48%7D%3D11.25%5C%20hours)
Thus, time taken by car to travel the distance= 11.25-2.25= 9 hours
![\\\Rightarrow\text{Speed of car}=\frac{540}{9}=60\ mph](https://tex.z-dn.net/?f=%5C%5C%5CRightarrow%5Ctext%7BSpeed%20of%20car%7D%3D%5Cfrac%7B540%7D%7B9%7D%3D60%5C%20mph)
Let t be the time at which they will meet if they are moving towards each other simultaneously.
Then Distance covered by Motorcycle+Distance covers by car= 540 miles
![\\\Rightarrow48t+60t=540\\\Rightarrow108t=540\\\Rightarrow\ t=5](https://tex.z-dn.net/?f=%5C%5C%5CRightarrow48t%2B60t%3D540%5C%5C%5CRightarrow108t%3D540%5C%5C%5CRightarrow%5C%20t%3D5)
Thus they will meet in 5 hours, after which time the motorcycle will have traveled ![48\times5=240\miles](https://tex.z-dn.net/?f=48%5Ctimes5%3D240%5Cmiles)
and the car will have traveled ![60\times5=300\miles](https://tex.z-dn.net/?f=60%5Ctimes5%3D300%5Cmiles)