Answer:vertical
Step-by-step explanation:
Answer:
$199.50
Step-by-step explanation:
10% discount of $34 = 10/100*34 = $3.40
so, a single shirt costs $34-$3.40 = $30.60
half off = 50% discount of $31 = 50/100*31 = $15.50
so, a single cap costs $31-$15.50 = $15.50
so, 5 shirts and 3 caps cost now
5*$30.60 + 3*$15.50 = $153 + $46.50 = $199.50
but careful - can this be a trick question ?
the phrasing of the problem description can also suggest that the discounts are only listed to confuse us and are already included in the mentioned prices ("worth" $34 - what does that mean ? because including the discounts they are currently "worth" their prices).
then it would just plainly be
5*$34 + 3*$31 = $170 + $93 = $263
Answer:
2=x
Step-by-step explanation:
-2x+5=4x-7
+2x +2x
5=6x-7
+7 +7
12=6x
/6
2=x
263.25 is the volume of the box in inches cubes you have to multiply 4.5 by 9 by 6.5
Answer:
Second choice:
![x=2t](https://tex.z-dn.net/?f=x%3D2t)
![y=4t^2+4t-3](https://tex.z-dn.net/?f=y%3D4t%5E2%2B4t-3)
Fifth choice:
![x=t+1](https://tex.z-dn.net/?f=x%3Dt%2B1)
![y=t^2+4t](https://tex.z-dn.net/?f=y%3Dt%5E2%2B4t)
Step-by-step explanation:
Let's look at choice 1.
![x=t+1](https://tex.z-dn.net/?f=x%3Dt%2B1)
![y=t^2+2t](https://tex.z-dn.net/?f=y%3Dt%5E2%2B2t)
I'm going to subtract 1 on both sides for the first equation giving me
. I will replace the
in the second equation with this substitution from equation 1.
![y=(x-1)^2+2(x-1)](https://tex.z-dn.net/?f=y%3D%28x-1%29%5E2%2B2%28x-1%29)
Expand using the distributive property and the identity
:
![y=(x^2-2x+1)+(2x-2)](https://tex.z-dn.net/?f=y%3D%28x%5E2-2x%2B1%29%2B%282x-2%29)
![y=x^2+(-2x+2x)+(1-2)](https://tex.z-dn.net/?f=y%3Dx%5E2%2B%28-2x%2B2x%29%2B%281-2%29)
![y=x^2+0+-1](https://tex.z-dn.net/?f=y%3Dx%5E2%2B0%2B-1)
![y=x^2](https://tex.z-dn.net/?f=y%3Dx%5E2)
So this not the desired result.
Let's look at choice 2.
![x=2t](https://tex.z-dn.net/?f=x%3D2t)
![y=4t^2+4t-3](https://tex.z-dn.net/?f=y%3D4t%5E2%2B4t-3)
Solve the first equation for
by dividing both sides by 2:
.
Let's plug this into equation 2:
![y=4(\frac{x}{2})^2+4(\frac{x}{2})-3](https://tex.z-dn.net/?f=y%3D4%28%5Cfrac%7Bx%7D%7B2%7D%29%5E2%2B4%28%5Cfrac%7Bx%7D%7B2%7D%29-3)
![y=4(\frac{x^2}{4})+2x-3](https://tex.z-dn.net/?f=y%3D4%28%5Cfrac%7Bx%5E2%7D%7B4%7D%29%2B2x-3)
![y=x^2+2x-3](https://tex.z-dn.net/?f=y%3Dx%5E2%2B2x-3)
This is the desired result.
Choice 3:
![x=t-3](https://tex.z-dn.net/?f=x%3Dt-3)
![y=t^2+2t](https://tex.z-dn.net/?f=y%3Dt%5E2%2B2t)
Solve the first equation for
by adding 3 on both sides:
.
Plug into second equation:
![y=(x+3)^2+2(x+3)](https://tex.z-dn.net/?f=y%3D%28x%2B3%29%5E2%2B2%28x%2B3%29)
Expanding using the distributive property and the earlier identity mentioned to expand the binomial square:
![y=(x^2+6x+9)+(2x+6)](https://tex.z-dn.net/?f=y%3D%28x%5E2%2B6x%2B9%29%2B%282x%2B6%29)
![y=(x^2)+(6x+2x)+(9+6)](https://tex.z-dn.net/?f=y%3D%28x%5E2%29%2B%286x%2B2x%29%2B%289%2B6%29)
![y=x^2+8x+15](https://tex.z-dn.net/?f=y%3Dx%5E2%2B8x%2B15)
Not the desired result.
Choice 4:
![x=t^2](https://tex.z-dn.net/?f=x%3Dt%5E2)
![y=2t-3](https://tex.z-dn.net/?f=y%3D2t-3)
I'm going to solve the bottom equation for
since I don't want to deal with square roots.
Add 3 on both sides:
![y+3=2t](https://tex.z-dn.net/?f=y%2B3%3D2t)
Divide both sides by 2:
![\frac{y+3}{2}=t](https://tex.z-dn.net/?f=%5Cfrac%7By%2B3%7D%7B2%7D%3Dt)
Plug into equation 1:
![x=(\frac{y+3}{2})^2](https://tex.z-dn.net/?f=x%3D%28%5Cfrac%7By%2B3%7D%7B2%7D%29%5E2)
This is not the desired result because the
variable will be squared now instead of the
variable.
Choice 5:
![x=t+1](https://tex.z-dn.net/?f=x%3Dt%2B1)
![y=t^2+4t](https://tex.z-dn.net/?f=y%3Dt%5E2%2B4t)
Solve the first equation for
by subtracting 1 on both sides:
.
Plug into equation 2:
![y=(x-1)^2+4(x-1)](https://tex.z-dn.net/?f=y%3D%28x-1%29%5E2%2B4%28x-1%29)
Distribute and use the binomial square identity used earlier:
![y=(x^2-2x+1)+(4x-4)](https://tex.z-dn.net/?f=y%3D%28x%5E2-2x%2B1%29%2B%284x-4%29)
![y=(x^2)+(-2x+4x)+(1-4)](https://tex.z-dn.net/?f=y%3D%28x%5E2%29%2B%28-2x%2B4x%29%2B%281-4%29)
![y=x^2+2x+-3](https://tex.z-dn.net/?f=y%3Dx%5E2%2B2x%2B-3)
.
This is the desired result.