Answer: each soda costs $1.5 and each hotdog costs $3.
Step-by-step explanation:
If H is the price for one hotdog and S is the price for one soda, we have the equations:
for Jack.
3*H + 2*S = $12
For Angie.
1*H + 4*S = $9
Now we can isolate one of the variables in one of the equations and then replace it in the other equation, let's isolate H in the second equation:
H = $9 - 4*S
now we replace it in the first eq
3*H + 2*S = $12
3*($9 - 4*S) + 2*S = $12
$27 - 12*S + 2*S = $12
-10*S = $12 - $27 = -$15
S = $15/10 = $1.5
Now we can replace it in the equation for H and get:
H = $9 - 4*$1.5 = $3
So each soda costs $1.5 and each hotdog costs $3.
<span>2(x - 5) + 7 = x + 8
Use distributed property
2x - 10 + 7 = x + 8
Add 7 to -10
2x - 3 = x + 8
Subtract x from both sides
x - 3 = 8
Add 3 to both sides
Final Answer: x=11</span>
Answer:
Step-by-step explanation:
3X + 6 + 4X + 20
7X + 26
In order to factorate the trinomial, let's first find its roots using the quadratic formula:
![\begin{gathered} b^2-4ac=12^2-4\cdot4\cdot9=144-144=0 \\ x_1=x_2=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}=\frac{-12+0}{2\cdot4}=-\frac{12}{8}=-\frac{3}{2} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20b%5E2-4ac%3D12%5E2-4%5Ccdot4%5Ccdot9%3D144-144%3D0%20%5C%5C%20x_1%3Dx_2%3D%5Cfrac%7B-b%5Cpm%5Csqrt%5B%5D%7Bb%5E2-4ac%7D%7D%7B2a%7D%3D%5Cfrac%7B-12%2B0%7D%7B2%5Ccdot4%7D%3D-%5Cfrac%7B12%7D%7B8%7D%3D-%5Cfrac%7B3%7D%7B2%7D%20%5Cend%7Bgathered%7D)
Now we can write the trinomial in the form:
So we have that:
So 2x + 3 is a factor of the trinomial, therefore the answer is D.
