What is the discriminant and number of solutions to the problem- y=2x2+6x+12

Answers

Answer 1

Answer: Δ = b² - 4ac
Δ = (6)² - 4(2)(12)
Δ = 36 - 4(24)
Δ = 36 - 96
Δ = -60

y = 2x² + 6x + 12
0 = 2x² + 6x + 12
0 = 2(x²) + 2(3x) + 2(6)
0 = 2(x² + 3x + 6)
2 2
0 = x² + 3x + 6
x = -(3) ± √((3)² - 4(1)(6))
2(1)
x = -3 ± √(9 - 4(6))
2
x = -3 ± √(9 - 24)
2
x = -3 ± √(-15)
2
x = -3 ± i√(15)
2
x = -1.5 ± 0.5i√(15)
x = -1.5 + 0.5i√(15) or x = -1.5 - 0.5i√(15)

The discriminant is -60 and the number of solutions is 2.

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I hope this helps you

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Answers

Answer:

Step-by-step explanation:

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Find the unknown side length, x. Write your answer in simplest radical form. A. 15 B. 11 square root 2 C. 2 square root 121 D. 15 square root 5

Answers

We have two right isosceles triangles. Hypotenuse of that triangle is a $√(2)$ or you can use the Pythagorean theorem: 11² + 11² = c²
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242 =c² c= $√(242)= √(121*2)=11 √(2)$ Answer is the same: B) 11 square root 2

Answer:

Step-by-step explanation:

imagine that the number 2 button on your calculator is damaged and cannot be used.use a flow chart to show 3 different ways in which you can calculate 24x12

Answers

$\left\begin{array}{ccc}24=3\cdot8\n12=3\cdot4\end{array}\right\}24\cdot12=3\cdot8\cdot3\cdot4\n\n\n\left\begin{array}{ccc}24=144:6\n12=36:3\end{array}\right\}24\cdot12=144:6\cdot36:6\n\n\n\left\begin{array}{ccc}24=96:4\n12=48:4\end{array}\right\}24\cdot12=96:4\cdot48:4\n\n\n\left\begin{array}{ccc}24=16+8\n12=9+3\end{array}\right\}24\cdot12=(16+8)\cdot(9+3)\nsequence\ of\ key:16+18=M+;\ 9+3=* MR=\n\n\n$

Gilda walks to the train station. If she walks at the rate of 3 mph, she misses her train by 7 minutes. However, if she walks at the rate of 4 mph, she reaches the station 5 minutes before the arrival of the train. Find the distance Gilda walks to the station.David knew he made a mistake when he calculated that Gilda walks 123 miles to the station. Read through David's calculations:Using d = rt, the distance is the same, but the rate and time are different.If Gilda misses the train, it means the time t needs 7 more minutes so d = 3(t + 7).If she gets to the station 5 minutes early means the time t can be 5 minutes less so d = 4(t - 5).3(t + 7) = 4(t - 5)3t + 21 = 4t - 20t = 41d = rt, so d = 3(41) = 123Find David's mistake in his calculations. In two or more complete sentences, explain his mistake. Include the correct calculations and solutions in your answer.

Answers

We'll represent the distance as d and the time as t.
d= 3(t+7) because Gilda is 7 minutes late when travelling 3 mph
d= 4(t-5) because Gilda is 5 minutes early at 4 mph

d= 3t + 21
d= 4t -20
3t +21 =4t -20
41=t
d= 3(41) +21= 144
The distance is 144 miles.

$d=3(t + 7)\ \ \ if\ Gilda\ walks\ of\ 3mph\n.\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ she\ is\ 7\ minutes\ after\ departure\ of\ the\ train\n\n d= 4(t - 5)\ \ \ if\ Gilda\ walks\ of\ 4mph\ \n.\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ she\ is\ 5\ minutes\ before\ the\ train\ \n\n3(t+7)=4(t-5)\n\n3t + 21 = 4t - 20 \n\nt = 41\ \ \ \Rightarrow\ \ \ d=3(t+7)=3\cdot(41+7)=3\cdot48=144\n\nAns.\ The\ distance\ to\ the\ station\ is\ 144\ miles.$

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