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alexandr402 [8]
3 years ago
9

Which line(s) intersect the parabola y = x^2 − 3x + 4 at two points? Select all that apply. A. y = –3x + 2 B. y = –3x + 3 C. y =

–3x + 5 D. y = –3x + 6
Mathematics
1 answer:
TEA [102]3 years ago
4 0

Answer:

C and D

Step-by-step explanation:

Equating the line A and the parabola, we get

-3x + 2 = x² - 3x + 4

0 = x² - 3x + 4 +3x - 2

0 = x² + 2

-2 = x²

which has no real solutions. Then, the line A and the parabola don't intersect each other.

Equating the line B and the parabola, we get

-3x + 3 = x² - 3x + 4

0 = x² - 3x + 4 + 3x - 3

0 = x² + 1

-1 = x²

which has no real solutions. Then, the line B and the parabola don't intersect each other.

Equating the line C and the parabola, we get

-3x + 5 = x² - 3x + 4

0 = x² - 3x + 4  + 3x - 5

0 = x² - 1

1 = x²

√1 = x

which has 2 solutions, x = 1 and x = -1. Then, the line C and the parabola intersect each other.

Equating the line D and the parabola, we get

-3x + 6 = x² - 3x + 4

0 = x² - 3x + 4  + 3x - 6

0 = x² - 2

2 = x²

√2 = x

which has 2 solutions, x ≈ 1.41 and x ≈ -1.41. Then, the line D and the parabola intersect each other.

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Solve the system using elimination.
KIM [24]
We can't eliminate as is so we have to change something up there in the equations to get either the x values the same number but opposite signs, or the y values the same number but opposite signs.  I chose to change the y values to the same number but different signs. In the first equation y is -3y and in the second one, y is -8y. The LCM of both of those numbers is 24, so we will multiply the first equation by an 8 (8*3=24) and the second equation by 3 (3*8=24) but since they are both negative right now, one of those multiplications has to involve a negative because - * - = +. Set it up like this:
8(-10x - 3y = -18)
-3(-7x - 8y = 11)
Multiply both of those all the way through to get new equations:
-80x - 24y = -144
 21x  +24y = -33
Now the y's cancel each other out leaving only the x's:
-59x = -177 and x = 3.  Now plug that 3 into either one of the original equations to find the y value.  Either equation will work; you'll get the same answer using either one. Promise. -7(3) - 8y = 11 gives a y value of -4.  so your solution is (3, -4) or B above.
7 0
3 years ago
Read 2 more answers
Deepak wrote out the steps to his solution of the equation – 3x – 5 + 4x = –.
MrMuchimi
X=5 if that's what you were asking for
3 0
3 years ago
So what exactly is a,b,c
Gala2k [10]
If you’re talking about answers a would be the option first b would be 2nd and c would be 3rd
4 0
2 years ago
PLEASE HELP!!!
viktelen [127]

The answer is 3/5.


\frac{1}{3} *\frac{3}{5} =\frac{3}{15} \\ \\ \frac{3}{15} *\frac{3}{5} =\frac{9}{75}


Continue this pattern and you'll see that it follows this geometric sequence

5 0
3 years ago
Read 2 more answers
Find the solution of 4x2y′′−4x2y′+y=0,x>04x2y″−4x2y′+y=0,x>0 of the form y1=xr(1+c1x+c2x2+c3x3+⋯)
BabaBlast [244]

Answer:

r = 1/2

c1 = 3/4

c2 = 27/64

c3 = 405/1408

Step-by-step explanation:

Find the solution of 4x2y′′−4x2y′+y=0,x>04x2y″−4x2y′+y=0,x>0 of the form y1=xr(1+c1x+c2x2+c3x3+⋯)

r = 1/2

c1 = 3/4

c2 = 27/64

c3 = 405/1408

The solution is attached.

5 0
3 years ago
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