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suter [353]
3 years ago
13

Find the set of values of k for which the y = kx – 4 intersects the curve of y = x2 – 2x at two distinct points.

Mathematics
1 answer:
Diano4ka-milaya [45]3 years ago
6 0

Answer:

For ax^2+bx+c=0,

x^2+x(-2-k)+4=0,

So, b=-2-k,

a=1, c=4, so

(-2-k)^2-(4*1*4)>0,

4+4k+k^2-16>0,

k*2+4k-12>0,

(k+6)*(k-2)>0,

the points of interest are

k=-6, k=2, so

look at k<-6, -6<k<2, and

k>2.

Just plug in values for each

interval and you will see

that k<-6 and k>2.

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Error Analysis Your friend says that the volume of this sphere is 44.58
Maurinko [17]

Answer:

  • the given dimension was used as the radius
  • 5.57 m³

Step-by-step explanation:

The volume of a sphere can be found using the formula ...

  V = 4/3πr³ . . . . . where r is the radius

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The figure points to a diameter line and indicates 2.2 m. The arrowhead is in the middle of a radius line, making it easy to interpret the dimension as the radius of the sphere.

If 2.2 m is used as the radius, the volume is computed to be ...

  V = 4/3π(2.2 m)³ ≈ 44.58 m³

This agrees with your friend's volume, suggesting the diameter was used in place of the radius in the computation.

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The correct volume, using 2.2 m as the diameter, is ...

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6 0
2 years ago
Hey, Its the same person. This is Algebra 2. Please Help!
suter [353]

Answer:

first option

Step-by-step explanation:

Given

f(x) = \frac{2x^2+5x-12}{x+4} ← factorise the numerator

     = \frac{(x + 4)(2x-3)}{x+4} ← cancel (x + 4) on numerator/ denominator

     = 2x - 3

Cancelling (x + 4) creates a discontinuity ( a hole ) at x + 4 = 0, that is

x = - 4

Substitute x = - 4 into the simplified f(x) for y- coordinate

f(- 4) = 2(- 4) - 3 = - 8 - 3 = - 11

The discontinuity occurs at (- 4, - 11 )

To obtain the zero let f(x) = 0, that is

2x - 3 = 0 ⇒ 2x = 3 ⇒ x = \frac{3}{2}

There is a zero at ( \frac{3}{2}, 0 )

Thus

discontinuity at (- 4, - 11 ), zero at ( \frac{3}{2}, 0 )

7 0
3 years ago
What is the value of x? Enter your answer, as a decimal, in the box.<br><br> ___ cm
lora16 [44]

Answer

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