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Mariulka [41]
3 years ago
8

When x3+ cx + 4 is divided by (x + 2), the remainder is 4. Find the value of c.

Mathematics
1 answer:
never [62]3 years ago
6 0

Answer:

-4

Step-by-step explanation:

x³ + cx + 4 divided by x + 2 has a remainder of 4, so:

(x³ + cx + 4) / (x + 2) = ax² + bx + d + 4 / (x + 2)

Multiply both sides by x + 2:

x³ + cx + 4 = (ax² + bx + d) (x + 2) + 4

Distribute:

x³ + cx + 4 = ax²(x + 2) + bx(x + 2) + d(x + 2) + 4

x³ + cx + 4 = ax³ + 2ax² + bx² + 2bx + dx + 2d + 4

x³ + cx + 4 = ax³ + (2a + b)x² + (2b + d)x + 2d + 4

Match the coefficients.

a = 1

2a + b = 0

2b + d = c

2d + 4 = 4

Solving, a = 1, b = -2, and d = 0.  So c = -4.

We can also solve this using long division (see picture).

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51 is 33 1/3 of what number?
Makovka662 [10]

1700, just use the inverse operation. The problem would look like this ( not inverse operation ) x ÷ 33 1/3 = 51

All you have to do is multiply the two numbers.

51 x 33 1/3 = 1700

Now plug it back in and check

1700 ÷ 33 1/3 does indeed equal 51.


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2 years ago
Is it congruent or not ? Remember that the diagram may not be drawn to scale . justify your conclusion.
Leno4ka [110]

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3 years ago
Which transformations could have been used to create A'B'C'? Choose all that apply.
Eduardwww [97]

The correct transformation is a rotation of 180° around the origin followed by a translation of 3 units up and 1 unit to the left.

<h3>Which transformation is used to get A'B'C'?</h3>

To analyze this we can only follow one of the vertices of the triangle.

Let's follow A.

A starts at (3, 4). If we apply a rotation of 180° about the origin, we end up in the third quadrant in the coordinates:

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Now if you look at A', you can see that the coordinates are:

A' = (-4, -1)

To go from (-3, -4) to (-4, -1), we move one unit to the left and 3 units up.

Then the complete transformation is:

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If you want to learn more about transformations:

brainly.com/question/4289712

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6 0
1 year ago
6 ice cream cones cost $10. How much will 9 cost?
jek_recluse [69]

Answer:

15 dollars

Step-by-step explanation:

We can write a ratio to solve

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------------   = --------------

10 dollars       x dollars

Using cross products

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Did you solve this? I need it too.
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