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3 years ago

Use the remainder theorem to find which of the following is NOT a factor of x^3 – 4x^2 – 4x + 16.

Mathematics

1 answer:

nataly862011 [7]3 years ago

3 0

Answer: x - 12 is not a factor.

Step-by-step explanation:

The equation

x³ - 4x² - 4x + 16

To know which of the following is a factor , we continue to find the value of x and substitute into the equation and see the one that gives zero. The one that gives zero is the factor.

(a) x + 2

If x + 2 = 0

x = -2, now substitute for x in the equation and find out if it will be zero.

x³ - 4x² - 4x + 16 = (-2)³ - 4(-2)² - 4(-2) + 16.

= -8 - 16 + 8 + 16

= 0.

Therefore, x + 2 is a factor.

(b) x - 12

If x - 12 = 0, then x = 12

x³ - 4x² - 4x + 16

(12)³ - 4(12)² - 4(12) + 16

1728 - 576 - 48 + 16

= 1,120 , not a factor.

If x - 2 = 0, then x = 2

x³ - 4x² - 4x + 16

(2)³ - 4(2)² - 4(2) + 16

8 - 16 - 8 + 16

= 0, Therefore, x - 2 is a factor.

(d) x - 4

If x - 4 = 0, x = 4

x³ - 4x² - 4x + 16

(4)³ - 4(4)² - 4(4) + 16

48 - 48 - 16 + 16

= 0,therefore, x - 4 is also a factor.

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A triangle has sides with lengths of 8 millimeters, 15 millimeters, and 17 millimeters. Is it a right triangle?

olga nikolaevna [1]

Answer:

yes.

Step-by-step explanation:

to find this answer, use the pythagoras theorem. the pythagoras theorem states that a² + b² = c².

to see if this is a right angled triangle, we will use this formula, as the pythagoras theorem only works for right angled triangles.

we are going to work out c, which is always the hypotenuse. the hypotenuse is the longest side of a triangle, that is larger than the other values. we know that the hypotenuse of this triangle is 17, so let’s see if that’s the answer we get.

calculation:

a² + b² = c²

a = 8 millimetres

b = 15 millilitres

c = ?

8² + 15² = c²

64 + 225 = c²

64 + 225 = 289.

289 = c²

√289 = c

√289 = 17.

the pythagoras theorem correctly identified the length of the hypothenuse. as i said earlier, this theorem only works on right angled triangles, therefore, this triangle is right angled.

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2 years ago

A boy owns 3 pairs of pants, 6 shirts, 4 ties, and 3 jackets. how many different outfits can the boy wear to school if each outf

scZoUnD [109]

multiply all numbers together:

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2 years ago

A line with a slope of 2 passes through the point (3,9).

Licemer1 [7]

Answer:

y-9=2(x-3)

Step-by-step explanation:

The point-slope formula is: y-y1=m(x-x1)

y1 and x1 is where you plug in the coordinate and m is the slope.

y1 is the second number of the coordinate (x, y)

So, y1 is 9 in this case

x1 is the first number of the coordinate (x, y)

So x1 is 3 in this case

Do you get it or do I need to explain further?

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3 years ago

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Elena-2011 [213]

Step-by-step explanation:

Here's the first question and how to solve the second.

So the first business start with 250, that's your b in slope.

y = mx + b

y = mx + 250

Now, they charge 14 an hour so that's your m.

y = 14x + 250

x is the number of hours it takes.

The second business is straight up 22 per hour, so it's just y = mx, where b is 0.

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Try plugging in different numbers and seeing how much it take to level out!

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3 years ago

Calculate the distance between the points C=(-7, 7) and M=(-2, 3) in the coordinate plane.

pishuonlain [190]

Answer:

d = Sqrt 41 = 6.4

Step-by-step explanation:

d = sqrt [(x-x)^2 + (y-y)^2]

d = sqrt [(-7 - - 2)^2 + (7-3)^2]

d = sqrt[(-7+2)^2 + (4)^2]

d = sqrt [(-5)^2 + (4)^2]

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d = sqrt 41 = 6.4

6 0

2 years ago