PLEASE HELP ASAP!!! :)Using the remainder theorem, what is the remainder of the quotient of x^3– 6x^2 + 4x– 5 and 1 - 3?

A.88
B. -20
c.-74
D. 34

Answers

Answer 1

Answer:

The remainder of the quotient is -20.

Option B is the correct answer.

What is an expression?

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

x³ - 6x² + 4x - 5 and x - 3

Now,

x - 3 ) x³ - 6x² + 4x - 5 ( x² - 3x - 5

x³ - 3x²

(-) (+)

-3x² + 4x

-3x² + 9x

(+) (-)

-5x - 5

-5x + 15

(+) (-)

-20

Thus,

The remainder is -20.

Learn more about expressions here:

brainly.com/question/3118662

#SPJ2

Answer 2

Answer:

Answer:

The correct answer is B. -20.

Step-by-step explanation:

I got it right on the Edmentum test.

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The perimeter of this isosceles triangle is 22 cm. If one side is 6 cm, what are the possible lengths of the other two sides? Part B Explain how you know. Provide at least one reason for your answer.

Please explain how to do this!!

Answers

9514 1404 393

Answer:

y = 55°

Step-by-step explanation:

You know the sum of angles in a triangle is 180°. So, ...

25° +30° +x = 180°

And, you know a linear pair of angles totals 180°:

x + y = 180°

Substituting for 180°, we have ...

25° +30° +x = x + y

Subtracting x from both sides, we get a relation that is useful to remember:

25° +30° = y

y = 55°

_____

This relation is usually described as ...

An exterior angle is equal to the sum of the remote interior angles.

Show that W is a subspace of R^3.

Answers

Answer:

Check the two conditions of Subspace.

Step-by-step explanation:

If W is a Subspace of a vector space, V then it should satisft the following conditions.

1) The zero element should be in W.

Zero element can be different for different vector spaces. For examples, zero vector in $\math{R^2}$ is (0, 0) whereas, zero element in $\math{R^3}$ is (0, 0 ,0).

2) For any two vectors, $w_1$ and $w_2$ in W, $w_1 + w_2$ should also be in W.

That is, it should be closed under addition.

3) For any vector $w_1$ in W and for any scalar, $k$ in V, $kw_1$ should be in W.

That is it should be closed in scalar multiplication.

The conditions are mathematically represented as follows:

1) 0 $\in$ W.

2) If $w_1 \in W; w_2 \in W$ then $w_1 + w_2 \in W$ .

3) $$ \forall k \in V, and \hspace{2mm} \forall w_1 \in W \implies kw_1 \in W$

Here V = $\math{R^3}$ and W = Set of all (x, y, z) such that $x - 2y + 5z = 0$

We check for the conditions one by one.

1) The zero vector belongs to the subspace, W. Because (0, 0, 0) satisfies the given equation.

i.e., 0 - 2(0) + 5(0) = 0

2) Let us assume $w_1 = (x_1, y_1, z_1)$ and $w_2 = (x_2, y_2, z_2)$ are in W.

That means: $x_1 - 2y_1 + 5z_1 = 0$ and

$x_2 - 2y_2 + 5z_2 = 0$

We should check if the vectors are closed under addition.

Adding the two vectors we get:

$w_1 + w_2 = x_1 + x_2 - 2(y_1 + y_2) + 5(z_1 + z_2)$

$= x_1 + x_2 - 2y_1 - 2y_2 + 5z_1 + 5z_2$

Rearranging these terms we get:

$x_1 - 2y_1 + 5z_1 + x_2 - 2y_2 + 5z_2$

So, the equation becomes, 0 + 0 = 0

So, it s closed under addition.

3) Let k be any scalar in V. And $w_1 = (x, y, z) \in W$

This means $x - 2y + 5z = 0$

$kw_1 = kx - 2ky + 5kz$

Taking k common outside, we get:

$kw_1 = k(x - 2y + 5z) = 0$

The equation becomes k(0) = 0.

So, it is closed under scalar multiplication.

Hence, W is a subspace of $\math{R^3}$ .

Q # 18,Graph the inequality on a coordinate plane, - y < 3 x - 5

Answers

For this case we have the following inequality:
- y <3 x - 5
Rewriting we have:
y > -3x + 5
The solution is given in this case by the set of points that belong to the shaded region shown in the graph.
Answer:
see attached image.

If n is a positive integer, which of following statement is individually sufficient to prove whether 289 is a factor of n?a. The greatest common divisor of n and 344 is 86. b. Least common multiple of n and 272 is 4624. c. The least common multiple of n and 289 is 289n.

Answers

Answer:

The statement b) is individually sufficient to prove than 289 is a factor of n

Step-by-step explanation:

The least common multiple of n and 272 is the smallest number that is a multiple of n and a multiple of 272. Therefore:

272 x X = 4624 ⇒ X = 17 but 272 = 17 · 16 and 289 = 17 · 17

Therefore 17·17 must be a factor of n. That means 289 is a factor of n

Stefania pours 2 liters of orange juice and 1.5 liters of pineapple juice into a punch bowl. How many kiloliters are in thepunch bowl? Use the metric table to help answer the question
hecto-
100
deka-
10
Metric Table
unit
1
deci-
0.1
centi-
0.01
milli-
0.001
1,000
0.0035 kiloliters
0.035 kiloliters
O 0.35 kiloliters
3.5 kiloliters