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3 years ago

The polynomial p(x) = 5x^3 – 9x^2 - 6x + 8 has a known factor of (x + 1).

Mathematics

2 answers:

alekssr [168]3 years ago

4 0

Answer:

$(x+1)(5x-4)(x-2)$

Step-by-step explanation:

We know that (x+1) is a factor, so we can use synthetic division to factor it out of $5x^3-9x^2-6x+8$ .

Once factored, we get $(x+1)(5x^2-14x+8)$

Now all we need to do is factor $(5x^2-14x+8)$

$(5x^2-14x+8)=(5x-4)(x-2)$

This gives us the answer $(x+1)(5x-4)(x-2)$ .

anzhelika [568]3 years ago

3 0

Answer:

(x+1)(5x-4)(x-2)

Step-by-step explanation:

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PLEASE HELP IM CRYING RN PLEASE ANSWER CORRECTLY AND YOU WILL GET BRAINLIEST AND 100 POINTS

Vlad [161]

Answer: B (x,y) --> (x + 4, y - 2)

Step-by-step explanation: When you add -5+4=-1, and when you subtract 2 from 4 it equals to 2, which gives you the second coordinates, this means that x+4 and y-2 is the answer.

8 0

3 years ago

Given points A(-1, -2) and B(2, 4) where AP: BP=1:2, find the locus of point P.

koban [17]

Answer:

$x^2 + 4x + y^2 +8y = 0$

Step-by-step explanation:

Given

$A = (-1,-2)$

$B = (2,4)$

$AP:BP = 1 : 2$

Required

The locus of P

$AP:BP = 1 : 2$

Express as fraction

$\frac{AP}{BP} = \frac{1}{2}$

Cross multiply

$2AP = BP$

Calculate AP and BP using the following distance formula:

$d = \sqrt{(x - x_1)^2 + (y - y_1)^2}$

So, we have:

$2 * \sqrt{(x - -1)^2 + (y - -2)^2} = \sqrt{(x - 2)^2 + (y - 4)^2}$

$2 * \sqrt{(x +1)^2 + (y +2)^2} = \sqrt{(x - 2)^2 + (y - 4)^2}$

Take square of both sides

$4 * [(x +1)^2 + (y +2)^2] = (x - 2)^2 + (y - 4)^2$

Evaluate all squares

$4 * [x^2 + 2x + 1 + y^2 +4y + 4] = x^2 - 4x + 4 + y^2 - 8y + 16$

Collect and evaluate like terms

$4 * [x^2 + 2x + y^2 +4y + 5] = x^2 - 4x + y^2 - 8y + 20$

Open brackets

$4x^2 + 8x + 4y^2 +16y + 20 = x^2 - 4x + y^2 - 8y + 20$

Collect like terms

$4x^2 - x^2 + 8x + 4x + 4y^2 -y^2 +16y + 8y + 20 - 20 = 0$

$3x^2 + 12x + 3y^2 +24y = 0$

Divide through by 3

$x^2 + 4x + y^2 +8y = 0$

3 0

3 years ago

Select all ordered pairs that correspond to input-output pairs of the function y = −7x + 6.

horrorfan [7]

Answer:

There are no options, so i will answer in a general way.

In a function:

y = f(x)

The output is y, and the input is x, and the ordered pair is written as (x, y)

In this case, we have the function:

y = -7*x + 6

Then we need to have different inputs and then find the outputs for each.

For example, if x = 1.

y = -7*1 + 6 = -1

Then we have the ordered pair (1, - 1)

if x = 0

y = -7*0 + 6 = 6

then we have the ordered pair (0, 6)

The general ordered pair is written as:

(x, y = -7*x + 6)

or:

(x, -7*x + 6)

Where you only need to replace the value of x.

8 0

3 years ago

What theorem shows that TPN ≅ TQM?

melisa1 [442]

Note: Consider the side of first triangle is TQ instead of TA.

Given:

Triangles TQM and TPN which share vertex T.

$TQ\cong TP,TM\cong TN$

To find:

The theorem which shows that $\Delta TPN\cong TQM$ .

Solution:

In triangle TQM and TPN,

$TQ\cong TP$ [Given]

$\angle QTM\cong \angle PTN$ [Given]

$TM\cong TN$ [Given]

Since two sides and their including angle are congruent in both triangles, therefore both triangles are congruent by SAS postulate.

$\Delta TPN\cong TQM$ [SAS]

Therefore, the correct option is C.

5 0

3 years ago

The probability of A is 7/20, the probability of A intersection B is 49/400 what is the probability of B?

tino4ka555 [31]

Answer:

n(A)+n(B)-49/400=n(AUB)

n(B)=1-7/20+49/400

n(B)=(400+49-140)/400

n(B)=309/400

5 0

3 years ago