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Alexus [3.1K]
3 years ago
11

PLEASE HELP ME WITH ALGEBRA PROBLEMS PLEASEEEE

Mathematics
2 answers:
Arisa [49]3 years ago
6 0

Answer:

1. The remainder is 1.

2. The remainder is 0.

3. The required number is 3.

Step-by-step explanation:

1.

The dividend is 3x^3-2x^2+x-1.

The divisor is (x-1).

The coefficient of dividend are 3,-2, 1 and -1. The divisor is (x-1), so we multiply dropped or added value by 1.

Write all the coefficients in top row. Drop down first coefficient as it is.

Multiply it by 1 and write the result in middle row, then add them.

Use synthetic method as shown in the below figure.

Bottom row represent the coefficients of quotient and remainder.

3x^3-2x^2+x-1=3x^2+x+2+\frac{1}{x-1}

The remainder is 1.

2.

If the divisor is a factor of given polynomial, then the polynomial is completely divides by divisor and the remainder is 0.

3.

The divisor is (x-3).

The divisor in the form of (x-c). The we multiply dropped or added value by c.

Since the divisor in the form of (x-3). The we multiply dropped or added value by 3.

Nat2105 [25]3 years ago
3 0

Answer:


Step-by-step explanation:

In the first part the given polynomial is 3x^{3}-2x^{2}+x-1, we have to divide this polynomial by (x-1) using synthetic division.

Here are the steps of synthetic division

Step 1: Set up the synthetic division table in which the coefficients are written in descending power of x.

Step 2: Drop down the leading coefficient i.e the coefficient of highest power of x to the bottom row.

Step 3:  Multiply a by the value just written on the bottom row and write this value just down of the number written next of leading coefficient.  Here, a is 1(taken from divisor)

Step 4:  Add the column made in step 3.  Repeat these steps until the last column reached.

In the second part,

It is given that divisor polynomial is the factor of given polynomial then we have to tell the remainder which is 0 because if divisor polynomial is the factor the it will completely divide the given polynomial which gives remainder 0.

In the third part,

Given when one uses the synthetic division to divide by (x-3) then what number is used to multiply each term that is dropped down or added.

As explained the steps of synthetic division in first part

x-3=0 ⇒ x=3 which is a

In step 3, Multiply a by the value just written on the bottom row and write this value just down of the number written next of leading coefficient. So, 3 is multiplied.

As explained in Step 2: Drop down the leading coefficient i.e the coefficient of highest power of x to the bottom row.

The columns which is formed by above steps are added.





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Answer:

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Find the value of x and y.
zysi [14]

Answer:

<em>x = 9</em>

<em>y = 36</em>

Step-by-step explanation:

<u>Lines and Angles</u>

Triangle CDE is isosceles. This means the two angles of the base DE are congruent (have the same measure):

7x + 1 = 4x + 28

Subtracting 4x + 1:

3x = 27

Dividing by 3:

x = 9

Substituting in the expression for the angles:

7x + 1 = 7*9 + 1 = 64°

The angles are 64° and 64°. The other internal angle at vertex C is 180°-64°-64°=52°. This angle is congruent with its vertical angle in the triangle ABC. We are given another angle of 43°. Thus the measure of angle A is 180°-52°-43°=85°

This last angle is equal to the expression of y:

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Subtracting 19:

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Removing the parentheses:

-6 + 2y = 66

Adding 6:

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Dividing by 2:

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The data show the traveler spend- ing in billions of dollars for a recent year for a sample of the states. Find the range, varia
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Solution :

Given data :

20.1     33.5     21.7      58.4     23.2     110.8     30.9

24.0    74.8     60.0

n = 10

Range : Arranging from lowest to highest.

20.1,   21.7,   23.2,    24.0,   30.9,    33.5,    58.4,    60.0,    74.8,   110.8

Range = low highest value - lowest value

           = 110.8 - 20.1

           = 90.7

Mean = $\frac{\sum x}{n}$

         $=\frac{20.1+21.7+23.2+24.0+30.9+33.5+58.4+60.0+74.8+110.8}{10}$

          $=\frac{457.4}{10}$

         $=45.74$

Sample standard deviation :

$S=\sqrt{\frac{1}{n-1}\sum(x-\mu)^2}$

$S=\sqrt{\frac{1}{10-1}(20.1-45.74)^2+(21.7-45.74)^2+(23.2-45.74)^2+(24.0-45.74)^2+(30.9-45)^2}$  

      \sqrt{(33.5-45.74)^2+(58.4-45.74)^2+(60.0-45.74)^2+(74.8-45.74)^2+(110.8-45.74)^2}

$S=\sqrt{\frac{1}{9}(657.4+577.9+508.0+472.6+220.2+149.8+160.2+203.3+844.4+4232.8)}$$S=\sqrt{\frac{1}{9}(8026.96)}$

$S=\sqrt{891.88}$

S = 29.8644

Variance = S^2

               =(29.8644)^2

               = 891.8823

6 0
3 years ago
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