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NeTakaya
3 years ago
11

1. Kalena was asked to prove ifx(x - 1)(x + 1) = x3 - X represents a polynomial identity. She

Mathematics
1 answer:
Verdich [7]3 years ago
6 0

Answer:

C. Kalena made a mistake in Step 3. The justification should state: -x²

+ x²

Step-by-step explanation:

Given the function x(x - 1)(x + 1) = x3 - X

To justify kelena proof

We will need to show if the two equations are equal.

Starting from the RHS with function x³-x

First we will factor out the common factor which is 'x' to have;

x(x²-1)

Factorising x²-1 using the difference of two square will give;

x(x+1)(x-1)

Note that for two real number a and b, the expansion of a²-b² using difference vof two square will give;

a²-b² = (a+b)(a-b) hence;

Factorising x²-1 using the difference of two square will give;

x(x+1)(x-1)

Factorising x(x+1) gives x²+x, therefore

x(x+1)(x-1) = (x²+x)(x-1)

(x²+x)(x-1) = x³-x²+x²-x

The function x³-x²+x²-x gotten shows that kelena made a mistake in step 3, the justification should be -x²+x² not -x-x²

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Is 4/6 is closer to a whole than 1/2
Andreas93 [3]

Answer:

yes

Step-by-step explanation:

1/2=3/6

4/6=4/6

4/6>3/6

therefore as long as both fractions are less than a whole the bigger the fraction is the closer it is to a whole.

6 0
3 years ago
Read 2 more answers
if angle A and angle B are supplementary, and angle A and angle C are supplementary. What conclusion is valid
Fantom [35]

Answer:

no angle c is not supplementary

Step-by-step explanation:

 

Angle A and angle B are supplementary

 

A+B=180°   Equation 1

 

The measure of angle B is equal to four times the complement of angle A

 

The complement of angle A=90°-A

 

B=4(90°-A)  

 

B=360°-4A

 

Substitute the value of B in equation 1

 

A+360°-4A=180°

 

-3A=-180°

 

A=60°

 

The measure of angle A=60°

 

B=360°-4A=360°-4(60°)=120°

 

The measure of angle B=120°

6 0
3 years ago
Read 2 more answers
A bag contains 2 red marbles, 7 blue marbles and 5 green marbles. If two marbles are drawn out of the bag, what is the exact pro
vivado [14]

Answer:

0.25 or 25%.

Step-by-step explanation:

2 Red + 3 Blue + 7 Green = 12 Total Marbles.

You have 3 blue marbles out of the total marbles, so 3/12, then simplify it. 3/12 = 1/4. This gives you 0.25, or 25%.  

The probability of drawing a blue marble is 0.25 or 25%

4 0
2 years ago
At an electronics store, a $165 television is marked up 110%. Dave purchases the TV and must pay 6.5% sales tax. What is his fin
Mariana [72]
Firstly, we need to know the price of the TV after the 110$ increase.
     $165 x 1.10 = $181.50
[This is an increase of $16.50]
[1.10 is the equivalent of 110%. 1 being 100% and the .10 being 10%]

Now for the sales tax. We apply a similar method.
     $181.50 x 0.065 = $11.79
     6.5% of $181.50 is $11.79, so we add the two together to find the final cost.

The final cost of the TV is $193.29
4 0
3 years ago
Complete the square to rewrite y-x^2-6x+14 in vertex form. then state whether the vertex is a maximum or minimum and give its co
ycow [4]

Answer:

y= x^2 -6x +(\frac{6}{2})^2 +14 -(\frac{6}{2})^2

And solving we have:

y= x^2 -6x +9 + 14 -9

y= (x-3)^2 +5

And we can write the expression like this:

y-5 = (x-3)^2

The vertex for this case would be:

V= (3,5)

And the minimum for the function would be 3 and there is no maximum value for the function

Step-by-step explanation:

For this case we have the following equation given:

y= x^2 -6x +14

We can complete the square like this:

y= x^2 -6x +(\frac{6}{2})^2 +14 -(\frac{6}{2})^2

And solving we have:

y= x^2 -6x +9 + 14 -9

y= (x-3)^2 +5

And we can write the expression like this:

y-5 = (x-3)^2

The vertex for this case would be:

V= (3,5)

And the minimum for the function would be 3 and there is no maximum value for the function

4 0
3 years ago
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