Ask question

Ask question

All categories

Makovka662 [10]

2 years ago

10

Jenny thinks that the expression below is equal to x²-4. If you agree, show that she is correct. If you disagree, show that she

is wrong by rewriting this expression as a polynomial in standard form.(x-2)³∕x-2

1 answer:

sergiy2304 [10]2 years ago

8 0

Answer:

Jenny is wrong the correct answer is x²+ 4 - 4 x.

Step-by-step explanation:

Given that

(x-2)³∕x-2

(x-2)³∕(x-2) =(x-2) (x-2)²∕(x-2)

(x-2)³∕(x-2) = (x-2)²

As we know that

(a-b)² = a²+b² - 2 ab

So

(x-2)² = x²+ 2² - 2 ˣ 2 ˣ x = x²+ 4 - 4 x

(x-2)² = x²+ 4 - 4 x

It means that

(x-2)³∕(x-2) = (x-2)² = x²+ 4 - 4 x

So Jenny is wrong the correct answer is x²+ 4 - 4 x.

You might be interested in

when a number is added to 1/5 of itself, the result is 24. the equation that models this problem is n 1/5 n = 24. what is the va

GuDViN [60]

Let n be unknown number, then 1/5 of this number is 1/5n. When you add these two numbers, you get

$n+\dfrac{1}{5} n.$

You know that this sum is equal to 24, so

$n+\dfrac{1}{5} n=24.$

1. Multiply this equation by 5:

$5n+n=120.$

2. Solve it:

$6n=120,\\n=120:6,\\n=20.$

Answer: n=20, correct choice is B.

4 0

2 years ago

Read 2 more answers

Francesca’s Labrador retriever has delivered a litter of five puppies. Two are chocolate, two are yellow, and one is black. The

anyanavicka [17]

Answer:

50-50 chance of black puppy

Step-by-step explanation:

4 0

2 years ago

Two pipes can fill a tank in 19 minutes if both are turned on. If only one is used, it would take 49 minutes longer for the smal

a_sh-v [17]

Answer:

The time taken by smaller pipe to fill the tank alone is 74.2 min

Step-by-step explanation:

Given as :

The time taken by two pipes to fill tank = 19 min

Let the time taken by larger pipe to fill tank = y

And the time taken by smaller pipe to fill tank = x

According to question

The smaller pipe takes 49 minutes longer than larger pipe

I.e x = y + 49

Now,

$\dfrac{1}{x}$ + $\dfrac{1}{y}$ = $\dfrac{1}{49}$

Or, $\dfrac{1}{y + 49}$ + $\dfrac{1}{y}$ = $\dfrac{1}{49}$

Or, $\dfrac{y + 49 + y}{y^{2} + 49 y }$ = $\dfrac{1}{49}$

Or, 2 y + 49 = $\dfrac{y^{2}+49y }{19}$

Or, 19 × ( 2 y + 49 ) = y² + 49 y

Or, 38 y + 931 = y² + 49 y

Or, y² + 49 y - 38 y - 931 = 0

or, y² + 11 y - 931 = 0

Or, Applying quadratic equation method to calculate the value of y

so, y = $\frac{- b \pm \sqrt{b^{2}-4\times a\times c}}{2\times a}$

Or, y = $\frac{- 11 \pm \sqrt{11^{2}-4\times 1\times (-931)}}{2\times 1}$

Or, y = $\frac{- 1 \pm \sqrt{121+3724}}{2}$

or, y = $\frac{- 1 \pm \sqrt{3845}}{2}$

or, y = $\frac{- 1 \pm 62.008}{2}$

∴ y = 25.2 , - 36.5

So, The time taken by larger pipe = y = 25.2 min

and the time taken by smaller pipe to fill the tank = y + 49 = 25.2 + 49 = 74.2 min

Hence The time taken by smaller pipe to fill the tank alone is 74.2 min answer

6 0

3 years ago

The sum of two positive numbers is 42. What is the smalles possible value of the sum of their squares?

Mkey [24]

Okie, it is not too hard.
Set these numbers a and b, notice a, b positive.
We have a+b=42.
You can see the next on my photo

Or you can use the formula of Cauchy

3 0

3 years ago

A rectangle has a height of k2 + 3 and a width of k2 + 7.

ElenaW [278]

Answer:

The area of the rectangle in polynomial form is $k^4 +10 k^2 + 21$

Step-by-step explanation:

Given

Shape: Rectangle

$Height: k^2 + 3$

$Width: k^2 + 7$

Required

Area of the rectangle

The area of a rectangle is calculated as thus;

$Area = Length * Width$

By substituting $k^2 + 3$ for height and $k^2 + 7$ for width; This gives

$Area = (k^2 + 3)(k^2 + 7)$

Expand the bracket

$Area = k^2(k^2 + 7) + 3(k^2 + 7)$

Open each bracket

$Area = k^2*k^2 + k^2*7 + 3*k^2 + 3*7$

$Area = k^4 +7 k^2 + 3k^2 + 21$

$Area = k^4 +10 k^2 + 21$

Hence, the area of the rectangle in polynomial form is $k^4 +10 k^2 + 21$

5 0

3 years ago