Ask question

Ask question

All categories

2 years ago

5

Which expression is equivalent to x² + 2x + 2?

1 answer:

melisa1 [442]2 years ago

4 0

Answer:

$(x+1-i)(x+1+i)$

Step-by-step explanation:

$(x+1-i)(x+1+i)\\\\=(x+1)^2 -i^2~~~~~~~~~~~~~;[a^2 -b^2 = (a+b)(a-b)]\\\\=x^2 +2x +1 -(-1)\\\\=x^2 +2x +1+1\\\\=x^2 +2x +2$

You might be interested in

Ashe feels she needs $45,000 per year in retirement. If she receives $2,500 a month from Social Security, at what interest rate

lesya692 [45]

Answer:

15,000 from her savings

Step-by-step explanation:2,500*12=30,000 45000-30,000=15,000

5 0

3 years ago

Kathleen worked for 4 hours and 45 minutes. How should she write that on her time card?

Yuri [45]

Answer:

4.75 hours.

Step-by-step explanation:

We have been given that Kathleen worked for 4 hours and 45 minutes.

We will convert 45 minutes to hours by dividing 45 by 60 as one hour has 60 minutes.

$\frac{\text{45 minutes}}{\frac{60\text{ minutes}}{\text{hour}}}$

$\frac{\text{45 minutes}}{60}\times \frac{\text{ hour}}{\text {minutes}}$

$\frac{3}{4}\times \text{ hour}$

$0.75\text{ hour}$

Therefore, she should write 4.75 hours on her time card.

6 0

3 years ago

Leonhard wants to place a triangular-based cabinet in the corner of his rectangle-shaped living room. The triangular base has a

almond37 [142]

Answer:

A. $x=\frac{-7+\sqrt{193}}{4}$

Step-by-step explanation:

We have, the dimensions of the living room are 30 ft and 20 ft.

Thus, area of the living room = length × width = 30 × 20 = 600 ft².

Now, it is given that the cabinet takes 6% of the living room i.e. 6% of 600 ft² = 0.06 × 600 = 36 ft².

As, the triangle has dimensions (2x+3) ft and (3x+6) ft.

So, the area of the triangle = $\frac{1}{2}\times base\times height$

i.e. Area of cabinet = $\frac{1}{2}\times (2x+3)\times (3x+6)$

i.e. Area of cabinet = $\frac{3}{2}\times (2x+3)\times (x+2)$

i.e. Area of cabinet = $\frac{3}{2}\times (2x^2+7x+6)$

Since, the cabinet takes 6% of the living room, we have,

$\frac{3}{2}\times (2x^2+7x+6)$ = 36

i.e. $2x^2+7x+6=36\times \frac{2}{3}$

i.e. $2x^2+7x+6=24$

i.e. $2x^2+7x-18=0$

Further, as the solution of a quadratic equation $ax^{2}+bx+c=0$ is given by $x=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}$

On comparing we have, a=2, b=7, c= -18.

Thus, $x=\frac{-7\pm \sqrt{7^{2}-4\times 2\times (-18)}}{2\times 2}$

i.e. $x=\frac{-7\pm \sqrt{49+144}}{4}$

i.e. $x=\frac{-7\pm \sqrt{193}}{4}$

i.e. $x=\frac{-7+\sqrt{193}}{4}$ and $x=\frac{-7-\sqrt{193}}{4}$

So, according to the options, we have,

A. $x=\frac{-7+\sqrt{193}}{4}$ is the correct value of x.

7 0

3 years ago

Can someone help me solve this problem please ? 3(8-6)=t

iVinArrow [24]

T= 6 that is the answer

7 0

4 years ago

Read 2 more answers

Whats the name of the fifth American president

-BARSIC- [3]

Answer:

the fifth president name was James Monroe

7 0

3 years ago