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2 years ago

12

Complete the square for x^2+12x-5.

1 answer:

Setler [38]2 years ago

3 0

Answer:

$x^2+12x-5=(x+6)^2-41$

Step-by-step explanation:

The given expression is $x^2+12x-5$

Comparing to $ax^2+bx+c$ , we have $a=1,b=12,c=-5$

We add and subtract $(\frac{b}{2a})^2$

$x^2+12x+6^2-6^2-5$

This implies that:

$\boxed{x^2+6x+36}-36-5$

The expression in the rectangle is a perfect square

$(x+6)^2-41$

Therefore $x^2+12x-5=(x+6)^2-41$

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Verify the identity. <br><br> sin (x+pi/2)=cos x

hram777 [196]

Given data
<span>sin (x+pi/2)=cos x
</span>now using sin law
sin(a+b)=sin(a)cos(b)+cos(a)sin(b)
now using above values
sin(pi/2+x)=sin(pi/2)cos(x)+cos(pi/2)sin(x)
as we know that
sin(pi/2)=1
cos(pi/2)=0
now putting these values
sin(pi/2+x)=1*cosx+0*1
sin(pi/2+x)=cosx
hence proved that

<span>sin (x+pi/2)=cos x</span>

4 0

3 years ago

3u+5u=64<br> What is the simplify of this <br> What does u

Nutka1998 [239]

Answer:

u = 8

Step-by-step explanation:

3u + 5u = 64

8u = 64

8u/8 = 64/8

u = 8

8 0

3 years ago

Jasmine rides her bike 9 miles in 50 minutes. what is jasmines speed per hour

Firdavs [7]

<u>Given</u>:

Given that Jasmine rides her bike 9 miles in 50 minutes.

We need to determine the speed per hour.

<u>Time per hour:</u>

The time taken is 50 minutes. We need to convert minutes into hours.

Thus, we have;

$\frac{50}{60}=\frac{5}{6} \ hr$

Thus, the time taken to cover 9 miles is $\frac{5}{6} h r$

<u>Speed:</u>

The speed can be determined using the formula,

$Speed =\frac{Distance}{Time}$

Substituting the values, we have;

$Speed =\frac{9}{(\frac{5}{6})}$

Simplifying, we get;

$Speed =9 \times {\frac{6}{5}}$

$Speed =\frac{54}{5}$

$Speed = 10.8$

Thus, Jasmine's speed is 10.8 miles per hour.

3 0

2 years ago

What is the length of the given segments EF and GH?

erastovalidia [21]

Answer:

$EF = 5$

$GH = 5$

Step-by-step explanation:

Length of EFis the distance between E(-4, -3) and F (-1, 1).

$EF = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

Let,

$E(-4, -3) = (x_1, y_1)$

$F(-1, 1) = (x_2, y_2)$

$EF = \sqrt{(-1 -(-4))^2 + (1 -(-3))^2}$

$EF = \sqrt{(3)^2 + (4)^2}$

$EF = \sqrt{9 + 16} = \sqrt{25}$

$EF = 5$

Distance between G(-2, -3) and H(3, -3)

$GH = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

Let,

$G(-2, -3) = (x_1, y_1)$

$H(3, -3) = (x_2, y_2)$

$GH = \sqrt{(3 -(-2))^2 + (-3 -(-3))^2}$

$GH = \sqrt{(5)^2 + (0)^2}$

$GH = \sqrt{25 + 0} = \sqrt{25}$

$GH = 5$

4 0

3 years ago

Karen earns her living as a salary plus commission employee. Her annual salary is $42,000, and she earns 5% commission on all sa

castortr0y [4]

Answer: c
;) hope this helps

7 0

2 years ago