Write x2 + 6x +13 in the form (x + a)

2 + b where a and b are integers.

Answer:

[tex]\displaystyle x=\left\{\frac{\pi}{6}+2n\pi, \frac{5\pi}{6}+2n\pi, \frac{3\pi}{2}+2n\pi\right\}, n\in\mathbb{Z}[/tex]

Step-by-step explanation:

We are given the equation:

[tex]2\cos^2(x)=\sin(x)+1[/tex]

And we want to find all solutions for x.

First, we should put the equation into terms of only one trigonometric ratio.

Since we are given cos²(x), we can turn this into sine. Recall the Pythagorean Identity which states:

[tex]\sin^2(x)+\cos^2(x)=1[/tex]

Therefore:

[tex]\cos^2(x)=1-\sin^2(x)[/tex]

By substitution:

[tex]2(1-\sin^2(x))=\sin(x)+1[/tex]

Distribute:

[tex]2-2\sin^2(x)=\sin(x)+1[/tex]

Isolate the equation:

[tex]2\sin^2(x)+\sin(x)-1=0[/tex]

We can factor:

[tex](2\sin(x)-1)(\sin(x)+1)=0[/tex]

Zero Product Property:

[tex]2\sin(x)-1=0\text{ or } \sin(x)+1=0[/tex]

Solve for each case:

[tex]\displaystyle \sin(x)=\frac{1}{2}\text{ or } \sin(x)=-1[/tex]

We can use the unit circle.

sin(x) = 1/2 for every π/6 and 5π/6. So, it will continue every 2π.

sin(x) = -1 every 3π/2. And this will also continue every 2π.

Hence, our solutions are:

[tex]\displaystyle x=\left\{\frac{\pi}{6}+2n\pi, \frac{5\pi}{6}+2n\pi, \frac{3\pi}{2}+2n\pi\right\}, n\in\mathbb{Z}[/tex]

Note:

If you only need the solutions within the interval [0, 2π), then it is:

[tex]\displaystyle x=\left\{\frac{\pi}{6}, \frac{5\pi}{6}, \frac{3\pi}{2}\right\}[/tex]

Answer:

The volume would be 36

Step-by-step explanation:

Trust me

The required expression is 2h+17 where h is the height of Chrissy.

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Given is a statement, 17 more than twice Chrissy's height, we are asked to convert this statement into an expression,

Let Chrissy's height be h,

Then,

2h+17

Hence, the required expression is 2h+17 where h is the height of Chrissy.

Learn more about expressions, click;

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Answer:

Step-by-step explanation:

a) x² - 10x + 25 = 0

(x-5)²=0

x-5=0

x=5

b) x² - 4x - 5 = 0

⇒ ( x 2 − 4 x + 4 ) − 5 − 4 = 0

⇒ ( x 2 − 4 x + 4 ) − 9 = 0

( x − 2 ) 2 − 9 = 0 ⇒

( x − 2 ) 2 = 9 ⇒

( x − 2 ) = ± √ 9 (don't forget the ± !) ⇒

x= − 1   x = 5

Answer:

Unfortunately, I can't be able to see the image. Please adjust.

Answer:

The number of large size candles sells are 12 and the number of small size candles are 5 .

Step-by-step explanation:

As given Sia sells large candles for $3 each and small candles for $2 each.She sold 17 candles for $46.00.Let us assume that the large size candle sells are x .Let us assume that the small size candle sells are y.             Equation becomes

x + y = 17

3x + 2y = 46

Multiply x + y = 17 by 3 and subtracted from 3x + 2y = 46 .

3x - 3x + 2y - 3y = 46 - 51

-y = - 5

y = 5

Put in the equation x + y = 17 .

x + 5 = 17

x = 17 - 5

x = 12

Therefore the number of large size candles sells are 12 and the number of small size candles are 5

Answer:

She used her bed for her dollhouse

Step-by-step explanation:

Answer:

5 units

Step-by-step explanation:

Calculate the distance d using the distance formula

d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1 )^2 }[/tex]

with (x₁, y₁ ) = (6, 4) and (x₂, y₂ ) = (3, 8)

d = [tex]\sqrt{(3-6)^2+(8-4)^2}[/tex]

   = [tex]\sqrt{(-3)^2+4^2}[/tex]

   = [tex]\sqrt{9+16}[/tex]

    = [tex]\sqrt{25}[/tex]

    = 5

Answer:

5

Step-by-step explanation:

Answer:

(ABOUT) 28.27433

Step-by-step explanation:

C = 2πr or dπ (because 2*r = d)

For this case:

C = dπ

C = 9π

C = 28.27433

You can round if you want to (like 28.3 or 29.27).

Answer:

c

Step-by-step explanation:

Answer:

A. way to pay in advance for using a car for a given time period

Step-by-step explanation:

I think so..

Answer:

C) a way to borrow money from a band or financial institution to pay for a car

Answer:

20

Step-by-step explanation:

Answer: it’s C

Step-by-step explanation:

Answer:

0.0416667

Step-by-step explanation:

Answer:

b. 4m

Step-by-step explanation:

congruent polygons means same shape, size, angles, and sides.

ANSWER:

Caso estadístico: Altura de las mujeres de la poblacion indigena Sikuani.

Step-by-step explanation:

Población: Mujeres de la comunidad sikuani

Muestra: se toma una muestra de 20 datos para calcular la altura ,este dato se toma de la población total  de 165 mujeres.

M: ( 1.30, 1.20, 1.50, 1.52, 1.60, 1.37, 1.28, 1.55,1.46, 1.26, 1.57, 1.58, 1.54, 1.38, 1.56, 1.23, 1.59, 1.62, 1.48, 1.40)

Variable: Altura

Recorrido de la  variable: El recorrido de la variable es la diferencia entre el valor máximo de la muestra y el valor mínimo.

Altura máxima: 1.62 m.

Altura mínima : 1.20

Como ya tenemos el valor máximo y el valor mínimo ,podemos hallar el recorrido de la variable.

                               R=( 1.62m -1.20m)

                                        R= 0.42

Answer: 268

Step-by-step explanation: substitute pi with 3.14, & then 4^3 as 64 in the second line. after, you multiply 3.14 x 64 you get 201 after you round. finally multiply 4 x 201 then divide your answer by 3. you get 268. (no one helped so i did)

Answer:  100%

97:97*100 =

(97*100):97 =

9700:97 = 100

Now we have: 97 is what percent of 97 = 100

Question: 97 is what percent of 97?

Percentage solution with steps:

Step 1: We make the assumption that 97 is 100% since it is our output value.

Step 2: We next represent the value we seek with $x$.

Step 3: From step 1, it follows that $100\%=97$.

Step 4: In the same vein, $x\%=97$.

Step 5: This gives us a pair of simple equations:

$100\%=97(1)$.

$x\%=97(2)$.

Step 6: By simply dividing equation 1 by equation 2 and taking note of the fact that both the LHS

(left hand side) of both equations have the same unit (%); we have

$\frac{100\%}{x\%}=\frac{97}{97}$

Step 7: Taking the inverse (or reciprocal) of both sides yields

$\frac{x\%}{100\%}=\frac{97}{97}$

$\Rightarrow x=100\%$

Therefore, $97$ is $100\%$ of $97$.

Answer:

100%

Step-by-step explanation:

Answer:

3333.4

Step-by-step explanation:

bc i said so

Answer:

ion lolz 7.4

Step-by-step explanation:

Answer:

403 miles

Step-by-step explanation:

500 mph is 500 miles per hour

30 minuites is half an hour, so that is 250 miles west

60 degrees west, 600 miles away

so it is a triagle of 30 60 and 90.

600 is the hypotenuse of the 30 60 90 triangle

we need to find the height of the 30 60 90 triangle

using the special rule, the height is 300

the length of the 30 60 90 triangle is 300rt3

so 300rt3 - 250  is the length of another triangle.

height is still 300

hypotenuse is the distance of the actual area minus the plane's current position

(300^2 + (300rt3-250)^2)^1/2 is about 403.351433

Answer:

with what??!!

Step-by-step explanation:

Answer:

This is essay thank you

Step-by-step explanation:

Answer:

JUST MULTIPLY 4x12=.... and youll find the answer

Step-by-step explanation:

4yarn x 12 inches= 48ft

Answer:

24 cans.

Step-by-step explanation:

6$ for each 12 cans, 12x4=48, so 6x4=24.

Answer:

$24

Step-by-step explanation:

Hope this helped you!

Answer:

pretty sure it is 1.8478125

Step-by-step explanation:

Answer:

1) Area = ½ b × h

= ½ × 6 × 4

= 12

2) Area = ½b × h

= ½ × 3 × 4

= 6

3) Area = ½b × h

= ½ × 4 × 7

= 14

Answer:

[tex]92[/tex]

Step-by-step explanation:

[tex]2 {a}^{2} + 5 {b}^{2} \\ 2 \times {( - 6)}^{2} + 5 \times {2}^{2} \\ 2 \times 36 + 5 \times 4 \\ 72 + 20 \\ = 92[/tex]

Hope this helps you.

Can I have the brainliest please?