Evaluate 5 x3 - 2 + 7 when x = -2.

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Work Shown:

sin(2x) = sin(x)

sin(2x) - sin(x) = 0

2*sin(x)*cos(x) - sin(x) = 0

sin(x)*(2cos(x) - 1) = 0

sin(x) = 0 or 2cos(x)-1 = 0

sin(x) = 0 or cos(x) = 1/2

Using the unit circle, the solutions to sin(x) = 0 are x = 0, x = pi, x = 2pi

Also, the solutions to cos(x) = 1/2 are x = pi/3, x = 5pi/3

So the entire solution set on the interval [0,2pi] is {0, pi/3, pi, 5pi/3, 2pi} when written in increasing order.

All solutions to the equation in the interval [0, 2[tex]\pi[/tex]]  is  {0, [tex]\frac{\pi }{3}, \pi , \frac{5\pi }{3} ,2\pi[/tex]}.

A solution is an assignment of values to the unknown variables that makes the equality in the equation true.

As sin2x = 2 sinx cosx,

sin2x = sinx is equivalent to

2 sinx cosx = sinx or 2 sinx cosx − sinx = 0 or

sinx (2cosx − 1) = 0 i.e.

either sinx = 0 and x = 0, π, 2π

or 2cosx − 1 = 0 i.e. cosx = [tex]\frac{1}{2}[/tex] i.e. x = [tex]\frac{\pi }{3} , \frac{5\pi }{3}[/tex]

Hence, solution to an equation is x = {0, [tex]\frac{\pi }{3}, \pi , \frac{5\pi }{3} ,2\pi[/tex]}

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Answer:

The series converges as any two consecutive elements of the sum are monotonically decreasing.

Step-by-step explanation:

The series converges since the consecutive element is monotonically decreasing. That is:

[tex]\forall\,i\in \mathbb{N}\,a_{i} > a_{i+1}[/tex] (1)

Where:

[tex]a_{i}[/tex] - The i-th component of the sum.

[tex]a_{i+1}[/tex] - The (i+1)-th component of the sum.

Answer: you can put it into addition form or multiplication just take the number from that place as the right amount of zeros behind it and you should be good so on 6 it could be 90 or if your suppose to be putting it in multiplication it would be 9x10

Step-by-step explanation:

Answer:

read below

Step-by-step explanation:

decomposed answ:

6. 9*10

7. 4*10

8. 89*10

9. 3*100

10. 7*1000

11. 37*100

decomposition:

12. 56*10

13. 43*100

14. 60*100

Answer:

is 0.24 yards in the option, becausw i am getting this as my answer

Answer:

6+18x

Step-by-step explanation:

=6(1+3x)

=6×1+6×3x

=6+18x

Answer:

Iliana cannot construct a triangle because the sum of the two smaller sides will not be greater than the third side.

Answer:

[tex]15\text{ grams}[/tex]

Step-by-step explanation:

Since the mass of the radioactive isotope is halved every 69 years, we want to multiply its initial mass by [tex]1/2[/tex] every 69 years.

We can model this using the following equation:

The remaining mass, [tex]f(x)[/tex], is equal to the initial mass multiplied by [tex]\frac{1}{2}^{(\frac{t}{69})}[/tex], where [tex]t[/tex] is the number of years that have passed from the initial mass. The reason why the exponent is [tex]\frac{t}{69}[/tex] is because we only want to half the mass every 69 years, so [tex]\frac{69}{69}=1[/tex] and [tex]\frac{1}{2}^1=\frac{1}{2}[/tex].

Thus, we have:

[tex]f(x)=20\cdot \frac{1}{2}^{(t/69)}[/tex]

Substituting [tex]t=30[/tex], we get:

[tex]f(x)=20\cdot \frac{1}{2}^{(30/69)}=20\cdot 0.73980522316=14.7961044632\approx \boxed{15\text{ grams}}[/tex]

Answer:

48160

Step-by-step explanation:

Answer:

6.55 cm

Step-by-step explanation:

A triangle is a polygon with three sides and three angles. Types of triangles are isosceles, acute, scalene, obtuse, right and equilateral triangle.

Cosine rule is used to show the relationship between sides and angles of a triangle. If a, b, and c are sides of a triangle, while A, B, and C are angles opposite to the corresponding sides. Then:

c² = a² + b² - 2ab*cos(C)

Given that PR = 13 cm, PQ = 12 cm and angle QPR = 30°, hence:

QR² = PR² + PQ² - 2(PR)(PQ)cos(∠QPR)

QR² = 13² + 12² - 2(13)(12)cos(30) = 169 + 144 - 270

QR² = 43

QR = 6.55 cm

Answer:

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Step-by-step explanation:

sorry di ko po alam yung sagot pasensiya na po

Given :

Parallel lines are

x – 2y = 3 and 2x – 4y = 12

Step-by-step explanation:

Lets write the given lines in slope intercept form y=mx+b

[tex]x -2y = 3 \\-2y=-x+3\\Divide \; both \; sides \; by -2\\y=\frac{x}{2} -\frac{3}{2}[/tex]

From the above equation , y intercept of first line is [tex]\frac{-3}{2}[/tex]

Solve the second equation for y and find out y intercept

[tex]2x-4y=12\\-4y=-2x+12\\Divide \; by \; -4\\y=\frac{1}{2} x-3[/tex]

y intercept of second line is -3

To find the distance between parallel lines, we subtract the y intercepts

[tex]\frac{-3}{2} -(-3)=\frac{-3}{2} +\frac{6}{2} =\frac{3}{2} =1.5[/tex]

Answer:

The distance between the parallel lines = 1.5

Reference:

https://brainly.com/question/24145911

Answer:

m<L, m<K, m<J

Step-by-step explanation:

The angle that sees the longest side length has the biggest measurement

so

for listing the angles from smallest to largest

m<L, m<K, m<J

Answer:K J L

Step-by-step explanation:

Answer:

Mariana takes the two pills together after 18 hours.

Step-by-step explanation:

Mariana must take two pills; one every 6 hours and another every 9 hours.

She take two pills together. Let she takes the two pills together after t hours at the time when she take initially.

To find the time to take the two pills together, take the least common multiple of 6 and 9.

6 = 2 x 3

9 = 3 x 3

So, the least common multiple is 2 x 3 x 3 = 18

So, she takes the two pills together after 18 hours.

Oh shucks man, I'm sorry bout that

Answer:

1<1.35<2

Step-by-step explanation:

Answer:

1.35 is closer to 1 than 2

So the bag of nuts weighed about 1 pound.

Step-by-step explanation:

The decimal is closer to the whole number 1 when plotted on a number line, so it rounds to 1.

Answer:

The table will be:

x |-2 | -1 | 0 | 1 | 2  

y | 1  | 4 | 5 | 4 | 2

Step-by-step explanation:

The function is:

[tex]y=5-x^{2}[/tex]

a) The x values of the table is:

x |-2 | -1 | 0 | 1 | 2

So, when x = -2, y will be:

[tex]y(-2)=5-(-2)^{2}=5-4=1[/tex]

Doing the same with the other x values we have:

[tex]y(-1)=5-(-1)^{2}=5-1=4[/tex]

[tex]y(0)=5-(0)^{2}=5[/tex]

[tex]y(1)=5-(1)^{2}=5-1=4[/tex]

[tex]y(2)=5-(2)^{2}=5-4=1[/tex]

The table will be:

x |-2 | -1 | 0 | 1 | 2  

y | 1  | 4 | 5 | 4 | 1

I hope it helps you!

Answer:

sorry

Step-by-step explanation:

hindi ko din alam

1. Answer is option 3

2. Answer is option 3

Answer:

for #1 it's the 3rd one and for #2 it's the 4th one (2.8 meters)

Answer:

The first one with the sequence 0.25,1,4,16

Answer:

the first one

Step-by-step explanation:

Answer:

[tex]P(G)=0.475[/tex]

Step-by-step explanation:

From the question we are told that:

Number of boys[tex]N_b=357[/tex]

Number of girls [tex]N_g=323[/tex]

Total Number of students

[tex]N_t=N_b+N_g[/tex]

[tex]N_t=680[/tex]

Generally the equation for Probability of Choosing a Girl is mathematically given by

[tex]P(G)=\frac{N_g}{N_t}[/tex]

[tex]P(G)=\frac{323}{680}[/tex]

[tex]P(G)=0.475[/tex]

Answer: i do not see a graph

Step-by-step explanation:

Answer:

96 cm 2

Option A is the correct answer

Step-by-step explanation:

Please mark me as Brainliest

Step-by-step explanation:

pls type the question

properly and I swear I will solve it

Answer:

7 times 5

35

divided by two

17.5

times 3

52.5 cubic inch

Answer:

12

Step-by-step explanation: