4. Find a pair of irrational numbers whose product is an integer.

Answer:

[tex]\displaystyle \theta = \left\{\frac{7\pi}{6}, \, \frac{3\pi}{2}, \frac{11\pi}{6}\right\}[/tex]

Step-by-step explanation:

We want to solve the equation:

[tex]2\sin ^2 \theta + 3\sin \theta + 1 = 0[/tex]

In the interval [0, 2π).

Notice that this is in quadratic form. Namely, by letting u = sin(θ), we acquire:

[tex]\displaystyle 2u^2 + 3u + 1 = 0[/tex]

Factor:

[tex]\displaystyle (2u+1)(u+1) = 0[/tex]

By the Zero Product Property:

[tex]\displaystyle 2u + 1 = 0\text{ or } u + 1 = 0[/tex]

Solve for each case:

[tex]\displaystyle u = -\frac{1}{2} \text{ or } u = -1[/tex]

Back-substitute:

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

Use the Unit Circle. Hence, our three solutions in the interval [0, 2π) are:

[tex]\displaystyle \theta = \left\{\frac{7\pi}{6}, \, \frac{3\pi}{2}, \frac{11\pi}{6}\right\}[/tex]

hi

formula for cicrle circumference is 2 *radius*Pi

as radius is 45, Pi is 3.14....

I let you do the math...

Answer:

Step-by-step explanation:

Possible largest numbers using digit 0 , 1 , 2

222  

221  

220  

212  

211  

210  

222 + 210  = 221 + 211  = 220  + 212 = 432

Largest total can be 432

Answer:

x = 47/7 or 6.714

Step-by-step explanation:

7 (x+3) = 72-4

7x + 21 = 68

7x = 68 - 21

7x = 47

x = 47/7 or 6.714

Answer:

Step-by-step explanation:

Supplement angle is 57degree 15'

Answer:

Month 1: 500 - 15 = 485

Month 2: 485 - 15 = 460

Month 3: 460 - 15 = 445

Month 4: 445 - 15 = 430

Step-by-step explanation:

Answer:

5 m/s²

Step-by-step explanation:

t (time) = 5 s

u (initial velocity) = 0m/s

v (final velocity) = 25m/s

a = (v-u)/t

a = (25-0)/5

a = 25/5

a = 5 m/s²

Answer:

[tex] \frac{25 {x}^{2} y}{729} [/tex]

Step-by-step explanation:

[tex]5xy \times \sqrt{ \frac{25 {x}^{2} }{ {9}^{6} } } [/tex]

[tex]5xy \times \frac{5x}{ {9}^{3} } [/tex]

[tex] \frac{25 {x}^{2} y}{ {9}^{3} } [/tex]

[tex] = \frac{25 {x}^{2}y }{729} [/tex]

Answer:

5

Step-by-step explanation:

Answer:

Corresponding angles for  similar triangles are equal

Corresponding angles and sides are equal for congruent triangles (they may be superimposed)

9514 1404 393

Answer:

  1. (f+g)(x) = 2x^2 +4x +2

  2. (f -g)(x) = -2x^2 +4x -4

  5. (f+g)(x) = x^2 +2x -1

  6. (g -f)(x) = x^2 -2x -1

Step-by-step explanation:

None of these are compositions. They are only sums or differences.

  (f±g)(x) = f(x) ± g(x)

__

1. (f+g)(x) = f(x) +g(x) = (4x -1) +(2x^2 +3)

  (f+g)(x) = 2x^2 +4x +2

__

2. (f -g)(x) = f(x) -g(x) = (4x -1) -(2x^2 +3)

  (f -g)(x) = -2x^2 +4x -4

__

5. (f +g)(x) = f(x) +g(x) = (2x) +(x^2 -1)

  (f+g)(x) = x^2 +2x -1

__

6. (g -f)(x) = g(x) -f(x) = (x^2 -1) -(2x)

  (g -f)(x) = x^2 -2x -1

Answer:

money = 1.45x - .20

Step-by-step explanation:

money made = first subscription + rest of subscriptions

Let x = number of subscriptions

We x-1 for the rest of the subscriptions since we already counted the first one

20 cents more than what was paid for the first one

money = 1.25 +(1.25+.20)(x-1)

money = 1.25 +(1.45)(x-1)

Distribute

money = 1.25 +1.45x-1.45

Combine like terms

money = 1.45x - .20

Answer:

D.

Step-by-step explanation:

the starting number is 370 and it gets multiplied by 1.11 every year so you would root the equation by t

The equation fourth represents the population of 370 animals that increases at an annual rate of 11% option fourth is correct.

It is defined as the function that rapidly increases and the value of the exponential function is always positive. It denotes with exponent y = a^x

where a is a constant and a>1

We have:

A population of 370 animals that increases at an annual rate of 11%

Initial value a = 370

rate r = 11% = 0.11

The equation:

[tex]\rm p = a(1 + r)^t[/tex]

[tex]\rm p = 370(1 + 0.11)^t[/tex]

Thus, the equation fourth represents the population of 370 animals that increases at an annual rate of 11% option fourth is correct.

Learn more about the exponential function here:

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x=7 is the solution for the given equation

x=4 is the extraneous solution .

Given :

[tex]\sqrt{x-3} +5=x[/tex]

Explanation :

To solve the given equation for x , we need to remove the square root first

Subtract 5 on both sides

[tex]\sqrt{x-3}+5=x\\ \sqrt{x-3}=x-5\\\\[/tex]

Take square on both sides to remove square root

[tex]x-3=(x-5)^2\\x-3=x^{2} -10x+25\\[/tex]

Subtract x  and add 3 on both sides

[tex]0=x^{2} -11x+28\\0=(x-7)(x-4)\\[/tex]

Set the factors =0 and solve for x

[tex]x-7 =0\\x=7\\\\\\x-4=0\\x=4[/tex]

x values are 4  and 7

Now we check the values using original equation and verify it

[tex]x=4\\\sqrt{x-3} +5=x\\\sqrt{4-3} +5=4\\\\6=4 \\[/tex]

x=4 does not satisfies the original equation

Now we check x=7

[tex]\sqrt{7-3} +5=7\\7=7[/tex]

x=7 is the solution  

Learn more :  brainly.com/question/13401711

Answer:

Step-by-step explanation:

Let the number of days is x.

Joseph tweets 13 times a day.

The number of tweets after x days would be:

t(x) - number of tweets after x days.

Answer:

C. 2

Step-by-step explanation:

2y and 0,0 are the same

Answer:

The answer is B) There is one proportional relationship

Step-by-step explanation:

The green line (the one at the top) does not go through the origin. This is not a proportional relationship.

Problem: It does not go through 0,0

----------------------------------------------------------------------------------------------------------------

The blue line (the one in the middle) is a straight line through the origin. This is a proportional relationship.

Reason: It goes through 0,0

----------------------------------------------------------------------------------------------------------------

The purple line (the one at the bottom) does not go through the origin. This is not a proportional relationship.

Problem: It does not go through 0,0

----------------------------------------------------------------------------------------------------------------

Conclusion: Since the green and purple lines are not proportional but the blue line is, this means only 1 line is proportional.

Note:

I know my answer is very late but I wanted to help anyone who needs it for future reference.

Answer:

Answer:

[tex]( - 8x + 3y) - (x + 4y) \\ = - 8x + 3y - x - 4y \\ = - 9x - y \\ thank \: you[/tex]

Answer:

34 1/2 miles

Step-by-step explanation:

92 miles = 2 2/3 hours

x miles = 1 hour

92 ÷ 2 2/3 = 34.5

34.5 x 1 = 34.5

34.5 miles = 1 hour

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

C.-3/4................

The required diagram could be used to represent the context if x represents how much each bottle of juice cost is D. Option D is correct.

Given that,
She bought a bag of popcorn for $3.39 and a 4-pack of juice bottles. The total cost before tax was $7.43.
To determine the diagram could be used to represent the context if x represents how much each bottle of juice costs.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,

Here,
Let the cost of each juice bottle be x.
Now,
accoding to the question,
4x = 7.43 - 3.39

Thus, the required diagram could be used to represent the context if x represents how much each bottle of juice cost is D. Option D is correct.

Learn more about arithmetic here:

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Answer:

340

Step-by-step explanation:

Anything greater or equal to 345 will be rounded to 350  

and anything less than 345 will be rounded to 340,  

So the numbers is:-

340

Answer: C

Hello,

Step-by-step explanation:

WZ=7-3=4

YW²=XW*WZ=3*4=12 ==> WY=2√3

In the right triangle YWZ, using the Pythagorean's theorem:

YZ²=WY²+WZ²=12+4²=28

YZ=2√7≅5.29150....

Answer C

Answer:

9

Step-by-step explanation:

Let Benjamin's age be=x.

Let Lucas's age be=y.

Then, x=2y-6

When x=12, 12+6=2y.

18/2=y, y=9

Answer:

[tex]-\frac{11}{3} \leq x\leq -1[/tex]

Hope this helps!! <3

Answer:

$3,140,835

Step-by-step explanation:

4,119,184-978,349=3,140,835

hope this helped!

Answer:

<

Step-by-step explanation:

167.462 is 0.062 larger than 167.400

Answer:

i have no idea that's why I need ur help

Answer:

irrational i think

Step-by-step explanation:

Answer:

-15,-13,-11

n + (n+2) + (n+4) = -51

3n + 6 = -51

3n = -57

n = -19

-19,-17,-15

Step-by-step explanation: