A book shop offers a 24% discount on books.
Sam has to pay $______????
if he purchases books with an original price of $84.

2 sin²(x) + 3 sin(x) + 1 = 0

(2 sin(x) + 1) (sin(x) + 1) = 0

2 sin(x) + 1 = 0   OR   sin(x) + 1 = 0

sin(x) = -1/2   OR   sin(x) = -1

The first equation gives two solution sets,

x = sin⁻¹(-1/2) + 2nπ = -π/6 + 2nπ

x = π - sin⁻¹(-1/2) + 2nπ = 5π/6 + 2nπ

(where n is any integer), while the second equation gives

x = sin⁻¹(-1) + 2nπ = -π/2 + 2nπ

2 cot(x) sec(x) + 2 sec(x) + cot(x) + 1 = 0

2 sec(x) (cot(x) + 1) + cot(x) + 1 = 0

(2 sec(x) + 1) (cot(x) + 1) = 0

2 sec(x) + 1 = 0   OR   cot(x) + 1 = 0

sec(x) = -1/2   OR   cot(x) = -1

cos(x) = -2   OR   tan(x) = -1

The first equation has no (real) solutions, since -1 ≤ cos(x) ≤ 1 for all (real) x. The second equation gives

x = tan⁻¹(-1) + nπ = -π/4 + nπ

sin(x) cos²(x) = sin(x)

sin(x) cos²(x) - sin(x) = 0

sin(x) (cos²(x) - 1) = 0

sin(x) (-sin²(x)) = 0

sin³(x) = 0

sin(x) = 0

x = sin⁻¹(0) + 2nπ = 2nπ

2 cos²(x) + 2 sin(x) - 12 = 0

2 (1 - sin²(x)) + 2 sin(x) - 12 = 0

-2 sin²(x) + 2 sin(x) - 10 = 0

sin²(x) - sin(x) + 5 = 0

Using the quadratic formula, we get

sin(x) = (1 ± √(1 - 20)) / 2 = (1 ± √(-19)) / 2

but the square root contains a negative number, which means there is no real solution.

2 csc²(x) + cot²(x) - 3 = 0

2 (cot²(x) + 1) + cot²(x) - 3 = 0

3 cot²(x) - 1 = 0

cot²(x) = 1/3

tan²(x) = 3

tan(x) = ± √3

x = tan⁻¹(√3) + nπ  OR   x = tan⁻¹(-√3) + nπ

x = π/3 + nπ   OR   x = -π/3 + nπ

Answer: 5x-30-9

-159

Step-by-step explanation:

-159 is the answer

Answer:

[tex]a = 1[/tex]

Step-by-step explanation:

Given

[tex]4x - 3(x + a) = 2[/tex]

[tex]x = 5[/tex]

Required

Determine the value of a

[tex]4x - 3(x + a) = 2[/tex]

Substitute 5 for x

[tex]4(5) - 3(5 + a) = 2[/tex]

Open all brackets

[tex]20 - 15 - 3a = 2[/tex]

[tex]5 - 3a = 2[/tex]

Collect Like Terms

[tex]-3a = 2 - 5[/tex]

[tex]-3a = -3[/tex]

Solve for a

[tex]a = -3/-3[/tex]

[tex]a = 1[/tex]

Answer:

The flywheel rate of the flywheel is 4 revolutions per second.

Step-by-step explanation:

From Rotation Physics we understand that flywheel rotates at constant rate. In this case, angular speed ([tex]\dot n[/tex]), measured in revolutions per second, is the number of revolutions done by the flywheel at a given interval of time. That is:

[tex]\dot n = \frac{n}{t}[/tex] (Eq. 1)

Where:

[tex]n[/tex] - Number of revolutions done, measured in revolutions.

[tex]t[/tex] - Time, measured in seconds.

If we know that [tex]n = 60\,rev[/tex] and [tex]t = 15\,s[/tex], then the angular speed of the flywheel is:

[tex]\dot n = \frac{60\,rev}{15\,s}[/tex]

[tex]\dot n = 4\,\frac{rev}{s}[/tex]

The flywheel rate of the flywheel is 4 revolutions per second.

Answer:

The answer for that question is 4 per second

Step-by-step explanation:

Just put that answer i know it on your choices i looked up goodle for this answer so your welcome

Hope this help

Pls leave a thanks if it did

Answer:

2 times 8 = 16 divided by 3 leaves a remander of 1

Step-by-step explanation:

The smallest whole number is 22.

Least Common Multiple is a mathematical term. The smallest number that is a multiple of both of two numbers is called the least common multiple.

For example, L.C.M of 16 and 20 will be 2 x 2 x 2 x 2 x 5 = 80, where 80 is the smallest common multiple for numbers 16 and 20.

Given:

First find the LCM of 7 and 3 .

LCM = 3 x 7 = 21

So, we will add remainder 1 (as given) to the LCM .

= 21+ 1

= 22

Learn more about LCM here:

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Answer:r/8>16

Step-by-step explanation:

r/8-16

It says 16 less, so we have to subtract 16 from r divided by 8.

That would be r/8-16.

Answer:

Step-by-step explanation:

at most 1.

8(3x - 6) = 6(x + 8)

24x - 48 = 4x + 48                   Subtract 4x

24x - 4x - 48 = 4x -4x + 48      Combine

20x - 48 = 48                           Add 48 to both sides.

20x = 96                                 divide by 20

x = 96/20

x = 4.8

No other answer is possible.    

True.

When you break it down, it's 0.45 compared to 0.50, so 0.5 is greater than 0.45 by 0.05. Also, 0.5 is closer to 0.

Answer:

3/4

Step-by-step explanation:

There are no answer choices so I just solved the equation

-3/4 divided by -8/12

Flip -8/12 to -12/8

Multiply -3/4 by -12/8

24/32

Simplify.

12/16

Simplify some more.

6/8

Simplify even more.

3/4

Hope I helped :)

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Answer:

1. constant: 2

2. you can use slope intercept

3. 4 pounds equal 40 cents

4. because it is linear

Step-by-step explanation:

Answer:

30°

Step-by-step explanation:

<4=<2=30

(vertical opposite angles are equal)

Answer:

30 degrees

Step-by-step explanation:

Since 4 is equal on the other side of 2, it would be congruent, which is the same as 2. So, 30 degrees.

Answer: $1.25

Step-by-step explanation:

Let the cost of cracker be a.

Let the cost of cookies be b.

Let the cost of candy bars be c.

From the question,

6a + 6b + 6c = $21

8a + 5b + 10c = $26

5a + 4b + 7c = $18.50

To solve this, we first pick any two pairs of equation. This will be:

6a + 6b + 6c = $21 ....... i

8a + 5b + 10c = $26 ....... ii

Multiply equation i by 8

Multiply equation ii by 6

48a + 48b + 48c = $168 ....... iii

48a + 30b + 60c = $156 ....... iv

Subtract equation iv from iii

18b - 12c = 12

We then pick another two pairs

8a + 5b + 10c = $26

5a + 4b + 7c = $18.50

Multiply equation i by 5

Multiply equation ii by 8

40a + 25b + 50c = $130

40a + 32b + 56c = $148

Subtract the equations

-7b - 6c = -18

Then, solve the new equations formed

18b - 12c = 12 ....... v

-7b - 6c = -18 ....... vi

Multiply equation i by -7

Multiply equation ii by 18

-126b + 84c = -84

-126b - 108c = -324

Subtract the equations

192c = 240

c = 240/129

c = $1.25

From equation v, put the value of c

18b - 12c = 12

18b - 12($1.25) = 12

18b - $15 = $12

18b = $27

b = $27/18

b = $1.5

Since,

6a + 6b + 6c = $21

6a + 6($1.5) + 6($1.25) = $21

6a + $9 + $7.5 = $21

6a + $16.5 = $21

6a = $21 - $16.5

6a = $4.5

a = $4.5/6

a = $0.75

One candy bar cost $1.25

The cost of one candy bar is $1.5 and this can be determined by forming the linear equation with the help of given data.

Given :

Form the linear equation in order to determine the cost of one candy bar. Let 'x' be the cost of crackers, 'y' be the cost of cookies, and 'z' be the cost of candy bars.

So, the linear equation that represents the situation "A snack bag containing 6 of each type of snack costs $21.00" is:

6x + 6y + 6z = 21  --- (1)

The linear equation that represents the situation "A snack bag containing 8 packages of crackers, 5 packages of cookies, and 10 candy bars costs $26.00" is:

8x + 5y + 10z = 26  --- (2)

The linear equation that represents the situation "A snack bag containing 5 packages of crackers, 4 packages of cookies, and 7 candy bars costs $18.50" is:

5x + 4y + 7z = 18.50  --- (3)

Simplify all three equations in order to determine the value of 'x', 'y', and 'z'.

z = $1.25

y = $1.5

x = $0.75

For more information, refer to the link given below:

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Answer:

0.625

Step-by-step explanation:

15 divided by 24 which equals 0.625

Answer:

Step-by-step explanation:

Sorry but please give detailed question

Answer:

B

Step-by-step explanation:

Answer:C

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

Since the entire length is 11, and one segment is 7, you'll subtract and end up with the answer 4.

The length of AB if Point B is on the line segment AC, BC = 7 and AC = 11, is 4.

A line segment is a measurable route between two points. Line segments can make up any polygon's sides because they have a set length.

Given:

Point B is on the line segment AC, BC = 7 and AC = 11,

Write the expression for the above phrase as shown below,

The length of the AC = The length of AB + the length of BC

11 = 7 + The length of AB

The length of AB = 11 - 7

The length of AB = 4

Thus, The length of AB is 4.

To know more about line segments:

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Answer: 22 Levels

Step-by-step explanation: He would need to go one level higher just to get to level one, and another 21 to get to the level that he wants to, so the total would be 22 levels.

Answer:

The elevator moved up 21 levels

Answer:

CORRECT OPTION is (C) The flight will be late on one of the three days.

Step-by-step explanation:

The 7am flight from Dallas to Chicago is on time 75% of the time.

A spinner with four sections was created by Fran to simulate this scenario.

Since the 4 sections were equal, it means each section was 25% of the spinner.

3 sections were shaded. That implies 25 × 3 = 75% of the spinner was shaded area.

This coincides with the 75% probability that the flight is on time on a given day.

In other words, if the spinner's pointer lands on shaded area, the flight will be on time. If the pointer lands on an unshaded portion, the flight will be late.

Now Fran spun the spinner 3 times so she has 3 outcomes. The outcomes are:

- Shaded   - Shaded   - Unshaded

CORRECT OPTION is (C) The flight will be late on one of the three days.

Answer:

C

Step-by-step explanation:

I did the test

Answer:

15

Step-by-step explanation:

Answer: yes because without the x the y does not have a corresonding oint

Answer:

The answer you chose is correct

Step-by-step explanation:

Answer:

10ft

Step-by-step explanation:

Given parameters:

Central angle  = 252°

Arc length  = 44ft

Unknown:

Radius = ?

Solution:

To find the radius of the circle, let us use the expression;

       Arc length  = [tex]\frac{central angle}{360}[/tex] x 2πr

 Insert the parameters and solve for r,

         44  = [tex]\frac{252}{360}[/tex] x 2 x 3.142 x r

          44  = 4.4r

               r  = 10ft

Answer:

0

Step-by-step explanation:

Answer:

C) $5/1 ticket

Step-by-step explanation:

$80 for 16 tickets is $5 for 1 ticket. We can find this by just simply dividing 80/16 together to get 5.

Answer:

$50

Step-by-step explanation:

Answer:

A) Upper limit = 7.39

Lower limit = 6.37

Margin of error = 0.51

B)Sample size = 87

C) Upper limit = 2218.50

Lower limit = 1909.50

Margin of error = 154.50

Step-by-step explanation:

We are given;

x¯ = $6.88 per 100 pounds

σ = $1.98 per 100 pounds

n = 45

A) We want to find a 90% Confidence interval. It means the significance level is; 1 - 0.9 = 0.1

Critical z-value for significance level of 0.1 is z = 1.645

Now, margin of error is;

MOE = zσ/√n

MOE = (1.645 × 1.98)/√40

MOE ≈ 0.51

Confidence interval is;

CI = x¯ ± MOE

CI = 6.88 ± 0.51

CI = ((6.88 + 0.51), (6.88 - 0.51))

CI = (7.39, 6.37)

Upper limit = 7.39

Lower limit = 6.37

B) We are given E = 0.35

Thus;

E = zσ/√n

Rearranging, we have;

n = (zσ/E)²

n = (1.645 × 1.98/0.35)²

n ≈ 87

Sample size = 87

C)We are told that the farm brings 15 tons of watermelon to market.

Also, 1 ton = 2000 pounds

Thus;

15 tons = 15 × 2000 pounds = 30000 pounds

Now this is per 100 pounds.

Thus, we can write as: 30000/100 = 300 pounds

So;

x¯ = 300 × 6.88

x¯ = 2064

σ = 1.98 × 300

σ = 594

Critical z-value for significance level of 0.1 is z = 1.645

Now, margin of error is;

MOE = zσ/√n

MOE = (1.645 × 594)/√40

MOE ≈ 154.50

Confidence interval is;

CI = x¯ ± MOE

CI = 2064 ± 154.50

CI = (2064 + 154.50, 2064 - 154.50)

CI = (2218.5, 1909.5)

Upper limit = 2218.50

Lower limit = 1909.50

Answer:

29

Step-by-step explanation:

Given the expression [tex]75_8 = 23_x[/tex] where x is the unknown base:

[tex]75_8 = 23_x\\7\times8^1 +5\times8^0 = 2\times x^1+3 \times x^0\\56+5 = 2x+3\\61 = 2x+3\\2x = 61-3\\2x = 58\\x = 58/2\\x = 29[/tex]

Hence the missing base is 29

Answer:

1/3

Step-by-step explanation:

thats the slope so im assuming :/