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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:

2.5 one decimal rounding off means to make it to one decimal place.the no is 24.9652 if you want to round of then you have to put decimal after 2 only then it will be one decimal place .this is because when we see a number after the point greater than 5 then we add 1 to the right side .now if we add 1 to the right side of 24.9652 by rounding off and making it to one decimal place then it will be 2.5.

Answer:

x = 2/3

Step-by-step explanation:

To find x-intercept/zero, subtract y = 0

0 = 3x + 2

Move variable to the left-hand side and change its sign

-3 = 2

Divide both ides of the equation by - 3

x = - 2/3

Solution

x = - 2/3

Alternate form

x = - 0.6

Answer:

16 pizzas.

Step-by-step explanation:

That is 4 divided by 1/4

= 4 * 4/1

= 16.

Answer:

16

Step-by-step explanation:

There are 4 pizzas per can and you have 4 cans.

4 x 4 = 16

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:The mixed number 2 3/7 can be converted to the improper fraction 17/7. The easiest way to do this is to multiply the denominator of the fraction (7 in...

Step-by-step explanation:

Answer:

[tex]Average = 10[/tex]

Step-by-step explanation:

Given

[tex]First\ Three = 14[/tex] --- Average

[tex]Next\ Seven= 4[/tex] --- Average

Required

Determine the overall average

Represent the sum of the first three with x.

So:

[tex]\frac{x}{3} = 14[/tex]

Solve for x

[tex]x = 14 * 3[/tex]

[tex]x = 42[/tex]

Represent the sum of the next seven with y.

So:

[tex]\frac{y}{7} = 4[/tex]

Solve for y

[tex]y = 4 * 7[/tex]

[tex]y = 28[/tex]

The overall average is calculated as thus:

[tex]Average = \frac{x + y}{7}[/tex]

[tex]Average = \frac{42 + 28}{7}[/tex]

[tex]Average = \frac{70}{7}[/tex]

[tex]Average = 10[/tex]

the Answear is B,D,A,C

Answer:

0.963

Step-by-step explanation:

It’s correct

Answer:

put one point at (0,3)

put another point at (1,-3)

draw a line between them

Step-by-step explanation:

could u vote me brainliest plz? thx :)

The standard formula for calculating the equation of a line is expressed as

y = mx + b

m is the slope of the line

b is the y-intercept of the line

Given the equation to graph expressed as g(x) = 3 - 6x

First, we need to get the x and y-intercept of the line expressed as:

For the x-intercept, y = 0

0 = 3 - 6x

6x = 3

x = 0.5

The x-intercept is at (0.5, 0)

For the y-intercept, x = 0

y = 3 - 6(0)

y = 3

The y-intercept is at (0, 3)

Plot the graph of a line passing through the coordinate points (0.5, 0) and (0, 3) as shown below;

Learn more here: https://brainly.com/question/17003809

Answer:

there are 30 boys

Step-by-step explanation:

If there is 24 girls you divide that by 4 and you get six so that means you multiply with six and you get 30.

A ratio of 4:5 means that for every 4 girls, there are 5 boys.

24 girls / 4 girls = 6

5 * 6 = 30 boys

There are 30 boys if there are 24 girls

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:

greater than

Step-by-step explanation:

1.994 is closer to 2 than 1.493 so it is greater!

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:

12.54

Step-by-step explanation:

Answer:

h(4) = -28

General Formulas and Concepts:

Order of Operations: BPEMDAS

Step-by-step explanation:

Step 1: Define

h(n) = -2n² + 4

h(4) is n = 4

Step 2: Solve

Answer:

Hypothesis

Step-by-step explanation:

 a polygon has five sides Conclusion: it is a pentagon If a polygon has five sides, then it is a pentagon.

hope this helps

Complete Question

Because of the relatively high interest rates, most consumers attempt to pay off their credit card bills promptly. However, this is not always possible. An analysis of the amount of interest paid monthly by a bank's Visa cardholders reveals that the amount is normally distributed with a mean of 25 dollars and a standard deviation of 8 dollars. (Round all decimals to at least 3 places.) (a) What proportion of the bank's Visa cardholders pay more than 28 dollars in interest

Answer:

0.354

Step-by-step explanation:

We solve for z score in this question.

The formula is given as:

z = (x-μ)/σ, where

x is the raw score = $28

μ is the population mean = $25

σ is the population standard deviation = $8

z= 28 - 25/8

z = 0.375

P-value from Z-Table:

P(x<28) = 0.64617

P(x>28) = 1 - P(x<28)

= 1 - 0.64617

= 0.35383

Approximately to 3 decimal places = 0.354

The proportion of the bank's Visa cardholders pay more than 28 dollars in interest is 0.354.

Answer:

The first one

Step-by-step explanation:

Answer:

Step-by-step explanation:To combine two intervals using inequality notation or set-builder notation, we use the word “or.” As we saw in earlier examples, we use the union symbol, \displaystyle \cup∪, to combine two unconnected intervals. For example, the union of the sets \displaystyle \left\{2,3,5\right\}{2,3,5} and \displaystyle \left\{4,6\right\}{4,6} is the set \displaystyle \left\{2,3,4,5,6\right\}{2,3,4,5,6}. It is the set of all elements that belong to one or the other (or both) of the original two sets. For sets with a finite number of elements like these, the elements do not have to be listed in ascending order of numerical value. If the original two sets have some elements in common, those elements should be listed only once in the union set. For sets of real numbers on intervals, another example of a union is

Answer:

The least common denominator is 77 so the fractions would become 63/77 and 66/77.

Answer:

0

Step-by-step explanation:

Answer:

20/25

Step-by-step explanation:

to get to a dinominator of 25, we have to multiply 5 by 5. so then we do 4 x 5 so now it is 20/25

Answer:

Step-by-step explanation:

132 / 4 = 33

Therefore,

The answer is,

Answer:

Step-by-step explanation:

Given

RS=9y+2, ST=2y+6, and RT= 52

The addition postulate is true for the number line.

RS+ST = RT

Substitute

9y+2+(2y+6) = 52

9y+2y+8 = 52

11y = 52-8

11y = 44

y = 44/11

y = 4

Find RS

RS = 9y+2

RS = 9(4)+2

RS = 36+2

RS = 38

Find ST:

ST = 2y+6

ST = 2(4)+6

ST = 8+6

ST = 14

Hence y = 4, RS = 38 and ST = 14

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:

0.0657534

Step-by-step explanation:

divide 2 by 30.417