4. Given that cos theta= 3/10 and 3pi/2 < theta < 2pi, find the exact value of each of the following:

a) sin 2theta

b) The quadrant in which the angle theta/2 is located.

B) cos theta/2

the other two angles of the triangle must also be equal, which means that the other two sides of the triangle must be equal as well. the length of the shorter sides is [tex]y = 16 feet[/tex] .

Let's start by using the information given to write equations for the perimeter of the heptagon in terms of the length of the sides:

Let x be the length of the four equal sides, and y be the length of the remaining three sides, which are half as long. Then, we have:

Perimeter  [tex]= 4x + 3y[/tex]

We also know that the perimeter is 88 feet, so we can set up the equation:

[tex]4x + 3y = 88[/tex]

Now we need to solve for y, which represents the length of the shorter sides.

We can simplify the equation by substituting y = (1/2)x:

[tex]4x + 3(1/2)x = 88[/tex]

Simplifying this expression, we get:

[tex]7x/2 = 88[/tex]

Multiplying both sides by 2/7, we get:

[tex]x = 32[/tex]

Now that we know x, we can find y by substituting it into the equation y   [tex]= (1/2)x[/tex]:

[tex]y = (1/2)(32) = 16[/tex]

Therefore, the length of the shorter sides is  [tex]y = 16[/tex] feet.

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232 child's plates were served and 103 adult's plates were served after rounding to the nearest whole number.

The substitution method involves solving one equation for one variable in terms of the other variable, and then substituting this expression into the other equation.

Let's use the following variables:

c = number of child's plates served

a = number of adult's plates served

We can set up a system of two equations based on the given information:

c + a = 335 (the total number of plates served was 335)

2.6c + 8.3a = 1458.1 (the total amount collected was $1458.10)

To solve this system, we can use the substitution method. Rearrange the first equation to solve for one variable in terms of the other:

c = 335 - a

Substitute this expression for c in the second equation and solve for a:

2.6(335 - a) + 8.3a = 1458.1

871 - 2.6a + 8.3a = 1458.1

5.7a = 587.1

a = 103

Now that we know there were 103 adult's plates served, we can substitute this value back into the first equation and solve for c:

c + 103 = 335

c = 232

Therefore, 232 child's plates were served and 103 adult's plates were served.

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The highest point of the quadratic equation that opens down can be (-5, 8)

We have a quadratic equation whose graph opens downwards, and we know that it also passes through the points (-2,5) and (-8, 5).

The highest point will be of the form (x, y).

Such that y is larger than 5, and the value of x is right between the two values above:

x = (-2 - 8)/2

x = -5

So the point is of the form (-5, y) where again y  > 5.

From the given options the only of this form is (-5, 8)

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Answer:

The answer is A

Step-by-step explanation:

You can use a graphing calculator (geogebra) It works

Answer:

To find the volume of Leah's new planter, we need to multiply the length, width, and height of the container:

V = 15 m x 4 m x 8 m x 11 m x 3 m

V = 11,880 cubic meters

Therefore, the total volume of Leah's new planter is 11,880 cubic meters.

Let's represent the volume of the large box as x cubic inches. Since the total volume of both boxes is 212 cubic inches, we can set up the following equation:

8 x 4 x 2 + x = 212

Simplifying the left side, we get:

64 + x = 212

Subtracting 64 from both sides, we get:

x = 148

Therefore, the volume of the large box is 148 cubic inches.

Answer:

x = -6

Step-by-step explanation:

2-3(x+4) = 8

2 - 3x - 12 = 8

-3x - 10 = 8

-3x = 18

x = -6

Answer:

x = -6

Step-by-step explanation:

2 - 3 (x + 4) = 8

2 - 3x - 12 = 8

- 10 - 3x = 8

- 3x = 8 + 10

- 3x = 18

x = -18/3

x = -6

___________

hope this helps!

The correct answer is (5x + 1) / (x+7).

The student made an error in adding the rational expressions. They attempted to add the numerators directly without finding a common denominator.

To add rational expressions, we must first find a common denominator, which is the Least Common Multiple (LCM) of the two denominators. Then, we can add the numerators.

Here is the correct solution:

Problem:

(5x) / (x+7) + 1 / (x+7)

First, note that both rational expressions have the same denominator (x+7). In this case, the LCM is simply (x+7). We can now add the numerators:

Work:

(5x) / (x+7) + 1 / (x+7) = (5x + 1) / (x+7)

Solution:

(5x + 1) / (x+7)

The correct answer is (5x + 1) / (x+7).

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Trigonometric ratios are mathematical functions that relate the angles of a right triangle to the lengths of its sides.

Tan 45 = x/13

x = 13 Tan 45

x = 13

Sin 30 = x/4

x = 4 Sin 30

x = 2

Tan 60 = 21/y

y = 21/Tan 60

y = 12.1

Cos 45 = x/22

x = 22Cos 45

= 15.6

Tan 45 = 5/x

x = 5/Tan 45

x = 5

Sin 30 = 9/x

x = 9/Sin 30

9 = 18

Cos 60 = y/22

y = 22Cos 60

y = 11

Sin 45 = x/16

x = 16Sin 45

x = 11.3

Tan 30 = x/42

x = 42 Tan 30

x = 24.2

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Answer:

Isosceles triangle is the shape which has exactly one line of symmetry.

Answer:

3.7

Step-by-step explanation:

1.5, 2.2, 2.8, 3.4, 5, 5.6, 6.8, 7

Q1 = 2.2+2.8 = 5.0 divided 2 = 2.5

Q3 = 5.6+6.8 = 12.40 divided 2 = 6.2

IQR = 6.2 - 2.5 = 3.7

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In the triangle, x has a value of 18.

A right triangle is one with a 90 degree inner angle. The hypotenuse, which is also the side of the right triangle that faces the right angle, is its longest side. The two arms of a right angle are made up of height and base.

We know that the respective sides of the two triangles in the diagram are proportional since they resemble one another. Namely, we have

AB / AE = BC / CD

Inputting the values provided yields:

x / 12 = 9 / 6

Finding x and simplifying results in:

x = 12 * (9/6) = 18

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Answer:

To add mixed numbers, we need to add the whole numbers separately and fractions separately.

Starting with the whole numbers, we have:

9 1/2 − 3 7/8 + 4 4/5 − 1 1/2

= (9 + 4) − (3 + 1) + (4/5 − 1/2) + (1/8 − 7/8) (grouping the terms)

= 10 − 4 + (8/10 − 5/10) + (−6/8) (converting fractions to have a common denominator)

= 6 + 3/10 − 3/4 (simplifying fractions and adding whole numbers)

= 5 7/20 (expressing the result as a mixed number in simplest form)

Therefore, the value of the expression is 5 7/20.

Answer:

0 ≤ x ≤ 10

Step-by-step explanation:

The domain is the possible values that the variable can take.

The statement "the number of internet users f(x) after x years from the year 2000" is telling us that the x-axis represents the number of years, so the domain of the function is the number of years from 2000 to 2010.

Number of years = 2010 - 2000 = 10 years

So we know that  is at most 10 years; therefore

Since years can't be negative, we can also infer that x must be 0 or bigger than 0, so

Now we can combine both inequalities to find the reasonable domain of the function:

Answer:

(a) 22 inches

(b) 770 inches

(c) 26,950 inches

Step-by-step explanation:

(a) To find the perimeter of the drawing, we add up the lengths of all four sides:

Perimeter of drawing = 7 + 4 + 7 + 4 = 22 inches

(b) The length and width of the actual garden are 35 times larger than the dimensions in the drawing. This means that the actual length is 7 x 35 = 245 inches and the actual width is 4 x 35 = 140 inches. To find the perimeter of the actual garden, we add up the lengths of all four sides:

Perimeter of actual garden = 245 + 140 + 245 + 140 = 770 inches

(c) When the dimensions of the garden are multiplied by 35, the perimeter of the garden will also be multiplied by 35. This is because each side will increase by a factor of 35, so the total length of all four sides will increase by a factor of 35 as well. Therefore, the new perimeter will be:

New perimeter = 35 x Perimeter of actual garden = 35 x 770 = 26,950 inches

The graph represents a proportional relationship.

What is proportional relationship?

A proportional relationship is a relationship between two variables where their ratio remains constant. This means that as one variable increases or decreases, the other variable changes proportionally in order to maintain a constant ratio. In other words, the two variables are directly proportional to each other. This relationship can be represented by a straight line passing through the origin on a graph. Proportional relationships are commonly used in various fields such as physics, finance, and engineering to analyze and predict outcomes.

Explaining the table, equation and graph to know which represents a proportional relationship :

The relationship between the values in the given table is not proportional. If it was a proportional relationship, then the ratio of y to x would be constant. However, in this case, the ratios are not equal. For example, the ratio of y to x for the first row is 3.6/3 = 1.2, but the ratio of y to x for the second row is 6/5 = 1.2, and the ratio of y to x for the third row is 7.2/8 = 0.9. Therefore, the ratios are not equal and the relationship is not proportional.

The equation y=2x+5 does not represent a proportional relationship. In a proportional relationship, there is a constant ratio between the two variables. However, in this equation, the ratio between y and x is not constant, but rather it increases as x increases.

The graph represents a proportional relationship as the ratio between y and x is  constant.

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Using the triangle inequality theorem, the possible values for the third side of the triangle are: 5 < x < 35.

The Triangle Inequality Theorem asserts that for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

Stated differently, the difference between the lengths of any two sides must be less than the length of the third side.

Thus, if you have the lengths of two sides of a triangle, as 20 and 15, we have:

20 - 15 < x < 20 + 15

5 < x < 35

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Answer:

y ≥ -x + 2

y < 2x - 1

Step-by-step explanation:

Solid line:

y ≥ -x + 2

Dashed line:

y < 2x - 1

The system of inequalities associated with the graph is y ≥ 2 and x < 3.

The system of inequalities associated with the graph can be determined by examining the shaded region on the graph. The shaded region represents all the possible solutions that satisfy the given inequalities. To determine the system of inequalities, we need to consider the boundaries of the shaded region. These boundaries are formed by the lines or curves on the graph.

1. Identify the lines or curves that form the boundaries of the shaded region. These lines or curves are usually represented by equations or inequalities. For example, if there is a solid line, it indicates that the boundary is included in the solution. If there is a dashed line, it indicates that the boundary is not included in the solution.

2. Determine the inequalities associated with each boundary line or curve. You can do this by examining the direction of the inequality symbol (<, >, ≤, or ≥) and the location of the line or curve in relation to the shaded region.

3. Write down the inequalities associated with each boundary line or curve. Make sure to include the correct inequality symbol and any necessary constants or variables.

4. Combine all the inequalities together to form the system of inequalities. This can be done by using logical operators such as "and" or "or" to connect the individual inequalities. The "and" operator is used when all the inequalities must be satisfied simultaneously, while the "or" operator is used when at least one of the inequalities must be satisfied. For example, let's say the graph has a solid horizontal line at y = 2, a dashed vertical line at x = 3, and the shaded region is above the horizontal line and to the left of the vertical line. In this case, the system of inequalities would be: - y ≥ 2 (since the shaded region is above the line) - x < 3 (since the shaded region is to the left of the line) Therefore, the system of inequalities associated with the graph is y ≥ 2 and x < 3.

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Therefore , the solution of the given problem of probability comes out to be there is a 0.44 percent chance of choosing a lady.

A procedure's criteria-based systems' main objective is to ascertain the likelihood that an assertion is accurate or that a particular event will take place. Chance can be represented by any number range between 0 and 1, where 0 is commonly used to indicate the possibility of something may be and 1 is usually employed to indicate a degree of confidence. A probability diagram shows the likelihood that a particular occurrence will occur.

Here,

By adding the probabilities of selecting a woman from each squad, weighted by the probabilities of selecting each team,

we can use the law of total probability to determine the likelihood of selecting a woman:

=> Woman = P(Red) * P(Woman from Red) + P(Blue) * P(Woman from Blue) + P(Yellow) * P(Woman from Yellow)

=>  P(Woman) = 0.2 + 0.12 + 0.12 P(Woman) = 0.44 P(Woman) = 0.4 * 0.5 + 0.4 * 0.3 + 0.2 * 0.6

As a result, there is a 0.44 percent chance of choosing a lady.

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Answer:

Numbers between 100 and 200 which are also equal to a square number multiplied by a prime number are:

Step-by-step explanation:

A square number is a number that has been multiplied by itself.

For example, 25 is a square number as 5 × 5 = 25.

The square numbers between zero and 200 are:

A prime number is a whole number greater than 1 that cannot be made by multiplying other whole numbers (its only factors are 1 and itself).

Since the smallest square number is 4, and our final number needs to be between 100 and 200, we only need to list the primes numbers that are less than 50 as 4 × 50 = 200.

Begin with the smallest prime number, 2. If we divide 100 and 200 by this prime number, we get 50 and 100. Therefore, to find a number between 100 and 200 that is equal to a square number multiplied by a prime number, the square number should be more than 50 and less than 100.  Therefore:

The next smallest prime number is 3. If we divide 100 and 200 by 3 we get 33.33.. and 66.66...  Therefore, the prime number 3 should be multiplied by a square number that is more than 33 and less than 67:

The next prime number is 5. If we divide 100 and 200 by 5 we get 20 and 40.  Therefore, the prime number 5 should be multiplied by a square number that is more than 20 and less than 40:

Continuing this way, all the numbers that are between 100 and 200, which are also equal to a square number multiplied by a prime number are:

Number between 100 and 200 which is also equal to a square number multiplied by a prime number is 147.

A prime number is a positive integer greater than 1 that has no positive integer divisors other than 1 and itself. In simpler terms, a prime number is a number that can only be evenly divided by 1 and itself.

To find this number, I first looked for square numbers between 100 and 200. The square numbers within this range are 121 (11 squared) and 169 (13 squared).

I then checked if either of these square numbers could be multiplied by a prime number to equal a number between 100 and 200. After some calculation, I found that 169 cannot be multiplied by a prime number to give a number between 100 and 200. However, 121 can be multiplied by 2 to give 242, which is greater than 200.

Finally, I checked if there were any other square numbers I missed. I found that 7 squared is equal to 49, which when multiplied by 3 (a prime number) gives 147, a number between 100 and 200 that satisfies the problem.

Therefore, the number between 100 and 200 which is also equal to a square number multiplied by a prime number is 147.

I hope this helps!

The answer to the question is 1/3.

There are three possible outcomes: 5, 6, or 7.

Out of these three outcomes, only two satisfy the condition of being odd or greater than 6: 7.

Therefore, the probability of picking a card that is odd or greater than 6 is 1/3, or approximately 0.333 or 33.3%.

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The quadratic function for the given graph is f(x) = -(x - 0.2)² + 6.2.

What is a quadratic function?

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the greatest degree term in a quadratic function is of second degree.

The graph crosses the y-axis at 6 so the graph has a y-intercept at (0,6).

The highest point in the graph is at (0.2,6.2) and the highest point is the maximum.

The graph crosses the x-axis at 2 and -1.5 so the graph has an x-intercept at (2,-1.5).

The graph's line of symmetry is x = 0.2 since the vertex is (0.2,6.2).

The zeros of a graph are its x-intercept so the graph has zeroes of 2 and -1.5.

The quadratic function is of the form a(x - h)² + k where (h, k) is the vertex.

Since, the graph is opening downwards so the value of a = -1 < 0.

The function f(x) = -(x - 0.2)² + 6.2 is the quadratic function of the graph.

Therefore, the function is obtained to be -(x - 0.2)² + 6.2.

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Therefore, the estimated length of the diagonal is approximately 1.414 units.

The square root of a number is a value that, when multiplied by itself, gives the original number. In other words, the square root of a number "x" is a value "y" such that y multiplied by y equals x. The symbol for square root is √.

For example, the square root of 25 is 5, because 5 multiplied by 5 equals 25. Similarly, the square root of 64 is 8, because 8 multiplied by 8 equals 64. The square root of a negative number is not a real number, as there is no real number that, when squared, equals a negative number.

Using the Pythagorean theorem, we can find the length of the diagonal of the square.

If we draw a diagonal from one corner of the square to the opposite corner, we create a right triangle. The two legs of the right triangle are the sides of the square, which have a length of 1. The hypotenuse, which is the diagonal of the square, is the side we are trying to find.

Using the Pythagorean theorem, we can write:

[tex]d^2 = 1^2 + 1^2[/tex]

where d is the length of the diagonal.

Simplifying, we get:

[tex]d^2 = 2[/tex]

Taking the square root of both sides, we get:

d ≈ 1.414

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Answer:

a-no for the first triangle, because the total of the inner angles must be 180, the last angle must be 90.

b-yes- a triangle with angles 90, 50, and 40 is possible

c-yes. 65+45+70=180.

Step-by-step explanation:

Answer:

36

Step-by-step explanation:

3/4 of 48 is 36

Answer:

Step-by-step explanation:

I'm sorry, but there seems to be some information missing from your question. Specifically, it is unclear what quantity or angle you want to determine the cosine of.

If you meant to ask for the value of the cosine of an angle given that its sine is 3/4, then we can use the Pythagorean identity to determine the cosine:

sin^2(x) + cos^2(x) = 1

Plugging in sin(x) = 3/4, we get:

(3/4)^2 + cos^2(x) = 1

Simplifying, we have:

9/16 + cos^2(x) = 1

Subtracting 9/16 from both sides, we get:

cos^2(x) = 7/16

Taking the square root of both sides, we get:

cos(x) = ±sqrt(7)/4

Since the sine is positive (3/4 is in the first quadrant), we know that the cosine must also be positive. Therefore:

cos(x) = sqrt(7)/4

I hope this helps! Let me know if you have any further questions.

Answer: g=18

Step-by-step explanation:

g*4=72

g=72/4

g=18

The wire can be divided into five equal parts, where one portion is one-fifth of the total length and the other four parts are four-fifths of the total length. the measure of the longer part of the wire after cutting is 2 meters.

If the wire was cut in a ratio of 1:4, then the total length of the wire can be divided into 5 parts, where one part is 1/5 of the total length, and four parts are 4/5 of the total length. Let's call the length of one part "x".

So, the total length of the wire is:

 [tex]5x = 2.5[/tex] meters

To find the length of the longer part of the wire, we need to find how many parts are in the longer portion. Since the wire was cut in a 1:4 ratio, the longer portion has four parts.

Therefore, the length of the longer part of the wire is:

[tex]4x = 4/5 \times 2.5 meters = 2 meters[/tex]

Therefore, the measure of the longer part of the wire after cutting is 2 meters.

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Scale factor of the similar polygon pairs is:

5. 6

6. 5/12

7. 4/15

8. 1/7

When both the original dimensions and the new dimensions are known, the scale factor may be determined.

The following is a basic formula to determine a figure's scale factor:

Scale factor is equal to the difference between the dimensions of the old and new shapes.

Here in the first figure,

The sides are in a ratio of 1:6. The sides have increased 6 times so the scale factor here is 6.

Similarly in the trapezium, the ratio of the sides is 5/12.

The scale factor here becomes 5/12.

In the next figure, the sides are in a ratio of 4/15. Scale factor for the pair here is 4/15.

In the last figure, the equivalent sides are in the ratio of 1/7. The scale factor between the pair is 1/7.

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