Solve each trigonometric function IN THE INTERVAL [0, 360).

17.) sec x + tan x = 1

The equation of a quadratic equation with a vertex and a point is

y = 1/4 (x - 11)² + 2

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 6 is an equation.

We have,

Vertex = (11, 2)

Point = (9, 3)

The equation of a quadratic equation with a vertex and a point is

y = a (x - h)² + k

Where (h, k) is the vertex and (x, y) is the point.

Now,

(11, 2) = (h, k)

(9, 3) = (x, y)

Substitute.

y = a (x - h)² + k

3 = a (9 - 11)² + 2

3 = a x 4 + 2

3 = 4a + 2

3 - 2 = 4a

a = 1/4

Now,

The equation of a quadratic equation is y = 1/4 (x - 11)² + 2.

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If the frame has 2 inches of width and its area is 208 inches of square. The dimensions of square without frame is 6.75 and 13.50.

Let the width of rectangle without frame is b.

Let the height of rectangle without frame is h.

Since the base of a square without frame is the double of its height. So

b = 2h...............(1)

The frame has 2 inches of width, so;

The width of rectangle with frame = b + 4

The height of rectangle with frame = h + 4

The area of the rectangle with frame = 208  inches of square

The formula of area of rectangle

A = Height × Width

(h + 4) × (b + 4) = 208

Putting the value of b from the equation 1

(h + 4) × (2h + 4) = 208

Simplify

h(2h + 4) + 4(2h + 4) = 208

2h^2 + 4h + 8h + 16 = 208

2h^2 + 12h + 16 = 208

Subtract 208 on both side, we get

2h^2 + 12h - 192 = 0

Taking common 2 from the equation, we get

h^2 + 6h - 86 = 0

After factoring the equation we get

h = (−3+√95, −3−√95)

h = 6.75, -12.75

The height can't be negative so we use the positive value of h.

Now putting the value of h in the equation 1.

b = 2×6.75

b = 13.50

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The complete question is:

The base of a square without frame is the double of its height, if the frame has 2 inches of width and its area is 208 inches of square. Find the dimensions of the square without frame.

Answer:  A=2 B=4 C=5

Step-by-step explanation:

The correct linear model for the table is f(x) = 5x + 1.

We have to note that when we have a table of values, it is possible that we can be able to obtain the equation that can be able to model the function. We know that we can be able to write the line equation in the form y = mx + c

Where y = g(x) we can write the equation to obtain the slope of the line as;

m = y2 - y1/x2 - x1

Then we have;

1 - (-4)/0 - (-1)

5/1

m = 5

The correct equation of the line is therefore;

f(x) = 5x + 1

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The total number of pencils that the three children have is represented by the expression p + 3 + 4p. This expression can be simplified to p + 3 + 4p.

The total number of pencils that the three children have is represented by the expression p + 3 + 4p. This expression can be simplified to p + 3 + 4p.

Jamila has p pencils. Haan has 3 fewer pencils than Jamila, so Haan has (p - 3) pencils. Naomi has 4 times as many pencils as Haan, so Naomi has (4(p - 3)) pencils.

Therefore, the total number of pencils the three children have is p + (p - 3) + (4(p - 3)). This can be simplified to p + 3 + 4p.

The total number of pencils that the three children have is represented by the expression p + 3 + 4p. This expression can be simplified to p + 3 + 4p.

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The equation for the graph after the shift would be y = x + 1. The answer is y = x + 1.

What happens when a function is shifted vertically?

Because this transformation involves adding a positive or negative constant to the function, a vertical shift, which moves the graph up or down, is the simplest shift. In other words, regardless of the input, the output result of the function receives the same constant.

The y-value adjusts when a function shifts vertically. While the y-value modifies the shift's magnitude, the x-value remains constant.

We add the value to the y-term if it changes upward. We shall deduct that amount from the y-term if it shifts downward.

The simplest transformation is a vertical shift, which entails moving the graph up or down. This is because this transformation only requires changing the function's sign from positive to negative.

The only variable that alters in vertical shifts of the fundamental linear equation y = mx + b is the b value, or the y-intercept.

The graph shown above is the graph of the parent function y=x after a vertical shift up 1 unit.

Hence, The equation for the graph after the shift would be y = x + 1. The answer is y = x + 1.

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The angles b and d have 80° degrees.

Trigonometry is the branch of mathematics that studies and defines the relations between the side lengths and angles of a triangle.

One key fact to know in all trigonometry problems is that all angles within a normal triangle = 180 degrees.

By creating algebraic equations based on the information given in the question, we can find missing values using this key fact.

Given:

Angle a = 20 deg

Angle b = Angle d = x

x = ?

We know that since two angles are equal, it is an isosceles triangle.

Using algebra and the given information, we create an equation:

20+2x=180

2x=180-20

2x=160

x=80

Therefore, we know that angles b and d are 80° degrees.

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Answer:  it takes 7.5 seconds for the object to reach the ground.

Step-by-step explanation:

The equation for the height of the object is h=-16t^2+900. To find the time when the object reaches the ground, we need to find the value of t when h=0.

Therefore, we can set h=-16t^2+900 = 0 and solve for t:

-16t^2+900 = 0

-16t^2 = -900

t^2 = 56.25

t = sqrt(56.25)

t = 7.5

So, it takes 7.5 seconds for the object to reach the ground.

To find out how many bicycles John can assemble in 1 hour, you can use the formula:

rate = work/time

where rate is the number of bicycles John can assemble in 1 hour, work is the total number of bicycles he assembled, and time is the total time it took him to assemble the bicycles.

In this case, the work is 10 bicycles and the time is 8 hours. So, we can substitute these values into the formula:

rate = 10 bicycles / 8 hours

rate = 1.25 bicycles/hour

So John can assemble 1.25 bicycles in 1 hour, assuming he works at a consistent pace.

Answer:

x ≥ -6

Step-by-step explanation:

Answer: x ≥-6

explanation: im pretty good at math

The percent of change when 51 is increased to 98, then there have increment of 92%. So the option d is correct.

The difference between a new and old amount, given as a percentage, is known as a percent change.

Calculating percent change involves determining the difference between the old and new quantities, dividing that difference by the old quantity, and multiplying that result by 100.

The number 51 is raised to 98; calculate the percentage change.

To start, subtract the new quantity from the previous one to determine the difference. 98 - 51 = 47, therefore the difference is 47.

The difference, 47, is then divided by the old amount, 51, yielding a result of 47/51=0.92.

Lastly, multiply the decimal by 100 × 0.92 to get the percentage change, which is increment of 92%.

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The prediction that Lucas can make about the next shipment of ornaments is that H. A delivery of 6 boxes will contain 6 more broken ornaments than a delivery of 3 boxes.

It should be noted that a word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real life scenario given.

In this case, since the department store receives a shipment of 3 boxes of glass ornaments and there are 25 ornaments in each box.

Lucas then opens the boxes and finds that 6 of the ornaments are broken. This implies that there are 2 broken for each box.

In this case, a delivery of 6 boxes will contain 6 more broken ornaments than a delivery of 3 boxes.

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Answer:

[tex]\boxed{n = - 5}[/tex]

Step-by-step explanation:

[tex]\textrm{We have the following equation:}\\\\\dfrac{n}{5}+\dfrac{\left(n-3\right)}{2}=n\\\\\textrm{ and we are asked to solve for n}[/tex]

Solution Steps

Multiply throughout by 10 which is the LCM of the denominators,  5 and 2

[tex]\dfrac{n}{5}\cdot \:10+\dfrac{n-3}{2}\cdot \:10=n\cdot \:10\\\\2n + 5(n-3) = 10n\\[/tex]

Expand the brackets: [tex]5(n-3) = 5n - 15\\\\[/tex]

The equation becomes:

2n + 5n - 15 = 10n

Add similar terms:

7n - 15 = 10n

Move 15 to the right side:

7n = 10n + 15

Move 10 to the left side

7n - 10n = 15

- 3n = 15

n = -15/3

[tex]\boxed{n = - 5}[/tex]

Each of the function should be evaluated as follows;

In Mathematics, the valid and true solutions to any function are referred to as the domain (input value) and they can be determined by substituting the x-values contained in the table into the function.

When x = 2, the range (output value) for this function is given by:

Function, f(2) = 5^x = 5^2 = 25.

When x = 1, the range (output value) for this function is given by:

Function, f(1) = 5^x = 5^1 = 5.

When x = 0, the range (output value) for this function is given by:

Function, f(0) = 5^x = 5^0 = 1.

When x = -1, the range (output value) for this function is given by:

Function, f(x) = 5^x = 5^-1 = 1/5.

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The inequality is y ≥ 1/2x.

We must first identify the linear equation that describes the line in the graph in order to determine the inequality it reflects.

So, using the two points (0, 0) and (2, 1), we first get the slope of the line:

m = y2 - y1 /x2 - x1 = 1-0 / 2-0 = 1/2

Now, we can determine the linear expression using one point, the slope, and the slope-point formula.

y - y1 = m( x - x1)

y - 0 = 1/2(x - 0 )

y = 1/2 x

Then, to evaluate the linear equation, we only need to select a test point from the shaded region, which will be (0,1):

y = 1/2 x

1 = 1 / 2 (0)

1 = 0

Because 1 is greater than 0 and the line is solid, we can infer that the inequality sign is in the proper position.

Therefore, the inequality is y ≥ 1/2x.

The Complete Question is inequality.

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Answer:

4x^2-3x+1+18?=2x+3

Step-by-step explanation:

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Gary would need 15.2 oz glue and 7.6 oz of glitter to make 4 bottles.

Multiplication of two numbers is defined as the addition of one of the number repeatedly until the times of the other number.

a × b means that a is added to itself b times or b is added to itself a times.

We have the information that,

Amount of glue needed for 1 bottle = 3.8 oz

Amount of glitter needed for 1 bottle = 1.9 oz

We have to find the amount of glue and glitter for 4 bottles.

Finding the product for 4 bottles.

Amount of glue needed for 4 bottles = 3.8 × 4 oz = 15.2 oz

Amount of glitter needed for 4 bottles = 1.9 × 4 oz = 7.6 oz

Hence Gary will need 15.2 oz glue and 7.6 oz of glitter to make 4 bottles.

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At two theaters Paige would be willing to buy a ticket and popcorn.

Consider the following table that shows ticket and popcorn prices at five movie theater chains.

Here, the inequality d < 4. 75 represents the prices d in dollars that Paige is willing to pay for popcorn.

And the inequality d < 8. 00 represents the prices d in dollars that Paige is willing to pay for a movie ticket.

To find: the number of theaters that would Paige be willing to buy a ticket and popcorn

We can observe that the number of theaters that has the movie ticket price less than 8 dollars are two.

The number of theaters that has the popcorn price less than 4.75 dollars are three.

And the number of theaters that has the popcorn price less than 4.75 dollars as well as the movie ticket price less than 8 dollars are two.

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x = 4,  y = 3 for the given equation 2x - 3 y = -1 , y = x - 1 .

Given data :

2x - 3 y = -1

y = x - 1

In a system of equations, there are multiple equations present. We actually look for the point at which these equations are identical when we attempt to solve a system of equations problem. In order to solve such an issue, we typically employ the substitution method, which involves inserting the values of one variable into the initial expression in order to determine the value of the second variable.

3y=2x+1

y= (2/3)x + 1/3 = x-1

x/3 =4/3

x = 4,  y=3

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Answer: Hi! I believe your answer would be y = −5/7x − 5

Step-by-step explanation: I hope this helps!

The equation of the translated function for this problem is given as follows:

y = ln(x + 8) + 12.

The four translation rules are defined as follows:

The parent function in this problem is given as follows:

y = ln(x).

The translations in this problem, and their effects, are given as follows:

Hence the translated function is defined as follows:

y = ln(x + 8) + 12.

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The graph of the inequality 0 > x ≥ 5 can be seen on the image at the end.

Here we want to graph the following inequality:

0 > x ≥ 5

So, x is strictly larger than 0 and smaller than or equal to 5.

Because x = 0 is not a solution, we will draw an open circle at x = 0.

Then a line that goes to the right until x = 5, where we will draw a closed circle, because that value belongs to the solution set, then the inequality is the one you can see below.

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Answer:

see below

Step-by-step explanation:

v=πr² (h/3)

h=3v/πr²

original equation measures v using bottom circle area multiply the height.

the equation for the height reverses the multiplication using volume divided by the area, so the result is a linear measurement.

Charlie must buy 7/3 yards long brown thread to weave a bracelet.

Based on number of pieces of brown thread and length of each piece, the formula that will be formed is -

Length of thread required = number of threads × length of each piece

Keep the values in formula to the length of piece required to weave a bracelet

Length of thread required = 7 × 1/3

Performing multiplication on Right Hand Side of the equation

Length of thread required = 7/3 yards

Thus, 7/3 yards of length is required to weave the bracelet.

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Answer:

0

Step-by-step explanation:

[tex]k + 7 = 16\\k = 9\\8k - 72\\8(9) - 72 = 0[/tex]

It can be interpreted as the average distance between each data point and the mean value of 80 for the 100 college students.

Standard deviation is a measure of the spread of values in a set of data, calculated as the square root of its variance. It indicates how much variation or dispersion there is from the mean of the set.

The standard deviation is a measure of the variability or dispersion of the data set around the mean. In this case, it can be interpreted as the average distance between each data point and the mean value of 80 for the 100 college students.

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Answer:

It has one solution, x = 4

Step-by-step explanation:

[tex]3(2x-7) = 3\\2x-7 = \frac{3}{3} \\2x-7 = 1\\2x = 8\\x = 4[/tex]

No other answer would work