Solve each trigonometric function IN THE INTERVAL [0, 2)

3 sec2x − 2 tan2x − 4 = 0

[tex] \pmb{ \underline{\color{green} \huge{Αηςωεr : ∼}}}[/tex]

[tex] \large \frak{ \red{x } - 4 = 8}[/tex]

[tex] \: [/tex]

[tex] \large \frak{ \red{x } = 8 + 4}[/tex]

[tex] \: [/tex]

[tex] \underline{ \boxed{ \large \frak{ \red{x } = \green{12}}}}[/tex]

[tex] \: [/tex]

hope it helps!

The value of sin and cosine of angle x are √2 and √2/2

from the question, we have the following parameters that can be used in our computation:

tan(x) = 2

Also, we have the interval to be

x = (0, ¤/2)

This means that the value of the angle x is from 0 to 90 degrees

Mathematically, we have

tan(x) = sin(x)/cos(x)

This means that

sin(x)/cos(x) = 1/2

So, we have

cos(x) = 2sin(x)

Let cos(x) = √2

This means that

sin(x) = √2/2

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Lengths of the legs of triangle are 6 cm and 8 cm by Pythagoras theorem of right triangle.

Let One short leg = x

then other = x+2

And hypotenuse is = 10 cm

so x²+(x+2)²=10²

Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“.

From Pythagoras theorem : a^2 + b^2 = c^2

Where c is the hypotenuse and a,b are the other sides of a right angle triangle.

x²+ x²+4x+4=100

[(a + b)^2 = a^2 +2.a.b +b^2]

2 x²+4x-96=0

x²+2x-48=0

(x+8)(x-6)=0

x= -8 or 6

Neglecting - value x=6 as the length can not be negative.

So legs of triangle are 6 cm and 8 cm.

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Answer: Billy drives 171 miles in 3 hours, so he could drive 256.5 miles in 4.5 hours.

Step-by-step explanation:

Speed = Distance/Time

The number of miles driven varies directly with the number of hours in the car. Billy drives 171 miles in 3 hours. Then the number of miles he can drive in 4.5 hours will be. This meas that x will be the number of miles covered in 4.5 hours.

x / 4.5 = 171 / 3

x = 256.5 miles

I hope this helps!

Answer:

78.4 meters

Step-by-step explanation:

The quotient and remainder on dividing 3x² + 6 by 3x – 3 are (x - 1) and 9 respectively.

To divide polynomials by a polynomial, we use the long division method.

When there is no common factor in both the numerator and the denominator, we can use the long division.

It may be used to find reminders and quotients while dividing.

Here we have

Divide 3x² + 6 by 3x – 3    

On dividing 3x² + 6 by 3x – 3 in long division method

we get the remainder as 9 and the quotient as (x - 1)

For more understanding understand the long division in the given picture.

Therefore,    

The quotient and remainder on dividing 3x² + 6 by 3x – 3 are (x - 1) and 9 respectively.

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-5-4-3- is the solution for {n\n<3} and 2-1-0 is the correct set for this solution {n\n≥3).

A set is a well-defined collection of distinct objects, known as elements or members of the set. The objects can be anything, such as numbers, letters, words, animals, or even other sets. The defining feature of a set is that its elements are unique and distinct, meaning that no element can appear more than once in the set.

The solution set to 6 + 2n > 12 is n > 3. The correct representations of this solution are:

{n | n ≥ 3}

(3, ∞)

Option 1 {n | n < 3} is incorrect, as it represents the solution set of n being less than 3, which is the opposite of the solution set provided.

Option 2 -5-4-3- is Correct, as it is not in the correct format to represent a solution set.

Option 3 (3,0⁰0) is correct because it represents a point, not a set.

Option 4 and 5 -5-4-3-2-1 0 1 2 3 4 5 and 0 2 3 4 5 are also incorrect as they are not in the correct format to represent a solution set, and does not include the value 3.

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Answer:

C

Step-by-step explanation:

Lets use process of elimination.
A would result in biased results as Lin is on the basketball team herself and thus, her teammates would be inclined to vote for her.

B would result in biased results as well. It doesn't say every third person in the line but rather every third girl. The girls might be inclined to vote for a female candidate.

That leaves C as the only viable option.

Answer:

Step-by-step explanation:

The value to write in the blank so the equation would be true is -4. Option A. no values of x

It is important to note that an algebraic expression is an expression comprising of coefficients, terms, factors, constants and variables.

These algebraic expression also consist of mathematical operations, such as;

From the information given, we have the equation;

4x - 4 = 4x + _

To make the equation true, then, the values must be the same on both sides, the value to add is (-4) because expanding the bracket would give the same value. We have;

4x - 4 = 4x + (-4)

expand the bracket

4x - 4 = 4x - 4

0 = 0

Hence, the value is -4

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Answer:

A=24+9t

B=40+5t

Step-by-step explanation:

see attached

The proof of ∠COP = ∠POD is below.

When viewed as a vector, a ray is a vector from a point to a point . In geometry, a ray is usually taken as a half-infinite line (also known as a half-line) with one of the two points and. taken to be at infinity.

Given is that AOB is a line. Ray OP is perpendicular to AB. OC is another ray between rays OA and OP. If ray OD is perpendicular to OC.

Refer to the figure attached.

In ΔOCP and ΔODP -

∠OPC = ∠OPD = 90°  {right angles}

OP = OP  {Common}

OC = OD

By SAS criteria, ΔOCP ≅ ΔODP.

So, we can write -

∠COP = ∠POD

Therefore, the proof of ∠COP = ∠POD is given above.

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Grams are the ideal unit for calculating the quantity of spices in a batch of cookies (g).

A system of measurements is called the metric system. It is employed in calculations and research across the globe. Here are some instances of measurements made with the metric system:

The unit used to measure lengths and distances is the meter. In daily life, we use this unit to measure things like the length of a piece of clothing, the distance from school to home, etc.

You may have noticed that the bag of your favorite food has a weight listed on it. 250 grams of potato chips, as an illustration. The unit of weight used here is the gram.

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Subtract the given angle from 180° and the missing angle measurements is 42°.

What is meant by angle ?

A+B+C=180°

57°+81°+C°=180°

138°+C=180°

C=138°-180°

C=42°.

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The reasonable domain for this function is 0 < x < 50

The domain of a function is defined as the set of all the possible input values that are valid for the given function.

The range of a function is defined as the set of all the possible output values that are valid for the given function.

Given;

A = 50W - W2

The area of a rectangle cannot be negative;

The practical domain of A is determined when;

50W-W^2>0

Taking common factor W

W(50-W)>0

Since W must be positive W>0

50-W>0

Or equivalently

50>w

W<50

The total interval is

0<W<50

Therefore, the domain of the function will be 0 < x < 50

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The term "solution set" refers to the collection of all possible solutions to an equation thus  {x|x≤4.5} holds it . The value is a solution because the equation holds true if both sides are equal.

Option B is correct.

The distinct items that make up a set are referred to as the set's members or elements. Set notation is a method for representing a set using a combination of symbols and numbers, and it can be used to define sets. "x | -5 x 4.5" is another way to show the solution set of the inequality -5 x 4.5 on a number line. Interval notation is the method by which all real numbers between two given values can be represented. The solution set can be read as "x such that -5 is less than x and x is less than or equal to 4.5" because "|" denotes "such that" and the vertical line denotes "and."

When the lines coincide and have the same y-intercept, the number of solutions to an equation system is infinite. If the slope and y-intercept of the two lines are the same, they are in fact on the same exact line.

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The required number of baskets made in 90 minutes are 27 baskets.

It is given that Juwan makes 12 baskets in 40 minutes and continues to make the baskets for 90 minutes.

Number of baskets made in 90 minutes = ?

So, let us calculate the number of baskets made in 1 minute.

40 min - 12 baskets

1 min - 12/40 baskets

Now, we need to find out the number of baskets made in 90 minutes.

90 min - ?

1 × 90 min - 90 × 12/40 = 27 baskets

Thus, the required number of baskets made in 90 minutes are 27 baskets.

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Correlations are used both as a hypothesis test to check the relationship between two variables, and also as internal reliability check, again to check the relationship between two items is true.

To evaluate a hypothesis about a population, hypothesis testing uses sample data. A hypothesis test evaluates the result's unusualness, determining if there is a reasonable amount of random variation or whether the result is too extreme to be accounted for by chance.

Reliability can be measured by internal consistency. When a measurement is said to be reliable, it means that it will always produce the same result, given all other factors being equal.

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The number of tables for 15 guests will be 3 tables.

The number of tables for 25 guests will be 5 guests

The number of tables for 50 guests will be 10.

Ratio in Mathematics simply demonstrates how many times one number can be able to fit into another number. It should be noted that ratios contrast two numbers by dividing them. In this case, A/B will be the formula if one is comparing one variable (A) to another variable (B).

In this case, Trey is having a party. He'll have 2 tables for every 10 guests. This means that 1 table will be for 10/2 = 5 guest

The number of tables for 15 guests will be:

= 15 / 5.

= 3 tables.

The number of tables for 25 guests will be:

= 25 / 5

= 5 guests

The number of tables for 50 guests will be:

= 50 / 5

= 10

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The domain of the function shown in the graph above include the following: D. {x|x ≥ -4}.

In Mathematics, a domain can be defined as the set of all real numbers for which a particular function is defined.

In Mathematics, the horizontal extent of any graph of a function represents all domain values and they are read and written from smaller to larger numerical values, and from the left of a graph to the right.

By using set builder notation, the domain of this function shown in the graph above can be written as follows;

Domain = {-4, ∞}

Domain = {x|x ≥ -4}

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The graph of constant of proportionality is determined and attached with a green check on the mark box

The ratio between two quantities that are directly proportional is the constant of proportionality.

When two quantities grow and shrink at the same rate, they are directly proportional. When y and x are two values that are directly proportional to one another, the proportionality constant k is defined as k=y/x.

The equation shows that y = kx and the y intercept is zero, because of this the graph will start from the origin

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The distance between the given points is 8.1 units

Distance between two points is the length of the line segment that connects the two points in a plane.

The formula to find the distance between the two points is usually given by d=√((x2 – x1)² + (y2 – y1)²)

From the given info, we have:

( 1 , 2 ) and (5, 9),

where x1 = 1, y1 = 2 and x2 = 5 and y2 = 9

d=√((x2 – x1)² + (y2 – y1)²)

d=√((5 – 1)² + (2 – 9)²)

d=√((4)² + (-7)²)

d = √65

d = 8.1 units

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Answer: To find the equation of the tangent line to a function at a specific point, we can use the following steps:

Find the derivative of the function f(x) = 3x3 − x2 + 2

f'(x) = 9x^2 - 2x

Substitute the point a = 0 into the derivative to find the slope of the tangent line at that point

f'(0) = 9(0)^2 - 2(0) = 0

Use the point-slope form of a linear equation, y - y1 = m(x - x1) to find the equation of the tangent line, where m is the slope and (x1, y1) is the point at which the tangent line touches the function.

y - f(a) = m(x - a)

y - (3*0^3 - 0^2 + 2) = 0(x - 0)

y - 2 = 0

So the equation of the tangent line to the function f(x) = 3x3 − x2 + 2 at a = 0 is:

y = 2

Therefore, the correct answer is A. y = 2

Step-by-step explanation:

Answer:

see attached

Step-by-step explanation:

The solution of an expression 1/2 x 2 is 1.

Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression for some number of times.

Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.

Given:

We have an expression 1/2 x 2.

We will apply the inverse property of multiplication.

= any number x its reciprocal

= 2 x 1/2

= 1

Therefore, 1 is the solution.

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Let x be the number of acres of Farm A planted with pine trees and birch trees, and let y be the number of acres of Farm B planted with pine trees and birch trees.

The system of equations would be as follows:

25x + 50y = 200 (the total number of pine trees planted)

75x + 75y = 450 (the total number of birch trees planted)

To solve this system of equations, we can use the method of substitution. Solving the first equation for x in terms of y:

x = (200 - 50y) / 25

We can substitute this expression for x into the second equation:

75((200 - 50y) / 25) + 75y = 450

Simplifying and solving for y:

(200 - 50y) + 75y = 450

25y = 250

y = 10

So 10 acres of Farm B are planted with pine and birch trees. To find the number of acres of Farm A that are planted with pine and birch trees, we can substitute this value of y back into the first equation:

25x + 50(10) = 200

25x = 50

x = 2

So 2 acres of Farm A are planted with pine and birch trees.

Therefore, the company will plant 25x = 50 pine trees and 75x = 225 birch trees on Farm A, and 50y = 500 pine trees and 75y = 750 birch trees on Farm B.

Answer: need photo

Step-by-step explanation:

Answer:

vanessa gest 80

Step-by-step explanation:

128/8 =16

5 * 16 =80

3*16. =48

Answer: £80

Step-by-step explanation:

Step 1:

Make a proportion:

5 - 8

x - 128

Step 2:

Cross multiply:

5*128=8x

640=8x

Step 3:

Divide by 8:

80=x or x=80

When the line to be examined's slope is known, and the provided point also serves as the y intercept, the slope intercept formula, y = mx + b, is utilized (0, b).

When should you use point-slope form?

When the slope of the line being studied is known, and the provided point is also the y intercept, the slope intercept formula, y = mx + b, is utilized (0, b). The y value of the y intercept point is represented by b in the equation.

One of the three ways we can express a straight line is using the point slope form, also known as the point-gradient form. By merely knowing one point on the line and the slope of the line, we may use this form to get the equation of the line.

The slope and y-intercept of the matching line can be rapidly determined when we have a linear equation in slope-intercept form. This enables us to graph it as well.

The equation of a line can be represented in either slope-intercept form or point-slope form.

Slope-intercept form:

The slope-intercept form of a line is given by y = mx + b, where m is the slope of the line and b is the y-intercept.

To find the equation of the line passing through the points (3,5) and (6,11) in slope-intercept form, we can use the point-slope formula to find the slope and then use one of the points to find the y-intercept.

Point-slope form:

The point-slope form of a line is given by y - y1 = m(x - x1), where m is the slope of the line and (x1, y1) is a point on the line.

To find the equation of the line passing through the points (3,5) and (6,11) in point-slope form, we can use the point-slope formula and one of the points.

Using the point-slope formula, the slope of the line is (11 - 5) / (6 - 3) = 6/3 = 2.

So, the equation of the line in slope-intercept form is:

y = 2x + b

We can use the point (3,5) to find the y-intercept:

5 = 2 * 3 + b

Solving for b, we get b = -1.

So the equation of the line in slope-intercept form is:

y = 2x - 1

In point-slope form, using the point (3,5), the equation of the line is:

y - 5 = 2(x - 3)

Both forms represent the same line, just in different ways.

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