1. f(x) = x3 - 3x2 - 8x - 60

Cosθ and secθ are positive when θ is in the third quadrant while other trigonometric ratios are negative.

The values of all trigonometric functions depending on the side ratio of a right-angled triangle are known as trigonometric ratios. The ratios of a right-angled triangle's sides to any acute angle are the angle's trigonometric ratios. Trigonometric ratios can be used to calculate the lengths of one (or both) of the acute angles in a right triangle if you know the lengths of two of its sides.

given

sinθ = - 4 / 5

cosθ = 3/5

tanθ = -4/3

secθ = 5/3

cotθ = -3/4

cosecθ  = - 5/4

as Cosθ and secθ are positive when θ is in the third quadrant while other trigonometric ratios are negative.

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Answer:

Step-by-step explanation:

To find the y-intercept on a graph, you must look at where the line intercepts through the y-axis.

For this problem it would be 16

Answer: AB : secant

OC : radius

AC : tangent

CD : chord

Point C : center

Point O : Point of tangency

D B You Try A : Not enough information provided to match the notation.

Step-by-step explanation:

The approximate angle between the base and a triangular face is; 79.43°

The dimensions of the pyramid are;

Side Length; a = 22 inches

Edge length; b = 61 inches

Using Pythagoras theorem:

h = height of pyramid

h = √(b² - 1/2a²)

h = √(61² - 22²/2)

h = √(3479)

h = 58.98

Slant height :

L = √(58.983² + 22²/4)

L =√(3479 + 121)

L = 60

Sinα = h/L

α = sin⁻¹(58.983/60)

α = 79.43°

That is the approximate angle found.

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Answer:  ∠M = 98°

Step-by-step explanation:

∠M = (3x-16)°

∠N = x°

∠O = (x+6)°

Sum of all angles in a triangle is 180°

Therefore, 180° = ∠M +∠N +∠O, substitute the given values

180° = (3x-16)° + x° + (x+6)° (add/combine like terms)

180° = (3x+x+x)° + (-16+6)°

180° = (5x)° + (-10°)

180° + 10° = (5x)° ( divide both sides by 5)

190°/5 = (5x)°/5

38° = x°

IF ∠M = (3x-16)°, substitute x°=38°,

Therefore, ∠M = 3(38)-16

                   ∠M = 114 - 16 = 98°

x<9

5(x+3)<60

x+3< 12

x<9

Which simply means x will always be less than 9 in this case.

These are the Simple inequation in one variable which can be simply solved by operating the same operations on both sides to get a simplified answer.

We follow the same algorithm even for equations where the left side and right sides are equal so we simply transfer the left digits to the right side simply by changing their operational signs like + will be -, * will be /.

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The change of base property is a formula that makes it possible to express a logarithm in terms of logs expressed in a different base.

It is possible to express a logarithm in terms of logs stated in a different base using the change of base property formula. This is especially useful when evaluating a log to a base other than 10 or e using a calculator. X, a, and b are all taken to be positive. The base change property can be used to simplify equations with different bases for the logarithmic terms. All the logarithmic terms of an equation with logarithmic functions should have the same base in order to be solved.

Examples given below:

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I decided to use Gallon Of Gas

The rate of change is 19.8 cents annually.

The average cost of a gallon of gas is $3.744 this year (2021).

Gas prices increased significantly in 2021, almost by $2 in some states, due to disease.

Gas prices forecast for the coming year!

Capital price at the average rate of change and economic fixtures: $4 per gallon (Real-Life Problems)

Detailed explanation:

Determine the average rate of change from 1960 to 2000 by computing the percentage change in the item's price for each decade.

A simple reveals the anticipated rise in petrol prices over the coming ten years.

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I made the decision to utilise a gallon of gas. The annual change is 19.8 cents. This year, a gallon of gasoline costs on average $3.744. (2021).

Disease caused a substantial rise in gas prices in 2021, almost by $2 in some places. Future gas prices, the average rate of change in capital prices, and economic indicators: At $4 per gallon (Real-Life Problems). By calculating the price change percentage for each decade, you can calculate the overall rate of change between 1960 and 2000.

A quick calculation shows how much gasoline prices are expected to climb over the next ten years. Subtract the original price from the new price to determine the percent change, then divide the result by the original price and multiply by 100. We must now calculate the percentage change when 25 is raised to 45. To determine the percentage change, we can easily use the formula.

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The domain and range of the given function are (-∞,∞),{x|x∈R} and (-∞,-28],{y|y≤-28} respectively.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

The given functions are h(z)=-3(z+13)²-28.

To find the x-intercept, substitute in 0 for y and solve for x. To find the y-intercept, substitute in 0 for x and solve for y.

x-intercept(s): None

y-intercept(s): (0,-535)

Find the domain by finding where the function is defined. The range is the set of values that correspond with the domain.

Domain: (-∞,∞),{x|x∈R}

Range: (-∞,-28],{y|y≤-28}

Therefore, the domain and range of the given function are (-∞,∞),{x|x∈R} and (-∞,-28],{y|y≤-28} respectively.

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No. of pages read on day of planning are represented by vertical intercept.

The difference between vertical intercept of original plan and line drawn by Lin is 10 unit.

The slope intercept form equation for a straight line with a slope, 'm', and 'c' as the y-intercept can be given as:

y = mx + c.

Given,

No. of pages Lin read on day of planning = 30

No. of pages she plans to read everyday = 40

If total pages are y for x days then,

y = 40x + 30

which is the original plan of Lin.

comparing it with slope-intercept form of line

y = mx + c

slope m = 40

vertical intercept of original plan c = 30 unit

slope m represents the no. of pages read everyday.

vertical intercept represents the no. of pages read on day of planning.

vertical intercept c' of line drawn by Lin = 40 unit

Comparing intercept of original plan to line drawn by Lin

= |c - c'|

= |30 - 40|

= 10 unit

Hence, the vertical intercept represents the no. of pages read on day of planning.

There is 10 unit difference between vertical intercept of original plan and line drawn by Lin.

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The four ways to depict an inequality: solution graph, interval notation, set notation, and equation notation.

In mathematics, an inequality displays the connection between two values in an unbalanced algebraic statement. One of the two variables on the two sides of the inequality may be greater than, greater than or equal to, less than, or less than or equal to another value, according to inequality signals.

There are four ways to depict an inequality: solution graph, interval notation, set notation, and equation notation.

A comparison of any two values, known as an inequality, demonstrates whether one value is less than, larger than, or equal to the value on the opposite side of the equation. A relationship in a real-world scenario can be demonstrated by writing an inequality.

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The null hypothesis is H0: p = 403

The alternative hypothesis is given as: H1: p < 403

The null hypothesis is a statement that there is no significant difference or relationship between two groups or variables. It represents the status quo or the default assumption that there is no effect.

The alternative hypothesis is the statement that there is a significant difference or relationship between the groups or variables. It is the opposite of the null hypothesis and represents the research hypothesis or the claim that you are trying to test.

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Answer:

  4f-7

Step-by-step explanation:

You want the perimeter of a triangle whose side lengths are f, 2f, and f-7.

The perimeter is the sum of the side lengths:

  P = f +2f +(f -7)

  P = 4f -7

The perimeter of the triangle is 4f-7.

__

Additional comment

No such triangle can exist. The sum of the two shortest sides is f+(f-7) = 2f-7, which is not greater than the longest side, 2f. The triangle inequality is not satisfied.

The equivalent expressions are 7(4c - 8), 28(c - 2), - 7(8-4c). Options A, B, E

Algebraic expressions are described as expressions that are made up of terms, variables, coefficients, factors and constants.

They are also composed of mathematical operations, such as;

Equivalent expressions are those with the same solution but different arrangement of values, we have the expression;

28c-56

Let's factor the terms, we get;

7(4c - 8)

Also,

28(c - 2)

Hence, the expressions are 7(4c - 8), 28(c - 2), - 7(8-4c)

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a. Drive Co.'s revenue function R(X) = (-x^2/5)-247x.

b. The price per drive when revenue is maximized is $370.6.

c. The maximum profit made from the sale of these drives if Drive Co. incurs production costs of $179 per drive and has fixed costs of $250 is $6030.

What is a function?

The characteristic that every input is associated to exactly one output defines a function as a relationship between a set of inputs and a set of allowable outputs.

Drive Co. sells portable 905 hard drives when the price is $66/drive and can sell 800 hard drives when the price is $87/drive.

Let p be the price of hard drive and x be the number of hard drives.

When x = 905, then p = 66.

So, (x1,p1) = (905,66)

Similarly, when x = 800, then p = 87.

So, (x2,p2) = (800,87)

So, the equation of line between x and p is given as -

p-p1=[(p2-p1)/(x2-x1)}(x-x1)

Plugging in the values -

p-66=[(87-66)/(800-905)](x-905)

p-66=(21/-105)(x-905)

-105p+6930=21x-19005

-105p-21x=-19005-6930

-105p-21x=-25935

p=(-21x/105)-247

p=(-x/5)-247

So, the price function p(x) = (-x/5)-247.

Now, derive the revenue function -

Revenue = Number of drives × price per drive

Revenue = x · p(x)

Revenue = x · (-x/5)-247

Revenue = (-x^2/5)-247x

Therefore, the revenue function R(x) = (-x^2/5)-247x.

For maximum revenue -

dR/dx = R'(x) = 0 and R''(x)<0

dR/dx = -2x/5-247 = 0

-2x/5 = 247

x = -1235/2

x = -617.5

Therefore, the number of drives at maximum revenue is 618 drives.

The price per drive is -

p(618) = {-618/5}-247

p(618) = -370.6

Therefore, the price per drive is $370.6.

Now, the profit S(x) = Revenue R(x) - Total Cost C(x)

C(x) = fixed cost + variable cost

Variable cost = number of drives × price per drive

C(x) = 250 + 179x

Substituting the values -

S(x) = [(-x^2/5)-247x] - [250+179x]

S(x) = (-x^2/5)-68x-250

In order to get maximum profit differentiate the equation and equate it to 0.

dS/dx = 0

dS/dx = -2x/5-68 = 0

-2x/5 = 68

x = 340/-2

x = -170

d^2S/dx^2 = -2/5<0

So, maximum profit will be at x = 170.

S max = S(170) = [(170)^2 /5] - 68 (170) - 250

= 5780 - 11560 - 250

= -6030

Therefore, the maximum profit earned is $6030.

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The 10 types of equation used in the mathematics are explained.

The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions.

Thus, the 10 types of equation are mentioned.

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Answer:

a. 1500 = 1000 × 1.05^x

b. 1500 = 1000 × 1.05^x

Divide both sides by 1000

1500/1000 = 1.05^x

Take the natural log of both sides

ln(1500/1000) = ln(1.05^x)

ln(1.5) = x ln(1.05)

x = ln(1.5) / ln(1.05)

x = 5.12 years

The value of x is 27

From the information given, we have that the triangle is an isosceles triangle.

The properties of an isosceles triangle are;

We have that;

First side = x + 2

Second side = 2x - 25

Equate the two sides, we get;

x+ 2 = 2x - 25

collect like terms

x - 2x = - 25 - 2

subtract like terms

-x= -27

make 'x' the subject

x = 27

Hence, the value is 27

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In given word problem Andre has more money than Elena after four weeks.

What is word problem?

A math word problem is a question that is written as one or more sentences and asks students to use their mathematical understanding to solve an issue from "real world." In order to understand the word problem, they must be familiar with the terminology that goes along with the mathematical symbols that they are used to.

Here,

Initial investment of Andre= $50

She add $5 per week for next 4 weeks , then

=> 4×5 = $20

Then total savings of Andre = $50+$20=$70.

Now Initial investment of Elena = $5

She adds $10 for each 4 weeks then

=> 10×4=$40.

Now total savings of Elena = $40+$5=$45.

Here $70>$45.

Hence after 4 weeks Andre has more money than Elena.

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Note that the above problems are solved using the knowledge of the sum of angles in a triangle.

10) when computed, x = 13°
11) when computed m∠S = 158°

12) when computed, ∠P = 115.625°; ∠Q = 21.125°; ∠R = 43.25°

13) when computed, angles L, J, K is 52°, 45°, 83° respectively.
14) When computed,

∠b = 108°

∠c = 36°

∠d = 36°

Note that the Triangles Theorem posits that the sum of Angles in a Triangle = 180°

10) To solve for x, we know that:

Given the above, we can state:

8x-44 = 180/3
8x-44 = 60

8x = 60 +44

x = 104/8

x = 13°

Thus x = 13°

11) For this problem, the key to solving for x is to note that the triangle is isosceles.

This means that,

15x - 31 = 9x + 11

Thus, collecting like terms, we have:

15x-9x = 11+ 31

24x = 42

x = 42/24

Thus,

x = 1.75

Since we are looking for m∠S, we can arrive at this by removing (15x - 31 ) + (9x + 11) from 180° based on the rule of the Sum of Angles in a triangle.
That is:

180 -  (15x - 31 ) + (9x + 11) = m∠S

To do this, we must impute the value of x in to the above equation:
⇒ m∠S = 180 -  ((15 * 1.75) - 31 ) + ((9 * 1.75) + 11)
⇒ m∠S = 180 -  (-4.75) + 26.75
m∠S = 180 -  22; thus

m∠S = 158°

12) <M, <P, <R, recall that the sum of the interior angles of triangle MPR will add up to 180 degrees

so <M + <P + <R = 180

We have ∠P is 14 less than five times x = 5x-15

∠Q is five less than x = x - 5

∠R is nine less than twice x =2x - 9

Recall the angle sum property of the triangle: The sum of all angles of a triangle is 180°

So, 5x -15 + x - 5 + 2x - 9 = 180°

Collect like terms to get

8x - 29 = 180

8x = 180+29

Thus,

x= 26.125

So,∠P  = 5x-15

=5 (26.125) -15

∠P = 115.625°

∠Q =x-5

=26.125 - 5

∠ Q =21.125°

∠R = 2x - 9

=2(26.125)-9

Thus

∠R = 43.25°

To confirm, if the above ∠ sum up to 180°, we say

Check 43.25+21.125+115.625

⇒ 43.25+21.125+115.625 = 180° is TRUE.

13) To solve for ∠J, ∠K  and ∠ L, recall that

The sum of the interior angles of triangle JKL will add up to 180 degrees

so <J + <K + <L = 180

L = measure of angle L

J = measure of angle J = L - 7

K = measure of angle K = 2L - 21

Thus, L + L-7 + 2L - 21 = 180; Collect like terms and we have

4L - 28 = 180

4L = 208

L = 52°,

If L is 52 then

J = L - 7 = 52 - 7

= 45°

K = 2L - 21 = 2(52) - 21

= 83

To check that they all sum up to 180° we say:

52+ 45+83

= 180°


14)

The sum of angle in a triangle is 180 degrees

Hence <b + <c + <d = 180

13x-35 + 5x - 19 + 2x + 14 = 180

13x+5x+2x-35-19+14 = 180

20x-40 = 180

20x = 180 + 40

20 x = 220

x = 220/20

x = 11

Get <b

<b = 13x-35

<b = 13(11) - 35

<b = 143-35

<b = 108 degrees

Get <c

c =5x-19

<c = 5(11)-19

<c = 55-19

<c = 36degrees

Get <d

<d = 2x+14

<d = 2(11) + 14

<d = 22+14

<d = 36 degrees

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Full Question for Number 14:
In ΔBCD if bc =bd angle b = 13x-35 angle c =5x-19 and angled d = 2x+14 find x and the measure of each angle

The 68-95-99.7 rule, also known as the empirical rule, is a shorthand for remembering the percentage of values in a normal distribution that lie within an interval estimate: 68%, 95%, and 99.7% of values lie within one, two, and three standard deviations of the mean, respectively.

The empirical rule, also known as the three-sigma rule or the 68-95-99.7 rule, is a statistical rule stating that for a normal distribution, nearly all observed data will fall within three standard deviations (denoted by σ) of the mean or average (denoted by µ).

The Empirical Rule states that 99.7% of data from a normal distribution is within 3 standard deviations of the mean.

68% of the data is within one standard deviation of the mean, 95% is within two standard deviations, and 99.7% is within three standard deviations, according to this rule.

Three-sigma limits that follow the empirical rule are used to define the upper and lower control limits in statistical quality control charts and risk analysis such as VaR.

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Answer:

[A] ((-2,5), (7, 5), (4, 0), (3, 1), (0,6))

Step-by-step explanation:

Given:

Which of the relations given by the following sets of ordered pairs is a function?

A. ((-2,5), (7, 5), (4, 0), (3, 1), (0,6))

B. ((1,2), (2, 3), (3,4), (2, 1), (1, 0))

C. ((2-8), (6, 4), (-3, 9), (2, 0), (5, 3))

D. ((1,3), (1, 1), (1, 1), (1,3), (1,5)}

Solve:

Knowing that; In order to know if a set of ordered pairs is a function or not we must see that if every x value have one or more than one y value that a function. If there is more than one same x value then it isn't a function.

Summary:

x value can't be duplicate but y can - in a working function

Hence, based on what we see in the answer choices;

[A] ((-2,5), (7, 5), (4, 0), (3, 1), (0,6)) is a function. Due to none repeat x values.

[B]((1,2), (2, 3), (3,4), (2, 1), (1, 0)) isn't a function. Due to repeat x -values (1 and 2)

[C] ((2-8), (6, 4), (-3, 9), (2, 0), (5, 3)) isn't a function. Due to repeat x-values (2)

[D]  ((1,3), (1, 1), (1, 1), (1,3), (1,5)} isn't a function. Due to repeat x-values (1)

RevyBreeze

64 marks must he score on her fourth exam to get exactly 80% in the course.

From the question, we are informed that Lisa is currently taking physics as one of her electives in school and that her grade at the end of the year is determined by the average of four exams, each worth 100 points.

First test = 84,

Second test = 92

Third test = 80

Forth test = y

And,

The fourth test is denoted by y.

Since we are told that she must get exactly 80% in the course and she took 4 exams, that means her total score will be: = 80 × 4 = 320

Therefore,

⇒ 84 + 92 + 80 + y = 320

⇒ 256 + y = 320

⇒ y = 320 - 256

⇒ y = 64

The fourth exam's score is 64.

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Answer: To keep both sides of the equation balanced

Step-by-step explanation:

The Golden Rule states that what you do to one side of an equation, that side being what is on one side of the equal sign, you must do to the other side. This is very important.

Therefore , as a result, the x, y, and z axes are the axis that the supplied coordinate plane problem is solved with.

The phrase "coordinate plane" describes a two-dimensional area made up of two rational numbers. It appears at the point where the X and Y axes connect, called the origin. A coordinate grid's numbers can be used to find points.

Here,

The x, y, and z axes of the Cartesian coordinate system,

which is used to represent three-dimensional space, are three axes that are mutually perpendicular to one another.

The origin is the location where the three axes converge.

Therefore , as a result, the x, y, and z axes are the axis that the supplied coordinate plane problem is solved with.

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The equation should be rearranged such that "y" is on the left and everything else is on the right.

Plot the "y=" line, using a solid line for y or y and a dashed line for y or y>. For "more than" or "less than" indications, shade above the line (y> or y), or below the line variable (y or y).

The symbols for less than and less than or equal to are "" and "," respectively. In contrast to less than or equal to, which requires that the variable or quantity be either equal to or less than the specified limit, less than means that the variable or quantity must have a value lower than the specified limit. There must be a difference between a and b's values.

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The complete question is " How do you graph the inequality y≥−5?"

It is not possible to construct a triangle whose sides are 8 cm 7 cm and 15 cm because the sum of two sides(8 cm and 7 cm) are equal to third side(15 cm).

In the given question, we have to check that it is possible to construct a triangle whose sides are 8 cm 7 cm and 15 cm.

The sum of the two sides must always be greater than the third side in order to determine whether or not the given sides may form a triangle.

To check this we firstly add the 8 and 7

8 + 7 = 15

15 = 15

Now we add 8 and 15

8 + 15 > 7

23 > 7

Now we add 7 and 15

7 + 15 > 8

22 > 8

It is not possible to construct a triangle whose sides are 8 cm 7 cm and 15 cm because the sum of two sides(8 cm and 7 cm) are equal to third side(15 cm).

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Answer: C = P$3.89

Step-by-step explanation:

Answer: 25

Step-by-step explanation:

The sum of all exterior angles = 360

Using this, we can get the equation

2x+20+x+40+3x+6x=360

12x+60=360

12x=300

Simplify, and you get

x = 25

In seventh grade, you received an A+:

1. Immediately after class, go through your notes.

2. Spend the most of your time studying throughout the day.

3. Read ahead rather than catching up.

4. Instruct someone else on the material.

5. Establish a study schedule from the start.

Grading in education is the practice of assigning standardized grades to students based on their degree of success in a course. Grades can be assigned in the form of letters, a range, a percentage, or a number out of a potential total. Grades are averaged in certain countries to get a grade point average. A 10-point grading scale is commonly used in Indian institutes (though some use a 4-point scale). Your GPA is derived by dividing the entire amount of your grades by the number of credits you took.

Here,

You get A+ in 7th grade:

1. Review your notes from class immediately after.

2. Do the bulk of your studying during the day.

3. Try to read ahead rather than play catch-up.

4. Teach the material to someone else.

5. Create a study schedule from day one.

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