Mathematics High School

In the given figure, AD is adjacent to BC.
if AB = 13 cm, BD = 5 cm and DC = 16 cm,
find the values of :
(I) sin B
(II) sec B
(III) cot B
(iv) cos C
(v) cosec C
(vi) tan C

Answers

Answer 1

By using the method of trigonometry,

(1)sin B=P/H=AD/AB=12/13

(2)sec B=H/B=AB/BD=13/5

(3)cot B=B/P=BD/AD=5/12

(4)cos C=B/H=CD/AC=16/20=4/5

(5)cosec C=H/P=AC/AD=20/12=5/3

(6)tan C =P/B=AD/DC=12/16=3/4

What is trigonometry?

Trigonometry is the study of angles and the angular relationships between planar and three-dimensional shapes. The cosecant, cosine, cotangent, secant, sine, and tangent are the trigonometric functions (sometimes known as the circle functions) that make up trigonometry. The unit circle is the most straight forward way to define the trigonometric functions. Let theta represent an angle that is calculated along a circle's arc counterclockwise from the x-axis.

Given that,

[tex]AD^{2}= AB^{2}- BD^{2}= 13^{2}- 5^{2}= 169-25= 144[/tex]

=>AD=12cm

(1)sin B=P/H=AD/AB=12/13

(2)sec B=H/B=AB/BD=13/5

(3)cot B=B/P=BD/AD=5/12

[tex]AC^{2}= AD^{2}+ DC^{2}= 12^{2}+ 16^{2}= 144+ 256= 400[/tex]

=>AC=20cm

(4)cos C=B/H=CD/AC=16/20=4/5

(5)cosec C=H/P=AC/AD=20/12=5/3

(6)tan C =P/B=AD/DC=12/16=3/4

note: P=perpendicular

B=base

H=hypotenuse

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Related Questions

Helpppp llsssssssssss

Answers

Answer:

Step-by-step explanation:

x = ( -b ± √b² - 4*a*c ) / 2a

3x² - x + 6 = 0

x = ( 1 ± √1 - 4 *3*6) / 2(6)

Select the correct answer. a charity organization is holding a food drive with a goal to collect at least 1,000 cans of food by the end of the month. it currently has 565 cans from donations and is having an event where 87 guests will attend and bring cans. which solution set represents the number of cans each guest must bring to meet the goal? a. a number line ranges from 0 through 10 from left to the right in increments of 1. a solid circular point is at 3. an arrow extends from the point toward the right. b. a number line ranges from 0 through 10 from left to the right in increments of 1. a hollow circular point is at 5. an arrow extends from the point toward the right. c. a number line ranges from 0 through 10 from left to the right in increments of 1. a hollow circular point is at 3. an arrow extends from the point toward the right. d. a number line ranges from 0 through 10 from left to the right in increments of 1. a solid circular point is at 5. an arrow extends from the point toward the right.

Answers

The number of cans each guest must bring to reach the goal must be greater than or equal to 5 by inequality.

What is inequality in math?

In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign ()" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.

Let

x -----> the number of cans each guest must bring to meet the goal

we know that

The number of guests multiplied by the the number of cans each guest must bring to meet the goal plus the currently cans must be greater than or equal to 1,000 cans

The inequality that represent this problem is

565 + 87x ≥ 1000

Solve for x

565 + 87x ≥ 1000

Subtract 565 both sides

87x ≥ 1000 - 565

87 ≥ 435

Divide by 87 both sides

x ≥ 435/87

x≥ 5

therefore, The number of cans each guest must bring to reach the goal must be greater than or equal to 5.

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The functions f and g are defined as follows.
g(x) = 4x+2
f(x)=3x²-3x
Find f(-5) and g(-4).
Simplify your answers as much as possible.

Answers

The value of functions f(-5) and g(-4) are 90 and -14 respectively.

What are functions and how to evaluate them?An expression, rule, or law in mathematics that establishes the relationship between an independent variable and a dependent variable.In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.Finding the value of f(x) =... or y =... that corresponds to a certain value of x is what it means to evaluate a function. To accomplish this, merely swap whatever value has been set to x into each of the x variables.

Given functions are:

g(x) = 4x+2

f(x) = 3x²-3x

We have to find f(-5) and g(-4).

f(x) = 3x²-3x, here in the function we replace the x variables with the value given.

f(-5) = 3x²-3x

= 3(-5)² - 3(-5)

= 75 + 15 = 90

g(x) = 4x+2

g(-4) = 4×(-4) + 2

= -16 + 2 = -14

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do you guys know how to solve this? 5/6x +1/2 = 4/5x - 1/6

Answers

Answer: x = -20

Step-by-step explanation:

Step 1: Move Like Terms to the Same Side

5/6x - 4/5x = -1/2 - 1/6

Step 2: Multiply by 30 to Remove Fractions

25x - 24x = -15 - 5

Step 3: Combine Like Terms

x = -20

Answer:

The answer is x = -20

Step-by-step explanation:

Did the math

which value is a solutions of 7/4x^2 -2 = 0.5 x+4

Answers

Answer:

x= 2 x= -1 5/7

Step-by-step explanation:

I believe this is the answer I used a math site.

x/50=20=40
i need help cux i dont get it

Answers

The given linear equation has solutions 1000 and 2000. This are values for which the equation is true.

Solving linear equations

Linear equations are equations that has a leading degree of 1. Given the equation below, we are to determine the value of x from the expression.

Given the linear equation

x/50=20=40

This can be splitted into x/50=20 and x/50 = 40

Solve both equations

x/50=20

Cross multiply

x = 50 * 20

x = 1000

Similarly;

x/50 = 40

Cross multiply

x = 50 * 40

x = 2000

Therefore the solutions to the given system of linear equation are 1000 and 2000

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Subtract using the number line. −1−(−6) Enter your answer in the box.

Answers

Using the number line we get the value as 5 .

In basic mathematics, real numbers are shown as a graphic of a graduated straight line called a number line.

Every point on a number line is considered to correspond to a real number, and every real number is assumed to correspond to a point.The integers are typically shown as lines of specially chosen, evenly spaced dots. Even though the picture only shows the integers, as well as numbers that are in between the integers, the line contains all real numbers, going forever in both directions. When teaching fundamental addition and subtraction with negative numbers, it is widely used as a teaching technique.

Now as represented in the number line we subtract the numbers to get

−1−(−6) = 5

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Witch is the equation of the given line?x = -3x = 3y = -3 y = -3x

Answers

y=-3

1) Since the graph shows us a horizontal line, where any value of x corresponds to y=-3

(2, -3), (3,-3) etc..

2) Then we have a constant function. y=-3

Answer:

y = - 3

Step-by-step explanation:

the line is horizontal and parallel to the x- axis with equation

y = c ( c is the value of the y- coordinates the line passes through.

the line passes through (- 4, - 3 ) and (2, - 3 ) both with y- coordinate - 3 , so

y = - 3 ← equation of line

What is the equation in slope-intercept form of a line (y = mx + b) that has aslope of 3 y-intercept of 6?

Answers

The equation of the line is y = 3x + 6

What are linear equations?

Linear equations are equations that have constant average rates of change.

Note that the constant average rates of change can also be regarded as the slope or the gradient

How to determine the equation of the line?

The given parameters are

Slope, m = 3

y-intercept, c = 6

A linear equation is represented as

y = slope * x + y-intercept

i.e.

y = mx + c

So, we have

y = 3x + 6

Hence. the linear equation is y = 3x + 6

Answers

When the pit stop duration is one minute other cars will gain 3/2 miles

Time duration of a pit stop during the car race = 10 seconds

The distance gained by other cars = 1/4 mile

Pit stop: During a race, a racing car makes a pit stop to get fuel, fresh tires, repairs, mechanical adjustments, a new driver, or any combination of the aforementioned. The pits typically consist of a row of garages where the work is done outside and a pit lane that runs parallel to the start/finish straight and is connected to the main track at each end.

When the duration is one minute or 60 seconds, then the distance gained by other cars will be:

Distance gained by other cars in 10 seconds*6 = 1/4*6 = 3/2 miles

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1. In a student election, Tyler defeated Julia by a ratio of 7 to 6. If there are 221 students
in the grade and all of them voted, how many votes did Julia receive?

A. 119
B. 107
C. 102
D. 89
E. 42

Answers

Answer:

Step-by-step explanation:

split 221 students in a ratio of 7:6

let x be 1/13th of the votes

221 = 7x + 6x

221 = 13x

17 = x

julia is the 6 in 7:6

6(17)

102

the answer is c

Rewrite the expression as the sum of two numbers. 4(5 + 8)

Answers

Answer:

20 + 32

Step-by-step explanation:

4(5 + 8)

20 + 32 = 52

I hope this helps!

Which of the following is a binomial in y
(1) y² + √2
1
(2) y + +2
y
(3) √5 + √2y
(4) y√y+1

Answers

Answer:

Binomial polynomial means that no negetive power on the no

(1) y² + √2 is correct answer

please help asap Evaluate the numerical expression open parentheses 2 to the power of 3 close parentheses to the power of one half.

4
cube root of 4
square root of 8
square root of 128

Answers

Answer:

C) square root of 8

=====================

Given expression

Open parentheses 2 to the power of 3 close parentheses to the power of one half.

Convert it to math language and simplify

[tex](2^3)^{\frac{1}{2} =[/tex] Expression as described[tex](8)^{\frac{1}{2} =[/tex] Cube of 2 is 8[tex]\sqrt{8}[/tex] Different form of square root

Correct choice is C

Help I can’t do this

Answers

Answer:

It looks like you want the point slope form of a line

y-4 = -2 (x +3)

Step-by-step explanation:

y -[tex]y_{1}[/tex] = m(x- [tex]x_{1}[/tex]) You plug in 4 for [tex]y_{1}[/tex], -2 for m and -3 for[tex]x_{1}[/tex]

y - 4 =(2(x - -3) x - -3 is the same at x + 3

y-4 + -2(x + 3)

7 9/16÷2 3/4 help me w my math

Answers

Answer is :

2.75

OR

2 3/4

If f(x)=-x and j(x)=f(x)+19 list the following attributes

f(x): Slope Y-intercept Zero J(x) Slope Y-intercept Zero

Answers

The slope of the functions f(x) and j(x) will be -1. And the y-intercept of the function j(x) will be 19.

What is a linear equation?

A relationship between two or more parameters that, when shown on a graph, produces a linear model. The degree of the variable will be one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

If f(x) = - x and j(x) = f(x) + 19

Then the function j(x) will be given as,

j(x) = f(x) + 19

j(x) = - x + 19

The slope of the functions f(x) and j(x) will be -1. And the y-intercept of the function j(x) will be 19.

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Jerald is having drain issues at his home and decides to call a plumber. The plumber charges $70 to come to his house and $50 for every hour they work. If the plumber charges Jerald a total of $285, how many hours did the plumber work?

Write and solve an equation to determine the number of hours worked by the plumber.

50x − 70 = 285; x = 7.1 hours
50x + 70 = 285; x = 4.3 hours
70x − 50 = 285; x = 4.8 hours
70x + 50 = 285; x = 3.4 hours

Answers

Answer: B

Step-by-step explanation:

A $70 is fixed, we have to add $50 each hour. So, it will be 70 + 50x. If he charged $285 overall, this means that 70 + 50x = 285

50x = 285 - 70

50x = 215

x = 215/50 = 4.3

Find the measure of

Answers

We can conclude that the angle ∠RST is 110°.

What are angles?An angle is a figure in plane geometry that is created by two rays or lines that have a common endpoint. The Latin word "angulus," which means "corner," is the source of the English word "angle." The common endpoint of two rays is known as the vertex, and the two rays are referred to as the sides of an angle.

So, as we can see line R and line T are parallel to each other.

Join, R and T with a line that makes a right angle with both lines.

(Refer to the image attached below)

Now, we know that ∠R = 90° and ∠SRT = 90 - 60 = 30°.Similarly, ∠T = 90° and ∠STR = 90 - 50 = 40°.

In triangle SRT, we know the two angles which are ∠R = 30° and ∠T = 40°.

We know that sum of all angles in a triangle is 180°.

So, ∠S in triangle SRT will be:

40 + 30 + ∠S = 18070 + ∠S = 180∠S = 180 - 70∠S = 110

Therefore, we can conclude that the angle ∠RST is 110°.

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1) If g(x) is a linear function, g(-2) = 6 and g(2) = 18, what is the rate of change? Is this function increasing or decreasing? Show your work!

Answers

Answers:

Rate of change = 3

The function is increasing

===================================================

Explanation:

The notation g(-2) = 6 means the input x = -2 leads to the output y = 6. Therefore, the point (-2,6) is on f(x). The other point given is (2,18).

For linear functions, the terms "rate of change" and "slope" are the same thing.

Let's use the slope formula on the two points (-2,6) and (2,18)

[tex](x_1,y_1) = (-2,6) \text{ and } (x_2,y_2) = (2,18)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{18 - 6}{2 - (-2)}\\\\m = \frac{18 - 6}{2 + 2}\\\\m = \frac{12}{4}\\\\m = 3\\\\[/tex]

The slope is 3, which can be written as 3/1

A slope of 3/1 means we go up 3 and to the right 1.

slope = rise/run = 3/1

rise = 3 = go up 3

run = 1 = go to the right 1

Since the slope is positive, this means the line is going uphill as we move to the right. In other words, the function is increasing.

can someone answer this pls Im dying

Answers

Answer: The rectangle has 2, and the triangle has 3

Step-by-step explanation:

½a + ¾b + ½a - ½b =
This all im looking for the answer

Answers

Answer:

(4a+b)/4

Step-by-step explanation:

HELP

What are the similarities and differences do you see between 3 and 4

For example:
Similar: both arithmetic/linear/common difference
Different: #1 is discrete #3 is continuous

WILL GIVE BRAIN

Answers

measures: _ , and .

Help me graph the relationship please! I've been stuck on this problem for a week now... :<

Answers

Rate of change (m) = 10

Starting amount (b) = 14

It takes 9 days to have 104 boondins.

The equation in slope-intercept form is: y = 10x + 14

Its graph is shown below.

How to Write the Equation of a Line?

Where m represents the rate of change and b represents the y-intercept or starting value, the equation of a line can be written in slope-intercept form as:

y = mx + b.

From the information given, the following are given about the line:

x = number of days

y = total number of boondins

If he had 74 boondins in 6 days and he bought 10 more every day, then:

x = 6

y = 74

Starting value (b) = ?

Rate of change (m) = 10

Substitute the values into y = mx + b to find the value of b:

74 = 10(6) + b

74 = 60 + b

74 - 60 = 60 + b - 60

14 = b

b = 14

Therefore:

Rate of change (m) = 10

Starting amount (b) = 14

To write the equation in slope-intercept form, substitute b = 14 and m = 10 into y = mx + b:

y = 10x + 14

To find how many days it takes to have 104 boondins, substitute y = 104 into the equation, y = 10x + 14:

104 = 10x + 14

Solve for x

104 - 14 = 10x

90 = 10x

90/10 = 10x/10

9 = x

x = 9

It takes 9 days.

For 10 days, it would take:

y = 10(10) + 14

y = 114 boondins

The table is:

(x, y)

(0, 14)

(10, 114)

The graph for y = 10x + 14 is given in the attachment.

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What is the value of x? (1 point)
1. 24
2. 9
3. 21
4. 14
(i forgot the picture the first time)

Answers

(5x+15)°+(3x-3)°=180°(CO-INTERIOR ANGLES)

[tex]5x + 15 + 3x - 3 = 180 \\ 5x + 3x = 180 - 15 + 3 \\ 8x = 168 \\ \frac{8x}{8} = \frac{168}{8} \\ x = 21[/tex]

ATTACHED IS THE SOLUTION

Combine like terms 8x=168
Divide both sides by 8
X=21

slope
P(-6, 16), Q(2, -4); R(-6, 14), S(-2, 4)

Answers

The slope of the given points is equal to -5/2 or -2.5.

What is a slope?

A slope is also referred to as gradient and it's typically used to describe both the direction, ratio, and steepness of the function of a straight line based on its coordinates or points.

How to calculate the slope of a line?

Mathematically, the slope of any straight line can be calculated by using this formula;

[tex]Slope = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]

For the given points P(-6, 16) and Q(2, -4), the slope is given by;

Slope = Δy/Δx

Slope = (-4 - 16)/(2 - (-6))

Slope = (-4 - 16)/(2 + 6)

Slope = -20/8

Slope = -5/2 or -2.5.

For the given points R(-6, 14) and S(-2, 4), the slope is given by;

Slope = Δy/Δx

Slope = (4 - 14)/(-2 - (-6))

Slope = (4 - 14)/(-2 + 6)

Slope = -10/4

Slope = -5/2 or -2.5.

In conclusion, the slope of the line that passes through the given points is equal to -5/2 or -2.5.

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Complete Question:

Find the slope of the given points. P(-6, 16), Q(2, -4); R(-6, 14), S(-2, 4)

What is the sequence of transformations that maps ABC to A’B’C’
Step 1:
A. Reflect across the line Y=X
B. Reflect across the x-axis
C. Rotate 90° clockwise about the origin.
D. Rotate 180° about the origin

Step 2:
A. Translate 6 units up
B. Translate 5 units up
C. Reflect across the line y=x
D. Reflect across the x-axis

Answers

Answer:

Yes, reflecting a shape across the x-axis and then rotating it 90° clockwise about the origin gives the same results as reflecting it

Step-by-step explanation:

Answer: step 1 = C step 2 = A

Step-by-step explanation: 190 abc 123

A bottled water company quality control officer wants to find out how well the label machines are working. He is studying every machine and every bottle to make sure it is usable to a customer. Which represents a population?

the first fifty bottles labeled on Monday morning
one hundred bottles
all the bottles with incorrectly placed labels
all the bottles produced in one day

Answers

All the bottles produced in one day represents the population in statistics .

In statistics, a population is a collection of similar things or events that are important to a specific experiment or topic.

A statistical population can be made up of actual objects (such all the stars in the Milky Way galaxy) or hypothetical groups of things that are assumed to be an infinite number of objects based on experience-based generalizations (e.g. the set of all possible hands in a game of poker). A common objective of statistical analysis is to gather information about a chosen community.In statistical inference, a subset of the population (a statistical sample) is chosen to represent the population in a statistical study.The statistical sample must also fairly and accurately represent the population.

Since the population represents all the data for a particular time period , in this case we can conclude that the population for the factory will be all the bottles produced in 1 day.

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Help please basic geometry

Answers

From the diagram in the image below, it can not be assumed that A C D is a right angle. Option A

This is further explained below.

What is a triangle's right angle?

Generally, In a triangle, a right triangle, also known as a right-angled triangle, an orthogonal triangle, or what was previously known as a rectangle triangle, is a triangle in which either one of the triangle's angles is a right angle or two of the sides are perpendicular to one another.

The relationship between the sides of a right triangle and the other angles provides the foundation for the study of trigonometry.

In conclusion, It is not possible to deduce from the diagram in the figure below that the angle ACD are right angles. Alternative A

Answers

Answer:

a₁₀ = 26

Step-by-step explanation:

to find a₁₀ substitute n = 10 into the nth term formula

a₁₀ = 3(10) - 4 = 30 - 4 = 26

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In the given figure, AD is adjacent to BC. if AB = 13 cm, BD = 5 cm and DC = 16 cm, find the values of : (I) sin B (II) sec B (III) cot B (iv) cos C (v) cosec C (vi) tan C

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In the given figure, AD is adjacent to BC.
if AB = 13 cm, BD = 5 cm and DC = 16 cm,
find the values of :
(I) sin B
(II) sec B
(III) cot B
(iv) cos C
(v) cosec C
(vi) tan C