Answer:
2
Step-by-step explanation:
slope = rise/run
rise = difference in y
run = difference in x
slope = (8 - 2)/(3 - 0)
slope = 6/3
slope = 2
Trigonometric ratios
class 9
please answer my questions
Step-by-step explanation:
Hi there!
Please see the answer in the picture.
Hope it helps!
1. Approach
One is given a trigonometric equation with and one is asked to prove that it is true. Using the attached image, combined with the knowledge of trigonometry, one can evaluate each trigonometric function. Then one can simplify each ratio to solve. To yield the most accurate result, one has to each of the ratios in a fractional form, rather than simplifying it into a decimal form. Remember the right angle trigonometric ratios, these ratios describe the relationship between the sides and angles in a right triangle. Such ratios are as follows,
[tex]sin(\theta)=\frac{opposite}{hypotenuse}\\\\cos(\theta)=\frac{adjacent}{hypotenuse}\\\\tan(\theta)=\frac{opposite}{adjacent}\\\\csc(\theta)=\frac{hypotenuse}{opposite}\\\\sec(\theta)=\frac{hypotenuse}{adjacent}\\\\cot(\theta)=\frac{adjacent}{opposite}[/tex]
Please note that the terms (opposite) and (adjacent) are relative to the angle uses in the ratio, however the term (hypotenuse) refers to the side opposite the right angle, this side never changes its name. Use these ratios to evaluate the trigonometric functions. Then simplify to prove the identity.
2. Problem (9)
[tex]\frac{sin(60)+cos(30)}{1+sin(30)+cos(60)}=sin(60)[/tex]
As per the attached image, the following statements regarding the value of each ratio can be made:
[tex]sin(60)=\frac{\sqrt{3}}{2}\\\\cos(30)=\frac{\sqrt{3}}{2}\\\\sin(30)=\frac{1}{2}\\\\cos(60)=\frac{1}{2}[/tex]
Substitute,
[tex]\frac{sin(60)+cos(30)}{1+sin(30)+cos(60)}=sin(60)[/tex]
[tex]\frac{\frac{\sqrt{3}}{2}+\frac{\sqrt{3}}{2}}{1+\frac{1}{2}+\frac{1}{2}}=\frac{\sqrt{3}}{2}[/tex]
Simplify,
[tex]\frac{\frac{\sqrt{3}}{2}+\frac{\sqrt{3}}{2}}{1+\frac{1}{2}+\frac{1}{2}}=\frac{\sqrt{3}}{2}[/tex]
[tex]\frac{\frac{2\sqrt{3}}{2}}{1+\frac{1}{2}+\frac{1}{2}}=\frac{\sqrt{3}}{2}[/tex]
[tex]\frac{\frac{2\sqrt{3}}{2}}{1+1}=\frac{\sqrt{3}}{2}[/tex]
[tex]\frac{\sqrt{3}}{1+1}=\frac{\sqrt{3}}{2}[/tex]
[tex]\frac{\sqrt{3}}{2}=\frac{\sqrt{3}}{2}[/tex]
Thus, this equation is true.
2. Problem (10)
Use a similar strategy to evaluate this equation,
[tex]\frac{1-cos(30)}{sin(30)}=\frac{1-cot(60)}{1+cot(60)}[/tex]
Use the attached image to evaluate the ratios.
[tex]cos(30)=\frac{\sqrt{3}}{2}\\\\sin(30)=\frac{1}{2}\\\\cot(60)=\frac{1}{\sqrt{3}}[/tex]
Substitute,
[tex]\frac{1-cos(30)}{sin(30)}=\frac{1-cot(60)}{1+cot(60)}[/tex]
[tex]\frac{1-\frac{\sqrt{3}}{2}}{\frac{1}{2}}=\frac{1-\frac{1}{\sqrt{3}}}{1+\frac{1}{\sqrt{3}}}[/tex]
Simplify,
[tex]\frac{1-\frac{\sqrt{3}}{2}}{\frac{1}{2}}=\frac{1-\frac{1}{\sqrt{3}}}{1+\frac{1}{\sqrt{3}}}[/tex]
[tex]\frac{\frac{2-\sqrt{3}}{2}}{\frac{1}{2}}=\frac{1-\frac{1}{\sqrt{3}}}{1+\frac{1}{\sqrt{3}}}[/tex]
[tex]\frac{\frac{2-\sqrt{3}}{2}}{\frac{1}{2}}=\frac{\frac{\sqrt{3}-1}{\sqrt{3}}}{1+\frac{1}{\sqrt{3}}}[/tex]
[tex]\frac{\frac{2-\sqrt{3}}{2}}{\frac{1}{2}}=\frac{\frac{\sqrt{3}-1}{\sqrt{3}}}{\frac{\sqrt{3}+1}{\sqrt{3}}}[/tex]
[tex]2-\sqrt{3}=\frac{\frac{\sqrt{3}-1}{\sqrt{3}}}{\frac{\sqrt{3}+1}{\sqrt{3}}}[/tex]
[tex]2-\sqrt{3}=\frac{\sqrt{3}-1}{\sqrt{3}}*\frac{\sqrt{3}}{\sqrt{3}+1}}[/tex]
[tex]2-\sqrt{3}=\frac{\sqrt{3}-1}{\sqrt{3}+1}[/tex]
Rationalize the denominator,
[tex]2-\sqrt{3}=\frac{\sqrt{3}-1}{\sqrt{3}+1}[/tex]
[tex]2-\sqrt{3}=\frac{\sqrt{3}-1}{\sqrt{3}+1}*\frac{\sqrt{3}-1}{\sqrt{3}-1}[/tex]
[tex]2-\sqrt{3}=\frac{(\sqrt{3}-1)^2}{3-1}[/tex]
[tex]2-\sqrt{3}=\frac{3-2\sqrt{3}+1}{2}[/tex]
[tex]2-\sqrt{3}=\frac{4-2\sqrt{3}}{2}[/tex]
[tex]2-\sqrt{3}=2-\sqrt{3}[/tex]
Therefore, this equation is also true.
30 Points cuz I need help ASAP
Answer:
the answer is option 1
Step-by-step explanation:
the negative angle => a quarter round angle (clockwise) = ¼ x ( -360°) = -90°
and
the positive angle => a full round angle + 270° = (360°)+270°
= 630°
Answer:
correct answer is -90 and 630
Step-by-step explanation:
find the missing side.
Answer:
I htink x ≈ 8
Step-by-step explanation:
Answer:
X is approximately 7.8.
Step-by-step explanation:
You can use SOH-CAH-TOA to help figure out what function (sin, cos, tan) you need to use in order to figure out the missing side.
For this one, we can see the angle is pointing to the opposite side (x length), and we have been given the hypotenuse (18). So we want to use the sin function.
[tex]sin\ (angle)=\frac{opposite}{hypotenouse}[/tex]
[tex]sin (26)=\frac{x}{18}[/tex]
[tex]0.438=\frac{x}{18}[/tex]
[tex]7.890... = x[/tex]
Using Pythagorean theorm, you can figure out the other side if need be :)
For reference:
[tex]sin (angle)=\frac{opposite}{hypotenuse}[/tex]
[tex]cos(angle)=\frac{adjacent}{hypotenuse}[/tex]
[tex]tan(angle)=\frac{opposite}{adjacent}[/tex]
Find the length of the third side. If necessary, round to the nearest tenth.
12
13
Answer:
Submit Answer
attempt 1 out of 2
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PLS HELP ASAP
Answer:
5
Step-by-step explanation:
Use pythagorean theorem. A^2+B^2=C^2
13 is c because it is the hypotenuse and across from the right angle
a is unknown and b is 12
A^2+12^2=13^2
A^2 +144 = 169
A^2 = 169- 144
A^2= 25
now take the sq root of both side
A = 5
Answer:
17.7
Step-by-step explanation:
Does this graph show a function? Explain how you know.
A. No; the graph fails the vertical line test.
• B. No; there are y-values that have more than one x-value.
• C. Yes; the graph passes the vertical line test.
D. Yes; there are no y-values that have more than one x-value.
Answer:
C. Yes; the graph passes the vertical line test.
Step-by-step explanation:
Reasons the others are wrong:
A. It does pass the vertical line test.
B. Y-values can have any x values. It is x-values that can't have multiple y-values.
D. There are y-values with more than one x-value on this graph so that's just false. Even if it were true, that still doesn't invalidate it due to the reasons given in Answer B.
Help me with this pls IM FAILING PYTHAGOREAN THEOREM
Answer: 33
Work Shown:
Apply the pythagorean theorem to get
[tex]a^2 + b^2 = c^2\\\\x^2 + 44^2 = 55^2\\\\x^2 + 1936 = 3025\\\\x^2 = 3025 - 1936\\\\x^2 = 1089\\\\x = 33[/tex]
Graph the solution to the following system of inequalities.
y-2x-9
y<2x+7
Answer:
Tb bight by icing I jb Yves j by by by navy by iffy i by by by
Will Mark Brainlest Help pls
Answer:
Hello,
[tex]\begin{bmatrix}-2&2\\3&5\\\end{bmatrix}\\\\[/tex]
Step-by-step explanation:
[tex]\begin{bmatrix}2&3\\5&7\end{bmatrix}-A=\begin{bmatrix}3&1\\-2&-3\end{bmatrix}+\begin{bmatrix}1&0\\0&1\end{bmatrix}\\\\\\\begin{bmatrix}2&3\\5&7\end{bmatrix}-A=\begin{bmatrix}2&3\\5&7\end{bmatrix}-\begin{bmatrix}4&1\\-2&-2\end{bmatrix}\\\\\\A=\begin{bmatrix}-2&2\\3&5\end{bmatrix}\\\\[/tex]
Find the measure of <3. 90 50 40 130
=============================================================
Explanation:
This figure is a kite since we have two pairs of adjacent sides that are congruent, but not all sides are the same length.
One property of kites is that the diagonals are always perpendicular (this applies to rhombuses as well). This means angle 3 is 90 degrees.
The measure of ∠3 is 90°
Because in a kite the diagonals bisects at 90°
Therefore ∠3 is 90°
Answered by Gauthmath must click thanks and mark brainliest
How many significant digits are there in the number 1.00250? OA) 7 OB) 6 OC) 5 OD) 4
Answer:
OB
Step-by-step explanation:
start counting from 1
Then your significant digit is 6
HELP PLS HELP MEEEEE IM FAILING PYTHAGOREAN THEOREM
7^2 + 6^2 = h^2
49 + 36 = h^2
85 = h^2
√85 = h
h = 9.21m
Answered by Gauthmath must click thanks and mark brainliest
Planes X and Yand points J, K, L, M, and N are shown.
Exactly how many planes contain points J, K, and N?
X
O 0
O 1
O 2
03
K
Υ
2
.M
.N
Answer:
0
Step-by-step explanation:
0
Number planes contain points J, K and N is 0. Therefore, option A is the correct answer.
What is a plane?A plane in geometry is a level surface that never ends. Other names for it include a two-dimensional surface. A plane has an unlimited width, an endless length, zero thickness, and no curvature.
Given that, X and Y are planes.
In the given figure, point J lies outside the X and Y planes.
Points K and N are lies on plane X.
So, J, K and N are not lying in the same plane.
Therefore, option A is the correct answer.
Learn more about the coordinate plane here:
https://brainly.com/question/24134413.
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A textbook store sold a combined total of 240 chemistry and history textbooks in a week. The number of chemistry textbooks sold
was two times the number of history textbooks sold. How many textbooks of each type were sold?
Answer:
160 chemistry books and 80 history books
Step-by-step explanation:
C=chemistry books sold, H=history books sold
C=2H
C+H=240, 3H=240, H=80, C=160
Add.
(3x2 – 2x) + (4x-3)
O A. 7x2- 5x
O B. 12x3 - 14x2 + 6x
O C. 3x2 - 6x + 3
O D. 3x2 + 2x-3
Answer:
O D. 3x2 + 2x-3
Answer:
A.7x2-5x questions 2of 20
HELP ITS DUE IN THE MORNING AND ITS 3:57
Answer:
A " (1,-2)
B " (4,0)
C " (6,-3)
Step-by-step explanation:
Hope it helped.
° ° °
pls explain me i will make u as brainlist
Answer:
hope this help you
have a great day
Alex can cut a cord into 7 pieces in 36 seconds. How long will it take him to cut the cord into 12 pieces? (the answer is NOT 61 or 62.)
Answer:
x=61.71428 or 61 5/7
Step-by-step explanation:
We can use a ratio to solve
7 pieces 12 pieces
----------------- = ---------------
36 seconds x seconds
Using cross products
7x = 36*12
7x = 432
Divide by 7
7x/7 = 432/7
61 5/7
x=61.71428
Answer:
66
Step-by-step explanation:
On another map, the distance between Saugerties and
Kingston is 2 inches. What would the distance from
Saugerties to Catskill be on this map?
Answer:
10miles
Step-by-step explanation:
Answer:
I have no clue what is going on wit dis g
Categorize the graph as linear increasing, linear decreasing, exponential growth, or exponential decay
Answer:
D. Exponential growth
Step-by-step explanation:
Hope this helps
Function that is similar to exponential.
Option (A) is correct.
What is exponential decay?Exponential decay describes the process of reducing an amount by a consistent percentage rate over a period of time. It can be expressed by the formula [tex]y=a(1-b)^{x}[/tex] wherein y is the final amount, a is the original amount, b is the decay factor, and x is the amount of time that has passed.
We can observe that
First, y increases as x increases
Last it is a function that is similar to exponential.
Function is an exponential decay.
Option (A) is correct.
Find out more information about exponential decay here
https://brainly.com/question/14355665
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Explain how to solve the equation
.
b – 7 = 12
Answer:
19
Step-by-step explanation:
Add 7 onto 12 to find answer.
Answer:
b = 19
Step-by-step explanation:
b = 12 + 7
Simplify 12+7 to 19.
Rewrite using exponents
AxAxAxAxAxAxA
need answer quick!!! please
Answer:
A^7
Step-by-step explanation:
-2z² + 4z + 2z² = ?
Anyone know this?
Answer:
4
Step-by-step explanation:
Let's simplify step-by-step.
−2z2+4z+2z2
Combine Like Terms:
=−2z2+4z+2z2
=(−2z2+2z2)+(4z)
=4z
Answer:
4z
Hope this helps <3 Need thanks?
Comment /hearthelp
[tex]\\ \sf\longmapsto -2z^2+4z+2z^2[/tex]
Combine like. variables[tex]\\ \sf\longmapsto -2z^2+2z^2+4z[/tex]
[tex]\\ \sf\longmapsto (-2+2)z^2+4z[/tex]
[tex]\\ \sf\longmapsto 0z^2+4z[/tex]
[tex]\\ \sf\longmapsto 4z[/tex]
What is the solution to the system that is created by the equation y = - x + 6
Answer:
If you draw the graph of y = -x + 6 on the above graph the solution to system will be the coordinates of the point of intersection.
the equation of the line drawn above is y = 0.5x
so you can also find the solution by solving the system
y = 0.5x
y = -x + 6
0.5x = -x + 6
1.5x = 6
x = 6/1.5 = 4
and y = 0.5*4 = 2
The answer is (4, 2) - the third choice.
Step-by-step explanation:
What is the length of BD?
Answer:
BD = 10 √3
Step-by-step explanation:
ABC ∆ ,
BD ÷ 20 = sin 60
BD = 20 sin 60
BD = (20 √3) / 2
= 10 √3
Divide Rs.45000 among 2 students Mina and Rita in the ratio of marks they got 40 and 50 respectively
Let
Money share of Mina=40xMoney shae of Rita=50xATQ
[tex]\\ \qquad\quad\sf{:}\twoheadrightarrow 40x+50x=45000[/tex]
[tex]\\ \qquad\quad\sf{:}\twoheadrightarrow 90x=45000[/tex]
[tex]\\ \qquad\quad\sf{:}\twoheadrightarrow x=\dfrac{45000}{90}[/tex]
[tex]\\ \qquad\quad\sf{:}\twoheadrightarrow x=500[/tex]
Now
[tex]\\ \qquad\quad\sf{:}\twoheadrightarrow Rita=50x=50(500)=25000[/tex]
[tex]\\ \qquad\quad\sf{:}\twoheadrightarrow Mina=40x=40(500)=20000[/tex]
u4gent help needed
help me with the question of o.math
Answer:
1≤f(x)≤5
Step-by-step explanation:
-1≤x≤1
-2≤2x≤2 (Multiplied by 2 both side)
-2+3≤2x+3≤2+3 (Adding three both sides)
1≤f(x)≤5
.The conversion of square feet to square yards can be represented by direct variation. Three square yards are equivalent to 27 square feet. Let y represent the number of square yards and x the number of square feet. Then y varies directly with x.
What is the constant of variation?
What is the equation representing the direct variation?
Answer:
The constant of variation is 1/9
The equation representing the direct variation is y/x= 1/9
Step-by-step explanation:
In direct variation, y/x=k denotes the equation, with k being the constant of variation. Here, y is the number of square yards and x is the number of square feet. Therefore, as we know that 27 square feet = 3 square yards, we can write one point (x₁, y₁) as (27 square feet, 3 square yards). Plugging x₁ and y₁ into our equation, we get
y/x = k
3 / 27 = k
(3/27) / (3/3) = 1/9* = k
Therefore, the constant of variation is 1/9
Next, as stated previously, y/x = k represents the equation of direct variation. Therefore, y / x = 1/9 as our equation
* because 3 is a factor of both 3 and 27, we can divide both the numerator and denominator by 3 to keep the fraction the same but also simplify it. One way to find the greatest common factor is to list the factors of each number and see the highest number that is a factor of both
The constant of variation is "1/9" and the equation representing the direct variation is y = (1/9)x.
What is the equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
The equation of direct variation is given by,
y = kx ....(i) where "k" is a constant.
Let y represent the number of square yards and x the number of square feet. Then y varies directly with x.
Given that y varies directly with x, and x = 27, then y = 3.
Substitute the values of y = 3 and x = 27 in the direct variation equation and solve for k:
⇒ 3 = 27k
⇒ k = 3/27
⇒ k = 1/9
Substitute the values of k = 1/9 in the direct variation equation :
⇒ y = (1/9)x
Thus, the constant of variation is "1/9" and the equation representing the direct variation is y = (1/9)x.
Learn more about the equations here:
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PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER PLS GIVE ME A STEP BY STEP EXPLANATION!!
The students in Shawn's class got to choose whether to visit the zoo or the aquarium. 3 students went to the zoo and 15 students went to the aquarium. What is the ratio of the number of students who went to the zoo to the number of students who did not go to the zoo?
A. 1:6
B. 1:1
C. 1:3
D. 1:5
Answer:
1 : 5
Step-by-step explanation:
3 students zoo
15 students aquarium
zoo : not zoo
3: 15
Divide each side by 3
3/3 : 15/3
1 : 5
value of the pronumeral and describe the rule.
4,1,-2,p,-8,-11
Answer:
p = -5
every element in the sequence is created by subtracting 3 from the pervious element.
Step-by-step explanation:
I am not sure you put every necessary information here.
but I'd the visible information is truly everything, then it's is trivial.
the difference between 4 and 1 is ... well, -3. meaning we subtract 3 from 4 to get 1.
we suspect this is the rule and keep trying.
1 -3 = -2
hey it works.
and -8 -3 = -11
hey, also correct.
and the difference between -2 and -8 is -6, and when we place another item in between (p), we cut that in half again to -3. so, it is all consistent.
therefore,
p = -2 -3 = -5
the rule is
an = an-1 - 3
Please help me to solve this question as soon as possible. Thank you
1.6 is a common factor of 36 and y. Find the possible value of y.
A. 25
B. 48
C.57
D. 81
Answer:
the answer is B
Step-by-step explanation:
because only 48 is dividable by 6