Answer:
[tex]\large\boxed{y=-\dfrac{8}{5}x+\dfrac{31}{5}}[/tex]
Step-by-step explanation:
[tex]\text{The slope-intercept form of an equation of a line:}\\\\y=mx+b\\\\m-slope\\b-y-intercept[/tex]
[tex]\text{Let}\\\\k:y=m_1x+b_1\\\\l:y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\l\ \parallel\ k\iff m_1=m_2\\\\--------------------------[/tex]
[tex]\text{We have:}\\\\y=\dfrac{5}{8}x-4\to m_1=\dfrac{5}{8}\\\\\text{The slope of a perpendicular line:}\ m_2=-\dfrac{1}{\frac{5}{8}}=-\dfrac{8}{5}\\\\\text{The equation:}\\\\y=-\dfrac{8}{5}x+b\\\\\text{Put the coordinates of the point (2, 3) to the equation:}\\\\3=-\dfrac{8}{5}(2)+b\qquad\text{solve for}\ b\\\\3=-\dfrac{16}{5}+b\qquad\text{add}\ \dfrac{16}{5}\ \text{to both sides}\\\\\dfrac{15}{5}+\dfrac{16}{5}=b\to b=\dfrac{31}{3}\\\\\text{Finally:}\\\\y=-\dfrac{8}{5}x+\dfrac{31}{5}[/tex]
Translate the sentence into an equation.
Twice the difference of a number and 3 equals 7.
Answer:
2(x - 3) = 7
Step-by-step explanation:
Set up the difference part first.
x - 3
Now deal with the "Twice."
2(x - 3)
Next equals
2(x - 3) =
And finally what it equals
2(x - 3) = 7
Answer:
2(x-3)=7
Step-by-step explanation:
Dont take my word for it double check with someone else.
Simplify (11+19i)/ (8-5i)
Answer:
To simplify the expression let's multiply and divide by (8+5i) as follows:
[tex]\frac{(11+19i)(8+5i)}{(8-5i)(8+5i)}= \frac{207i-7}{89}= 2.32i - 0.08[/tex]'
Now, we have successfully removed the imaginary number from the denominator.
HELP ASAP AND GETS SOME POINTS AND BRAINLEST!!!!
Answer:
9x² + 28x - 32
Step-by-step explanation:
Given
(9x - 8)(x + 4)
Each term in the second factor is multiplied by each term in the first factor, that is
9x(x + 4) - 8(x + 4) ← distribute both parenthesis
= 9x² + 36x - 8x - 32 ← collect like terms
= 9x² + 28x - 32
Answer:
Option D
Step-by-step explanation:
Between 2000 and 2014, the number of twin births in a certain country increased by 15%, to approximately 133975. About how many twin births were there in 2000?
Answer:
116500
Step-by-step explanation:
We are looking for the number of twin births in 2000.
Let the number of twin births in 2000 be x.
The number of twin births in 2000 is 100% of the number of births in 2000 since 100% of something is the entire thing.
The number of twin births went up 15% from 2000 to 2014, so in 2014, the number of twin births was 100% of the number of twin births plus another 15% of the number of twin births.
100% + 15% = 115%
The number of twin births in 2014 was 115% of x.
The number of twin births in 2014 was 133975.
115% of x = 133975
115% * x = 133975
1.15x = 133975
x = 133975/1.15
x = 116500
The number of twin births in 2000 was 116500.
An increase by 15% means 15 added to per cent (per = each; cent=100).
If the population was 100 in the year 2000 then it would be 115 in the year 2014. (adding 15 to 100)
The population was 116500 in the year 2000 and it increased to 133975 in the year 2014.
Let the population be x in the year 2000.
Using ratio and proportion
Year 2000 : Year 2014
100 : 115
x : 133975
Applying cross product rule
x × 115= 100× 133975
x= 100× 133975/115
x= 116500
The population was 116500 in the year 2000 and it increased to 133975 in the year 2014.
https://brainly.com/question/14039286
-2(10r + 4) + 10(7r + 2)
Answer:
[tex]\large\boxed{-2(10r+4)+10(7r+2)=50r+12}[/tex]
Step-by-step explanation:
[tex]-2(10r+4)+10(7r+2)\qquad\text{use the distributive property}\ a(b+c)=ab+ac\\\\=(-2)(10r)+(-2)(4)+(10)(7r)+(10)(2)\\\\=-20r-8+70r+20\qquad\text{combine like terms}\\\\=(-20r+70r)+(-8+20)\\\\=50r+12[/tex]
write a linear equation in point slope form for the line that goes through (-1, 1) and (1, -3)
Answer:
y - 1 = -2(x + 1).
Step-by-step explanation:
The slope = (-3-1)/(1 - -1)
= -4 / 2
= -2.
In point slope form:
y - y1 = m(x - x1)
Using m = -2 and the point (-1, 1):
y - 1 = -2(x + 1).
Answer:
see explanation
Step-by-step explanation:
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
Calculate m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (- 1, 1) and (x₂, y₂ ) = (1, - 3)
m = [tex]\frac{-3-1}{1+1}[/tex] = [tex]\frac{-4}{2}[/tex] = - 2
Using either of the 2 points as a point on the line, then
Using (- 1, 1)
y - 1 = - 2(x - (- 1)), that is
y - 1 = - 2(x + 1) ← in point- slope form
A circle with a radius of 10 inches is placed inside a square with a side length of 20 inches. Find the area of the square.
a. 400
b. 413
c. 314
d. 143
Answer:
The correct answer is option a. 400
Step-by-step explanation:
Points to remember
Area of square = a²
Where 'a' is the side length of square
To find the area of square
It is given that, the side length of square is 20 inches.
Here a = 20 inches
Area = a²
= 20²
= 400
Therefore the correct answer is option a. 400
Ashley is diving in the ocean. She wants to reach a coral reef that is 60 feet below sea level,that is , the reefs elevation is -60 feet. She decides to safely descend to the reef from the oceans surface in increments of 10 feet. Ashley dives in increments of 10 feet. What rational number represents diving 10 feet below sea level?
Answer:
-10 is the answer
Step-by-step explanation:
Diving 10 feet below sea level increases the pressure by 1 atmosphere (ATA), causing the body's air pockets to compress. Divers must equalize the pressure by adding air to these airspaces on the descent.
Explanation:When diving 10 feet below sea level, the pressure increases by 1 atmosphere (ATA). According to Boyle's law, the volume of gases decreases as pressure increases. The increase in pressure can compress the body's air pockets, such as those in the ears and lungs, which can cause discomfort or injury. Divers must equalize the pressure by adding air to these airspaces on the descent.
Learn more about Pressure and equalization in scuba diving here:https://brainly.com/question/30262529
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Given a= 108 degree, b=9 and c = 15, use the law of cosines to solve the triangle for the value of A. Round answer two decimal places.
a. 19.13
b. 14.92
c. 19.73
d. 18.53
Answer:
c. 19.73
Step-by-step explanation:
The Cosine rule shows states that:
a²=b²+c²-2bcCos A, where a, b and c are the sides of the triangle and A is the angle at vertex A.
A=108°
b=9
c=15
Substituting with the values above gives:
a²=9²+15²-(2×9×15 Cos 108)
a²=389.4346
a=19.73
Identify the least common multiple of x2 − 10x + 24 and x2 − x − 12.
Answer:
(x-4)(x-6)(x+3) or in more compressed form x³-7x²-6x+72
Step-by-step explanation:
To find the L.C.M, w first factorize each of the expressions.
x²-10x+24
Two numbers that when added give -10 but when multiplied give 24
will be, -4 and -6
Thus the expression becomes:
x²-4x-6x+24
x(x-4)-6(x-4)
=(x-4)(x-6)
Let us factorize the second expression.
x²-x-12
Two numbers when added give -1 and when multiplied give -12
are 3 and -4
Thus the expression becomes: x²-4x+3x-12
x(x-4)+3(x-4)
(x-4)(x+3)
Therefore the LCM between (x-4)(x-6) and (x-4)(x+3)
will be
(x-4)(x-6)(x+3)
We can multiply the expression as follows.
(x-4)(x-6)
x²-6x-4x+24 = x²-10x+24
(x+3)(x²-10x+24)
=x³-10x²+24x+3x²-30x+72
=x³-7x²+-6x+72
3. Which layer of the skin contains hair follicles?
Answer:
The second layer of skin is the dermis, located under the epidermis. It contains connective tissue, nerve endings, and hair follicles.
The dermis layer of the skin contains hair follicles.
Explanation:The layer of the skin that contains hair follicles is the dermis.
The dermis is the layer of skin directly under the epidermis, and it is made of tough connective tissue. It contains hair follicles, sweat glands, oil glands, and blood vessels.
For example, when you pluck a hair from your skin, you are pulling it out from the dermis.
f(x) = 2x – 1 g(x) = 7x – 12 What is h(x) = f(x) + g(x)?
A. h(x) = 9x – 13
B. h(x) = 9x – 12
C. h(x) = –5x + 11
D. h(x) = 5x – 13
The answer is:
A.
[tex]h(x)=9x-13[/tex]
Why?To solve the problem, we need to perform the shown operation.
We have the functions:
[tex]f(x)=2x-1\\g(x)=7x-12[/tex]
So, performing the following operation, we have:
[tex]f(x)+g(x)=h(x)[/tex]
[tex]h(x)=f(x)+g(x)=(2x-1)+(7x-12)=7x+2x-1-12=9x-13[/tex]
[tex]h(x)=9x-13[/tex]
Hence, we have that the correct option is:
A. [tex]h(x)=9x-13[/tex]
Have a nice day!
Answer: A
Step-by-step explanation:
Two angles are said to be congruent if
Answer:
Two line segments are congruent if they have the same length. Two angles are congruent if they have the same measure.
Two angles are said to be congruent if they are equal. For example, if two triangles each have an angle of 42 degrees, then those angles are congruent.
Calculate the median and mode for the following data set: Data Set = 2, 9, 10, 4, 8, 4, 12
Answer:
The mode is 4 and the median is 8
Step-by-step explanation:
The mode is the number the occurs the most in the set, and as you can see 4 appears twice. The median is the number that lies in the middle of the set when put together from least to greatest. When you write it out it results in 2,4,4,8,9,10,12. As you can see the number 8 lies right in the middle, with three numbers on it's left and three numbers on it's right. Hope this helps :)
Final answer:
median: 8
mode: 4
Explanation:
Calculate the median and mode for a data set, including step-by-step instructions.
Median: To find the median, arrange the data set in numerical order first. As the data set has seven values, the median will be the fourth value, which is 8. Median represents the middle most value of the data
Mode: The mode is the value that appears most frequently in the data set. In this case, the mode is 4 as it occurs twice. Mode represents the maximum frequency.
A customer needs to seed an area 75 feet by 50 feet in size. Each bag of seed can cover 25 square feet of land. How many bags of seed do you need to cover the lot
Answer:
150 bags
Step-by-step explanation:
Given the total area:
The area will be:
=75*50
= 3750 square feet
As it is given that one bag covers 25 square feet. To find the total number of bags we have to find how many 25s will be in 3750 square feet.
So,
Total number of bags = 3750 / 25
= 150 bags
Hence, total number of bags that will be used are 150 ..
the length of a lap is 15 meters. if lisa wants to swim 450 meters this week,how many laps must she swim
Lisa must swim 30 laps to cover the distance of 450 meters, by dividing the total distance she wants to swim by the length of one lap.
To calculate how many laps Lisa must swim to cover a distance of 450 meters, we divide the total distance she wants to swim by the length of one lap. Since the length of one lap is 15 meters, we perform the following calculation:
Divide the total distance (450 meters) by the length of one lap (15 meters).450 meters / 15 meters per lap = 30 laps.Therefore, Lisa needs to swim 30 laps to reach her goal of swimming 450 meters this week.
At a certain distance from a pole, the angle of elevation to the top of the pole is 28° . If the pole is 6.3 ft tall, what is the distance from the pole?
Answer:
11.84 feet
Step-by-step explanation:
The given scenario will form a right angled triangle where the distance and the point from where the angle of elevation is measured will be the base of the triangle.
We know
Angle of elevation = x = 28 °
Height of pole = p = 6.3 feet
Distance from pole = d= ?
So,
[tex]tan\ x = \frac{p}{b}\\ tan\ 28 = \frac{6.3}{b} \\0.5317 = \frac{6.3}{b}\\b = \frac{6.3}{0.5317}\\b=11.84\ feet[/tex]
Therefore, the distance from the pole is 11.84 feet ..
What is the length of the unknown leg in the right triangle?
Answer:
a = 20 cm
Step-by-step explanation:
Since the triangle is right use Pythagoras' identity to solve for a
The square on the hypotenuse is equal to the sum of the squares on the other two sides, that is
a² + 21² = 29²
a² + 441 = 841 ( subtract 441 from both sides )
a² = 400 ( take the square root of both sides )
a = [tex]\sqrt{400}[/tex] = 20
At 6:00 A.M., the temperature was -9°F.
At noon, the temperature was 10°F. Use
the number line to model the change in
temperature from 6:00 A.M. to noon. what was the temperature change
Answer: The temperature change is 19 degrees Fahrenheit.
Step-by-step explanation: Put a circle at -9 and 10. You can count the numbers in between them to get 19. Or you can add the two numbers. 9 + 10 = 19.
Jessa bought her home for $125,000 in 2010 Property values have increased 15% every year since she has owned the home. Which of the following equations can be used to represent the price of the home x years after 2010?
y = 125,000(1 15)
y = 125 000(125)
y = 125,000(085)
y = 125.000(075)
Answer:
y= 125,000 (1.15x)
Step-by-step explanation:
Answer:
A. [tex]y=125,000\cdot (1.15)^x[/tex]
Step-by-step explanation:
We have been given that Jessa bought her home for $125,000 in 2010 Property values have increased 15% every year since she has owned the home.
We can see that increase in value of house is not constant, so the value of house in increasing exponentially.
We know that an exponential function is in form [tex]y=a\cdot b^x[/tex], where,
a = Initial value,
b = For growth b is in form [tex](1+r)[/tex], where r represents growth rate in decimal form.
[tex]r=\frac{15}{100}=0.15[/tex]
[tex]y=125,000\cdot (1+0.15)^x[/tex]
[tex]y=125,000\cdot (1.15)^x[/tex]
Therefore, the equation [tex]y=125,000\cdot (1.15)^x[/tex] represents the price of the home x years after 2010.
If f(x)=3x - 15', thenNf^(-1)(x)=
Enter the correct answer.
Answer:
[tex]\large\boxed{f^{-1}(x)=\dfrac{1}{3}x+5}[/tex]
Step-by-step explanation:
[tex]f(x)=3x-15\to y=3x-15\\\\\text{exchange x to y and vice versa:}\ x=3y-15\\\\\text{solve for}\ y:\\\\3y-15=x\qquad\text{add 15 to both sides}\\\\3y=x+15\qquad\text{divide both sides by 3}\\\\y=\dfrac{x}{3}+5\\\\y=\dfrac{1}{3}x+5[/tex]
HURRY!!!!!
A carpenter cuts the corners of a rectangle to make the
trapezoid shown.
What is the value of x?
5.375
5.5
011
(7x + 4)
13
Answer:
[tex]x = 11[/tex]
Step-by-step explanation:
The bases of a trapezoid are parallel
The angles,
[tex](9x) \degree[/tex]
and
[tex](7x + 4) \degree[/tex]
are same side interior angles. These two angles are supplementary.
[tex](7x + 4) + 9x = 180 \degree[/tex]
[tex]7x + 9x = 180 - 4[/tex]
[tex]16x = 176[/tex]
Divide both sides by 16.
[tex]x = \frac{176}{16} [/tex]
[tex]x = 11[/tex]
Answer:
[tex]x=11[/tex]
Step-by-step explanation:
We have been given that a carpenter cuts the corners of a rectangle to make the trapezoid. We are asked to find the value of x.
Since trapezoid is made of rectangle, so both bases will be parallel to each other.
We know that two consecutive interior angle of parallel lines are supplementary. We can set an equation to solve for x as:
[tex]9x+7x+4=180[/tex]
[tex]16x+4=180[/tex]
[tex]16x+4-4=180-4[/tex]
[tex]16x=176[/tex]
[tex]\frac{16x}{16}=\frac{176}{16}[/tex]
[tex]x=11[/tex]
Therefore, the value of x is 11.
Triangle ABC is to be dilated through point P with a scale factor of 3. How many units away from point A along ray PA will A’ be located?
Answer:
Point A' will be located 10 units away from point A along ray PA
Step-by-step explanation:
we have
The scale factor is 3
step 1
Find out the distance PA'
we know that
The distance PA' is equal to multiply the distance PA by the scale factor
so
[tex]PA'=PA*3[/tex]
we have
[tex]PA=5\ units[/tex]
substitute the given values
[tex]PA'=(5)*3=15\ units[/tex]
step 2
Find out how many units away from point A along ray PA will A’ be located
we know that
[tex]PA'=PA+AA'[/tex]
we have
[tex]PA=5\ units[/tex]
[tex]PA'=15\ units[/tex]
substitute the given values and solve for AA'
[tex]15=5+AA'[/tex]
[tex]AA'=15-5=10\ units[/tex]
therefore
Point A' will be located 10 units away from point A along ray PA
Answer:
10 units
Step-by-step explanation:
Two points on a line are given by the ordered pairs (-3, 2) and (-3, -5). What type of line is this?
horizontal
vertical
slanted
none of these
[tex]\huge{\boxed{\text{vertical}}}[/tex]
Explanation:[tex]\text{A vertical line is a line where all of the x values are the same.}[/tex]
[tex]\text{In this case, both of the points have an x value of -3, so this is a vertical line.}[/tex]
Zahra compares two wireless data plans Which equation gives the correct value of n
the number of GB for which Plans A and B cost the same
(G8 means 'gigabytes of data)
Wireless Plan A
No initiate fee and 8$ for each GB
Wireless Plan B
$20 for the
first 2 GB
$6 for each
additional GB
after the first 2
A) 8n = 20 + 60
B) 8n= 20(2n) + 6
C) 8n = 20 + 6(n-2)
D) 8n = 20 + 2n+6
Answer:
8n=20+6(n-2)
Step-by-step explanation:
n is the number of GB
Plan A has no initial fee and charges 8$ per each GB
So A has an equation that is y=0+8n or just y=8n.
Plan B has 20 for the first 2 GB and $6 for each addition GB after the first 2.
So B has an equation that is y=0+20+6(n-2) assuming n is 2 are greater.
So the two equations are y=8n and y=20+6(n-2).
We want Plan A to be the same as Plan B.
So we need to solve:
8n=20+6(n-2).
Let's check our equation:
Distribute:
8n=20+6n-12
Subtract 6n on both sides:
2n=20-12
2n=8
Divide both sides by 2:
n=4
Plan A charges 8 dollars ber GB, so plan A charges 4(8)=32 dollars.
Plan B charges 20 dollars for the first 2GB and 6 dollars for each GB after so we used 4 which means we are spending 20+6(2)=20+12=32 dollars.
They are the amount so n=4 is right.
I am very late to answer this, but I want to help others who struggle on this question! The answer and explanation is in the picture, thank me later! :)
I am confusion pls help me i am sad help
Answer:
A should be the answer
Step-by-step explanation:
ok so first find area of a circle the area of this circle
pi r sqared
the area of the circle is 3.14
since the raduis is diamter ÷ 2
the area of the small rectangle would be 2a sqared
so if i did it right the answer should be A
I could be wrong tho
hope this helped
The mean ages with standard deviations of four swim teams at a swim club are given below.
Team
Mean
Standard Deviation
Stars
16
4.1
Dolphins
18
1.5
Giants
14
0.3
Mackerels
15
2.3
Which statement is most likely to be true?
The ages of the Mackerels are the most dispersed from the team’s mean.
The ages of the Stars are the most dispersed from the team’s mean.
The ages of the Dolphins are the most dispersed from the team’s mean.
The ages of the Giants are the most dispersed from the team’s mean.
Answer:
Statement 2 (The ages of the Stars are the most dispersed from the team’s mean).
Step-by-step explanation:
Standard deviation is one way to measure the average of the data by determining the spread of the data. It actually explains how much the observation points are further away from the mean of the data. Higher the standard deviation, higher the spread of the data and higher is the uncertainty. This means that the team with the highest standard deviation will have the most dispersion. In this case, the standard deviation of 4.1 is the largest number, therefore, the statement "The ages of the Stars are the most dispersed from the team’s mean." is true i.e. the option 2!!!
Answer:
B.The ages of the Stars are the most dispersed from the team’s mean
Step-by-step explanation:
Which of these is least likely to be the average salary of another of the groups?
Answer:
$104,000
The probability that the average salary between two groups is the same, is actually low. It could be close, but it's quite difficult to get the same exact amount.
I am equation of the line that passes through the point (2,3) with slope 3 please answer
[tex]\huge{\boxed{y-3=m(x-2)}}[/tex]
Point-slope form is [tex]y-y_1=m(x-x_1)[/tex], where [tex]m[/tex] is the slope and [tex](x_1, y_1)[/tex] is a point on the line.
Substitute the values. [tex]\boxed{y-3=m(x-2)}[/tex]
Note: This is in point-slope form. Let me know if you need a different form. Also, if you have any more problems similar to this, I encourage you to try them on your own, and ask on here if you are having trouble.
Answer:
y-3 = 3(x-2) point slope form
y = 3x-3 slope intercept form
Step-by-step explanation:
We can use the point slope form of the equation for a line
y-y1 = m(x-x1)
where m is the slope and (x1,y1) is the point
y-3 = 3(x-2) point slope form
If we want the line in slope intercept form
Distribute
y-3 = 3x-6
Add 3 to each side
y-3+3 = 3x-6+3
y = 3x-3 slope intercept form
Let theta be an angle in quadrant II such that cos theta = -2/3
Find the exact values of csc theta and tan theta.
Answer:
So we have [tex]\csc(\theta)=\frac{3 \sqrt{5}}{5} \text{ and } \tan(\theta)=\frac{-\sqrt{5}}{2}[/tex].
Step-by-step explanation:
Ok so we are in quadrant 2, that means sine is positive while cosine is negative.
We are given [tex]\cos(\theta)=\frac{-2}{3}(\frac{\text{adjacent}}{\text{hypotenuse}})[/tex].
So to find the opposite we will just use the Pythagorean Theorem.
[tex]a^2+b^2=c^2[/tex]
[tex](2)^2+b^2=(3)^2[/tex]
[tex]4+b^2=9[/tex]
[tex]b^2=5[/tex]
[tex]b=\sqrt{5}[/tex] This is the opposite side.
Now to find [tex]\csc(\theta)[/tex] and [tex]\tan(\theta)[/tex].
[tex]\csc(\theta)=\frac{\text{hypotenuse}}{\text{opposite}}=\frac{3}{\sqrt{5}}[/tex].
Some teachers do not like the radical on bottom so we will rationalize the denominator by multiplying the numerator and denominator by sqrt(5).
So [tex]\csc(\theta)=\frac{3}{\sqrt{5}} \cdot \frac{\sqrt{5}}{\sqrt{5}}=\frac{3 \sqrt{5}}{5}[/tex].
And now [tex]\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}=\frac{\sqrt{5}}{-2}=\frac{-\sqrt{5}}{2}[/tex].
So we have [tex]\csc(\theta)=\frac{3 \sqrt{5}}{5} \text{ and } \tan(\theta)=\frac{-\sqrt{5}}{2}[/tex].
Answer:
[tex]tan\theta{3}=-\frac{\sqrt5}{2}[/tex]
[tex]cosec\theta=\frac{3}{\sqrt5}[/tex]
Step-by-step explanation:
We are given that [tex]\theta[/tex] be an angle in quadrant II and [tex]cos\theta=-\frac{2}{3}[/tex]
We have to find the exact values of [tex]cosec\theta[/tex] and [tex]tan\theta[/tex].
[tex]sec\theta=\frac{1}{cos\theta}[/tex]
Then substitute the value of cos theta and we get
[tex]sec\theta=\frac{1}{-\frac{2}{3}}[/tex]
[tex]sec\theta=-\frac{3}{2}[/tex]
Now, [tex]1+tan^2\theta=sec^2\theta[/tex]
[tex]tan^2\theta=sec^2\theta-1[/tex]
Substitute the value of sec theta then we get
[tex]tan^2\theta= (-\frac{3}{2})^2-1[/tex]
[tex]tan^2\theta=\frac{9}{4}-1=\frac{9-4}{4}=\frac{5}{4}[/tex]
[tex]tan\theta=\sqrt{\frac{5}{4}}=-\frac{\sqrt5}{2}[/tex]
Because[tex] tan\theta [/tex] in quadrant II is negative.
[tex]sin^2\theta=1-cos^2\theta[/tex]
[tex]sin^2\theta=1-(\farc{-2}{3})^2[/tex]
[tex]sin^2\theta=1-\frac{4}{9}[/tex]
[tex]sin^2\theta=\frac{9-4}{9}=\frac{5}{9}[/tex]
[tex]sin\theta=\sqrt{\frac{5}{9}}[/tex]
[tex]sin\theta=\frac{\sqrt5}{3}[/tex]
Because in quadrant II [tex]sin\theta[/tex] is positive.
[tex]cosec\theta=\frac{1}{sin\theta}=\frac{1}{\frac{\sqrt5}{3}}[/tex]
[tex]cosec\theta=\frac{3}{\sqrt5}[/tex]
[tex]cosec\theta[/tex] is positive in II quadrant.