Question 28
Let be an angle in quadrant such that.
Find the exact values of and.

Question 28Let Be An Angle In Quadrant Such That.Find The Exact Values Of And.

Answers

Answer 1

Answer:

see explanation

Step-by-step explanation:

Since Θ is an angle in the third quadrant, then secΘ < 0 and tanΘ > 0

Using the identity

sec x = [tex]\frac{1}{cosx}[/tex] , then

cos x = - [tex]\sqrt{1-sin^2x}[/tex]

         = - [tex]\sqrt{1-(-3/5)^2}[/tex] = - [tex]\sqrt{1-\frac{9}{25} }[/tex] = - [tex]\sqrt{\frac{16}{25} }[/tex] = - [tex]\frac{4}{5}[/tex], thus

secΘ = [tex]\frac{1}{-\frac{4}{5} }[/tex] = - [tex]\frac{5}{4}[/tex]

---------------------------

Using the identity

tan x = [tex]\frac{sinx}{cosx}[/tex] , then

tanΘ = [tex]\frac{-\frac{3}{5} }{-\frac{4}{5} }[/tex] = - [tex]\frac{3}{5}[/tex] × - [tex]\frac{5}{4}[/tex] = [tex]\frac{3}{4}[/tex]

Answer 2

The value of sec(x) is (5/4) and tan(x) will be (-3)(4).

What is trigonometry?

The branch of mathematics sets up a relationship between the sides and the angles of the right-angle triangle termed trigonometry.

Sine, cosine, tangent, cosecant, secant, and cotangent are some of their names. The adjacent side, opposite side, and hypotenuse side of the right triangle are used to define each of these trigonometric ratios.

The six trigonometric ratios are the source of all fundamental trigonometric identities.

The given value of sin (x) is ( -3 / 5 ). The values of sec(x) and tan(x) will be calculated as below:-

sec(x) = 1 / cos(x)

[tex]cosx = \sqrt{1-sin^2x}[/tex]

[tex]cosx = \sqrt{1-(\dfrac{-3}{5})^2}[/tex]

cos(x) = 4 / 5

sec(x) = 1 / ( 4 / 5 ) = ( 5/ 4)

The value of tan(x) will be calculated as:-

tan(x) = sin(x)/cos(x) = ( -3 / 5 ) / (4 / 5 )

tan(x) = (-3/4)

Therefore, the value of sec(x) is (5/4) and tan(x) will be (-3)(4).

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Related Questions

for the data set 46, 31, 44, 35, 39, 43, 33, 41 what is the mean absolute deviation

Answers

Answer: i believe the answer is 39

Step-by-step explanation:

sum divided by the terms

Please help will mark brainliest!!!
How would you describe the graph of the function at interval 3? Select all that apply.
image below

Answers

Answer:

B and E

Step-by-step explanation:

In the graph, the altitude represents Y axis while time represents the X axis. we can see that at interval 1 the function is dramatically decreasing. At Interval 2 the function is constant. At interval 3 the function is increasing but I can't say definitively if the slope is positive or negative. Hope this helped!

Help with this question please!!

Answers

Answer:

Width = 160

Length = 110

Step-by-step explanation:

Perimeter is the sum of all the sides

They tell you that the length is 50 m shorter than the width

so L = W - 50

W = W

540 = W + W + W-50 + W-50

540 = 2W + 2(W-50)

540 = 2W + 2W - 100

540 = 4W - 100

640 = 4W

W = 160

L = 160 - 50

L = 110

Answer:

Length: 110 m

Width: 160 m

Step-by-step explanation:

The formula for perimeter of a rectangle is P = 2L + 2W.

We can write the length in terms of width if width is w:

Length: w - 50

Width: w

Plug the values into the formula.

540 = 2(w - 50) + 2w

540 = 2w - 100 + 2w

540 = 4w - 100

640 = 4w

w = 160

find length by subtracting 50 from the width

160-50=110

Therefore, the length is 110 and the width is 160.

What is the probability of rolling a number cube and getting a number greater than four?

Answers

The probability would be 8/12

You spin the spinner below once. What is the probability that the arrow will land on 3

Answers

Answer:

how many numbers are there and if there is more of the same number then that will be ur probability

Step-by-step explanation:

What type of sequence is 0,12,24,36,48 geometric or arithmetic?

Answers

Answer:

Arithmetic

Step-by-step explanation:

Since each number is 12 larger than the last, this is an arithmetic sequence. A geometric sequence is one in which each next number in the sequence is the previous one multiplied by a certain set coefficient, while in an arithmetic sequence it's a certain number added. Hope this helps!

Answer:

It is arithmetic because to get from one term to the next, you add 12, and in an arithmetic sequence, you add/subtract a common difference to get from one term to the next. Hope this helps!

the radius of a circle with a circumstance of 28 pie into units

Answers

Answer:

The radius is 14

Step-by-step explanation:

The circumference of the circle is 28 pi

C = 2* pi *r  where r is the radius

28 pi = 2 pi *r

Divide each side by 2 pi

28 pi/2pi = 2 pi *r/2pi

14 = r

Can you please help me

Answers

Answer:

the length of the car in Ivan's drawing is 12 cm, or the second option.

Step-by-step explanation:

Scale drawing length : actual car length = 2 cm:1 cm

Since it's the same car, we know that the length would be 6 cm.

Therefore, we can set up a proportion and solve for x.

2/1=x/6

x=12

Therefore, the length of the car in Ivan's drawing is 12 cm, or the second option.

I hope this helped and have a good rest of your day!

Mark has invested $300 at age 16 into a money market account earning 6%. How many times will Mark's investment double before age 52? What will his investment be worth? What would Mark's investment be if he had invested at age 28?

Answers

Answer:

A.3times

B.$1214.68

Step-by-step Explanation

A

Using compound interest formula

A=P(1+I)^n

A is the amount

P is the principal=$300

I is the interest=0.06

n is the time ( between 52 and 16years)=36years

A=300(1+0.06)^36

A=$2444.175

Which means 300 would have become

$2444.175 which is 8 folds.

That means it would have doubled 3times(2×2×2) at age of 52.

B. The time would change to (52-28)=24

Using compound interest formula

A=300(1+0.06)^24

A=$1214.68

Therefore his investment would have been $1214.68.

Imani sells shirts packed in boxes that are each 15in. x 10in. x 2in. Imani stacked 3 boxes and wrapped them with one piece of paper. How much paper did she use, not including overlap?

Answers

Answer:

She used 600 square inches of paper.

Step-by-step explanation:

Since the box are 15 in x 10 in x 2 in and are stacked on top of each other, they form a bigger rectangular prism with 15 in x 10 in x 6 in. In order to calculate how much paper she used, we need to calculate the surface area of this prism, this is done by using the following formulla:

surface area = 2*width*length + 2*width*height + 2*length*height

surface area = 2*15*10 + 2*15*6 + 2*10*6 = 300 + 180 + 120

surface area = 600 in².

She used 600 square inches of paper.

what is the 15th n term of the sequence 22 18 14 10 6

Answers

Answer:

-34

Step-by-step explanation:

All you have to do is subtract by 4 until you count to 15 which then leads you to the number -34

I'm am like, really serious. WHO THE FREAK IS JOE?

Answers

Answer: My momma of course

Step-by-step explanation:

Mary's dog weighs 185 pounds. Her dog needs to lose between 9 and 15 pounds. Between what two percentages, rounded to the nearest whole numbers, should Mary's dog lose weight with respect to its current weight of 185 pounds. Select your answers from the drop-down lists.

Answers

Answer:

5-8% of the weight

Step-by-step explanation:

The dog needs to lose a weight within the values 9-15 pounds

To answer this question, what we just need to do is to know the percentage of 185 pounds that is 9 and the percentage of 185 pounds that is 15

The percentage decrease can be calculated using the formula;

(difference)/old value * 100%

For the 9 pound loss, we have ;

9/185 * 100% = 4.86 which is approximately 5%

For the 15 pound loss, we have;

15/185 * 100% = 8.11% which is approximately 8%

Thus, the dog is losing between 5-8% of its weight

A manufacturer claims that its cleaning product is best because over half of the cleaning services surveyed used the product. Which BEST decreases the validity of the claim? A.Only 50 cleaning services were surveyed. B.Cleaning services were selected at random. C.A well-known company conducted the survey. D.Only one cleaning product was asked about in the survey.

Answers

Answer:

D. Only one cleaning product was asked about in the survey.

Any given company can use more than one cleaning product or even use a combination of different cleaning products. The question was not specific enough, since it should have probably asked which cleaning products are used and which ones are used more frequently.

Step-by-step explanation:

the other options are wrong because:

A. Only 50 cleaning services were surveyed. ⇒ This actually would increase the validity of the claim because it satisfies the the condition for a valid confidence interval [np and n(1 - p) are larger than 10]-B. Cleaning services were selected at random. ⇒ This actually would increase the validity of the claim. C. A well-known company conducted the survey. ⇒ This actually would increase the validity of the claim.

Leila and Jo are two of the partners in a business. Leila makes $4 in profits for every $5 that Jo makes. If Jo makes $60 profit, how much profit does Leila make?

Answers

Answer:

Leila would make a profit of $48

Step-by-step explanation:

~ Knowing that there is some sort of proportion that can be formed through Leila and Jo's profit, we could form even a proportionality to compute the profit Leila makes given jo's profit of $60 ~

If is is known that Leila: Jo, 4: 5, we could form such a proportion:

4                5       ⇒     where x - Leila's profit knowing Jo's profit of $60

x               60

Now let us solve for x, through cross multiplication:

5x = 60 * 4,

5x = 240,

x = profit of $48

find out three rational numbers lying between 2/3 and 3/4

PLEASE HELP...... I NEED TO SUBMIT IT NOW......

Answers

Answer:

33/48, 34/48, 35/48

Step-by-step explanation:

2/3 is equal to 32/48 and 3/4 is equal to 36/48. The fractions in between them are all rational numbers. Hope this helped <3

2/3 = 2000/3000
3/4 = 2250/3000

Here are 248 rational numbers between them:
2001/3000
2002/3000
2003/3000
2004/3000
2005/3000
2006/3000
2007/3000
2008/3000
2009/3000
2010/3000
2011/3000
2012/3000
2013/3000
2014/3000
2015/3000
2016/3000
2017/3000
2018/3000
2019/3000
2020/3000
2021/3000
2022/3000
2023/3000
2024/3000
2025/3000
2026/3000
2027/3000
2028/3000
2029/3000
2030/3000
2031/3000
2032/3000
2033/3000
2034/3000
2035/3000
2036/3000
2037/3000
2038/3000
2039/3000
2040/3000
2041/3000
2042/3000
2043/3000
2044/3000
2045/3000
2046/3000
2047/3000
2048/3000
2049/3000
2050/3000
2051/3000
2052/3000
2053/3000
2054/3000
2055/3000
2056/3000
2057/3000
2058/3000
2059/3000
2060/3000
2061/3000
2062/3000
2063/3000
2064/3000
2065/3000
2066/3000
2067/3000
2068/3000
2069/3000
2070/3000
2071/3000
2072/3000
2073/3000
2074/3000
2075/3000
2076/3000
2077/3000
2078/3000
2079/3000
2080/3000
2081/3000
2082/3000
2083/3000
2084/3000
2085/3000
2086/3000
2087/3000
2088/3000
2089/3000
2090/3000
2091/3000
2092/3000
2093/3000
2094/3000
2095/3000
2096/3000
2097/3000
2098/3000
2099/3000
2100/3000
2101/3000
2102/3000
2103/3000
2104/3000
2105/3000
2106/3000
2107/3000
2108/3000
2109/3000
2110/3000
2111/3000
2112/3000
2113/3000
2114/3000
2115/3000
2116/3000
2117/3000
2118/3000
2119/3000
2120/3000
2121/3000
2122/3000
2123/3000
2124/3000
2125/3000
2126/3000
2127/3000
2128/3000
2129/3000
2130/3000
2131/3000
2132/3000
2133/3000
2134/3000
2135/3000
2136/3000
2137/3000
2138/3000
2139/3000
2140/3000
2141/3000
2142/3000
2143/3000
2144/3000
2145/3000
2146/3000
2147/3000
2148/3000
2149/3000
2150/3000
2151/3000
2152/3000
2153/3000
2154/3000
2155/3000
2156/3000
2157/3000
2158/3000
2159/3000
2160/3000
2161/3000
2162/3000
2163/3000
2164/3000
2165/3000
2166/3000
2167/3000
2168/3000
2169/3000
2170/3000
2171/3000
2172/3000
2173/3000
2174/3000
2175/3000
2176/3000
2177/3000
2178/3000
2179/3000
2180/3000
2181/3000
2182/3000
2183/3000
2184/3000
2185/3000
2186/3000
2187/3000
2188/3000
2189/3000
2190/3000
2191/3000
2192/3000
2193/3000
2194/3000
2195/3000
2196/3000
2197/3000
2198/3000
2199/3000
2200/3000
2201/3000
2202/3000
2203/3000
2204/3000
2205/3000
2206/3000
2207/3000
2208/3000
2209/3000
2210/3000
2211/3000
2212/3000
2213/3000
2214/3000
2215/3000
2216/3000
2217/3000
2218/3000
2219/3000
2220/3000
2221/3000
2222/3000
2223/3000
2224/3000
2225/3000
2226/3000
2227/3000
2228/3000
2229/3000
2230/3000
2231/3000
2232/3000
2233/3000
2234/3000
2235/3000
2236/3000
2237/3000
2238/3000
2239/3000
2240/3000
2241/3000
2242/3000
2243/3000
2244/3000
2245/3000
2246/3000
2247/3000
2248/3000
2249/3000

what is the answer of 24a-18b ​

Answers

Answer:

6(4a−3b)

Step-by-step explanation:

You have to factor out this expression, so i would recommend the UMBRELLA  method.

Answer:

6(4a-3b)

Step-by-step explanation:

This is the answer because

find what number is divisible by both 24 and 18. The answer there is 6So then you write an equation that would equal 24a-18bTherefore since 24a is part one of the equation you would do what times 6 equals 24a. 6 times 4a=24aSo place four a in the parenthesis. Then find out what times 6 = -18bThe answer to that is -3b because a negative times a positive is always positive. So your final answer is 6(4a-3b)

Michael has three quarters two dimes + 3 nickels in his pocket he randomly draws two coins from his pocket at one time and they are both times he says the probability of that occurring as 1 out of 4 because two of the eight coins are dimes is he correct explain

Answers

Answer:

He is correct

Step-by-step explanation:

Here, we have 3 types of coins which are;

3 quarters

2 dimes

3 nickels

Now, we want to obtain the probability that if two coins are selected, both will be dimes.

Now, this probability is kind of delicate. This is because he is selecting only at a single time, the two coins.

Thus, the probability of the two coins coming out at the same time and they are both dimes will be 2/8 = 1/4

This shows that she is correct.

Kindly note that our answer is 1/4 because she is making the selection at the same time and not once at a time

3. This table shows a linear relationship between the amount of water in a tank and
time.
time (minutes) water (gallons)
0 T| 30 G
5 T| 20 G
10T| 10 G
Which of these statements is true?
OD
A.The water in the tank is increasing at a rate of 2 gallons per minute.

B.The water in the tank is increasing at a rate of 10 gallons per minute.

C.The water in the tank is decreasing at a rate of 2 gallons per minute.

D.The water in the tank is decreasing at a rate of 10 gallons per minute.
OL

Answers

Answer:

c because 10gallons per min is to much

Step-by-step explanation:

The water in the tank is decreasing at a rate of 2 gallons per minute. Therefore, option C is the correct answer.

What is the equation of a line?

The general equation of a straight line is y=mx+c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.

The given table shows a linear relationship between the amount of water in a tank and time.

From the table we have (0, 30), (5, 20) and (10, 10).

Now, slope m=(20-30)/(5-0)

m= -2

Substitute (x, y)=(0, 30) and m=-2 in y=mx+c, we get

30=-10(0)+c

c=30

Now equation is y=-2x+30

Here, the water in the tank is decreasing at a rate of 2 gallons per minute.

Therefore, option C is the correct answer.

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Is it possible to triangulate a quadrilateral and get more or fewer than two triangles? Determine whether this investigation verifies that the sum of the interior angles of a quadrilateral is always 360°.

Answers

Answer:

No.

Step-by-step explanation:

It’s not possible. No matter what type of quadrilateral it is, there will only be two triangles formed, verifying that the sum of the interior angles of a quadrilateral is always 360°.

It’s not possible to triangulate a quadrilateral and get more or fewer than two triangles. It is verifies that the sum of the interior angles of a quadrilateral is always 360°.

What is a quadrilateral?

Any closed figure made by 4 line segments joined end to end in series is called a quadrilateral.

It’s not possible to triangulate a quadrilateral and get more or fewer than two triangles. No matter what type of quadrilateral it is, there will only be two triangles formed.

We know that The sum of internal angle of a quadrilateral is 360°.

The sum of angle in a triangle is 180°. By Adding the two triangle angle together, we will get the sum as 360°.

The Sum of the interior angle of a polygon = 180(n-2) .

It is verifies that the sum of the interior angles of a quadrilateral is always 360°.

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7(5+2x)+x=65 someone please help me with this equation

Answers

Answer:

x=2

Step-by-step explanation:

7(5+2x)+x=65

35+14x+x=65

35+15x=65

15x=65-35

15x=30/15

x=2

Answer:

x=2

Step-by-step explanation:

7×5=35

7×2x=14x+=65

so the equation would be

35+14x+x=65

add the variables together so:

35+15x=65

subtract 35 from 65 which makes it 30 so:

15x=30

now divide both sides by 15

which makes the anwer x=2

s= ut + 1/2 at x2
u=10
a=-2
t=1/2
work out the value of s

Answers

Answer:

s = 4 3/4.

Step-by-step explanation:

The formula is s = ut + 1/2 at^2

so s =  10^1/2 + 1/2 * -2 * (1/2)^2

s = 5 - 1/4

= 4  3/4.

Three fifths of the sum of 13 and 6

Answers

Answer: 11.4

Step-by-step explanation:

change to numbers [tex]\frac{3}{5} (13+6)[/tex]

simplify [tex]\frac{3}{5} (19)\\11.4[/tex]

HELPP MEE FASTT I HAVE LESS THAN 10 MIN

Farrah borrowed $155 from her brother. She has already paid back $15. She plans to pay back $35 each month until the debt is paid off.

Which describes the number of months it will take to pay off the debt? Select three options.
x + 15 + 35 = 155
35 x + 15 = 155
35 x = 155 minus 15
It will take 8 months to pay off the debt.
It will take 4 months to pay off the debt.

Answers

Answer:

35x + 15 = 155

35x = 155 minus 15

it will take 4 months to pay off the debt.

Hope this helps. Mark brainliest please!

Answer:

35x + 15 = 155

35x = 155 - 15

It will take 4 months to pay off debt

Step-by-step explanation:

Its mental so idk but trust me <3


How many fourths are in 2 1/2?

Answers

Answer:

There are 10 fourths.

Step-by-step explanation:

There are four 1/4ths in 1. So 2.5 x 4 = 10.

Answer:

2 1/2 is the same as 5/2 which is the same as 10/4, so 10 is the answer :)

Step-by step solution

The ratio of cars to trucks passing the intersection of Reyes Adobe and TO Blvd is 7:2. If 108 vehicles pass this intersection, how many are cars?

Answers

Answer:

84 cars

Step-by-step explanation:

the the ratio is 7 to 2. There were 108 vehicles. 108/ 9=12

12 x 7= 84.... or at least that's how I think of it.

The center of the circle is (3,2). The circle passes through (7,6). What is the radius ?

Answers

Answer:

Step-by-step explanation:

i’m not sure but add them

Answer:

square root of 32

Step-by-step explanation:

you have to take center and the point it passes and solve them

Simplify. 6x+3−(x+1) =

Answers

Answer:

5x +2

Step-by-step explanation:

6x+3−(x+1) =

Distribute the minus sign

6x +3 -x -1

5x +2

Answer:

[tex]5x + 2[/tex]

Step-by-step explanation:

[tex]6x + 3 - (x + 1) \\ 6x + 3 - x - 1 \\ = 5x + 2[/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

Someone help me pleaseeee

Answers

Answer: x=44°

explanation: because the angles in a triangle add up to 180° and since the latter or whatever goes straight up it is 90° and the other angle is 46° so 180=90+46+x.

Subtract 90 from both sides of the = and it becomes 90=46+x.

Then you subtract 46 on both sides and you get 44=x

Use the Pythagorean Theorem to find the length of the hypotenuse of a
right triangle if the lengths of the legs are 5 and 12 meters.

Answers

Answer:

13

Step-by-step explanation:

x^2=5^2+12^2

x^2=25+144

x^2=169

x=13

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