Evaluate cosθ if sinθ = [tex]\frac{ \sqrt{5} }{3} [/tex]

Answers

Answer 1
We are told that sin theta = sqrt(5) / 3.  Thus, the opp side of this angle is sqrt(5), and the hypo is 3.  Use the Pythagorean Theorem to find the adj side:

[sqrt(5)]^2 + adj^2 = 3^2, or 5 + adj^2 = 3^2.  Thus, 5 + adj^2 = 9.  Solving for adj, we get adj = plus or minus 2.

The angle theta could be in either QI or QIII, because the sine is positive.  

If the angle theta is in QI, the cosine of theta is -2/3; if in QIII, 2/3.

Related Questions

How do you solve step by step (-10)+14+25+(-16)

Answers

(-10) + 14 + 25 + (-16)   Add 14 and 25
    (-10) + 39 + (-16)      Change 39 + (-10) to 39 - 10
      (-10) + 39 - 16        Subtract 16 from 39
          (-10) + 23          Change (-10) + 23 to 23 - 10
            23 - 10            Subtract 10 from 23
                13 

*Remember, you can rearrange expressions like this as long as each number keeps its sign. Notice that (-10) had its negative sign the whole time, even though we moved it around.

Multiply or find the special product. (Simplify your answer completely.)
[(x − 8y) + z][(x − 8y) − z]

Answers

You can use formula (a-b)(a+b) = a² - b²

[(x − 8y) + z][(x − 8y) − z]
= (x - 8y)² - z²
= x² - 16xy + 64y² - z²  ←  answer

Simplify . 4y4 4y8 8y4 8y8

Answers

Answer:

B

Step-by-step explanation:

Just did it.

Answer:

b

Step-by-step explanation:

Which of the following fractions is closest to the decimal 0.35

Answers

These are the options that I found for this question.

1/3

3/5

3/8

5/1/2

You just have to make the division and compare the results>

1 / 3 = 0.333..

3 / 5 = 0.6

3 / 8 = 0.375

5 / 12 = 0.416.....

So which is closest to 0.35? The answer is 1/3

A number and it's absolute value are equal. If you subtract 2 from the number, the new number and it's absolute value are not equal. What do you know about the number? What is a possible number that satisfies these conditions?

Answers

This means that the number is positive. 

The absolute value is the distance away from 0 the number is.

So 1's absolute value would be 1, yet -5's absolute value would be 5.

So the number that's equal to its absolute value is positive, and the one that's not is negative.

So if you subtract 2 from the positive number, it must turn negative.

So 1 is a number that satisfies these conditions.

what number must you add to complete the square x^2+24x=17




Answers

We have
x² + 24x = 17                          (1)

Note that
(x + 12)² = x² + 24x + 144
By adding 144 to the left side of equation (1), it becomes a perfect square.

Therefore
x² + 24x = (x+12)² - 144         (2)

Substitute (2) into (1).
(x + 12)² - 144 = 17 
(x + 12)² = 17 +144
(x + 12)² = 161

Answer:
We added 144 to the left side of equation (1) in order to make it a perfect square.

evaluate the expression
(4+49) - 4X10

Answers

4 +49 = 53 -40=24



hope this works

In a recent survey, two-thirds of the 234 students in a freshman class said they watch television shows on their computer. Determine the correct arithmetic set up for determining how many students watch television on their computer

Answers

We know that 2/3 of all students watch TV shows on their computers.
And 234 students were in that survey.
2 / 3 * 234 = 156
Answer: 156 students watch shows on their computer.
Essentially, arithmetic set here means "number", so what we will be interested in is the answer to this question can be found here:

'two-thirds of the 234'.

that's all we need to know here. So let's count:
[tex] \frac{2}{3} *234=2*78=156[/tex]

so the answer is simply 156!

if x equals 3= xequals 4 then use the equation 2x y -6 x equals 18 Z to find the value of y

Answers

Greetings!

"If x equals 3 and z equals 4, find the value of y in the equation: [tex]12xy-6x=18z.[/tex]"

Input the value of the variables we were given:
[tex]12(3)y-6(3)=18(4)[/tex]
Simplify.
[tex]36y-18=72[/tex]
Add 18 to both sides.
[tex](36y-18)+18=(72)+18[/tex]
Simplify.
[tex]36y=90[/tex]
Divide both sides by 36.
[tex](36y)/36=(90)/36[/tex]
Simplify.
[tex]y=5/2[/tex]
[tex]y=2.5[/tex]

The variable, y is equal to 2.5.

Hope this helps.
-Benjamin

What is the absolute difference between 1/2 and 1/3?

Answers

1/2 - 1/3 = 3/6-2/6 = 1/6

 absolute value is 1/6

Tyler used 17.04 gallons of gas.Maria used 6.2 times as many gallon of gas as Tyler. How many gallons of gas did Maria use?

Answers

Tyler (T)= 17.04 gallons
Maria=6.2(T), Maria= 6.2x17.04=105.65 gallons

If i buy a box of candy for $30 and make $52 selling the candy what is my profit

Answers

it is $82 for your profit

Jenny charges for delivering the cakes.

 

Bob lives 12 miles away.


How much will Jenny charge to deliver the cakes? delivery charges £4 mixed cost + 60p per mile

Answers

Final answer:

To deliver the cakes to Bob, Jenny will charge £11.20.

Explanation:

To calculate the delivery charges, we need to find the distance between Jenny's location and Bob's location. Since Bob lives 12 miles away, the delivery distance will be 12 miles. Jenny charges £4 as a mixed cost plus 60p per mile. So, the delivery charge will be £4 + (12 miles * 60p) = £4 + £7.20 = £11.20.

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0.4 ( 8 - 0.2w ) = -4

Answers

Hello there! 
 
[tex]Subtract[/tex] by the [tex]number [/tex] [tex]3.2 [/tex] to your [tex]sides [/tex]

Like → [tex]-0.08w + 3.2 - 3.2 \\ \\ = 4 - 3.2[/tex]

We get this→ [tex]-0.08w = -7.2 [/tex]

Since the [tex]-0.08 [/tex]  goes into both of the number we would have to [tex]divide [/tex] by the decimal [tex]-0.08 [/tex] onto your [tex]sides [/tex]

Like → [tex] \frac{-0.08w}{-0.08} = \frac{-7.2}{-0.08} [/tex]

Now the we got those [tex]few [/tex] [tex]steps [/tex] out of the way we can solve our answer! 

[tex] \frac{-0.08w}{-0.08} \\ (CancelOut) \\ \\ \\ \\ \frac{-7.2}{-0.08} \\ (Keep)[/tex]

[tex] \frac{-7.2}{-0.08} = 90 \\ \\ \\ Answer: w = 90 [/tex]

Good luck on your assignment and enjoy your day! 

                       ~[tex]MeIsKaitlyn:)[/tex]

In how many different ways can the curator of a museum arrange five of eight paintings horizontally on the wall?

Answers

8C5=8!/(3!5!)=56
There are 56 ways a curator can arrange the paintings.

The requried number of ways that 5 paintings to be chosen is 56 ways.

What are permutation and combination?

In arithmetic, combination and permutation are two different ways of grouping elements of a set into subsets. In combination, the components of the subset can be recorded in any order. In a permutation, the components of the subset are listed in a distinctive order.

Here,
Total number of paintings = 8
Total number of paintings to be arranged = 5
Number of ways = 8C5
                         = 8!/[8-5]!5!     [nCr = n!/[n-r]!r!]

                         = 56 ways

Thus, the requried number of ways that 5 paintings to be chosen is 56 ways.

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At a local school supply store, a highlighter costs $1.25, a ballpoint pen costs $0.80, and a spiral notebook costs $2.75. Explain how you can use the Commutative Property of Addition to find the total cost if three of each item are purchased!

Answers

Since the communative property shows you can add or multipy in any order, this means you can add all three of these in a different order and still get the same answer.....For example, you can do $1.25 + $0.80 + $2.75 or you can switch it around and do it in another way

The addition of all costs using commutative property will be $4.8.

What is the arithmetic operator?

Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,

Summation = addition of two or more numbers or variable

For example = 2 + 8 + 9

Subtraction = Minus of any two or more numbers with each other called subtraction.

For example = 4 - 8

Division = divide any two numbers or variable called division.

For example 4/8

Multiplication = to multiply any two or more numbers or variables called multiplication.

For example 5 × 7.

Given,

Cost of one highlighter = $1.25

Cost of one ballpoint pen = $0.80

Cost of one spiral notebook = $2.75

The cumulative property states that the resultant of summation or multiplication does change by changing order.

Addition = 1.25 + 0.80 + 2.75

Total cost = $4.8.

Hence"The addition of all costs using commutative property will be $4.8".

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Find the average.

11,16,15,22

A.64
B.15
C.17
D.16

Answers

Your answer is D)16. To find the average, add up all the numbers and divivde by the number of numbers there is
To find the average, add all of the numbers and then divide by how many numbers there were. 
So:
11 + 16 + 15 + 22 = 64
64 / 4 = 16

Your answer is D. 16. Hope this helps!

Hans needs to memorize words on a vocabulary list for Latin class. He has memorized 20 of the words which is 1/4 of the list. How many words are in the list?

Answers

If hans memorized 20 of the words which is 1/4 of the list that means you need to multiply by 4 to get the total number of words which would be 80.
Answer:  There are "80words in the list
______________________________________
Explanation:
______________________________________
(1/4) x = 20 ;  solve for "x" ;

Multiply each side of the equation by "4" ; to isolate "x" on ONE SIDE of the equation; and to solve for "x"; 

  =====>  4 * { (1/4) x } = 20 *4 ; 

                   ===>  x = 80 .
______________________________
There are "80" words in the list
______________________________

Solve the given initial-value problem. give the largest interval i over which the solution is defined. x dy dx + y = 6x + 1, y(1) = 8

Answers

[tex]x\dfrac{\mathrm dy}{\mathrm dx}+y=6x+1[/tex]
[tex]\dfrac{\mathrm d}{\mathrm dx}(xy)=6x+1[/tex]
[tex]xy=\displaystyle\int(6x+1)\,\mathrm dx[/tex]
[tex]xy=3x^2+x+C[/tex]

Given that [tex]y(1)=8[/tex], we have

[tex]8=3+1+C\implies C=4[/tex]

so that the particular solution is

[tex]xy=3x^2+x+4[/tex]
[tex]y=3x+1+\dfrac4x[/tex]

which is valid as long as [tex]x\neq0[/tex], which in turn suggests the largest interval over which the solution may be valid is [tex](0,\infty)[/tex].

A rational number can be written as the ratio of one blank to another and be represented by a repeating or blank decimal. What are the two vocabulary for this sentence?

Answers

The answer is a rational number is one integer divided by another, and can be represented in either decimal of fraction form. The explanation behind this is visualize you are using long division to divide one number by one more.  You divide, and then you acquire a remainder. Then you carry down a zero (multiply by ten) and divide again.  Well, there are only so many balances you could perhaps have.  For example, for 5, your choices are 0, 1, 2, 3, and 4.  Sooner or later, you will replicate a remainder, at which fact you will just keep dividing the same method you did last time you saw that remainder -- and that's the reason why it repeats.

You started on a bike trip, riding at a rate of 9 miles per hour. Your friend left one hour later and rode at the rate of 12 miles per hour. How long did it take your friend to catch up with you?

Answers

They need 3 hours to catch.

What is Unitary method?

It is a method where we find the value of a single unit from the value of multiple units and the value of multiple units from the value of a single unit.

Steps to Use Unitary Method

First, let us make a note of the information we have. There are 5 ice-creams. 5 ice-creams cost $125.

Step 1: Let’s find the cost of 1 ice cream. In order to do that, divide the total cost of ice-creams by the total number of ice-creams. The cost of 1 ice-cream = Total cost of ice-creams/Total number of ice-creams = 125/5 = 25. Therefore, the cost of 1 ice cream is $25.

Step 2: To find the cost of 3 ice-creams, multiply the cost of 1 ice cream by the number of ice-creams. The cost of 3 ice-creams is cost of 1 ice-cream × number of ice-creams = 25 × 3 = $75. Finally, we have the cost of 3 ice-creams i.e. $75.

Given:

riding at a rate of 9 miles per hour

the friend left at rate of 12 miles per hour

Difference between

=12-9

=3 mph

So, the time they need to take

=9/3

= 3 hours

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From a rectangular piece of cardboard having dimensions a × b, where a = 20 inches and b = 70 inches, an open box is to be made by cutting out an identical square of area x2 from each corner and turning up the sides (see the figure). Express the volume V of the box as a function of x.

Answers

check the picture below.

The volume of the box as a function of x will be 1400x - 180x² - 4x³.

First and foremost, you should note that the volume of a rectangular prism is given as:

= Length × Width × Height

where,

Length = 70 - 2x

Width = 20 - 2x

Height = x

Volume = Length × Width × Height

Volume = (x)(20 - 2x)(70 - 2x)

Volume = 1400x - 40x² - 140x² + 4x³

Volume = 1400x - 180x² - 4x³

Therefore, the volume of the box as a function of x will be 1400x - 180x² - 4x³.

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Enfaite je ne comprend pas cet exercice qui peut m'aider c'est deja la rentré et je galère merci de bien vouloir m'aider

Answers

La surface de la pizza est de 110x88 = 9 680 cm²
9 680  en facteurs premier donne 9680 = 2⁴ x 5 x 11² ou 4² x 5 x 11²

Donc on peut diviser l'aire de la pizza ( au minimum) avec des carres de 4 cm de cote et au maximum avec des carres de 11 cm de cote:

Donc 9680÷ 4² = 9680 ÷ 16 = 605 carres de 4 cm chacun

et 9680 ÷ 11² = 9680 ÷ 121 = 80 carres de 11 cm chacun


what he said ^^^^^^^^

Write an even number between 7 and 16. Draw a picture and then write a sentence to explain why it's an odd number

Answers

a even number could be 9 it is odd because it cant be divided by 2, 4, 6, 8, 10, 12, 14, 16,...

Answer:

9, 11, 13 and 15

Step-by-step explanation:

Given numbers,

7 and 16,

In the number line the numbers are arranged in ascending order from left to right,

Thus, the numbers greater than 7 are,

8, 9, 10, 11, 12, 13, 14, 15, 16, 17....

Also, the number less than 16,

.......6, 7, 8, 9, 10, 11, 12, 13, 14, 15,

So, the numbers between 7 and 16,

8, 9, 10, 11, 12, 13, 14, 15

Now, a number with 1, 3, 5 or 7 in the ones place is an odd number.

Hence, the odd number between 7 and 16 are,

9, 11, 13 and 15



Which equation correctly applies the distributive property?

A.​ 50+1.015=(50⋅1)+(50⋅0.01)+(50⋅0.005) ​
B.​−1.2⋅0.57⋅0.5=−1.2⋅0.5⋅0.57​
​C. (0.5⋅0.5)+(0.5⋅0.3)+(0.5⋅0.2)=0.5⋅(0.5+0.3+0.2) ​
D.​ −2.5⋅(4⋅1.045)=(−2.5⋅4)⋅1.045 ​

Answers

C. (0.5⋅0.5)+(0.5⋅0.3)+(0.5⋅0.2)=0.5⋅(0.5+0.3+0.2) ​
​C. (0.5⋅0.5)+(0.5⋅0.3)+(0.5⋅0.2)=0.5⋅(0.5+0.3+0.2) ​ is the correct answer


hope this helps

You can take out a 0.5 from each expression

Suppose a card is drawn from a deck of 52 playing cards. what is the probability of drawing a 4 or an ace?

Answers

The answer is 4 out of 52 because there are 4 suites

of the 30 girls who tried out for the lacrosse team at euclid Middle School, 12 were selected. Of the 40 boys who tried out but, 16 were selected. Are the ratios of the numbers of students on the team to the number of students trying out the same for both boys and girls? How do you know?

Answers

12/30 = 2/5
16/40 = 2/5

yes the ratio is the same, because they both simplify to 2/5

hope this helps

Joe bought 20 ounces of nuts at the store. How much is this in pounds? Write your answer as a whole number or a mixed number in simplest form. Include the correct unit in your answer.

Answers

The answer would be 1/4 pounds((One and one quarter pounds)) I hope this helps :3

If Joe bought 20 ounces of nuts at the store then the nuts in pounds is  1. 25 lb

What is Unit of Measurement?

A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.

Joe bought 20 ounces of nuts at the store.

We have to find in pounds.

As we know that 1 ounce is equal to 0.0625 pounds.

Now we have to convert 20 ounces to pounds.

To do this we have to multiply 20 with 0.0625

20×0.0625

1.25 pounds

20 oz is equal to 1. 25 lb

Hence, the nuts in pounds is  1. 25 lb if Joe bought 20 ounces of nuts at the store.

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Jody, a statistics​ major, grows tomatoes in her spare time. she keeps a record of the weight of each tomato she grows. what percentage of all her tomatoes will be within one standard deviation of the mean​ weight? choose the correct answer below.
a. 50
b. 99.7
c. 95
d. 68
e. 10

Answers

Refer to the figure below.
μ = the mean
σ = the standard deviation

If the weights of the tomatoes are normally distributed, then about 68% of the weights will be within one standard deviation from the mean.
That is,
P(μ-σ ≤ x ≤ μ+σ) = 0.68

Answer: c. 68

F is the midpoint EG Find the length EG given that the length FG IS10.9

Answers

2x10.9=21.8
that's the answer(dont forget your unit)
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