Answer:
[tex]\theta =2n\pi, \;\frac{\pi}2+2n\pi \;\;\text{for all}\; n=0,1,2,...[/tex]
Step-by-step explanation:
[tex]\frac 1{\text{cosec} \theta}+\cot \theta-\frac 1{\sin \theta}=\frac 1{\sin \theta}-\frac 1{\text{cosec} \theta}-\cot \theta[/tex]
[tex]\Rightarrow \frac 2{\text{cosec} \theta}+2\cot \theta-\frac 2{\sin \theta}=0[/tex]
[tex]\Rightarrow \frac 1{\text{cosec} \theta}+\cot \theta-\frac 1{\sin \theta}=0[/tex]
[tex]\Rightarrow \sin \theta -\frac 1{\sin \theta}+\frac{\cos \theta}{\sin \theta}=0[/tex]
[tex]\Rightarrow \frac{\sin ^2\theta-1+\cos \theta}{\sin \theta}=0[/tex]
[tex]\Rightarrow \frac{-\cos ^2\theta+\cos \theta}{\sin \theta}=0\Rightarrow\frac{\cos \theta-\cos ^2\theta}{\sin \theta}=0[/tex]
[tex]\Rightarrow \cot \theta(1-\cos \theta)=0[/tex]
[tex]\text{If} \;\;1-\cos \theta=0\Rightarrow \cos \theta=1[/tex]
[tex]\Rightarrow \theta=2n\pi\;\; \text{for all}\; n=0,1,2,.....[/tex]
[tex]\text{If} \cot \theta=0\Rightarrow \frac{\cos \theta}{\sin \theta}=0\Rightarrow \cos \theta=0[/tex]
[tex]\Righarrow \theta =\frac{\pi}2+2n\pi\;\;\text{for all}\; n=0,1,2,...[/tex]
Hence, [tex]\theta =2n\pi, \;\frac{\pi}2+2n\pi \;\;\text{for all}\; n=0,1,2,...[/tex]
Latoya created a factor tree and wrote the prime factorization of 90 shown below. A factor tree of 90. 90 branches to 9 and 10. 9 branches to 3 and 3. 10 branches to 2 and 5. The equation is 90 = 2 times 3 times 5. What is Latoya's error? She should not have found the factors of 9. She should have included an exponent of 2 on the 3. She should have included 9 and 10 in the prime factorization. She should have started the tree with 2 times 45.
Answer:
B) She should have included an exponent of 2 on the 3.
Step-by-step explanation:
Just took the test. Good luck!
A flower garden is 22.50m long. Sheila wants to make a border along one side using bricks that are 0.25m long. Find the number of bricks needed. a) 9 (b) 90 (c) 900 (d) none of these
Answer:
(b) 90
Step-by-step explanation:
Four bricks are needed for each meter of length:
4 × 22.5 = 90
90 bricks are needed.
32. At 8 AM, the temperature was 3°F below zero. By 1pm, the temperature rose
14F and by 10 PM, dropped 12. Plot points and draw arrows on the number
line below to model this situation.
What was the temperature at 10 PM? Explain how the number line helped you
find your answer.
Answer: - 1°F
Step-by-step explanation:
Given that:
At 8a.m:
Temperature = 3°F below 0
By 1p.m ; Temperature rose by 14F ;
By 10pm ; temperature dropped by 12F
Temperature at 10 pm:
3°F below 0 = - 3°F
Temperature at 1pm: temperature increased by 14°F
-3°F + 14°F = 11°F
Temperature at 10pm: temperature dropped by 12°F
11°F - 12 = - 1°F
A spinner with 8 equally sized slices has 2 yellow slices, 3 blue slices, and 3 red slices. The dial is spun and stops on a slice at random. What is the probability that the dial stops on a yellow or blue slice?
The probability that the dial stops on a yellow or blue slice will be 5/8.
What is mean by Probability?The term probability refers to the likelihood of an event occurring.
Given that;
A spinner with 8 equally sized slices.
It has 2 yellow slices, 3 blue slices, and 3 red slices.
Now,
Since, The dial is spun and stops on a slice at random.
Here, Number of yellow and blue slice = 2 + 3
= 5
And, Total number of slices = 8
So, The probability that the dial stops on a yellow or blue slice = 5 / 8
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-28 + 2x = -18 what is x?
Answer: x=5
Step-by-step explanation:
To solve for x, we want to use algebraic properties to isolate x.
-28+2x=-18 [add both sides by 28]
2x=10 [divide both sides by 2]
x=5
Now, we know that x=5.
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \text{x = 5}}}}}[/tex]
Step-by-step explanation:
[tex] \star{ \sf \: - 28 + 2x = - 18 }[/tex]
[tex] \tt{Step \: 1}[/tex] : Move 28 to right hand side and change it's sign
[tex] \hookrightarrow{ \sf{2x = - 18 + 28}}[/tex]
[tex] \tt{Step \:2}[/tex] : Subtract 18 from 28
The negative and positive integers are always subtracted but posses the sign of the bigger integer
[tex] \hookrightarrow{ \sf{2x = 10}}[/tex]
[tex] \tt{Step \: 3}[/tex] Divide both sides by 2
[tex] \hookrightarrow{ \sf{ \frac{2x}{2} = \frac{10}{2}}} [/tex]
[tex] \tt{Step \: 4}[/tex] Calculate
[tex] \hookrightarrow{ \sf{x = 5}}[/tex]
[tex] \tt{∴ \: The \: value \: of \: x \: is \: \bold{5}}[/tex]
[tex] \sf{Hope \: I \: helped !!}[/tex]
[tex] \sf{Best \: regards !!}[/tex]
~[tex] \text{TheAnimeGirl}[/tex]
or each hour he babysits, Anderson earns $1 more than half of Carey’s hourly rate. Anderson earns $6 per hour. Which equation can be used to solve for Carey’s hourly rate, c?
Answer:
6=[tex]\frac{c}{2}[/tex]+1
Step-by-step explanation:
anderson's $6 per hour is one half of carey's hourly rate, plus one.
Answer:
A)
6 = c/2 + 1
Step-by-step explanation:
edg2020
Which Angel number supplementary to angel to AED
Answer:
Angle number 5
Step-by-step explanation:
The sum of supplementary angles equal 180°.
Angle AED, in the diagram given is labelled angle 4.
The angle labelled 4 forms a linear pair with the angle labelled 5.
Since a linear pair of angles = 180°, therefore:
m<AED + m<AEI = 180°.
That is:
m<4 + m<5 = 180°.
Both angles are supplementary.
Therefore, angle number 5 is supplementary to angle AED.
John's teacher bought three 64 ounce bottles of soda for a class party. At the end of the party, 1/6 of the soda remained. How many ounces of soda remained?
Answer: 10
Step-by-step explanation:
64/6=10 therefore it is 10
2. |X-6|+ 1 =- 2x + 4
Answer:
i dont understand the question you are asking
Step-by-step explanation:
Priya starts with $50 in her bank account. She then deposits $20 each week for 12 weeks.
Write an equation that represents the relationship between the dollar amount in her bank
account and the number of weeks of saving.
O 50w + 20 -T
20w - 50 -T
O 50 + 20w -T
O 50w - 20-T
find the domain of f(x)=5x/x-2
Hey there!
ANSWER:Interval Notation: [tex](-[/tex]∞[tex],0)[/tex]∪[tex](0,[/tex]∞)
EXPLANATION:[tex]f(x)=\frac{5x}{x}-2[/tex]
Interval Notation: [tex](-[/tex]∞[tex],0)[/tex]∪[tex](0,[/tex]∞[tex])[/tex]
Hope this helps!
[tex]\text {-TestedHyperr}[/tex]
8/9p=12/18 whats the p value?
Answer:
p = 12/18
Step-by-step explanation:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
8/9*p-(12/18)=0
Simplify.
Simplify more.
Find the Least Common Multiple
The left denominator is : 9
The right denominator is : 3
What is the coefficient in the expression 8x + 10
What's more selfish? Committing Death or forcing someone to stay in a world where they are so unhappy?
Answer:forcing someone to stay in the world they dont wanna be in
Step-by-step explanation:
____________________ A letter that represents one or more numbers. pick from these: Absolute Value Distributive Property Equation Evaluate Equivalent Simplify Expression Integers Like Terms Inequality Reciprocal Coefficient Variable Solution Ratio
Answer:
The answer is a Variable
Step-by-step explanation:
In algebra, symbols (usually letters) are used to represent numbers. To solve math problems, you should know what variables and constants are. Here is an introduction to the terms variables and constants. A variable is a letter or symbol used as a placeholder for an unknown value.
I hope this helps you :)
What does an arrow as an endpoint
imply for a function? How does it
effect your domain and range?
I
Answer:
Step-by-step explanation:
Another way to identify the domain and range of functions is by using graphs. Because the domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the x-axis. The range is the set of possible output values, which are shown on the y-axis
Answer:
It menas that it keeps going.
Step-by-step explanation:
If you have a line with an arrow at the end it means that the numbers keep on going. So say that you had a number line that ended at ten but there is an arrow, this means that there is more or less.
<- ->
10 less than ten 10, more than ten.
53, -82, 103, -7, 22, 0 in ascending order
Answer:
-82, -7, 0, 22, 53, 103
Step-by-step explanation:
smaller to bigger
-7=y/-10
Help me, please
Answer:
70
Step-by-step explanation:
Solve any pre-algebraic equation with inverse operations:
-7 = y/-10
multiply both sides by -10
-7 * -10 = y
now simplify:
remember that multiplying two negatives with result in a positive
70 = y
what is the slope intercept form of the equation 15x-4y=32
Answer: y = 15/4 x - 8
Step-by-step explanation:
Robert had $58.62 in his bank account. He got paid $142.76. He then bought a new jacket for $63.76. He also bought 2 new movies for $6.99 each. He then babysat for his sister and was paid $12. How much money does Robert have now?
In how many ways can 5 people sit around a circular table
Answer:
120 ways
Step-by-step explanation:
In the scenario described, there are 120 ways that 5 people can sit around a round table.
Please i need help thank you
At a carnival, Andrew went on rides and played games.
• Each ride cost $2.
• Each game cost $2.
• Andrew went on 3 rides and played g games.
Andrew wrote the expression below to represent the total
amount of money, in dollars, he spent at the carnival.
6 + 2g
Which of the following is another way Andrew could represent
the total amount of money, in dollars, that he spent at the
carnival?
a. 2 × 3g
b. 2(3 + g)
c. 4 × 3g
d. 4(3 + g)
Answer:
I thinks its b cause you have to multiply them both by 2 and add 3 and g together. hope it helps
The expression can also be 2(3 + g).
What is Expression?A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:
An absolute numerical number is referred to as a constant.
Variable: A symbol without a set value is referred to as a variable.
Term: A term can be made up of a single constant, a single variable, or a mix of variables and constants multiplied or divided.
Coefficient: In an expression, a coefficient is a number that is multiplied by a variable.
Given:
Each ride cost $2.
Each game cost $2.
Andrew went on 3 rides and played g games.
So, the ride costs = $6
and, games costs = $2g
Andrew pay in total = 6 + 2g
= 2 (3 + g)
Hence, the expression can also be 2(3 + g).
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-3x + 7= 28
what does x equal
Answer:
x = -7
Step-by-step explanation:
[tex]-3x+7=8[/tex] subtract 7 on both sides
[tex]-3x=21[/tex] divide -3 into both sides
[tex]x=-7[/tex]
To check
-3(-7) = 21 + 7=28
The product of eight and a number x
Answer:
To write this down as an algebraic expression you would simply need to multiply the two terms together.
So in this case it would be 8 multiples by x which is 8x
Step-by-step explanation:
1) Find out the variables in the Expression
2) Find the operation that is done to the variables
3) Apply the operation to those variables.
The product of 8 and an unknown number x is 8x.
What is multiplication?Multiplication gives us a resultant number that will be very big as compared to the number which is going to be multiplied if and only if the number which is going to be multiplied is more than one.
Given the product of 8 and x
Product is also called multiplication.
Multiplication is an arithmetic operator which is applied in between two numbers or variables.
For example 2 × 4, 4 × 5.
So,
Product of 8 and x must be
8 × x = 8x
Hence "The product of 8 and an unknown number x is 8x".
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Choosing a car that coasts _____ instead of a car that costs _____ means that you’ll have more money available for other purchase. A. $12,000; $11,000 B. $9000; $7000 C. 10,000; $14,000 D. 18,000; $12,000
Answer:
C. : Choosing a car that costs 10,000 instead of a car that costs 14,000 means that you'll have more money available for other purchases
Step-by-step explanation:
5 x (-1/3) do u know
Answer:
~-1.67
Step-by-step explanation:
Multiply. Note that when you multiply a negative and positive number, your answer will be negative:
5 x (-1/3) = (5 * -1)/3
Multiply, then divide:
5 * -1 = -5
-5/3 = ~-1.67 (rounded to the nearest hundredths).
~
Answer:
-5x/3
It just is, trust me.
In the neighborhood 72 families, 18 one or more cats as a fraction then express the fraction as a decimal
Answer:
poopie
Step-by-step explanation:
what is the LCM of 25 and 35
Answer:
175
Step-by-step explanation:
find three consecutive odd integers with a sum of 75
Answer:
23, 25, 27
Step-by-step explanation:
first integer will be X, second will be (X+2), and the third will be (X+4). They will all be summed up and set equal to 75.
[tex](x) + (x + 2) + (x + 4) = 75[/tex]
combine like terms:
[tex]3x + 6 = 75[/tex]
subtract 6:
[tex]3x = 69[/tex]
divide by 3 to find value of X:
[tex] \frac{3x}{3} = \frac{69}{3} [/tex]
[tex]x = 23[/tex]
plug in X in o red der to finger the rest of the integers.
(X+2)= (23+2)=25
(X+4)= (23+4)=27