Answer:
[tex]\dfrac{\pi}{6}, \dfrac{5\pi}{6}, \dfrac{3\pi}{2}[/tex]
Step-by-step explanation:
Given the quadratic equation as:
[tex]2sin^2x+sinx=1\\OR\\2sin^2x+sinx-1=0[/tex]
Let us put [tex]sinx=y[/tex] for simplicity of the equation:
Now, the equation becomes:
[tex]2y^2+y-1=0[/tex]
Now, let us try to solve the quadratic equation:
[tex]\Rightarrow 2y^2+2y-y-1=0\\\Rightarrow 2y(y+1)-1(y+1)=0\\\Rightarrow (2y-1)(y+1)=0\\\Rightarrow 2y-1 = 0, y+1 = 0\\\Rightarrow y = \dfrac{1}{2}, y = -1[/tex]
So, the solution to the given trigonometric quadratic equation is:
[tex]sinx = \dfrac{1}{2}[/tex]
and
[tex]sinx=-1[/tex]
Let us try to find the values of [tex]x[/tex] in the interval [tex][0, 2\pi)[/tex].
[tex]sin\theta[/tex] can have a value equal to [tex]\frac{1}{2}[/tex] in 1st and 2nd quadrant.
So, [tex]x[/tex] can be
[tex]30^\circ, 150^\circ\\OR\\\dfrac{\pi}{6}, \dfrac{5\pi}{6}[/tex]
For [tex]sinx=-1[/tex],
[tex]x = 270^\circ\ or\ \dfrac{3 \pi}{2}[/tex]
So, the answer is:
[tex]\dfrac{\pi}{6}, \dfrac{5\pi}{6}, \dfrac{3\pi}{2}[/tex]
Solving by Completing the Square
Answer:
16
Step-by-step explanation:
Hello,
[tex]x^2-8x=10 \text{ *** we complete the square ***}\\ \\(x-4)^2-4^2=10 <=> (x-4)^2-16=10 \text{ *** we add 16 to both sides ***}\\\\(x-4)^2-16\boxed{+16}=(x-4)^2=10\boxed{+16}=26[/tex]
Thanks
I need help with example 4 plz
Answer:
a) [tex]y=1[/tex]
b) [tex]x=-3[/tex]
Step-by-step explanation:
Recall the forms of vertical and horizontal lines
Horizontal lines come in the form of [tex]y=0x+b[/tex], so the slope of the equation is zero. The value of b will be the y-value of the point that you're given.
This means that the equation for a would be y=1
Vertical lines come in the form of [tex]x=a[/tex]. For this line, the value of a would be equivalent to the x-value of the given point. Therefore, b. would be [tex]x=-3[/tex]
math problem At a nba game the ratio of the score of team b was 16.21. of a team a got 80 points. how many points did team b get?
Answer:
105 points.
Step-by-step explanation:
The scores of team A and B is 16 and 21.
if 16 = 80, The ratio of 16 to 21 is 5.
So, that means 16 x 5 is 80.
How many points did team B get?
score x gap between 16 to 21
= 21 x 5 = 105.
the team B got 105 points.
The population of a colony of bacteria can be modeled by the function P(t) = 19,300(5)^t, where t is the elapsed time
in hours. What is the inverse function?
Answer:
C. P–1(t) = log5 (StartFraction t Over 19,300 EndFraction)
Step-by-step explanation:
The inverse function of P(t) is [tex]P^{-1} (t)=log_{5}( \frac{t}{19300})[/tex]
What is an inverse function?The inverse function is a function obtained by reversing the given function. An inverse is a function that serves to “undo” another function. The domain of the original function becomes the range of inverse function and the range of the given function becomes the domain of the inverse function.
For the given situation,
The function P(t) = 19,300(5)^t, where t is the elapsed time in hours.
Steps to find inverse function:
Step 1: Replace P(t) as y
[tex]P(t) = 19,300(5)^t[/tex]
⇒ [tex]y= 19,300(5)^{t}[/tex]
Step 2: interchange t and y
⇒ [tex]t = 19,300(5)^y[/tex]
Step 3: Now solve for y
⇒ [tex]\frac{t}{19300} =5^y[/tex]
By law of logarithm,
[tex]a^{x} = y[/tex]
⇒ [tex]log_{a} y=x[/tex]
Thus the equation becomes,
⇒ [tex]log_{5} \frac{t}{19300}=y[/tex]
Step 4: Now replace y as [tex]P^{-1}( t)[/tex]
⇒ [tex]P^{-1} (t)=log_{5}( \frac{t}{19300})[/tex]
Hence we can conclude that the inverse function of P(t) is [tex]P^{-1} (t)=log_{5}( \frac{t}{19300})[/tex].
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A magic square is a square array of numbers arranged so that the numbers in all rows, all columns, and the two diagonals have the same sum. Create a 3-by-3 magic square using nine of the ten numbers, 20, 21, 22, 23, 24, 25, 26, 27, 28, and 29. Explain your solution and reasoning. List the strategies used.
Answer:
strategies used are : identifying a sub-goal and Guess and check
Step-by-step explanation:
To create a 3 by 3 magic square using nine of the ten numbers
20,21,22,22,23,24,25,26,27,28 and 29
In order to achieve a 3 by 3 magic square table we will pick Nine consecutive numbers out of the ten numbers given and apply the format below
n+1,n-4,n+3,n+2,n,n-2,n-3,n+4,n-1
we will take n = 24
attached below is the magic square
please help with 1-3 thank you!
Answer:
x the probleme
Step-by-step explanation:
Answer:
2 is 3/5 and 3 is (0,-6) and the slop is 4/3
Step-by-step explanation:
x/9 + 7 ≥ 10
A. x ≤ 83
B. x ≥ 27
C. x ≤ 27
D. x ≥ 83
Answer:
its B.x> 27
Step-by-step explanation:
Plot the following points to create a rectangle. Find the missing vertex.(5,3);(-5,3);(-5,-1)
Answer:
(5,1)
Step-by-step explanation:
I took the test
Jackson claims that the order of the best deal to the worst deal (based on cost/oz) is 10 oz bottle, 89 oz bottle, 59 oz bottle, case of 24 10 oz bottles, and 64 oz carton. Which statement about Jackson’s claim is true?
Answer:
Jackson is incorrect.
Step-by-step explanation:
He should compare the values in equal place values to compare all the decimals, not just those of the same length. For example, 0.0561 < 0.05625 < 0.0564.
Answer:
C
Step-by-step explanation:
hanks pickup can travel 68 miles on 4 gallons of gas. How many gallons will hanks pickup need to travel 34 miles?
Answer: This is a ratio of miles (m) per gallon (g), which can be written as the fraction m/g. So Hank's truck can do 68 miles per 4 gallons, or 68/4. The other ration of miles per gallon is 34 miles to (x) amount of gallons. If you set these ratios equal to each other, the resulting equation can help you solve for the number of gallons.
Answer:
2 gallons
Step-by-step explanation:
What is the quotient of 8,688 ÷ 24?
362
434
450
8,664
Answer:
362
Step-by-step explanation:
Answer:
362
Step-by-step explanation:
(4x - 2) + (6x - 2). Please help brainly
Answer:
2 (5 x - 2) = 10 x - 4 or x = 2/5 (if you need to solve for x)
Step-by-step explanation:
Simplify the following:
4 x - 2 + 6 x - 2
Hint: | Group like terms in 4 x - 2 + 6 x - 2.
Grouping like terms, 4 x - 2 + 6 x - 2 = (4 x + 6 x) + (-2 - 2):
(4 x + 6 x) + (-2 - 2)
Hint: | Add like terms in 4 x + 6 x.
4 x + 6 x = 10 x:
10 x + (-2 - 2)
Hint: | Group the negative terms in -2 - 2 together and factor out the minus sign.
-2 - 2 = -(2 + 2):
10 x + -(2 + 2)
Hint: | Evaluate 2 + 2.
2 + 2 = 4:
10 x - 4
Hint: | Factor out the greatest common divisor of the coefficients of 10 x - 4.
Factor 2 out of 10 x - 4:
Answer: 2 (5 x - 2)
________________________________
if you need to solve for x then:
Solve for x:
10 x - 4 = 0
Add 4 to both sides:
10 x + (4 - 4) = 4
4 - 4 = 0:
10 x = 4
Divide both sides of 10 x = 4 by 10:
(10 x)/10 = 4/10
10/10 = 1:
x = 4/10
The gcd of 4 and 10 is 2, so 4/10 = (2×2)/(2×5) = 2/2×2/5 = 2/5:
Answer: x = 2/5
Estimate. Then find the difference 456,912 -37,800
Help, please! College precalc! TIA.
Answer:
I believe that the answer is 0
Step-by-step explanation:
All you have to do is add f and g and substitute -2 for x. When you substitute -2, simplify.
Step-by-step explanation:
(f+g)=(x-4)+(x^2-x)=x^2+x-x-4=x^2-4
when x=-2
(f+g)(-2)=(-2)^2-4=0 ans.
Don ate 4/22 of the pie.what percent of the pie did he eat?
Answer:
9.090909090909%
Step-by-step explanation:
2/22 = 1/11 = 9.090909090909%
Hope This Helps :)
For an apartment complex, the association collects $158,000 from all of its 211 residents. What is the average rent per capita for this apartment complex?
Answer:
$748.42
Step-by-step explanation:
The average rent per capita is used to measure the average rent paid by a group of people in an apartment or an area. The rent per capita estimates the average rent charged for each resident. It is ratio of the total rent paid by the people in the area to the number of residents. Hence:
The average rent per capita = Total rent / number of residents = $158000 / 211 residents = $748.42
If (6, 1) is dilated by a scale factor of 3 the new point would be:
A(3,3)
B (18,3)
C (15,3)
D (9.4)
The sum of two integers is 10. Their difference is 4.
What are the two integers?
answer = 7&3
step by step solution
let's take X and Y two intigers
X+Y=10
X-Y=4
adding both equation
X=7
Y=3
Find the unit rate and use it answer the question
35 copies in 7 minutes, how may copies in 10 minutes
Answer:
50 copies in 10 minutes
Step-by-step explanation:
becuase it takes 7 minutes for 35 copies and 5 copies times 7 is 35 so 5 copies per minute and it would take 10 minutes for 50 copies
The temperature is -14 degrees. Over the next three days, the temperature drops 5 degrees, then 3 degrees, and finally 1 degree. What is the temperature now?
Answer:
-23 degree
Step-by-step explanation:
=>-14-5-3-1
=>-23
Answer:
-23°
Step-by-step explanation:
= -14 - (5+3+1)
= -14 - 9
= -23°
The measure of an angle is 103°. What is the measure of its supplementary angle?
Answer:
77
Step-by-step explanation:
Let's let the unknown number be x.
Supplementary angles add up to a total of 180 degrees. Since we already know one angle is 103, this means that:
[tex]103+x=180[/tex]
Subtract 103 from both sides:
[tex]x=77\textdegree[/tex]
So, the measure of its supplementary angle is 77 degrees.
And we are done!
Answer:77
Step-by-step explanation:
The US courts are reviewing a case to see whether a work has been refused fairly. What is an example of something they might consider when trying to decide whether the use was fair?
Answer:
The Purpose and Character of the usage of the work.
Step-by-step explanation:
In the United States of America, there is a terminology used in court called Fair use. This is a law in the USA that permits a limited use of one or more copyrighted materials without the need to first acquire permission from the holder of the copyright.
Thus, an example of something they might consider when trying to decide whether the use was fair is:
The Purpose and Character of the usage of the work.
This is because the original purpose of the work may have been altered to mean something new or different or it was just copied exactly into another work.
So knowing the purpose and character of usage of the work or material in question would be something they would consider
part 2. Laws of sines. Please show work. Round answer to the nearest tenth.
Answer:
5) 30.0m
6) 34.0mi
7) 11.0ft
8) 17.0 km
(all rounded off to the nearest tenth)
Step-by-step explanation:
Please see attached pictures for the full solution.
10/2i?
(dividing complex numbers)
Note that; i = √-1
Divide using the rule
10/2i = -5i
Best of Luck!
Is 7.787887888… a rational number? PLEASE ANSWER ASAP!! WILL GIVE BRAINLIEST!!!!!
Answer:
yes it is a rational number because the number has a repeating pattern
Step-by-step explanation:
The number 7.787887888... is rational, Yes; it has a pattern that is repeating.
What is an irrational number?It is defined as the numbers in all real numbers which cannot be represented as rational numbers, in other words, the irrational number cannot be expressed in the form of p/q form.
A rational number is a sort of real number that has the form p/q and does not equal zero.
It is given that:
The number is 7.787887888
As we know,
The rational number can be represented in the form of p/q where q cannot be equal to zero.
If the number is terminated after some decimal places then it is said to be a rational number.
If the number is repeating its digit after decimal then it is said to be an irrational number.
Thus, the number 7.787887888... is rational, Yes; it has a pattern that is repeating.
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A bag contains three types of candy (gumdrops, jelly beans, and jawbreakers). If
chosen at random, the probability of getting a gumdrop is, and the probability
of getting a jellybean is 3. What is the probability of getting a jawbreaker?
Answer:
1/2
Step-by-step explanation:
First, I added the two numbers tat we had already.
1/6+1/3=1/6+2/6=3/6=1/2
Then, I subtracted the sum (1/2) from the total (1).
1-1/2=1/2
So, the probability of getting a jawbreaker is 1/2.
On a number line where is the number 14 relative to the number -23
Answer:
14 is to the right of -23
Step-by-step explanation:
On the number line, the number 14 will appear on the right side of -23 with respect to zero from front.
What is a number line?Integers are arranged at equal intervals along horizontal straight lines called number lines. A number line can be used to represent every number in a series.
Number line is a graphical representation of whole numbers, natural numbers, rational and irrational numbers. which represents both negative and positive numbers such that, positive numbers from 1 to infinity lie on the right-hand side of zero and negative numbers from (- 1) to (- infinity) lie on the left-hand side of zero.
Therefore, zero is considered as the reference point.
Number 14 is positive natural number, it appears on the right side of zero and (-23) appears on the left side of zero.
Thus, On a number line, the number 14 lies to the right of number -23.
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5x-11=19. Solve for x. Please explain how you got x
Answer:
x = 6
Step-by-step explanation:
5x - 11 = 19
+11 = +11
5x = 30
5x/5 = 30/5
x = 6
A pyramid has a square base with an area of 169ft. What is the perimeter of the base of the pyramid?
Answer:52 ft.
Step-by-step explanation: If the area of the base of the pyramid is
169
ft
2
then each side of the base is
13
ft
long because the base of the pyramid is a square.
Length of the side,
s
=
√
169
=
13
Iif we take the area of a square
A
=
s
2
where
s
=
13
we get the area of the base to be
169
ft
2
thus proving that each side of the base is
13
ft
long.
So to find the perimeter of the base of the pyramid we use the formula:
P
=
4
s
where
s
=
13
ft
and thus,
p
=
4
⋅
13
ft
=
52
ft
Are lines GH and G'H' perpendicular? Why or why not? Yes, they intersect at one point. Yes, their slopes are negative reciprocals. No, their slopes are not negative reciprocals. No, their slopes are not equal.
Answer:
Step-by-step explanation:
B yes their slopes are negative reciprocals
Answer:
b
Step-by-step explanation:
on edge