The equation is an illustration of trigonometry ratios, and the non-negative values of x are 30 and 270 degrees
How to solve the equation?The equation is given as:
2sin²(x) + sin(x) = 1
Let y = sin(x)
So, the equation becomes
2y² + y = 1
Rewrite as:
2y² + y - 1 = 0
Expand
2y² + 2y - y - 1 = 0
Factorize
2y(y + 1) - 1(y + 1) = 0
Expand
(2y - 1)(y + 1) = 0
Split
2y - 1 = 0 or y + 1 = 0
Solve for y
y = 0.5 or y = -1
Recall that: y = sin(x)
So, we have:
sin(x) = 0.5 and sin(x) = -1
Take the arcsin of both sides
x = sin⁻¹(0.5) and x = sin⁻¹(-1)
x = 30 degrees and x = 270
Hence, the non-negative values of x are 30 and 270 degrees
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PLEASE HELP CHOOSING BRAINLIEST
Answer:
C
Step-by-step explanation:
The denominator is the same and the expression can be rewritten as 2n⁴ + 6 - 7 in the numerator, which simplifies to 2n⁴ - 1 over n⁴ + 3.
Algebraically:
[tex]\frac{2n^4+6}{n^4+3} -\frac{7}{n^4+3}[/tex]
[tex]\frac{2n^4+6-7}{n^4+3}[/tex]
[tex]\frac{2n^4-1}{n^4+3}[/tex]
I hope this helps!
A movie theater is open x hours Monday through Thursday and y hours Friday through Sunday. Write an algebraic expression that represents the number of hours per week the theater is open
Answer: 4×+3y
Step-by-step explanation:
1. There are 4 days from Mon to Thurs. Since x hours are opened on each of the 4 days, we get 4x.
2. There are 3 days from Fri to Sun. Since y hours are opened on each of the 3 days, we get 3y.
In a week, it will just be the sum of 1 and 2, which is 4x+3y
The population of the high school increases by 10% each year what would B= in the form of y=a(b)^x
[tex]\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &a\\ r=rate\to 10\%\to \frac{10}{100}\dotfill &0.10\\ t=\textit{elapsed time}\dotfill &x\\ \end{cases} \\\\\\ A=a(1 + 0.10)^{x}\implies A=a(1.1)^x~\hfill \boxed{y=a(1.1)^x}[/tex]
Each grass square measures 1 foot by 1 foot. How much fence is needed to go around the garden?
Answer:
42 feet
Step-by-step explanation:
The length of fence is equal to the perimeter of the shape. That can be found by adding the lengths of the edges.
__
Clockwise from the upper left corner, the sum of edge lengths is ...
2 +6 + 3 + 6 + 2 + 7 + 1 + 1 + 5 + 1 + 1 + 7 . . . . feet
= 8 + 9 + 9 + 2 + 6 + 8 . . . . added pairwise
= 17 + 11 + 14
= 28 + 14 = 42 . . . feet
42 feet of fence is needed to go around the garden
The point P is on the unit circle. If the y-coordinate of P is -3/7
and P is in quadrant IV, then
T=
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Answer: [tex]\bold{x=\frac{2 \sqrt{10}}{7}}[/tex]
Step-by-step explanation:
[tex]\text { Let } p=\left(x,-\frac{3}{7}\right) \text { as given } y \text {-coordinate is }=-\frac{3}{7}[/tex]
[tex]r=1 \ \ \text{(as $p$ is on unit circle)} \\$$\therefore x^{2}+y^{2}=1^{2}[/tex]
[tex]\begin{aligned}&\Rightarrow x^{2}+\left(-\frac{3}{7}\right)^{2}=1 \Rightarrow x^{2}=1-\frac{9}{49}=\frac{40}{49} \\&\Rightarrow x^{2}=\pm \sqrt{\frac{40}{49}} \Rightarrow x=\pm \frac{2 \sqrt{10}}{7}\end{aligned}[/tex]
[tex]$$Since the point is in quadrant $4$ $\therefore \text{the} \ x$-coordinate will be positive$$\therefore x=\frac{2 \sqrt{10}}{7} \text$$[/tex]
pls simplify this will give brainly and a lot of points!!!!! 5:00min
Answer:
More details please ._.
Step-by-step explanation:
[tex] \frac{{b}^{4} }{ {a}^{2} {c}^{2} } [/tex]
explanation:
There's 4 as in the denominator which cancels out the 2 in the numerator. Thus leaving you with 2 as in the denominator. Then there's only 1 b I the denominator which is canceled out by the ones in the numerator, leaving you with only 4 b's in the numerator. Finally there is only 1 c in the numerator which is canceled out by the ones in the denominator. Thus leaving you with 2 c's in the denominator.
Select the reason that best supports Statement 6 in the given proof.
Answer: D. Subtraction property of equality
Step-by-step explanation:
They are subtracting 6 from both sides of the equality.
Find the equation of line a and line b.
HELP PLEASE
Answer:
Blue-y=1/2-1
Red-x=-3
Step-by-step explanation:
Find the exact value of the expression sin(sin225 - 120)
Step-by-step explanation:
I use desmos . com so it's easier.
A) 1.29
B) 0.91
C) 0.97
D) 1.05
Good Luck!
PLEASE HELP!!! I NEED TO KNOW HOW TO SOLVE IT
Name of the shape:
Triangular Prism - a three sided prism "triangular base"
Surface Area of Right Triangular Prism:
⇒ Base x Height + Length(perimeter of the base)
4 x 3 + 11(3 + 5 + 4)12 + 11(12)12 + 132144 cm²There surface area of this shape is 144 cm²
#a
Triangular prism#b
If sides be L,B,H
Then
TSA=BH+L(Perimeter of base)#c
Now
TSA=4(3)+11(3+5+4)TSA=12+11(12)TSA=144cm²Felix has $100 in an account that earns 5% interest compounded annually.
To the nearest cent, how much interest will he earn in 2 years?
Based on the amount that Felix deposited in the account and the 5% compounded annual interest, the interest Felix will earn in 2 years is $10.25
How to find the interest earned?First, find the amount the $100 would have accrued to in 2 years:
= Amount deposited x (1 + rate) ^ number of years
Solving gives:
= 100 x (1 + 5%)²
= $110.25
The interest earned is:
= Amount in 2 years - Amount deposited
= 110.25 - 100
= $10.25
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Answer:10.25
Step-by-step explanation:
The table represents a linear function that shows the number of stamps y that a student collects after x months. Complete the table.
Answer:
24
Step-by-step explanation:
a linear function has the form: y = ax + b
According to the table: b = 5 and a = (43 − 5)/(2 − 0) = 38/2 = 19
Then our function is of the form: y = 19x + 5
Now ,we replace x by 1 in the function to get the missing value :
Missing value = 19(1) + 5 = 19 + 5 = 24.
For tanisha's lemonade recipe, 14 lemons are required to make 7 cups of lemonade. at what rate are lemons being used in lemons per cup of lemonade?
Without using a calculator, order the following expressions from least to greatest.
11/3, square root 20, square root 17
Answer:
[tex]\displaystyle \large{\frac{11}{3} < \sqrt{17} < \sqrt{20}}[/tex]
Step-by-step explanation:
( 1 ) 11/3
[tex]\displaystyle \large{\frac{11}{3}}[/tex] can be converted to mixed fractions to [tex]\displaystyle \large{3\frac{2}{3}}[/tex]
Therefore, 11/3 is at least around 3, almost 4. It could be more than 3.5 by approximation but not exactly 4.
( 2 ) √20
[tex]\displaystyle \large{\sqrt{20}=\sqrt{5\cdot 4}}\\\displaystyle \large{\sqrt{20}=\sqrt{5\cdot 2\cdot 2}}\\\displaystyle \large{\sqrt{20}=2\sqrt{5}}[/tex]
We know that [tex]\displaystyle \large{\sqrt{4}=2}[/tex] so [tex]\displaystyle \large{\sqrt{5} > \sqrt{4}}[/tex] which means approximately, [tex]\displaystyle \large{\sqrt{20}}[/tex] can be either at least 4.3 up to 4.4
( 3 ) √17
We know that [tex]\displaystyle \large{\sqrt{16} = 4}[/tex] so [tex]\displaystyle \large{\sqrt{17}}[/tex] can be at least 4.1 up to 4.2, but it’s obvious that the square root of 17 is less than square root of 20 since [tex]\displaystyle \large{\sqrt{a} > \sqrt{b}}[/tex] for a > b
Hence, from least to greatest:
[tex]\displaystyle \large{\frac{11}{3} < \sqrt{17} < \sqrt{20}}[/tex]
In a spot check of cartons of eggs, Matilda found that 6 out of 200 eggs were cracked.
If the store has 3,000 eggs for sale, how many can expect to be cracked?
0.046×0.3
Show your work
help pleaseee thankssssssss :))))))
Answer:
it is 20
Step-by-step explanation:
because it rounds from the ten value which is to the left of the decimal which means it has to be either 10 or 20 and 8 is greater than 5 so the answer if 20
This question is asking you to round to the nearest ten, not the nearest tenth. To do this, all you have to do is round to the nearest product of ten - in this case, 20.
Bill has to choose between a 10% off coupon and a coupon that saves $10.00. Which of the following totals would allow Bill to save more with the $10 coupon? Answer choices:
$140 $120 $100 $80
Answer:
$80
Step-by-step explanation
(chart)
10% -$10
$140 $126 $130
$120 $108 $110
$100 $90 $90
$80 $72 $70
Bradley bought 8 quarts of lemonade. How many cups did Bradley buy?
Answer: 32 cups
Step-by-step explanation:
1 quart: 4cups
8 x 4 : 36 cups
Bobby says, “when you multiply two numbers, the product is greater than both factors “ Bobby’s claim is not always true select the two multiplication expressions that show Bobby’s claim is not always true
Answer:
0*1=0 7*1 basically anything multiplied by 0 or 1 will not be greater than both factors
Step-by-step explanation:
Based on how I do not know the options I am going to say what I believe you might have as options for example, anything multiplied by 0 is less than and anything multiplied by 1 is not greater it is equal to.
I NEED HELP IM STUCK ON THIS
Step-by-step explanation:
[tex]12 \frac{1}{25} - 7 \frac{2}{15} [/tex]
[tex] \frac{368}{75} [/tex]
If each customer takes 3 minutes to check out, what is the probability that it will take more than 9 minutes for all the customers currently in line to check out?
Using a discrete probability distribution, it is found that there is a 0.15 = 15% probability that it will take more than 9 minutes for all the customers currently in line to check out.
What is the discrete probability distribution?Researching the problem on the internet, it is found that the distribution for the number of customers in line at the store is given by:
P(X = 0) = 0.2;P(X = 1) = 0.15;P(X = 2) = 0.30;P(X = 3) = 0.20;P(X = 4) = 0.10;P(X = 5) = 0.05;Hence, since each customer takes 3 minutes to check out, the probability that it will take more than 9 minutes for all the customers currently in line to check out is the probability that there are more than 3 customers, hence:
P(X > 3) = P(X = 4) + P(X = 5) = 0.10 + 0.05 = 0.15.
0.15 = 15% probability that it will take more than 9 minutes for all the customers currently in line to check out.
More can be learned about a discrete probability distribution at https://brainly.com/question/24855677
Find the volume of the cone.
Use 3.14 for π. Round your answer to the nearest tenth if needed. Do not enter units.
Answer:
94.2 cm³
Step-by-step explanation:
Volume of cone= ⅓πr²h
Let's identify the radius of the base and the height of the cone!
r= 3 cm
h= 10 cm
Next, substitute r= 3 and h= 10 into the volume of cone formula.
Volume of cone
= ⅓(3.14)(3²)(10)
= 94.2 cm³
find a area of a circumference that is 13 ft for 3.14 π
Answer:
4.14x3.14=12.9996
Step-by-step explanation:
This is the closest to 13 ft via circumference
Here is a few equations a dn formulas to remind you.
Area=3.14xRxR or Pi*rr
This is Pi times the radius times the radius.
The radius is half of the circle or half of the Diameter.
Area(semi-circle)=1/2x3.14xrxr
Circumfrence=3.14xDor 3.14xdiameter
If this answer helped pls give brainlest.
9. The value of U.S. postage stamps increases -5% per year. The current price is 55€. Estimate what the price will be in 20 years
[tex]\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &\$0.55\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ t=years\dotfill &20\\ \end{cases} \\\\\\ A=0.55(1 + 0.05)^{20}\implies A=0.55(1.05)^{20}\implies A\approx 1.46[/tex]
What is the sum of 3,45,26,712 and 1,00,98,756??
Answer:
34,526,712 + 10,098,756 = 44,625,468
James buys 7 baseballs and 1 bat.
• Each baseball costs the same amount.
• The bat costs $42.00.
• The total cost is $66.50, before tax.
What is the cost of each baseball?
$3.50
$6.00
$9.50
$15.50
The cost of each baseball is $3.50, option A is correct.
Given that the Number of baseballs are 7.
Cost of the bat = $42.00
Total cost before tax = $66.50
The total cost of the baseballs can be calculated by multiplying the cost of each baseball by the number of baseballs:
Total cost of baseballs = 7 × x
The total cost of all items, including the baseballs and the bat, is the sum of the individual costs:
Total cost = Total cost of baseballs + Cost of the bat
$66.50 = 7x + $42.00
We need to solve this equation for x.
Subtracting $42.00 from both sides:
$66.50 - $42.00 = 7x
$24.50 = 7x
Dividing both sides by 7:
$24.50 / 7 = x
x = $3.50
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The means and mean absolute deviations of sidney’s and phil’s grades are shown in the table below. means and mean absolute deviations of sidney’s and phil’s grades sidney phil mean 82 78 mean absolute deviation 3.28 3.96 which expression represents the ratio of the difference of the two means to sidney’s mean absolute deviation? startfraction 82 over 3.28 endfraction startfraction 4 over 3.28 endfraction startfraction 4 over 0.68 endfraction startfraction 82 over 0.68 endfraction
The expression that represents the ratio of the difference of the two means to Sidney’s mean absolute deviation is given by: Option B: 4/3.28
What is mean absolute deviation?Mean absolute deviation is the average of the absolute deviation of each observation from their mean, for a considered set of observations.
For this case, the table of mean and mean absolute deviation is given as:
[tex]\begin{array}{ccc}&Mean&M.A.D.\\\text{Sidney}&82&3.28\\\text{Phill}&78&3.96\end{array}[/tex]
(M.A.D refers to Mean Absolute Deviation).
So, difference in their mean is 82 - 78 = 4
Absolute deviation for Sidney is 3.28
Thier ratio is: 4/3.28
Thus, the expression that represents the ratio of the difference of the two means to Sidney’s mean absolute deviation is given by: Option B: 4/3.28
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Answer:
Option B: 4/3.28
Step-by-step explanation:
If b= 110 degrees and a= 50 degrees, what is the value of x?
I think you're question is incomplete or is missing an attachment.
Jina makes eight dollars for each hour of work. Write an equation to represent her total pay ‘p’ after working ‘h’ hours
Answer:
p = 8h
Step-by-step explanation:
Simple math my guy
Answer:
p=8h
Step-by-step explanation:
For each hour, she gets paid $8. So the total pay would be the number of hours multiplied by 8.
