All apply values to the equation are:
0 ⇒ A
π/3 ⇒ B
5π/3 ⇒ E
What is an equation?
A formula known as an equation shows the equality of two expressions by joining them with the equals sign =.
Main Body:
∵ 0 ≤ x ≤ 2π is the domain for angle x
∴ 0 ≤x/2 ≤ π is the domain of angle
∵ sin(x/2) + cos(x) - 1 = 0
→ To solve the equation we should use the rule of cosine double angle
∵ cos(x) = 1 - 2 sin²(x/2)
→ Substitute it in the equation above
∴ sin(x/2) + (1 - 2 sin²(x/2) = 0
∴ sin(x/2) + 1 - 2 sin²(x/2) = 0
→ Add the like terms
∴ sin(x/2) + (1 - 1) - 2 sin²(x/2) = 0
∴ sin(x/2) - 2 sin²(x/2) = 0
→ Take sin(x/2) as a common factor
∴ sin(x/2) [1 - 2sin(x/2)] = 0
→ Equate each factor by 0
∵ sin(x/2) = 0
→ The value of sine equal zero on the x-axis
∴ x/2 = 0, π, 2π
∵ The domain of x/2 is 0 ≤ (x/2) ≤ π
∴ x/2 = 0 and π ⇒ 2π refused because ∉ the domain
→ Multiply both sides by 2 to find x
∴ x = 0 and 2π
∵ 1 - 2sin(x/2) = 0
→ Subtract 1 from both sides
∴ - 2sin(x/2) = -1
→ Divide both sides by -2
∴ sin(x/2) = 1/2
→ The sine is positive in the 1st and 2nd quadrants
∴ (x/2) lies on the 1st OR 2nd quadrants
∵ (x/2) = sin⁻¹(1/2)
∴ (x/2) = π/6 = ⇒ 1st quadrant
→ Multiply both sides by 2
∴ x = π/3
∵ (x/2) = π -π/6 = 5π/6 ⇒ 2nd quadrant
→ Multiply both sides by 2
∴ x = 5π/3
∴ The values of x are 0,π/3 , 5π/3 , 2π
Hence apply values are:
0 ⇒ A
π/3⇒ B
5π/3⇒ E
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1. Determine the solution for the system of equations shown in this graph. Enter your answer as a coordinate pair without any spaces, infinite solutions, or no solutions.
The solution for the system of equations shown in this graph is (-2, 1)
In this question, we need to determine the solution for the system of equations shown in this graph.
From given graph of system of equations we can observe that the system of equations represent lines intersected at point.
This means that the system of equations has a solution.
The point of intersection of given line is (-2, 1)
Therefore, the solution for the system of equations shown in this graph is (-2, 1)
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find the number that is exactly between 1/10 and 2/5
Answer:
1/4
Step-by-step explanation:
[tex] \frac{1}{2} ( \frac{1}{10} + \frac{2}{5} )[/tex]
[tex] \frac{1}{2} ( \frac{1}{10} + \frac{4}{10} ) = \frac{1}{2} ( \frac{5}{10} ) = \frac{1}{2} ( \frac{1}{2} ) = \frac{1}{4} [/tex]
When can you use proportional reasoning to solve a problem?
A. When two quantities add to 1
B. When one quantity is a constant multiple of the other
C. When the two quantities multiplied equal a constant
D. When one quantity is 1 more than the other
We can use proportional reasoning to describe that when the two quantities multiplied equal a constant.
Hence, Option (C) is correct.
What is a proportion?
A proportion is a type of ratio in which the denominator also contains the numerator. For example, the proportion of male deaths would be deaths to males divided by deaths to males plus deaths to females (i.e. the total population).
Let 'x' be the numerator and 'y' be denominator,
then one ratio is 'x/y' and its reciprocal by using the proportion would be 'y/x'
and then their multiplication will be
[tex]=\frac{x}{y}*\frac{y}{x} \\\\\=1[/tex]
Multiplication gave us '1', which is a constant.
Hence option (C) is the correct answer.
We can use proportional reasoning to describe that when the two quantities multiplied equal a constant.
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Sally adds 3.13 moles of argon to a 5.29 liter balloon that already contained 2.51 moles of argon. What
is the volume of the balloon after the addition of the extra gas?
The volume of the balloon after the addition of the extra gas is 11.87 liters
The initial volume of the balloon = 5.29 liters
Initial quantity of argon in the balloon = 2.51 mole
Here we have to use the unitary method
The volume of the 1 mole of argon = The initial weight of the balloon / Initial quantity of argon in the balloon
Substitute the values in the equation
The volume of the 1 mole of argon = 5.29 / 2.51
= 2.11 liters
Additional argon added = 2.51 mole
Total quantity of argon = 2.51 + 3.13
= 5.64 mole
The volume of the 5.64 mole of argon = 5.64 × 2.11
= 11.87 liters
Hence, the volume of the balloon after the addition of the extra gas is 11.87 liters
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I would like to know the answer..
Answer:
Ann’s work is correct
Step-by-step explanation:
Which system of linear inequalities is graphed?
A.
x<-3
y ≤-x+1
B.
x<-3
y ≤-x-1
C.
x<-2
y ≤-x-1
D.
x ≤-3
y ≤-x-3
Answer:
A x<-3
y ≤-x+1
Step-by-step explanation:
x<-3
y ≤-x+1
51.765 rounded 2 decimal places
Answer:
The answer would be 52 if you rounded by the nearest whole number.
Step-by-step explanation:
Find your place
Look next door (to the minor digit)
Four or less just ignore
Five or more let it sore.
Given the explicit formula u(n) = 4n - 1, where u(1) = 1, find the recursive formula for u(n).
A. u(1) = 1 and u(n + 1) = 4u(n), for n = 1, 2, 3, . . .
B. u(1) = 1 and u(n + 1) = u(n) + 4, for n = 1, 2, 3, . . .
C. u(1) = 1 and u(n + 1) = u(n) + 8, for n = 1, 2, 3, . . .
D. u(1) = 1 and u(n + 1) = 8u(n), for n = 1, 2, 3, . . .
The Recursive formula for the given explicit formula is u(1) = 1 and u(n+1) = u(n) + 4 , for n = 1 , 2 , 3 .... , the correct option is (b) .
In the question ,
it is given that ,
the explicit formula is u(n) = 4n - 1 .
and u(n) = 1 ,
we need to find the recursive formula ,
We substitute n + 1 in place of n , in the equation u(n) = 4n - 1
after substitution , we get
u(n+1) = 4(n + 1) - 1
u(n+1) = 4n + 4 - 1
u(n+1) = 4n + 3
Subtracting u(n) = 4n - 1 from u(n+1) = 4n + 3 ,
we get
u(n+1) - u(n) = 4n + 3 - (4n - 1)
u(n+1) - u(n) = 4n + 3 - 4n + 1
u(n+1) - u(n) = 3 + 1
u(n+1) - u(n) = 4
u(n+1) = u(n) + 4
Therefore , The Recursive formula for the given explicit formula is u(1) = 1 and u(n+1) = u(n) + 4 , for n = 1 , 2 , 3 ....
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All stereos are 20
%
off of the original price. If stereos normally cost $160, what is the sale price?
Answer:
128 dollars
Step-by-step explanation:
hope it helped! :)
Simplify without a calculator 2x X 3x
- 2x²
Answer:
4x²
Step-by-step explanation:
2x × 3x - 2x²
= 6x² - 2x²
= 4x²
Find the simple interest of Rs. 20,000 for 5 years at 10% per annum? Also, at what time will Rs. 50,000 earn the same amount of interest at 5% of simple interest per annum?
Answer:
below
Step-by-step explanation:
Simple interest = 20 000 * .1 * 5 (.1 is 10% in decimal)
at 1/2 the 10% interest it will take twice as long = 10 years
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The amount owed at the end of the 6 years duration is $10865
How to determine the amount owed in six years?The given parameters about the compound interest are
Principal Amount, P = $5300
Interest Rate, R = 8%
Time, t = 6 years
To calculate the amount owed, we make use of the following formula
A = P + CI
Where
Compound interest, CI = P(1 + R)^t - P
So, the equation becomes
A = P + P(1 + R)^t - P
Evaluate the like terms
A = P(1 + R)^t
In this question, the formula is given as
A = P(1 + r/n)^nt
Where
n = 12, i.e compounded monthly
Substitute the known values in the above equation
A = 5300 * (1 + 8%/12)^(6*12)
Express 8% as decimal
A = 5300 * (1 + 0.08/12)^(6*12)
Evaluate the sum
A = 5300 * (1.01)^(6*12)
Evaluate the exponent
A = 5300 * 2.05
Evaluate the product
A = 10865
Hence, the value of the amount after 6 years is $10865
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solve
5/x+2 + 4/x+1 =2
Answer:
1.5,3
Step-by-step explanation:
Hope this helps it's all I could find I'm sorry
Ooo! It's fall and Thanksgiving time! I gotta get ready for Thanksgiving and for my friends to come over! Fun! - Ash the Fox
Sari made pancake batter. She has 1 cup of batter left. How much batter did she use?
If this problem cannot be solved with the information provided, write additional information
and then solve the problem.
Answer:
3 cups
Step-by-step explanation:
let's assume that sari made pancake batter in a jar.
1 jar is equivalent to 4 cups
so if 1 cup of batter is left, it can be concluded that Sari uses 3 cups of batter in making pancakes.
In a class of 29 students, 9 play an instrument and 14 play a sport. There are 8 students who do not play an instrument or a sport. What is the probability that a student does not play an instrument given that they play a sport?.
The probability of a student playing a sport but not playing an instrument is around 0.4286.
The likelihood of a student not playing an instrument, provided they play a sport, is:
[tex]Probability=\dfrac{Number\ of\ students\ who\ play\ a\ sport\ but\ do\ not\ play\ an\ instrument}{Number of \students\ who\ play\ a\ sport}[/tex]
It is known that 14 students participate in a sport, while 8 students do not engage in either a musical instrument or a sport. Thus, the number of students who play a sport but do not play an instrument is:
Number of students who play a sport but do not play an instrument = 14- 6
= 6
Now, let's calculate the probability:
Probability = 6/14
= 0.4286
Rounded to four decimal places, the likelihood of a student playing a sport but not playing an instrument is approximately 0.4286.
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An irregular polygon has exterior angle measures of 92, 73, 63, and 104 degrees. What is the measure of the fifth interior angle?
Answer:
152°
Step-by-step explanation:
the sum of the exterior angles of a polygon = 360°
let x be the measure of the fifth exterior angle , then
92° + 73° + 63° + 104° + x = 360°
332° + x = 360° ( subtract 332° from both sides )
x = 28°
then
interior angle + exterior angle = 180° , that is
interior angle + 28° = 180° ( subtract 28° from both sides )
interior angle = 152°
the exterior angles of a polygon is 360°
92 + 73 + 63 + 104 = 332
360 - 332 = 28° is the measure of the fifth interior angle.
help please (see picture)
Also if it’s not clear cus of the smudge, it says “6” and “U”
The perimeter of the triangle is 64 when the triangle is ZTW.
Given that,
In the picture we have a triangle ZWT.
The U and V are mid points of WT and Y and X are midpoints of ZW.
We have to find the perimeter of the triangle.
We get the sides
ZT=22
We have,
TU/ZY= UV/YX= VW/XW (Thales theorem)
6/8= a/12= 3/b
3/4=a/12= 3/b
Take,
3/4=a/12
a=3/4×12
a=3×3
a=9
Take,
3/4=3/b
b=3×4/3
b=4
The side TW=6+9+3=18
The side ZW=8+12+4=24
The perimeter of the triangle is sum of the sides.
The perimeter of the triangle=ZT+ZW+TW
The perimeter of the triangle= 22+24+18
The perimeter of the triangle= 64
Therefore, The perimeter of the triangle is 64 when the triangle is ZTW.
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Multiple Choice 1. 2(y +2) for y=3 (1 point) O -4 O8 O 10 O 2
Answer:
10
Step-by-step explanation:
If y is three, add 2+3, then multiply by 2, so the answer would be ten.
Last year at a certain high school, there were 125 boys on the honor roll and 50 girls on the honor roll. This year, the number of boys on the honor roll increased by 12% and the number of girls on the honor roll increased by 8%. By what percentage did the total number of students on the honor roll increase? round your answer to the nearest tenth (if necessary).
The total student increases by 10.85% from last year.
What is percentage?A relative value indicating hundredth parts of any quantity is called percentage.
Given that, last there were 125 boys and 50 girls, and it increased by 12% and 8% next year,
Total students last year = 125+50 = 175
Boys increased = 125x112/100 = 140
Girls increased = 50x108/100 = 54
Total students current year = 140+54 = 194
Percentage increase = (194-175)/175x100 = 10.85%
Hence, The total student increases by 10.85% from last year.
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Four fifths plus one thirds plus eleven twelfths
Answer: 1/3
Step-by-step explanation: 4/5 + 3/15 is equal to 12/15 + 3/15
12/15 + 3/15 = 1
1/1 - 2/3 is equal to 3/3 - 2/3
3/3 - 2/3 = 1/3
a farmer raises chickens and sheep on his farm. the ratio of the total number of legs of the chickens to the total number of legs of the sheep is 4:7. find the minimum number of chickens and sheep he has.
Answer:
8 chickens, and 28 sheep.
Step-by-step explanation:
The chickens have the ratio of 4. Chickens have 2 legs, so 4 x 2 = 8 chickens.
The sheep have the ratio of 7. Sheep have 4 legs, so 7 x 4 = 28 sheep.
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The completed table of coordinates for the exponential function can be presented as follows;
x; -2, -1, 0, 1, 2
y ; 16/9, 4/3, 1, 3/4, 9/16
Please find attached the graph of the function created with MS Excel
The correct graph is therefore, option D
What is an exponential function?
An exponential function is one that has the argumant as an exponent
The values in the table can be found as follows;
[tex]f(x) = \left(\frac{3}{4} \right)^x[/tex]
[tex]f(x) = \left(\frac{3}{4} \right)^{-2} = \dfrac{16}{9}[/tex]
[tex]f(x) = \left(\frac{3}{4} \right)^{-1} = \dfrac{4}{3}[/tex]
[tex]f(x) = \left(\frac{3}{4} \right)^{0} = 1[/tex] The y-intercept
[tex]f(x) = \left(\frac{3}{4} \right)^{1} = \dfrac{3}{4}[/tex]
[tex]f(x) = \left(\frac{3}{4} \right)^{2} = \dfrac{9}{16}[/tex]
The completed table is therefore;
x; -2, -1, 0, 1, 2
y ; 16/9, 4/3, 1, 3/4, 9/16
The graph of the function , [tex]f(x) = \left(\frac{3}{4} \right)^x[/tex], therefore, has a y-intercept of 1, and a maximum value of 16/9 at x = -2
The best cprect option for the graph is therefore option D
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Caroline leaves her house and walks north 6 blocks. She turns and heads east 8 blocks until she reaches mattie’s house. What is the shortest distance between caroline’s and mattie’s houses?.
Caroline leaves her house and walks north 6 blocks. She turns and heads east 8 blocks until she reaches mattie’s house.
The shortest distance between Caroline’s and Mattie’s house is 10 blocks.
If we assume this as a right angle triangle then height(BA) is 6 blocks long and base(BC) is 8 blocks
long.
Then, the shortest distance between Caroline’s and Mattie’s house will be the hypotenuse(AC) of this
triangle.
So, by applying Pythagoras theorem:
(AC)² = (BA)² + (BC)² = (6)²+(8)² = 36+64 = 100
Thus, AC = √100 = 10 block
Hence, the shortest distance we can take from Caroline’s house to reach Mattie’s house is 10 blocks.
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Please answer the second question ASAP
25th second part
Thank you!
If D is the midpoint of the segment BC then 2(BM + MD) = 2DC.
What is geometry?Geometry is one of the oldest branches of mathematics, along with arithmetic. It is concerned with spatial qualities such as figure distance, shape, size, and relative position. A geometer is a mathematician who works in the field of geometry.
In the given image we have a triangle in which line BC is cut into two halves at point D. This Means that D is the mid-point of line BC.
Here if segment BC is divided by point D into two halves then,
BM + MD = DC
The value of 2DC will be,
2DC = 2 (BM + MD)
Therefore, the value of 2DC will be equal to 2(BM + MD).
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the breaking strength x of a certain rivet used in a machine engine has a mean 5000 psi and standard deviation 400 psi. a random sample of 36 rivets is taken. consider the distribution of , the sample mean breaking strength. what is the probability that the sample mean falls between 4800 psi and 5200 psi?
The probability that the sample mean falls between 4800 psi and 5200 psi is 0. 0.9973.
Probability refers to the numerical descriptions of how likely an event is to occur. For the given information, the mean µ = 5000 psi and standard deviation σ = 400 psi.
For a random sample, n = 36, in order to determine the probability that the sample mean falls between 4800 psi and 5200 psi, the z test statistics for the range must be calculated.
z = (x - µ)/ (σ/√n) = (4800 - 5000)/ (400/√36) = -3
z = (x - µ)/ (σ/√n) = (5200 - 5000)/ (400/√36) = 3
Hence, the probability that the sample mean falls between 4800 psi and 5200 psi would be p ( -3< z < 3).
From the table,
p ( -2.4 < z < 2.4) = 0.9973
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The ten digit of a two-digit number exceeds twice the units digit by 1. If the digits are reversed, the sum of the new number and the original number is 143. Find the original number.
If the digits are reversed, the sum of the new number and the original number is 143. The original number is 94.
How to find the original number?Let x represent the unit digit of the original number
Let tens digit =2x+1
Let the number = 10(2x+1)+x=21x+10
Assuming the digits are reversed
Tens digit = x
Unit digit =2x+1
Reversed number = 10x+2x+1=12x+1
So,
(21x+10)+(12x+1)=143
Collect like terms
33x+11=143
33x=132
Divide bot side by 33x
x = 143/33
x=4
Original number:
Original number =21×4+10
Original number = 84 +10
Original number =94
Therefore the original number is 94.
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Solve for x. Help me and I will do anything for you.
x = 8
Step-by-step -e-x-p-l-a-n-a-t-i-o-n- below
The angles shown are vertical angles
Vertical angles are congruent (equal to each other)
This means that 8x + 36 = 5x + 60
Using this equation we can solve for x
8x + 36 = 5x + 60
==> subtract 36 from both sides
8x = 5x + 24
==> subtract 5x from both sides
3x = 24
==> divide both sides by 3
x = 8
Answer:
[tex]\huge\boxed{\sf x = 8}[/tex]
Step-by-step explanation:
From the diagram,8x + 36 = 5x + 60 (Vertically opposite angles are equal)
Subtract 5x to both sides
8x - 5x + 36 = 60
3x + 36 = 60
Subtract 36 to both sides
3x = 60 - 36
3x = 24
Divide 3 to both sides
x = 24/3
x = 8[tex]\rule[225]{225}{2}[/tex]
PLEASE HELP!!!! I BEG YOU!!!
What is the solution to the system of equations graphed below? Give the answer as a coordinate point (x, y)
Answer:
(1,3)
Step-by-step explanation:
The solution to a system of equations graph is the point of intersection of the two lines.
In this case the point where both lines meet is at x = 1 and y = 3
hence the answer being (1,3)
Write a rate that represents the situation.
Need help on 5 & 6
Answer:
5. (6 hours)/(1 day)
6. (8 quarts)/(1 container)
Step-by-step explanation:
5. The number line shows both hours and days. It does not indicate why the relationship exists. Perhaps the hours are the ones worked in a day. What’s important is whether the relationship between the two is the same for all data pairs. E.g., 12/2 = 6; 36/6 = 6; 60/6 - 5, and so forth. They are all the same ratio, or rate: (6 hours)/(1 day)
6. The number line shows both quarts and containers. The relationship between the two is the same for all data pairs. E.g., 8/5, 16/10 or 8/5; 24/15 or 8/5; 32/20 or 8/5, and 40/25 or 8/5. They are all the same ratio, or rate: (8 quarts)/(1 container).
Write the equation in standard form for the circle with center (–
6,0) and radius 5.
Answer:
[tex](x - 6)^2 + y^2 = 25[/tex]
Step-by-step explanation:
The standard form of a circle is [tex](x - x_1)^2 + (y - y_1)^2 = \text{R}^2[/tex], where [tex](x_1\text{, }y_1)[/tex] is the center point of the circle, and [tex]\text{R}[/tex] is the circle's radius.
We're given the center of our circle is (6, 0) and its radius is 5, therefore, the circle's equation in standard form is:
[tex](x - 6)^2 + (y - 0)^2 = 5^2\\\to (x - 6)^2 + y^2 = 25[/tex]
Answer:
(x - 6)² + y² = 25
Step-by-step explanation:
the equation of a circle in standard form is
(x - h)² +(y - h)² = r²
where (h, k ) are the coordinates of the centre and r is the radius
here (h, k ) = (6, 0 ) and r = 5 , then
(x - 6)² + (y - 0)² = 5² , that is
(x - 6)² + y² = 25
