In the accompanying diagram of a unit circle, the ordered pair (x,y) represents the point where the terminal side of 0 intersects the unit circle. If 0=150, what is the value of x.
A.
B.
C.
D.
Answer:
Below in bold.
Step-by-step explanation:
tan 150 = -tan 30
= -1/√3 = y/x (1)
This is a unit circle so the hypotenuse = 1.
so sin 150 = y/1 = y
y = 1/2
So substituting in equation (1)
1/2 / x = -1/√3
-x = √3/2
x = -√3/2.
The value of x in the unit circle is -√3/2.
Option B is the correct answer.
What is a circle?A circle is a two-dimensional figure with a radius and circumference of 2pir.
The area of a circle is πr².
We have,
Since the angle is 150 degrees, we know that it is in the second quadrant, where the x-coordinate is negative and the y-coordinate is positive.
Since the circle has a radius of 1, the y-coordinate is sin(150) = 1/2.
To find the x-coordinate, we can use the formula x = cos(θ), where θ is the angle in radians.
To convert 150 degrees to radians, we multiply by π/180:
150 degrees x π/180 = 5π/6 radians
So,
x = cos(5π/6) = -√3/2.
Therefore,
The value of x is -√3/2.
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Ram spent 1/3 of his salary on food, ,1/4 of his salary on rent and electricity, and 1/20 of his salary on the telephone. Since April -2022 is the month of Ramadan, irrespective of religion and cast Ram has donated 1/10 of his salary to an orphanage and 5000Aed to RCA Charity. He was left with 3000AED with him. What is his monthly salary?
STEP BY STEP PLS
The total monthly salary earned by Ram in the month of April 2022 is an amount of 30000 AED before payments and donations.
How to solve a word problem
Word problems are statements that embody a set of algebraic expressions that offers at least one solution. In this case, we have to read the statement, find the equivalent formula and solve for the resulting variable.
After a careful reading, the statement is equivalent to the following formula:
x = x / 3 + x / 4 + x / 20 + x / 10 + 5000 + 3000
4 · x / 15 = 8000 (1)
Where x is Ram's monthly salary.
The solution of (1) is x = 30000.
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Write an equation of a line in slope-intercept form given the slope (m) and the y-intercept (b).
Slope, m =
y-intercept, b =
Answer:
y = 5x + 3
Step-by-step explanation:
If the slope is 5 and the y-intercept is 3, we can substitute the value of the variables into the formula.
y = mx + b
y = (5)x + 3
y = 5x + 3
I hope this helps!
Which expression is equivalent to
Answer:
First option
Step-by-step explanation:
The expression can be simplified to:
[tex]\frac{8g^{15} }{64h^6}[/tex] = [tex]\frac{g^{15} }{8h^{6} }[/tex]
You can't simplify this further since the indices if you think about it is g 15 times or h 6 times so you can't simply them further.
Solve log x = 4. plese help
Answer:
x = 10^4 = 10000
Step-by-step explanation:
log(x) = 4
x = 10^4
100 PTS!! If line segment AB is dilated with a scale factor 3/2, what is the length of the new line segment A’B’?
A)7.5cm
B)15cm
C)20cm
D)30cm
Length of AB is not given so insufficient info provided
Let's see how to solve then
Scale factor is 3/2 means 3/2 is multiplied with AB to form A'B'
If length of AB is n the. then length of A'B' is 3n/2
help me pleaseeeeeeeeee
Answer:
slope = [tex]\frac{8}{3}[/tex]
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 5, - 4) and (x₂, y₂ ) = (- 2, 4) ← 2 points on the line
m = [tex]\frac{4-(-4)}{-2-(-5)}[/tex] = [tex]\frac{4+4}{-2+5}[/tex] = [tex]\frac{8}{3}[/tex]
Find the area of the polygon: Hint: Area = (Length)(Width)
-
( 3x+8 ) ( 7x-2 )
= 21x² + 56x - 6x -16
= 21x² + 50x -16
HOPE IT HELPS :)
A square number and a prime number equals to 17
Answer:
2 & 13
Step-by-step explanation:
The square of 2 plus the prime number 13 add up to 17
[tex]2^{2}+13=4+13 =17[/tex]
Hope this helps
Answer:
Square number = 4
Primer number = 13
Step-by-step explanation:
A square number is the result when a number has been multiplied by itself.
A prime number is a whole number greater than 1 that only has two factors, itself and 1.
List all the square numbers and prime numbers below 17:
Square numbers: 1, 4, 9, 16, ...
Prime numbers: 2, 3, 5, 7, 11, 13, ...
Therefore, the only combination of square number and prime number that sums to 17 is: 4 + 13 = 17
Solution
Square number = 4
Primer number = 13
I dont understand this to save my life, Please help !
6. Find the H.C.F. of: (a) a² + 2ab + b2-c?, b? + 2bc + ? - a and c? +2ac + a-b? +
Answer:
- (a + b)^2
- (b + c)^2
- (a - b + c) (a + b + c)
The answer is given in the photos below (for verification),
I hope my answer helps you.
state the restrictions on the domain of the equation.
Answer: Choice E
[tex]x \ne -4, -1[/tex]
This is the same as saying [tex]x \ne -4 \text{ and } x \ne -1[/tex]
======================================================
Reason:
If we plugged x = -4 into the function, then the x+4 in the denominator turns to 0.
x+4 = -4+4 = 0
Dividing by zero is not allowed. It leads to a division by zero error. Therefore, we need to exclude -4 from the domain. Similar reasoning will exclude -1 as well because it makes the x+1 in the denominator to be zero.
Any other x value is valid.
Side note: The (x+1) terms cancel, which may appear that x = -1 is valid. However, your calculator will likely not perform such a simplification. It will simply try to directly compute the result using PEMDAS. That means x = -1 is likely to produce a division by zero error.
chen and megan each have a set of numbered counters chen has= 1 2 3 4 megan has= 1 2 3 4 5 they each take thier own counters without looking chen says im more likley to get a 4 is he correct? explain your answer
Answer:
Yes, Chen is correct.
Step-by-step explanation:
Chen has 1/4 chance of getting a 4, whereas Megan has 1/5 chance of getting a 4.
1/4 = 0.25
1/5 = 0.20
Therefore, Chen is correct.
Say that the economy is in an expansion, causing wages to increase by six percent. if you previously received a monthly salary of $1,375.00, what will your new monthly salary be? round all dollar values to the nearest cent. a. $2,365.00 b. $1,604.17 c. $1,462.77 d. $1,457.50 please select the best answer from the choices provided a b c d
The new monthly salary will be $1,457.50.
You received a monthly salary of $1,375.00
Now by economy expansion, causing wages to increase by = 6%
Increment of the salary = 6% of 1,375.00
[tex]= \frac{6}{100} \times 1,375[/tex]
[tex]= 0.06 \times 1,375 =\$82.50[/tex]
What is the monthly salary?Monthly Salary means Employee's monthly salary, before deductions.
Therefore our new monthly salary would be
[tex]= $1,375.00 + $82.50\\ = $1,457.50[/tex]
Therefore our new monthly salary will be $1457.50.
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Matt is given a jar with eight marbles, six of which are red and two of which are green. Matt then randomly draws marbles without replacement. If he selects a red marble, he puts it in the first box; similarly, he continues to place all red marbles he selects into the first box until a green marble is chosen. When a green marble is chosen, he puts the first box aside. He then selects and places red marbles in the second box until the second green marble is chosen. When the second green marble is selected, he will put the second box aside and place all remaining red marbled in a third box. After all marbles are drawn, what is the probability that each box contains two red marbles? Express your answer as a common fraction.
Answer:
as a percentage it is: 0.25 x 0.2 =0.05 or 5%
but as a common fraction it is: 5/100 or 1/20
Step-by-step explanation:
What is the surface area of this right prism?
48 in²
84 in²
96 in²
120 in²
Answer:
It's 96
Step-by-step explanation:
-The left and right rectangles
5*4=20
(5*4)*2=40
-Triangle (front and back)
8*3/2=12
(8*3)/2*2=24
-Bottom Triangle (base)
8*4=32
-Area
=40+24+32
=96
Answer: 96 in^2
Step-by-step explanation: I took the quiz and got it right!! Hope this helps you, have a beautiful day!! :)
A right rectangular prisim has a length of 2 1/2 feet a width of 3 feet and a height of 1 1/2 feet. Unit cubes with side lengths of 1/2 foot are added to completely fill the prisim with no space remaining. What is the volume in cubic feet of the right rectangular prisim?
PLEASE HELP ASAP FIRST CORRECT ANSWER GETS BRAINLEIST
k²= 6²+5²
k²= 36+25
k²= 61
k= V61
k=7.81
Choose all lengths that are equal to
3 yards 16 inches.
A.
124 in.
B.
4 yd 4 in.
C.
3 yd 1 1/2 ft
D.
2 yd 52 in.
E.
10 ft 4 in.
(15 points)
Answer: The answer you would be looking for is A. D. E.
Step-by-step explanation:
I hope i helped and can i have brainliest please <3
What should be done to solve the following equation?
=
C-730
7
What should be done to solve the following equations?
C - 7 and 3/4= 0
A) add 7 and 3/4 to both sides of the equation
B)Add O to both sides of the equation.
C)Subtract from both sides of the equation
D) Subtract 7 from both sides of the equation
The equation C -7 - 3/4 = 0 is an algebraic equation
To solve the equation we (a) add 7 and 3/4 to both sides of the equation
How to determine the action on the equation?The equation is given as:
C -7 - 3/4 = 0
Make C the subject of formula by adding 7 and 3/4 to both sides of equation
C = 7 + 3/4
Now, we can solve for C
Hence, to solve the equation we (a) add 7 and 3/4 to both sides of the equation
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Which equation has a vertex at (3, –2) and directrix of y = 0?
y + 2 = StartFraction 1 Over 8 EndFraction (x minus 3) squared
y + 2 = 8 (x minus 3) squared
y + 2 = negative StartFraction 1 Over 8 EndFraction (x minus 3) squared
y + 2 = negative 8 (x minus 3) squared
Answer: C
Answer:
The square below represents one whole.
What percent is represented by the shaded area?
The square below represents one whole.
What percent is represented by the shaded area?The square below represents one whole.
What percent is represented by the shaded area?The square below represents one whole.
What percent is represented by the shaded area?The square below represents one whole.
What percent is represented by the shaded area?vvvvStep-by-step explanation:
fing the midpoint of A(1-4) and B(-2;-7)
Omar and Ted have a total of 25 books. Omar has 5 less than twice the number of books Ted has. Use a graph to find how many books each boy has. y
Answer:
Ted has 10 books and Omar has 15 books
Step-by-step explanation:
Hey there!
In order to find how many books each of the boys have, we can make a system of equations
First equation: O+T=25
Second equation: O=2T-5
After making the equations, you can use substitution by plugging in 2T-5 For O in the first equation:
2T-5+T=25
Simplify LHS
3T-5=25
Take 5 to the other side
3T=30
Divide by 3 on both sides to get T by itself
T=10
So this means that Ted has 10 books
Now we can plug this into the second equation
*note that you can plug 10 into the first equation too*
O=2(10)-5
Simplify RHS
O=20-5
Combine like terms
O=15
This means that Omar has 15 books
So, Ted has 10 books and Omar has 15 books
PLSSS HELP IF YOU TURLY KNOW THISS
Answer:
1 1/2 or 1.5
As a simplified fraction
If this helped pls give brainlest.
HELP PLSSS - WILL MARK BRAINLIEST
Select the correct answer
which situation is best modeled by a nonlinear function with time as the independent variable?
A. The value of a gift card that decreases by three dollars each month
B. The value of a $20 bill
C. The value of a collectible baseball card that increases by constant factor of 1.1, or by 10%, each year
D. The value of an investment that increases by two dollars each week
Answer: Most likely it is A
Step-by-step explanation:
Although it should be B, because a non linear function doesn't have a rate of change. I already looked up this question many times so we know It's NOT C.
The best modeled by a nonlinear function with time as the independent variable is:
The value of a collectible baseball card that increases by a constant factor of 1.1, or by 10%, each year.
A nonlinear function is one that does not follow a straight line.
In this case, t
A) describes a linear function since the value of the gift card decreases by a fixed amount each month, resulting in a straight-line relationship.
B) describes a constant value, which is a special case of a linear function where there is no change over time.
C) The value of the collectible baseball card increases by a constant factor of 1.1 each year, which results in exponential growth. This behavior is best modeled by a nonlinear function.
D) describes a linear function since the value of the investment increases by a fixed amount each week, resulting in a straight-line relationship.
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Danielle and Esther are selling fruit for a fundraiser. Danielle sold 3 boxes of apples and 2 boxes of oranges for $44.50. Esther sold 5 boxes of apples and 4 boxes of oranges for $81.50. How much did a box of oranges cost?
Let x be the cost of a box of apples and y be the cost of a box of oranges.
Danielle : 3x + 2y = 44.5
Esther: 5x + 4y = 81.5
3x + 2y = 44.5 --- 1
5x + 4y = 81.5 --- 2
6x + 4y = 89 --- 3
From 2 and 3, we have:
x = 7.5
Subsitute x = 7.5 into 1
3(7.5) + 2y = 44.5
2y = 22
y = 11
Therefore, a box of oranges costs 11 dollars
Find the measure of angle x.
155° X x
x = [?]
? "
Answer:
x = 155°
Step-by-step explanation:
This is called a vertically opposite angle.
Marcel made an error when he used the distributive property to write an equivalent expression. which sentence describes the error? 32x−16====(8x⋅4)−(8⋅2)8x(4−2)8x(2)16x clear check both terms aren’t multiplied by 8x, so 8x can’t go in front of the parentheses. 8x(2) does not equal 16x. 32x does not equal 8x⋅4. 32x and 16 have no factors in common
Answer:
I think he made a mistake in the first one
Step-by-step explanation:
Marcel made an error which is both terms aren’t multiplied by 8x, so 8x can’t go in front of the parentheses" option (A) is correct.
What is distributive property?The distributive property is the property that expresses the distributive law of algebraic multiplication. Similarly, in polynomial expression we can use the distributive property, for example, we can write a(c+b) in the form of (ac+bc).
The expression is:
= 32x - 16
= 8x(4) - 2(8)
= 8(4x - 2)
The error is "both terms aren’t multiplied by 8x, so 8x can’t go in front of the parentheses"
Thus, Marcel made an error which is both terms aren’t multiplied by 8x, so 8x can’t go in front of the parentheses" option (A) is correct.
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Jack has $15,000 to invest. If he invests two-thirds of it into a high-yield savings account with an annual interest rate of 8%, compound continuously, and the other third in a regular savings account at 6% simple interest, how much does Jack earn after one year?
Based on the amounts that Jack invested into the different investment vehicles, the amount Jack earns a year would be $1,132.87.
How much does Jack earn from the high-yield savings account?The amount invested is:
= 2 / 3 x 15,000
= $10,000
Amount after a year:
= Amount x e ^ (rate x time)
= 10,000 x e ⁰.⁰⁸ ˣ ¹
= $10,832.87
How much does Jack make from the regular savings account?Amount invested:
= 1/3 x 15,000
= $5,000
Amount after a year:
= 5,000 x (1 + 6%)
= $5,300
How much did Jack earn in a year:= (10,832.87 + 5,300) - 15,000
= $1,132.87
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Lydia is planning an event for 275 people. She wants to find out the food preferences for the guests, so she surveys 60 guests and discovers that 45 of those guests prefer chicken and 15 prefer fish. What is the sample for the survey?
Answer:
sample size is the number of individuals in the sample and the sample is 60 guests.
Step-by-step explanation:
She wants to find out the food preferences for the guests, so she surveys 60 guests and discover 45 of those guests prefer chicken and 15 prefer fish.
The sample is 60 guests.