The sine and cosine functions with the ordered pairs A(1,4) and B(0,-4) are given as follows:
Sine: f(x) = 4sin(π(x + π/2)).Cosine: g(x) = -4cos(πx).What is the definition of the trigonometric functions?Both the sine and the cosine functions have similar definitions, given as follows:
f(x) = asin(b(x+c))+d.g(x) = acos(b(x+c))+d.The meaning of the coefficients of the functions are presented as follows:
a is the amplitude of the trigonometric function.b: The period of the trigonometric function is of 2π/b.c is the phase shift of the trigonometric function.d is the vertical shift of the trigonometric function.The functions vary between -4 and 4, hence the amplitude is given as follows:
a = 4.
This is the standard oscillation for a trigonometric function with amplitude 4, between -4 and 4, hence the vertical shift is of:
d = 0.
The difference between the x-coordinates of the maximum and the minimum value is half the period, hence the period is of 2 x 1 = 2, and the coefficient b is:
2π/b = 2
b = π.
The cosine function has no phase shift, it just is inverted, as it should assume a value of 4 at x = 0, hence the definition is:
g(x) = -4cos(πx).
The sine function has a phase shift, as it should assume a value of -4 at -π/2, not π/2, hence it is shifted shift π/2 units, hence the definition is:
f(x) = 4sin(π(x + π/2)).
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Find the common difference of the arithmetic sequence -4, 1, 6,...
Hannah borrows $999 from her parents to buy a phone. She will repay $225 to start, and then another $43 per week.
A. Write an equation that can be used to determine w, the number of weeks it will take for Hannah to repay the entire amount.
B. What number of weeks will it take Hannah to repay the entire amount?
A. The equation that can be used to determine the number of weeks is $999=225+42w
B. The number of weeks it will take Hannah to repay is 18weeks
What is linear equation?An equation is a mathematical statement, which has an equal sign (=) between the algebraic expression. Linear equations are the equations of degree 1. It is the equation for the straight line. The solutions of linear equations will generate values, which when substituted for the unknown values, make the equation true. In the case of one variable, there is only one solution. For example, the equation x + 3 = 0 has only one solution as x = -2.
the total amount of money Hannah repaid is $225+$43×w, where w is the number of weeks to repay $43.
therefore $999= $225+$43w
$43w=$ (999+225)
$43w= $1224
divide both side by $43
w= $1224/$43
w= 18 weeks
therefore it will take Hannah 18weeks to repay the money.
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-2(9x-1)=-(x-9) - 7x
Answer:
Step-by-step explanation: 34
Answer:
x = [tex]\frac{11}{26}[/tex]
Step-by-step explanation
Expand 2(9x - 1): 18x - 2
Expand - ( x - 9 - 7x: -8 + 9
Add 2 to both sides 18x - 2 +2 = -8x + 9 + 2
Simplify
18x = -8x + 11
Add 8x to both sides
18x + 8x = -8x + 11 + 8x
Simplify
26x = 11
Divide both sides by 26
[tex]\frac{26x}{26}[/tex] = [tex]\frac{11}{26}[/tex]
Simplify
x = [tex]\frac{11}{26}[/tex]
What’s the unit rate for three dollars for 2 1/2 hours of work
The unit rate for three dollars for 2 1/2 hours of work will be $1.2 using the concept of unitary method.
What is unitary method?The unitary method is a technique that involves determining the value of a single unit and then calculating the value of the requisite number of units based on that value. The term unitary refers to a single or unique entity. As a result, the goal of this approach is to determine values in reference to a single unit. The unitary technique is a method for determining the value of any necessary quantity by first obtaining the value of the unit (one) quantity.
Here,
$3 for 2.5 hours of work,
1 hour will cost $x,
3/2.5=x/1
2.5x=3
x=$1.2
Using the unitary technique, the unit rate for three dollars for two and a half hours of labour will be $1.2.
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fill in the blank, somebody help please. will mark brainliest + 20pt
Answer:
c) divide both sides by 8
hope this helps!
Answer:
Its the 3 option
If x= 1 is a zero of the polynomial function f(x) = 3x³+4x² - 5x-2, which of the following is another zero of f(x)? (6 points)
Answer: x=1 x=-2 x=-1/3
Step-by-step explanation:
[tex]f(x)=3x^3+4x^2-5x-2\\\\3x^3+4x^2-5x-2=0\\\\3x^3+(-3x^2+7x^2)-5x-2=0\\\\(3x^3-3x^2)+7x^2-5x-2=0\\\\3x^2(x-1)+7x^2+(-7x+2x)-2=0\\\\3x^2(x-1)+(7x^2-7x)+(2x-2)=0\\\\3x^2(x-1)+7x(x-1)+2(x-1)=0\\\\(x-1)(3x^2+7x+2)=0\\\\x-1=0\\\\x=1\\\\3x^2+7x+2=0\\\\3x^2+(6x+x)+2=0\\\\(3x^2+6x)+(x+2)=0\\\\3x(x+2)+(x+2)=0\\\\(x+2)(3x+1)=0\\\\x+2=0\\\\x=-2\\\\3x+1=0\\\\3x=-1\\\\[/tex]
Divide both parts of the equation by 3:
[tex]\displaystyle\\x=-\frac{1}{3}[/tex]
determine whether the value is a discrete random variable, continuous random variable, or not a random variable. a. the b. the c. the d. the e. the f. the
a. The amount of rain in City Upper B during April
b. The number of statistics students now reading a book
c. The eye color of people on commercial aircraft flights
d. The time it takes for a light bulb to burn out
e. The square footage of a house
f. The time it takes to fly from City Upper A to City Upper B
a) Continuous random variable
b) Discrete variable
c) Discrete random variable
d) Continuous random variable
e) Continuous random variable
f) Continue random variables
A variable is something whose value changes.
A discrete variable is a variable whose value can be obtained by counting.
Example: Number of students in attendance
Number of red marbles in a jar
A continuous variable is a variable whose value is determined by measurements.
Example: Height of a student in a class
Weight of a student in a class
Random variable : A random variable is a variable whose value is the numerical result of a random phenomenon.
Random variables are marked with capital letters.The probability distribution of a random variable X gives the possible values of X and how probabilities are assigned to those values.Random variables can be discrete or continuous.
A discrete random variable X has a countable number of possible values.
Example: Let X be the sum of two dice.
A continuous random variable X takes all values at a specific number interval.
The probability distribution of a continuous random variable is represented by a density curve. The probability that a continuous random variable X is exactly equal to a number is zero.On the basis of above definition we can easily evaluate that the given examples are random variable, continuous random variable or Discrete variable.
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What integer values satisfy both inequalities? − 2 < x < 3 x < 2
Answer:
-1, 0, 1
Step-by-step explanation:
find slope of points (10,8) and (1,1)
Answer: Slope=7/9
Step-by-step explanation:
m=[tex]y_{2} - y_{1} / x_{2} - x_{1}[/tex]
We can insert your equation to get:
m=8-1/10-1
Simplify:
m=7/9
the weather report sugested that your city temperture increase by -10 degrees and went to 20 degrees celsuis . what is the rise in temperture
Answer:just add if i am right?
Step-by-step explanation:
2 -3 - > › Solve for x 5(x + 2) = 6x +1 X =
Answer:
the is 20 because you need to multiple
10 - 2(4 + 12x)
pls give me an equation answer, not the solution!!!
Answer:
-2 ( 12x - 1 )
Step-by-step explanation:
1) Simplify the equation
To simplify the equation, we have to get rid of any brackets. To do this multiply the term to left of it with everything inside the bracket
-2 x 4 = -8-2 x 12x = -24xNow we can plug these numbers into our equation
2) Collect like terms
The equation we are left with from the previous step would be 10-8-24x
The terms that are similar are 10 and -8.
To collect like terms simplify the terms down to one term
10 - 8 = 23) Find common factor and simplify
What we are left with from the previous step is -24x+2
To find the common factor you have to find a number that goes it both numbers which for 2 and 24 would be 12.
-24x ÷ 2 = -12x2 ÷ 2 = 1We are left with -2 ( 12x - 1 )Hope this helps, have a great day!
Mike's Fitness Center charges $30 per month for a
membership. All-Day Fitness Club charges $22 per month
plus an $80 initiation fee for a membership. After
type your answer...
months will the total amount
paid to the two fitness clubs will be $
type your answer...
For the given fees charged by two fitness clubs , number of months required by two fitness clubs to pay the same total amount is equal to 10 months.
As given in the question,
Number of fitness club = 2
Let 'x' represents the number of months
Charges for a month membership charged by Mike's Fitness center is equal to $30.
Charges for a month membership charged by All-Day Fitness club is equal to $22 plus $80 initiation fee.
Required equation when two clubs have same amount of charges is given by:
30x = 22x + 80
⇒ 30x -22x = 80
⇒ 8x = 80
⇒ x = 10 months
Therefore, number of months required by two fitness clubs to pay the same total amount is equal to 10 months.
The complete question is:
Mikes fitness center charges $30 per month for a membership. All-Day fitness club charges $22 per month plus an $80 initiation fee for a membership. After how many months will the total amount paid to the two fitness clubs be the same?
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14. What is the y-intercept on the equation y = 3x - 6*
Answer:
-6 is the y-intercept, as in the point that crosses the y axis
What is the answer to this question
Answer:
Angle 6 is 78 degrees Angle 7 is 102 degrees
Step-by-step explanation:
Since both lines are parallel, you can assume that Angle 6 plus Angle 7 are a linear pair. Angle 1 corresponds to Angle 5 by the corresponding parts. Angle 5 is congruent to Angle 7 by Vertical angles so therefore Angle 7 is 102. Since Angle 6 + Angle 7 equal 180 degrees, you can put the equation like this,
[tex]Angle 6 + 102 = 108. Angle 6 = 78.[/tex]
Therefore you get your two answers
Graph the equation y = 2x + 2 Iready
Answer:
picture it to pixilated
Step-by-step explanation:
The x-intercept and y-intercept of the equation will be (-1, 0) and (0, 2). The graph is given below.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
x/a + y/b = 1
Where 'a' is the x-intercept of the line and ‘b’ is the y-intercept of the line.
The linear equation is given below.
y = 2x + 2
Convert the equation into intercept form, then we have
y = 2x + 2
y - 2x = 2
y / 2 - x / 1 = 1
The x-capture and y-block of the situation will be (- 1, 0) and (0, 2). The chart is given beneath.
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y + 2.1 > 0.8 Solve the inequality for y.
Simplify your answer as much as possible.
Answer:
y>-1.3
Step-by-step explanation:
y+2.1>0.8
-2.1. -2.1
y>-1.3
Hopes this helps please mark brainliest
Answer:
Hi! Okay so the Inequality form would be: Y>-1.3
and the Interval Notation would be: (-1.3, ∞)
Sorry if it doesn't work btw
Step-by-step explanation:
How many solutions are there to the system of equations shown?
Answer:
There are two solutions. The parabola and the line intersect at two different points.
Answer:
Two
Step-by-step explanation:
there are two slope lines, so you need two equations for each lines.
a 12oz box of cereal costs $3.50. An 18oz box of cereal costs $5.40. Set up equations to determine which is the better buy.
Answer:
12oz box of cereal for $3.50 is the better buy
Step-by-step explanation:
12oz=$3.50
36oz = $10.50
----------------------------
18oz=$5.40
36oz=$10.80
please help me
what ∞ times x = what
An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Infinity is denoted by ∞.
∞ = 1/0
∞ times x is ∞
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Infinity is denoted by ∞.
∞ = 1/0
Now,
∞ times x = ∞
Whatever we multiply with infinity will always give us infinity.
Thus,
∞ times x is ∞
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tickets for a baseball game are $69 for main level seats and $39 for terrace level seats. a group of fifteen friends went to the game and spent a total of $735 for the tickets. how many of main level and how many terrace level tickets did they buy?
Tickets for a ball game are $69 for Primary Level seats and $39 for Porch Level seats. A total of $804 was spent on the tickets by a group of 16 friends who attended the game.
How many tickets were purchased for the Main Level and the Terrace Level?
No. of tickets for the Main Level = X
No. total price = 804 = 39(16 - X) + 69X = 624 - 39X + 69X = 624 + 30X 30X = 804 - 624 = 180 X = 180/30 = 6
No. of Terrace Level Tickets = 16 - X
Main Level Tickets Prace = 69X
Terrace Level Tickets Prace = 39X
Total Price = 804 = 39(16 - X) + 69X = 624 - 39X + 69X =of tickets for the Main Level, X = 6
No. of tickets for the Terrace Level: 16 - X = 16 - 6 = 10 Check:39x10 + 69x6 = 390 + 414 = 804
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Dr. Ellison says that the equation y = -3x + 7 has a solution f(2) = 5/3. Is Dr. Ellison right or wrong?
Dr. Ellison's equation that f(2) = 5/3 is wrong
How to determine if the doctor is right or wrong?From the question, we have the following equation that can be used in our computation:
y = -3x + 7
This equation can be expressed as a function
So, we have
f(x) = -3x + 7
In Dr. Ellison's equation, we have
f(2) = 5/3
This means that
x = 2
So, we have
f(2) = -3 * 2 + 7
Evaluate
f(2) = 1
The calculated value is different from Dr. Ellison's equation
Hence, the solution is wrong
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a box is given a sudden push up a ramp. friction between the box and the ramp is not negligible. which of the following diagrams best represents the directions of the actual forces acting on the box as it moves upward after the push?
For a box given a sudden push up a ramp and the friction between the box and the ramp is not negligible, the diagrams which best represent the directions of the actual forces acting on the box as it moves upward after the push is Option A.
Friction refers to the force of resistance in the relative motion of solid surfaces in contact and sliding or rolling against each other. Frictional forces are affected by the surface texture and the amount of force impelling them together and the angle and position of the object. The actual forces acting on the box will be the normal force (always perpendicular to the surface), weight force (acting downward) and frictional force (acting opposite to the direction of push).
Note: The question is missing options which are provided in the figure.
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A recording studio charges musicians an initial fee of $ 100 to record and album. Studio time also coasts an additional $75 per hour
Write a slope intercept form equitation to model this situation
The linear model that represents the total cost of recording is f(x) = 75x + 50.
The initial fee is $50 for recording an album.
There is an additional cost per hour i.e. $75.
number of hours = x
Now based on the above information, the linear model should be f(x)=75x+50
Here 50 represent the initial fee i.e. equivalent to y-intercept
And, 75 represent the slope
Therefore we can conclude that the linear model that represents the total cost of recording is f(x) = 75x + 50.
A SALESMAN BOUGHT A COMPUTER FROM A MANUFACTURER. THE SALESMAN THEN SOLD THE COMPUTER FOR $15,600 MAKING A LOSS OF 25%. WHAT AMOUNT DID THE SALESMAN PAY THE MANUFACTURER FOR THE COMPUTER?
Answer:
20800 dollars
Step-by-step explanation:
15600*(1/0.75)
=20800
the original price was 20800 dollars.
weirdly expensive computer though
change this root into a power
Answer:
[tex]2^{\frac{4}{3}}[/tex]
Step-by-step explanation:
we do the reverse of what is in the photo
Denominator of exponent is 3 and numerator 4
2^4/3
hopes this helps please mark brainliest
Find the slope of the line on the graph.
Write your answer as a fraction or a whole
number, not a mixed number or decimal.
Answer:
Slope: 1
Step-by-step explanation:
If you take 2 points on the graph, for example (0,3) and (-3,0), you can find the slope. Use the rise over run method (y2-y1/x2-x1). 0-3=-3 and -3-0=-3. After I did that, I divided it: -3/-3=1.
please help me fast!!
Answer:
4(y+3)(y+5)
Step-by-step explanation:
4y^2+32y+60 = 4(y^2+8y+15) = 4(y+3)(y+5)
y^2+8y+15 = (y+3)(y+5)
LCD = 4(y+3)(y+5)
The function h(x)=x² +5 maps the domain given by the set {-2, -1, 0, 1, 2}. Which of the following sets
represents the range of h(x)?
(1) {0, 6, 10, 12)
(2) {5,6,7}
(3) {5, 6,9}
(4) {1, 4, 5, 6,9}
For the given function h(x) = x² +5 ,the domain of the function h(x) maps by the set { -2, -1, 0, 1, 2 } then the range of the function h(x) is given by the set { 5, 6, 9 } .
As given in the question,
Given function is equal to :
h(x) = x² +5
Domain of the function h(x) = x² +5 maps by the set { -2, -1, 0, 1, 2 }
Range of the function h(x) = x² +5 is represented by the set as follow :
Substitute the value x = -2, -1, 0, 1, 2 in the function h(x) = x² +5 we get,
h(-2) = (-2)² + 5
= 9
h(-1) = (-1)² + 5
= 6
h(0) = (0)² + 5
= 5
h(1) = (1)² + 5
= 6
h(2) = (2)² + 5
= 9
Range of the function is represented by the set : { 5, 6, 9 }
Therefore, for the given function h(x) = x² +5 ,the domain of the function h(x) maps by the set { -2, -1, 0, 1, 2 } then the range of the function h(x) is given by the set { 5, 6, 9 }.
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There is a line whose y-intercept is -2 and whose slope is 1. What is its equation in
slope-intercept form?