It has a period of 2pi
the equation to find the period of a sin/cos function is
[tex]period = \frac{2\pi}{b} [/tex]
y = -2 sin(x) has a normal period of 2pi because the b value in this equation isn't stated, making it equal to 1
the basic equation for a sin function is
[tex]y = a \: \sin(b(x - c) ) + d[/tex]
4sin2xcosx+sin3x=sin<3,14+x>
The solution to 4sin2xcosx+sin3x=sin<3,14+x> is x = nπ, where n = ±{0, 0.5, 1, 1.5....}
How to solve the equation?The equation is given as:
4sin2xcosx+sin3x=sin<3,14+x>
Rewrite properly as:
4sin(2x)cos(x)+sin(3x)=sin(3.14+x)
Next, we split the equation as follows:
y = 4sin(2x)cos(x)+sin(3x)
y = sin(3.14+x)
Next, we plot the graph of both equations (see attachment)
From the attached graph, we have:
x = nπ, where n = ±{0, 0.5, 1, 1.5....}
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For what values of x does f(x) = 0?
O-4, 0, 2
O-2, 0, 4
O-5, 0, 17
O-17, 0,5
The values of x does f(x) = 0 will be -4,0,2.Option A is corect.
What is a graph?A diagram depicting the relationship between two or more variables, each measured along with one of a pair of axes at right angles.
The graph shows the cubic polynomial equation found as;
⇒(x+4)(x)(x-2)
The points f(x) = 0 is;
⇒(x+4)(x)(x-2)
⇒(-4+4)(0)(2-2)
⇒0
The values of x does f(x) = 0 will be -4,0,2.
Hence, option A is corect.
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solve simulteneusly equation 6p-4r=4 and p-2r=5
Answer:
r = - 3.25, p = -1.5
Step-by-step explanation:
→ Rearrange p - 2r = 5
p = 5 + 2r
→ Substitute into 6p - 4r = 4
6 ( 5 + 2r ) - 4r = 4
→ Expand
30 + 12r - 4r = 4
→ Simplify and solve
r = - 3.25
→ Substitute into p - 2r = 5
p + 6.5 = 5
→ Minus 6.5 from both sides
p = -1.5
Samuel and 4 of his friends entered a chili cook-off. The rules allowed them
to spend a certain amount on supplies. If each person spent $15 for
supplies, how much did they spend in all?
Answer:
$75
[It is easy to say $60, but don't forget to add Samuel to the total]
Step-by-step explanation:
There are 5 people in total:
1 Samuel
4 friends
5 people who can spend up to $15 each.
(5 people)*($15/person) = $75 total spent on supplies
identify the slope and y-intercept of the function y=5x-10
Answer:
slope = 5 , y- intercept = - 10
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = 5x - 10 ← is in slope- intercept form
with slope m = 5 and y- intercept c = - 10
The slope and y intercept of the function y = 5x - 10 is 5 and -10 respectively.
What is Slope?Slope of a line is the ratio of the change in y coordinates to the change in the x coordinates of two points given.
Equation of a line in slope intercept form is,
y = mx + b,
where m is the slope of the line and b is the y intercept,
y intercept is the y coordinate of the point where it touches the Y axis.
Given equation is y = 5x - 10.
Comparing with slope intercept form,
m = 5 and b = -10
Hence the slope of the line is 5 and y intercept is -10.
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Step 1: 4 x minus x + 2 + 6 = 6 x + 16
Step 2: 3 x + 8 = 6 x + 16
Step 3: 8 minus 16 = 6 x minus 3 x
Step 4: Negative 8 = 3 x
Step 5: Negative StartFraction 8 Over 3 EndFraction = x
Jorge verifies his solution by substituting Negative StartFraction 8 Over 3 EndFraction into the original equation for x. He determines that his solution is incorrect. Which best describes Jorge’s error?
Jorge distributed incorrectly.
Jorge incorrectly combined like terms.
Jorge incorrectly applied the addition and subtraction properties of equality.
Jorge incorrectly applied the multiplication and division properties of equality
The error from Jorge's arithmetic operation on the given algebraic expression is that he distributed it incorrectly.
What is an algebraic expression?An algebraic expression is a mathematical equation that is made up of variables together with arithmetic operations.
From the given expression, we have:
4x - x + 2 + 6 = 6x + 16
Add similar elements together;
3x + 8 = 6x + 16
Using distributive property, subtract 8 from both sides:
3x + 8 - 8 = 6x + 16 - 8
3x = 6x + 8
Simplify
3x-6x = 8
-3x = 8
Divide both sides by -3
-3/-3x = -8/3
x = -8/3
So from Jorge's calculation, because he distributed incorrectly, we can conclude that could be his error.
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What is the value of x
Enter your answer in the box
X= _ degrees
Answer:
x = 55 degrees
Step-by-step explanation:
The sum of the internal angles of a triangle results in 180°
x + 50° + 75° = 180°
x + 125° =180°
x = 180° - 125°
x = 55°
Which statement describes the graph?
<-10
10-
-10+
10
OA. The graph crosses the y-axis at (0, -5), decreasing from x = -10 to
x= -2 and increasing from x= -2 to x = 10.
B. The graph crosses the y-axis at (0, -5), decreasing from x = -10 to
x = 0 and remaining constant from x = 0 to x = 10.
C. The graph crosses the y-axis at (-6, 0), decreasing from x= -10 to
x = -2 and remaining constant from x=-2 to x = 10.
OD. The graph crosses the y-axis at (0, -5), decreasing from x = -10 to
x= -2 and remaining constant from x=-2 to x= 10.
Correct answer is option D.
The graph crosses the y-axis at (0, 5), increasing from x = -10 to x = 2 and remaining constant from x = 2 to x = 10.
What is Increasing Function?A function f(x) is said to be increasing on an interval I if for any two numbers x and y in I such that x < y, we have f(x) ≤ f(y).
For this case, the first thing you should observe is that you have a different function in two distinct intervals.
We have then:
For [-10, 2]:
The linear function has a positive slope, therefore it grows and cuts the y-axis at the point (0, 5)
For [2, 10]:
We have a constant function whose equation is:
y = 5
Thus, the correct Answer is:
D. The graph crosses the y-axis at (0, 5), increasing from x = -10 to x = 2 and remaining constant from x = 2 to x = 10.
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Find the measure of angle RPQ.
Answer:
20°
Step-by-step explanation:
Measure of QR is 180 - 108 = 72°
then using intercepted arc - external angle theorem:
angle RPQ then equals 1/2 ( 108 - 72) = 20 °
It takes 1.5 seconds for a grandfather clock's pendulum to swing from left (initial position) to right, covering a horizontal distance of 10 inches. which function models the horizontal displacement as a function of time in seconds?
The function that models the horizontal displacement as a function of time in seconds is y = 5cos(2π/3 x)
How to model the function?The given parameters are:
Time, t = 1.5 secondsHorizontal distance, h = 10 inchesStart by calculating the amplitude, A using:
A = h/2
This gives
A = 10/2
A = 5
Next, we calculate the period using:
B = π/t
This gives
B = π/1.5
Evaluate
B = 2π/3
The pendulum is at the middle.
So, it has no vertical displacement
The function is then represented as:
y = Acos(Bx)
This gives
y = 5cos(2π/3 x)
Hence, the function that models the horizontal displacement as a function of time in seconds is y = 5cos(2π/3 x)
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HELPPP i need to find standard form and general form, please help
The equation in slope-intercept form is y = 13/8x -17/8 and the equation in standard form is 13x -8y = 17
Equation of a line
A line is the shortest distance between two points. The equation of a line in slope-intercept form is y = mx + b while as a standard notation is Ax+By = C
Given the coordinate points (-3, -7) and (5, 6)
Determine the slope
Slope = 6-(-7)/5-(-3)
Slope = 13/8
For the y-intercept
6 = 13/8(5) + b
6 = 65/8 + b
b = 6 - 65/8
b = -17/8
The equation in slope-intercept form is y = 13/8x -17/8
Write in standard form
Recall y = 13/8x - 17/8
Multiply through by 8
8y = 13x - 17
-13x + 8y = -17
13x -8y = 17
Hence the equation in standard form is 13x -8y = 17
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Draw a line representing the “rise” and a line representing the “run” of the line. State the slope of the line in simplest form.
The slope of the line in its simplest form is 3.
The slope of a line is [tex]Slope=\frac{Rise}{Run}[/tex].
We need to find the slope of the line in its simplest form.
What is the slope?In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line. The slope is often denoted by the letter m; there is no clear answer to the question of why the letter m is used for slope.
Select any two points on the line like A and B.
From the below figure it is clear that
Rise = Change in y = -2-(-5) = 3
Run = Change in x = 9-0 = 9
Now, [tex]\frac{9}{3} =3[/tex]
Therefore, the slope of the line in simplest form is 3.
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g Lovely Lawns, Inc., intends to use sales of lawn fertilizer to predict lawn mower sales. The store manager estimates a probable six-week lag between fertilizer sales and mower sales. The pertinent data are: PeriodFertilizer SalesNumber of Mowers Sold 11.915 21.612 31.713 41.915 52.116 61.813 71.914 81.713 91.815 101.412 111.814 121.714 131.714 141.612 a. Determine the correlation between the two variables.
The correlation between variables (r) = 0.959, and signifies a positive relationship between the variables.
What is correlation?The correlation of two pairs of data values tells about the degree of movement(along or opposite) that can occur in one of the data values when other data value is increased or decreased respectively.
The pertinent data are:
Period Fertilizer Sales Number of Mowers Sold
1 1.6 12.0
2 1.3 10.0
3 1.8 13.0
4 2.0 15.0
5 2.2 15.0
6 1.5 11.0
7 1.6 12.0
8 1.4 10.0
9 1.8 13.0
10 1.4 10.0
11 1.9 15.0
12 1.4 11.0
13 1.7 14.0
14 1.4 13.0
To determine the correlation between the two variables
Regression equation ( y ) = a + bx
y = dependent variable ( mower )
x = independent variable ( fertilizer)
a = intercept point ( y-axis and regression line )
b = slope ( regression line )
From the given data;
N = 14 , Σ x = 22.8,
Σy = 131, Σy^2 = 1269,
Σx^2 = 38.18, (Σx)^2 = 519.84
Σxy = 219.8, (Σy)^2 = 17161
Hence, The correlation between variables (r) = 0.959, and signifies a positive relationship between the variables.
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Question 4(Multiple Choice Worth 1 points)
(02.04 LC)
Write the equation of a line that goes through point (4, 0) and has an undefined slope.
Ox=4
Ox=0
Oy=4
Oy=0
Answer:
Ox=4 is the answer for the question
Exercise 1.2 1 Round each of these numbers to the degree of accuracy shown in brackets. a) 7765 (nearest hundred). b) 1099 (nearest thousand). c) 487 (nearest ten) d) 34 766 (nearest hundred) e) 45620000 (nearest million please help me
Answer:
a. 700
b. 1000
c. 80
d. 700
e.
The quotient of 7 more than three times a number m and the number 27 less than n
An expression is defined as a set of numbers, variables, and mathematical operations. The given statement can be modeled as (3m+7)/27 < n.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The given statement "The quotient of 7 more than three times a number m and the number 27 less than n" can be modeled as an algebraic expression as shown below.
(3m+7)/27 < n
Hence, the given statement can be modeled as (3m+7)/27 < n.
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A triangular prism and two nets are shown:
A right triangular prism is shown with two nets. The triangular base of the prism has height 5 inches, base 12 inches, and hypotenuse 13 inches. The length of the prism is 18 inches. Net A has 3 rectangles having dimensions 5 by 18, 18 by 12, and 18 by 13, and two triangles having legs 12 inches and 5 inches. Net B has 3 rectangles having dimensions 5 by 13, 13 by 12, and 13 by 18, and two triangles having legs 5 inches and 12 inches.
Which is the correct net of the prism and what is the surface area of the prism?
The surface area of the triangular prism is 480 square inches and net A is the correct net of the prism
What is a triangular prism?When a triangle is, stretch it out to produce a stack of triangles, one on top of the other. A triangular prism is a name given to this novel 3D object.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
We have given a triangular prism with its net.
After analyzing the correct net will be net A because the inner rectangle length should be 14 in not 13 in.
The surface area of the triangular prism:
[tex]= 2[\dfrac{1}{2}(5\times12)]+ 5\times 14+ 12 \times 14+ 13\times 14[/tex]
After solving:
The surface area = 480 square inches.
Thus, the surface area of the triangular prism is 480 square inches and net A is the correct net of the prism
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At a gymnastics meet, twenty gymnasts compete for first, second, and third place.
How many ways can first, second, and third place be assigned
There 6840 ways can first, second, and third place be assigned.
What is Permutation?A permutation is a mathematical technique that determines the number of possible arrangements in a set when the order of the arrangements matters.
We will use the concept of permutation
[tex]^{20}P_3[/tex]= 20!/ (20-3)!
= 20*19*18*17!/ 17!
= 6840 ways.
Hence, there are 6840 ways.
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Find the value of x
Find the value of y
Answer:
x = 9
y = 61
Step-by-step explanation:
let me know if you want an explanation!
A shopkeeper sold a watch for rupees 992 allowing 20% discount find its marked price
Answer:
⇒ Let marked price be Rs.x.
⇒ Discount = 20% of marked price.
⇒ Discount=
100
20
×x=
100
20x
⇒ Selling price = Marked price - Discount.
⇒ 192=x−
100
20x
⇒ 192=
100
80x
⇒ x=
80
19200
=Rs.240
MARK IT AS BRAINLIESTAND FOLLOW ME.Answer:
S.p = 992
discount = 20%
marked price = S. p + discount
= 992 + 20/100*992
= 992 + 198.4
= 1190.4
2(x-4) + 3x-x² for x = 3.
Answer:
-2
Step-by-step explanation:
[tex]2(3-4) +3(3)-3^2\\= 2(-1) + 3(3) -3^2\\= -2 + 9 - 9\\= -2[/tex]
Keiko+has+a+health+insurance+premium+of+$3298+annually. +if+her+employer+pays+90%+of+the+premium,+how+much+does+she+pay+annually?
Answer: $329.8
[tex]3298-(\frac{90}{100} *3298)\\= 3298 - 2968.2\\= 329.8[/tex]
The amount Keiko pays annually is $329.8
To answer the question, we need to know the amount Keiko pays annually
How to calculate how much Keiko pays annually.Since Keiko health insurance premium annually is $3298 and if his employer pays 90% of the premium, we want to know how much Keiko pays.
Since the employer pays 90% of the premium, the employer pays x = 90% of $3298
= 0.9 × 3298
= $2968.2
So, the amount Keiko pays annually is y = premium - amount employer pays, x
= $3298 - $2968.2
= $329.8
So, the amount Keiko pays annually is $329.8
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Please help I will mark brainliest!!!!!
Answer:
#1 (4b + 6a) #2 150y
Step-by-step explanation:
#1 :area of right triangle: ab/2
4x2/2 = 4b
area of rectangle: length x width
2 x 3 = 6a
#2:
5y + 2.5y = 7.5y x 2 = 15y
so the top and bottom are both 15 y
the sides are each 5y so thats 10 y
15x10= 150y
2ⁿ+2ⁿ+2ⁿ+2ⁿ=2¹⁶
value of n?
Answer:
[tex]n = 14[/tex]
Step-by-step explanation:
[tex]~~~~~~~2^n+2^n+2^n+2^n = 2^{16}\\\\\implies 4 \cdot 2^n = 2^{16}\\\\\implies 2^2 \cdot 2^n = 2^{16}\\\\\implies 2^{n+2} = 2^{16}~~~~~~~~~~~~~~~~~~~~~~~~~~~~;[a^m \cdot a^n = a^{m+n}]\\\\\implies n+ 2 = 16\\\\\implies n = 16-2 \\\\\implies n = 14[/tex]
7litres of petrol cos t £3.50. Find the cost of 23 litresof petrol of the same grade.
Answer:
£11.50
Step-by-step explanation:
7litres of petrol cos t £3.50. The cost of 1 liter will be:
= £3.50/7
= £0.50
The cost of 23 litres of petrol of the same grade will be:
= £0.50 × 23
= £11.50
What is the length of the missing side of this triangle?
A
2
B
10
C
50
D
100
top side is 26 bottom side is 24 left side is whats missing
Answer:
B
Step-by-step explanation:
pythagorus theorem
a² + b² = c²
c² - b² = a²
26² - 24² = a²
676 - 576 = a²
a² = 100
a = 10
Solve the following inequality |x| < 13
Answer:
x < 13 and x > -13
Step-by-step explanation:
Split the absolute value equation into 2 equations to account for the positive and negative answers possible with absolute values.
Write the positive value first by removing the absolute value symbol.
x < 13
Flip the inequality and make the 13 negative for the other side.
x > -13
The function f(x) is shown on the graph.
On a coordinate plane, a curved line shaped like a w, labeled f of x, crosses the x-axis at (negative 2, 0), (negative 1, 0), crosses the y-axis at (0, 12), and crosses the x-axis at (2, 0) and (3, 0).
What is f(0)?
The value of f(0) is 12.
What is graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
By considering the graph we have to find f(0) which means we have to find that point where x- coordinate is zero.
Also, which shows that 12 the function f(x)
So, taking the point is (0,12) we can get f(0)= 12.
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Which of the following best describes the slope of the line below?
Select the correct answer. What is the slope-intercept form of the equation of a line that passes through (5, -4) and has a slope of `3/4`? A. `y = -(3)/(4) x -(1)/(4)` B. `y = 3/4 x +(1)/(4)` C. `y = 3/4 x -(31)/(4)` D. `y = 3/4 x +(31)/(4)`
-------------------------------------------------------------------------------------------------------------
Answer: [tex]\textsf{y = 3/4x - 7.75}[/tex]
-------------------------------------------------------------------------------------------------------------
Given: [tex]\textsf{Passes through (5, -4) with a slope of 3/4}[/tex]
Find: [tex]\textsf{The equation in slope-intercept form}[/tex]
Solution: In order to determine the equation we need to first plug the values into the point-slope form, simplify, distribute, and solve for y to get our final result.
Plug in the values
[tex]\textsf{y - y}_1\textsf{ = m(x - x}_1\textsf{)}[/tex][tex]\textsf{y - (-4) = 3/4(x - 5)}[/tex]Simplify the expression and distribute
[tex]\textsf{y + 4 = 3/4(x - 5)}[/tex][tex]\textsf{y + 4 = (3/4 * x) + (3/4 * -5)}[/tex][tex]\textsf{y + 4 = 3/4x - 3.75}[/tex]Subtract 4 from both sides
[tex]\textsf{y + 4 - 4 = 3/4x - 3.75 - 4}[/tex][tex]\textsf{y = 3/4x - 3.75 - 4}[/tex][tex]\textsf{y = 3/4x - 7.75}[/tex]The equation in slope-intercept form that follows the information that was provided is y = 3/4x - 7.75
