Given the equation y = 6sin(2x - 10) + 3
We have the equation:
[tex]y=6\sin(2x-10)+3[/tex]We have to find the amplitude, the period, the horizontal shift and the midline.
The amplitude can be calculated as half the difference between the maximum and minimum value of the function.
The maximum value will happen when the sine is equal to 1 and the minimum when the sine is equal to -1.
We can then calculate the amplitude A as:
[tex]\begin{gathered} A=\frac{y_{max}-y_{min}}{2} \\ A=\frac{6(1)+3-(6(-1)+3)}{2} \\ A=\frac{6+3-(-6+3)}{2} \\ A=\frac{9-(-3)}{2} \\ A=\frac{12}{2} \\ A=6 \end{gathered}[/tex]Now we have to calculate the period.
The period will be equal to the horizontal distance at which the function starts repeating itself (or complete a period).
As we have a sine function we know that:
[tex]\sin(u)=\sin(u+2n\pi)\text{ }n\in Z[/tex]That means that it will repeat itself for any multiple of 2π.
We can calculate the period as:
[tex]\begin{gathered} y(x+2\pi)=y(x+T) \\ 6(2x-10+2\pi)+3=6(2(x+T)-10)+3 \\ 2x-10+2\pi=2(x+T)-10 \\ 2x+2\pi=2x+2T \\ 2\pi=2T \\ T=\pi \end{gathered}[/tex]The period is π.
The horizontal shift will be given by the constant value inside the argument of the sine function. We can ignore the other terms and factors and use only the sine function in this case.
For example, for sin(2x) = 0, this value corresponds to x = 0.
In the case of sin(2x-10) = 0 this corresponds to an x that is 5.
That is because the function has a frequency that is twice as the frequency of the hpure sine function.
If the function wasn't periodice we would see it translated by 10 to the right.
We can calculate the midline as the average of the function.
This average value will be given by the average value of the sine function, which is 0, so we can calculate the midline as:
[tex]y_{avg}=6(0)+3=3[/tex]Answer:
The amplitude is 6.
The period is π.
The horizontal shift is 10 units to the right.
The midline is y = 3.
name the sets of numbers to which the number 62 belongs
62
real numbers (not imaginary or infinity)
rational numbers
Integers ( no fraction, included negative numbers)
Whole numbers (no fraction)
Natural numbers (counting and whole numbers)
Calculate the net price and trade discount (use net price equivalent rate and single equivalent discount rate) for the following: Sony Hd flat-screen list price: 899 chain discount: 5/4 net price: Trade discount
The net price and trade discount for the good is.539.4 and 359.6 respectively.
How to calculate the net price?From the information given, tuw.Sony Hd flat-screen list price is 899 and has a discount: 5/4 net price:
The net price will be:
= List price × (1 - Discount rate)
= 899 × (1 - 40%)
= 899 × 60%
= 899 × 0.6
= 539.4
The trade discount will be:
= List price - Net price
= 899 - 539.4
= 359.6
Learn more about discount on:
brainly.com/question/7459025
#SPJ1
Complete question:
Calculate the net price and trade discount (use net price equivalent rate and single equivalent discount rate) for the following: Sony Hd flat-screen list price: 899 chain discount: 5/4 net price and discount 40%
Is my answer correct help me please
Pls help me!!!!!!!!!
2. 4+ (-10)
3. 3+(-15)
4.2+5
5. (-10)+(-5)
Kaylee read 1 book in 4 months. What was her rate of reading, in books per month? Give your answer as a whole number or a FRACTION in simplest form.On the double number line below, fill in the given values, then use multiplication or division to find the missing value.
If Kaylee read 1 book in 4 months, this means that in 1 month, she read 1/4 of the book. We can see this in the following figure:
An architect is designing the roof for a house what is the height of the roof?
An architect is designing the roof for a house
what is the height of the roof?
From the diagram,
We have that tan 30 = h/ 12
0.5774 = h/ 12
cross-multiply,
h = 12 x 0.5774
h = 6.9288 feet
Find the oth term of the geometric sequence 5,--25, 125,
Given the geometric progression below
[tex]5,-25,125,\ldots[/tex]The nth term of a geometric progression is given below
[tex]T_n=ar^{n-1},\begin{cases}a=\text{first term} \\ r=\text{common ratio}\end{cases}[/tex]From the geometric progression, we can deduce the following
[tex]\begin{gathered} T_1=a=5 \\ T_2=ar=-25 \\ T_3=ar^2=125 \end{gathered}[/tex]To find the value of r, we will take ratios of two consecutive terms
[tex]\begin{gathered} \frac{T_2}{T_1}=\frac{ar}{a}=\frac{-25}{5} \\ \Rightarrow r=-5 \end{gathered}[/tex]To find the 9th term of the geometric, we will have that;
[tex]\begin{gathered} T_9=ar^8=5\times(-5)^8=5\times390625 \\ =1953125 \end{gathered}[/tex]Hence, the 9th term of the geometric progression is 1953125
Dave jogs 8 feet per second. Give each rate in miles per hour.
Answer:
Step-by-step explanation:
first find seconds in an hour
60(seconds in a minute) *60(minutes in an hour) = 3600 seconds in an hour
then multiply 8 by 3600 to see how many feet per hour
28,800
we need miles so there are 5280 feet in a mile
28800/5280 is 5.45454545 or 5.455 miles per hour
Please help answer the questions 1-6
The equations for each slope - intercept pair are discussed below.
What is the general equation of a straight line?The general equation of a straight line is -
y = mx + c
Where -
[m] is the slope of the line.
[c] is the y - intercept
Given are the slopes and [y] intercepts of some lines.
We can write the equation for each pair as discussed above in the general equation.
[1] → The equation of the straight line with slope [m] = -3 and y- intercept
[c] = 4 will be → y = -3x + 4.
[2] → The equation of the straight line with slope [m] = 0 and y- intercept
[c] = 0 will be → y = 0.
[3] → The equation of the straight line with slope [m] = 7/3 and y- intercept [c] = 3 will be → y = 7/3x + 3.
[4] → The equation of the straight line with slope [m] = -1/2 and y- intercept [c] = 5 will be → y = -1/2x + 5.
[5] → The equation of the straight line with slope [m] = -1/4 and y- intercept [c] = 4 will be → y = -1/4x + 4.
[6] → The equation of the straight line with slope [m] = -4/3 and y- intercept [c] = 1 will be → y = -4/3x + 1.
Therefore, the equations for each slope - intercept pair are discussed above.
To solve more questions on straight line graphs, visit the link below-
https://brainly.com/question/27730503
#SPJ1
Number 14. Need help finding the area of the shaded area. Forgot how to solve it. Please help.
To find the area of the shaded region we need to calculate the area of the square and subtract to it the area of the circle.
The area of a square is calculated as follows:
[tex]A=b^2[/tex]where b is the length of each side.
Substituting with b = 16 cm (given that the radius of the circle is 8 cm, then the length of the square's side is 2x8 = 16 cm):
[tex]\begin{gathered} A_1=16^2 \\ A_1=256\operatorname{cm}^2 \end{gathered}[/tex]The area of a circle is calculated as follows:
[tex]A=\pi r^2[/tex]where r is the radius of the circle.
Substituting with r = 8 cm, we get:
[tex]\begin{gathered} A_2=\pi\cdot8^2 \\ A_2=\pi\cdot64 \\ A_2\approx201\operatorname{cm}^2 \end{gathered}[/tex]Finally, the area of the shaded region is:
[tex]\begin{gathered} A_3=A_1-A_2 \\ A_3=256-201 \\ A_3=55\operatorname{cm}^2 \end{gathered}[/tex]SOMEONE please help.
The class interval of the median is 1 ≤ x ≤ 2 and the mean of the distribution is 1.8
How to determine the class interval of the median class?From the question, we have
Number of students = 30
This represents the total frequency
So, we have
Total frequency = 30
The median position is then calculated as
Median = (Total frequency + 1)/2
Substitute the known values in the above equation
So, we have
Median = (30 + 1)/2
Evaluate
Median = 15.5th
The 15.5th element is located in the second class
i.e. the class with the interval 1 ≤ x ≤ 2
So, the class interval in this case is 1 ≤ x ≤ 2
The mean of the distributionTo do this, we start by calculating the average of the class interval
This is represented as
0 ≤ x ≤ 1 ⇒ 0.5
1 ≤ x ≤ 2 ⇒ 1.5
2 ≤ x ≤ 3 ⇒ 2.5
3 ≤ x ≤ 4 ⇒ 3.5
So, we have
x f
0.5 6
1.5 13
2.5 7
3.5 4
The mean is calculated as
Mean = ∑fx/∑f
So, we have
Mean = (0.5 * 6 + 1.5 * 13 + 2.5 * 7 + 3.5 * 4)/30
Evaluate
Mean = 1.8
Hence, the mean value is 1.8
Read more about grouped frequency at
https://brainly.com/question/16410093
#SPJ1
If m ll n, which statement is true? 3 1 5 2. 4 6 O A.
∠1 and ∠2 have equal measures because they are corresponding angles
Write the equation in point slope and slope intercept form of a line that passes through the given point and has given slope m.(5,-6);m=-1
Given:
A line passes through the point,
[tex](x_1,y_1)=(5,-6)[/tex]The slope of the line is m = -1.
The objective is to find the equation of the line in point-slope and slope-intercept form.
Explanation:
To find equation in point-slope form:
The general formula of point-slope form is,
[tex]y-y_1=m(x-x_1)\text{ . . . . . . ..(1)}[/tex]On plugging the given values in equation (1),
[tex]\begin{gathered} y-(-6)=-1(x-5) \\ y+6=-x+5\text{ . . . . . .(2)} \end{gathered}[/tex]To find the equation in slope-intercept form,
The general formula of slope-intercept form is,
[tex]y=mx+b\text{ . . . . (3)}[/tex]On further solving the equation (2),
[tex]\begin{gathered} y+6=-x+5 \\ y=-x+5-6 \\ y=-x-1 \end{gathered}[/tex]Hence,
The equation of the line in point-slope form is y+6 = -x+5.
The equation of the line in slope-intercept form is y = -x-1.
The sum of three
numbers is 18. The largest
is 5 times the smallest,
while the sum of the
smallest and twice the
largest is 22. Write a
system of equations to find
the numbers, then solve.
The required system of equation is x+y+z=18, z=5x, x+2z=22 and the required values of x=2, y=6 and z=10 by using the substitution method of solving equations and according to given conditions: The sum of three numbers is 18. The largest is 5 times the smallest, while the sum of the smallest and twice the largest is 22. .
What is system of equation?A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, also known as a system of equations or an equation system.
What is substitution method?The algebraic approach to solving simultaneous linear equations is known as substitution method. The value of one variable from one equation is substituted in the other equation in this method, as the name implies.
x+y+z=18
z=5x
x+2z=22
x+10x=22
x=2
y=6
z=10
The required system of equations is x+y+z=18, z=5x, x+2z=22, with the required values of x=2, y=6, and z=10 when solving equations using the substitution method under the conditions stated: Three numbers added together equal 18. The sum of the smallest and twice-largest numbers is 22, while the largest is five times the smallest.
To know more about system of equation,
https://brainly.com/question/10413253?referrer=searchResults
#SPJ13
what should be done to solve the following e q u a t i o n x + 8 equals 4
we have the equation
x+8=14
step 1
subtract 8 both sides
x+8-8=14-8
x=6
therefore the answer is the last option
JCPenney sells jeans for $49.50 that cost $38.00. What is the percent markup on cost? Check the cost.
The percent markup of the jeans is 30.2%
How to calculate the markup on cost ?
The selling price of the jeans is $49.50
The cost price is $38
Markup can be described as the difference between the selling price and the cost price of a product
The markup can be calculated by subtracting the cost price from the selling price
= 49.50 - 38
= 11.5
The percent markup can be calculated as follows
11.5/38 × 100
= 0.302 × 100
= 30.2%
Hence the percent markup is 30.2%
Read more on percent markup here
https://brainly.com/question/28949918
#SPJ1
个 == CR Algebra 1 B (GP) 21-22 / 8:Radical Expressions and Equations 104 6 2 -10-8-6 -4 - 2 0 N 4 6 8 10 2 -4 6 -8 -10 Match the graph with its function by translating the graph of y = Vx. 3. O y = √x-1+7 O y = x-7+1 = 7 O O y=√x+1+7 O y = x+7+1 Search the web and Windows a
SOLUTION
The transformation of the function
[tex]y=\sqrt[]{x}[/tex]To give the graph in the question is as follows.
The graph is move to the left from the origin by 1 unit on the x-axis, which is to add 1 to x, we have
[tex]y=\sqrt[]{x+1}[/tex]Also,
The graph is the move upward along the y-axis by 7 unit, which is addition of 7 to the function
Then, the equations becomes
[tex]y=\sqrt[]{x+1}+7[/tex]Therefore
The function that produce the graph in the image is
y = (√x+1) + 7
Tools Pencil Guideline Eliminator Sticky Notes Formulas Graphing Calculator Graph Paper Х y 5 Clear Mark 3 -4.5 5 -9.5 7 - 14.5 9 - 19.5 What are the slope and the y-intercept of the graph of this function? A Slope = 2, y-intercept = -4.5 5 B Slope = y-intercept = 3 2 © Slope = 2, y-intercept = -5 D Slope = 2 5 y-intercept = 3
Explanation:
The equation for a line in the slope-intercept form is:
[tex]y=mx+b[/tex]Where 'm' is the slope and 'b' is the y-intercept.
We can find both with only two points from the line. The slope is:
[tex]m=\frac{\Delta y}{\Delta x}=\frac{y_1-y_2}{x_1-x_2}[/tex](x1, y1) and (x2, y2) are points on the line.
With only one of these points, once we know the slope, we can find the y-intercept by replacing x and y by the point. For example:
[tex]y_1=mx_1+b[/tex]And then solve for b.
In this problem we can use any pair of points from the table. I'll use the first two:
• (3, -4.5)
,• (5, -9.5)
The slope is:
[tex]m=\frac{-4.5-(-9.5)}{3-5}=\frac{-4.5+9.5}{-2}=\frac{5}{-2}=-\frac{5}{2}[/tex]And the y-intercept - I'll use point (3, -4.5) to find it;
[tex]\begin{gathered} -4.5=-\frac{5}{2}\cdot3+b \\ -4.5=-\frac{15}{2}+b \\ b=-4.5+\frac{15}{2}=-\frac{9}{2}+\frac{15}{2}=\frac{6}{2}=3 \end{gathered}[/tex]Answer:
• Slope: -5/2
,• y-intercept: 3
The correct answer is option B
Referring to the figure, the polygons shown are similar. Findthe ratio (large to small) of their perimeters and areas.
SOLUTION
Consider the image below
The ratio of the side is given by
[tex]\begin{gathered} \text{large to small} \\ \frac{\text{large}}{small}=\frac{length\text{ of the side of the large triangle}}{Length\text{ of the side of small triangle }}=\frac{10}{5}=\frac{2}{1} \\ \\ \end{gathered}[/tex]Since the ratio of the side is the scale factor
[tex]\text{the scale factor =}\frac{2}{1}[/tex]hence The raio of the perimeters is the scale factor
Therefore
The ratio of their parimeter is 2 : 1
The ratio of the Areas is square of the scale factor
[tex]\text{Ratio of Area =(scale factor )}^2[/tex]
Hence
[tex]\begin{gathered} \text{ Since scale factor=}\frac{2}{1} \\ \text{Ratio of Area=}(\frac{2}{1})^2=\frac{2^2}{1^2}=\frac{4}{1} \\ \text{Hence} \\ \text{Ratio of their areas is 4 : 1} \end{gathered}[/tex]Therefore
The ratio of their Areas is 4 :1
What is the 100th term of the arithmetic sequence below? 2x, 3x + 4, 13x - 1
We are given an arithmetic progression and are requested to find the 100th term of the progression. We need to find the value of x from the question by equating differences.
[tex]\begin{gathered} T_2-T_1=T_3-T_2 \\ 3x+4-2x=13x-1-(3x+4)=13x-1-3x-4 \\ x+4=10x-5 \\ \text{Collecting like terms gives us:} \\ 10x-x=4+5 \\ 9x=9 \\ x=1 \end{gathered}[/tex]Now we will find the actual value of our terms.
[tex]\begin{gathered} T_1=a=2(1)=2 \\ T_2=3(1)+4=7 \\ T_3=13(1)-1=12 \\ \text{Therefore,} \\ \text{ d = }T_2-T_1=T_3-T_2 \\ d=7-2=12-7=5 \end{gathered}[/tex]Common difference, d = 5
Lastly, we employ our AP formula to find the 100th term.
[tex]\begin{gathered} Tn=a+(n-1)d \\ T_{100}=2+(100-1)5 \\ T_{100}=2+(99)5=497 \end{gathered}[/tex]The 100th term is 497
two slices of dans famous pizza have 230 calories how many calories would you expect to be in 5 slices of pizza
We can answer this question, using proportions. We can see it graphically as follows:
Then, we have that 5 slices will have 575 calories.
10)BONUSKelll walks into science class and they have 6 hershey kisses and 6 reese cups on a scale that reads82.4 ounces. She wants some chocolate so she eats 2 hersey kisses and 1 reese cup and now thescale reads 63.8 ounces.a) Define your variables and set up a system of equations.
Leah, this is the solution:
Variables:
Let x to represent the weight of one Hershey kiss
Let y to represent the weight of one Reese cup
System of equations:
6x + 6y = 82.4
4x + 5y = 63.8
______________
Let's multiply the second equation by - 3/2, therefore:
6x + 6y = 82.4
-6x - 15y/2 = -95.7
________________
-15/2 + 6 = -3/2
_________________
-3y/2 = -13.3
Dividing by -3/2 at both sides:
-3y/2 / -3/2 = -13.3 / -3/2
y = 8.87
______________
Replacing y in the first equation and solving for x:
6x + 6 * 8.87 = 82.4
6x + 53.22 = 82.4
Subtracting 53.22 at both sides:
6x +53.22 - 53.22= 82.4 - 53.22
6x = 29.18
Dividing by 6 at both sides:
6x/6 = 29.18/6
x = 4.86
_________________
In conclusion, one Hershey kiss weights 4.86 ounces and one Reese cup weights 8.87 ounces.
Please helpMe if your good with mathI appreciate it thank u!
Let x be the number of tshirt sold.
A/q,
[tex]\begin{gathered} 5x+40=125 \\ \Rightarrow5x=85 \\ \Rightarrow x=17 \end{gathered}[/tex]Thus the number of tshirt sold is 17.
A quadrilateral has two angles that measure 110° and 120°. The other two angles are in aratio of 6:7. What are the measures of those two angles?andSubmit
From the problem, two angles in a quadrilateral are 110 and 120 degrees.
Note that the sum of interior angles in a quadrilateral is 360 degrees.
Then the sum of the other two angles will be :
[tex]360-(110+120)=130[/tex]And the angles are in a ratio of 6 : 7.
Multiply the ratio by a common factor "x"
[tex]6x\colon7x[/tex]Then take the sum and equate it to 130 degrees.
[tex]6x+7x=130[/tex]Solve for x :
[tex]\begin{gathered} 13x=130 \\ x=\frac{130}{13} \\ x=10 \end{gathered}[/tex]Now, substitute x = 10 to the ratio.
[tex]\begin{gathered} 6(10)\colon7(10) \\ 60\colon70 \end{gathered}[/tex]Therefore, the other two angles are 60 and 70 degrees.
ANSWER :
60 and 70 degrees
In Exercises 25–26, the domain of each piecewise function is (-⬁,⬁). a. Graph each function. b. Use the graph to determine the function’s range.
We have to graph this piecewise function.
It will be two horizontal lines that change when x = -1: to the left it will be y = 5, as x ≤ 1, and to the right, it will be y = -3.
We can see it graphed as:
b) The range is the set of values that f(x) takes for the domain for which it is defined.
We can see that f(x) only takes two values: y = -3 and y = 5, so the set {-3,5} is the range of f(x).
Answer:
a) Graph
b) Range = {-3, 5}
Find the slope of the line that goes through the given points 9,7 and 8,7
we have the points
(9,7) and (8,7)
Note that: The y-coordinates of both points are equal
that means
we have a horizontal line
therefore
The slope is zeroUse Polya's four-step problem-solving strategy and the problem-solving procedures presented in this section to solve the following exercise.A shirt and a tie together cost $68. The shirt costs $30 more than the tie. What is the cost of the shirt (in dollars).
Let x and y be the cost of a shirt and a tie, respectively; therefore, the two equations are
[tex]\begin{gathered} x+y=68 \\ \text{and} \\ x=30+y \end{gathered}[/tex]We have two variables and two equations; we need to solve the system of equations to find the values of x and y.
Solve using the substitution method.
Use the second equation into the first equation, as shown below
[tex]\begin{gathered} x=30+y \\ \Rightarrow(30+y)+y=68 \\ \Rightarrow30+2y=68 \\ \Rightarrow2y=68-30=38 \\ \Rightarrow y=\frac{38}{2} \\ \Rightarrow y=19 \end{gathered}[/tex]Now, use this value of y in the second equation
[tex]\begin{gathered} y=19 \\ \Rightarrow x=30+y=30+19 \\ \Rightarrow x=49 \end{gathered}[/tex]Remember that x is the cost of a shirt and y is the cost of a tie. Therefore, the answers are
Cost of a shirt: $49
Cost of a tie: $19
One can verify the answer by noticing that a shirt and a tie cost $49+$19=$68, and that a shirt costs $30+$19=$49
Elisa has 24 black and white photographs and 72 photographs that are in color. She is arranging the photographs in an album and wants to contain the same combination of color and black and white photographs. What is the greatest number of pages elisa can fill with photographs
you are running a fuel economy study. one of the cars you find where blue
Answer:
Explanation:
For Blue Car:
Distance = 33 & 1/2 miles
Gasoline = 1 & 1/4 gallons
For Red Car:
Distance = 22 & 2/5 miles
Gasoline = 4/5 gallon
To determine the rate unit rate for miles per gallon for each car, we use the following formula:
[tex]Unit\text{ Rate = }\frac{\text{Distance}}{\text{Gasoline consumption}}[/tex]First, we find the unit rate for blue car:
[tex]\begin{gathered} \text{Unit Rate=}\frac{33\text{ }\frac{1}{2}\text{ miles}}{1\text{ }\frac{1}{4}\text{ gallons}} \\ \end{gathered}[/tex]Convert mixed numbers to improper fractions: 33 & 1/2 = 67/2 and 1 & 1/4 = 5/4
[tex]\begin{gathered} \text{Unit Rate = }\frac{\frac{67}{2}}{\frac{5}{4}} \\ \text{Simplify and rearrange:} \\ =\frac{67(4)}{2(5)} \\ \text{Calculate} \\ =\frac{134\text{ miles}}{5\text{ gallon}}\text{ } \\ or\text{ }26.8\text{ miles/gallon} \end{gathered}[/tex]Next, we find the unit rate for red car:
[tex]\begin{gathered} \text{Unit Rate = }\frac{22\frac{2}{5}}{\frac{4}{5}} \\ \text{Simplify and rearrange} \\ =\frac{\frac{112}{5}}{\frac{4}{5}} \\ =\frac{112(5)}{5(4)} \\ \text{Calculate} \\ =28\text{ miles/gallon} \end{gathered}[/tex]Therefore, the car that could travel the greater distance on 1 gallon of gasoline is the red car.
