Which of the following functions is represented in the graph shown?
f(x) = −2cos(2x) + 1
f(x) = −4cos(2x) − 1
f(x) = −2cos(x) − 1
f(x) = −4cos(x) + 1
Answers
Answer:
[tex]f(x)=-2\cos(2x)+1[/tex]
Step-by-step explanation:
Recall the general cosine equation
Function: [tex]f(x)=a\cos(bx+c)+d[/tex]Amplitude: [tex]|a|[/tex]Period: [tex]\frac{2\pi}{|b|}[/tex]Vertical Shift: [tex]-\frac{c}{b}[/tex]Midline: [tex]y=d[/tex]Identify amplitude
[tex]\text{Amplitude}=\frac{\text{Max-Min}}{2}=\frac{3-(-1)}{2}=\frac{4}{2}=2[/tex]
Identify period and solve for b
[tex]\frac{3\pi}{2}-\frac{\pi}{2}=\pi\\ \\\frac{2\pi}{|b|}=\pi\\ \\2\pi=b\pi\\\\2=b[/tex]
Identify midline
[tex]y=d=1[/tex]
Final Equation
[tex]f(x)=-2\cos(2x)+1[/tex]
Also, the reason why [tex]a=-2[/tex] is because a cosine function starts at its maximum, but since it starts at its minimum, the value of [tex]a[/tex] must be negative and causes the wave to flip about the midline.
Related Questions
is the ordered pair (2,1) a solution for
[tex] y \leqslant \frac{3}{2} x + 3 \: show \: your \: work[/tex]
Answers
Answer:
put x= 2 and y = 1
and see this inequality will holds
Help me please help me
Answers
Answer:
m = -10.7
Step-by-step explanation:
m + 4.1 = -6.6
Subtract 4.1 from both sides:
m + 4.1 = -6.6
- 4.1 - 4.1
m = -10.7
Final answer: m = -10.7
Hope this helps!
What are the values y = 3x
Answers
Answer:
when x=1
y= 3 × 1 = 3
when x=2
y= 3 × 2 = 6
when x=3
y= 3 × 3=9
i hope my answer was helpful and please mark me as brainliest
can someone help me w/t this
Answers
Answer:
72 cm²
Step-by-step explanation:
The shaded area is 1/4 of the rectangle, so the unshaded area is 3/4 of the rectangle--3 times the area that is shaded.
__
Unshaded area = 3 × 24 cm² = 72 cm²
The region that is not shaded has an area of 72 cm².
_____
You can mark the midpoint of MR as point S, and draw segment PS. That will divide the rectangle into 4 congruent triangles, one of which is shaded. The congruent triangles all have the same area, so the shaded area is 1/4 of the total area, and the unshaded area is 3 times the shaded area.
42, 53, 54, 55, 59, 59, 60, 63, 65, 67, 70, 71, 73
Mode=
A. 60
B. 59
C. 60.85
Answers
Reason:
The mode is the number that shows up the most.
In this case, it would be 59 because it shows up twice, which is the most compared to any other number (which only show up once).
6. Find the surface area of the regular pyramid shown to the nearest whole number. The figure is (1 point)
not drawn to scale.
11 m
12 m
6√3
01,540 m²
0770 m²
0396 m²
0749 m²
Answers
Area of hexagon
6(1/2BH)3BH3(6√3)(12)216√3m²Now
area of upper 6 triangles
3BH3(11)(12)396m²Total area
396+216√3770.112m²770m²Answer:
770 m²
Step-by-step explanation:
The surface area of a regular pyramid comprises the area of the base (regular polygon) and the area of each of the slanted sides (triangles).
Apothem: The line segment from the center of the regular polygon to the midpoint of one of its sides.
Area of the base
The base of the prism is a regular polygon with 6 sides (hexagon).
[tex]\textsf{Area of a regular polygon}=\sf \dfrac{1}{2}nsa[/tex]
where:
n = number of sidess = side lengtha = apothemGiven:
n = 6s = 12 ma = 6√3Substitute the given values into the formula:
[tex]\begin{aligned}\implies \textsf{Base area}& =\sf \dfrac{1}{2}\cdot 6 \cdot 12 \cdot 6\sqrt{3}\\ & = \sf 216\sqrt{3}\:m^2\end{aligned}[/tex]
Area of one side
The sides of the regular pyramid are congruent triangles.
[tex]\textsf{Area of a triangle} = \sf \dfrac{1}{2} \times base \times height[/tex]
Given:
base = 12 mheight = 11 mSubstitute the given values into the formula:
[tex]\implies \textsf{Area of a triangle} = \sf \dfrac{1}{2} \times 12 \times 11=66\:m^2[/tex]
Total Surface Area
[tex]\begin{aligned}\implies \textsf{Total Surface Area} & = \sf base \: area + 6 \times side \: area\\& = \sf 216\sqrt{3}+6 \cdot 66\\& = \sf 216\sqrt{3}+396\\& = \sf 770\:m^2\:(nearest\:whole\:number)\end{aligned}[/tex]
Diego wondered how far sixth-grade students could throw a ball. he decided to collect data to find out. he asked 10 friends to throw a ball as far as they could and measured the distance from the starting line to where the ball landed. the table shows the distances he recorded in feet.
40 76 40 63 47 57 49 55 50 53
find the median and iqr of the data set.
on a later day, he asked the same group of 10 friends to throw a ball again and collected another set of data. the median of the second data set is 49 feet, and the iqr is 6 feet.
did the 10 friends, as a group, perform better (or throw farther) in the second round compared to the first round? explain how you know.
were the distances in the second data set more variable or less variable compared to those in the first round? explain how you know.
Answers
The median of the number recorded in the question is 51.5 feet. This is obtained by dividing the sum of two numbers that occur centrally in half.
What is median?The central value in a list ordered from smallest to largest is the median of a set of values.
What is the Inter-quartile Range (IQR) of an observation?The formula for the Inter-quartile range is given as:
IQR = Q₃- Q₁ (that is Median of the Upper Half Less the Median of the lower half)
Step 1 - First, let's arrange the numbers sequentially
→ 40, 40, 47, 49, 50, 53, 55, 57, 63, 76
Step 2 - Determine the upper and lower halves and their median
If the Lower half is 40, 40, 47, 49, 50, then it's median is 47
If the Upper half is 53, 55, 57, 63, 76, then its median is 57.
Hence:
IQR = 57 - 47
= 10 feet.
Given that the median of the second data set is 49 feet, and the IQR is 6 feet. Did the 10 friends, as a group, perform better (or throw farther) in the second?No, the friends didn't perform better in the second round because the was a significant drop in the median and the IQR. The median dropped from 51.5 to 47 and the IQR from 10 to 6.
Were the distances in the second data set more variable or less variable compared to those in the first round?
It can be concluded that the distance in the second set of data is less variable when juxtaposed with those form the first set.
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A refreshment company had declared that their soda drink is 250 oz. A group of students in CNHS wants to prove that the soda is less than advertised. They took 100 of such sodas in their study.
Answers
Answer:
200^2
Step-by-step explanation:
Write the quadratic equation in standard form:
-3x^2-16=−3x
Answers
Answer:
3x² - 3x + 16 = 0
Step-by-step explanation:
Standard form :
Ax² + Bx + C = 0Solving :
-3x² - 16 = -3x3x² - 3x + 16 = 0Standard form ax²+bx+c=0
-3x²+3x=16-3x²+3x-16=03x²-3x+16=0Done
can someone give me the step by step for 10
Answers
x^2 = (16)^2 + (16)^2
x^2 = 256 + 256
x^2 = 512
x = 16√2
Match each problem with its solution.
200
6
5
15
Jason is a party planner. In 124 packages, he has a total
of 1,860 balloons. If each package has the same number
of balloons, how many balloons are there in each package?
arrowRight
A plane has to travel 2,800 miles at an average speed of
560 miles per hour. How many hours will it take to reach
its destination?
arrowRight
An adult seal at a marine park consumes 2,400 kilograms
of food in one year. If it consumes the same amount of
food every month, how many kilograms of food does the
seal consume per month?
arrowRight
Andy and his roommates consume 180 bottles of orange
juice in 30 days. If they consume the same amount of
orange juice each day, how many bottles of orange juice
do they consume each day?
please let me know if you have an answer
Answers
The number of balloons on each package will be 15
How to calculate the problems?From the information, Jason is a party planner. In 124 packages, he has a total of 1,860 balloons and each package has the same number.
Therefore, the number of balloons on each package will be:
= 1860 / 124
= 15
When a plane has to travel 2,800 miles at an average speed of 560 miles per hour. The number of hours used will be:
= 2800/560
= 5
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Explain what the following statement means:
Polynomials are closed under the operations of addition and subtraction.
Provide one addition example and one subtraction example to demonstrate.
a set is closed under certain operation if the operation performed on two elements of the set gives an element of the same set
addition,subtractio sa well as multiplication of polynomials result into another polynomial.Therefore,the set of polynomials is closed under addition,subtraction and multiplication.
division of a polynomial need not be a polynomial (sometimes it is ,but not always).Therefore,the set of polynomials is not closed under division.see the example in the box beside.
Sample Response: If you add two polynomials, the sum is always a polynomial. Example: (2x2 + 3x) + (8x2 - 4x) = 10x2 - x If you subtract two polynomials, the difference is always a polynomial. Example: (2x2 + 3x) - (8x2 - 4x) = -6x2 + 7x
Compare your response to the sample response above. Did your response …
… explain what closure means for addition and give an example?
… explain what closure means for subtraction and give an example?
Answers
Polynomials are the algebraic expressions that consist of variables and coefficients.
How to explain the polynomial?
The Closure property of addition states that in a defined set, for example, the set of all positive numbers is closed with respect to addition since the sum obtained adding any 2 positive numbers is also a positive number which is a part of the same set.
Closure property of subtraction states that if any two real numbers a and b are subtracted from each other, the difference or result will be a real number as well. For example, 9 - 4 = 5.
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3. Determine the probability that a randomly selected person has a birthday on the 29th day of a month.
Answers
Answer:
0.0308.
Step-by-step explanation:
There are 11 months out of the year which have a 29th day except for a leap year when all 12 have it.
Required probability = number of '29th' days in 4 years / total days in 4 years
= (3*11 + 12) / (3*365 + 366)
= 45/1461
= 0.0308.
NEED THE ANSWER NOW 50 POINTS PLEASE HELP!
Answers
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
Let's solve ~
[tex]\qquad \sf \dashrightarrow \: \dfrac{3 {x}^{2} y {}^{ - 1}}{27x {}^{ - 3} {y}^{8} } [/tex]
Now, let's get the common terms out :
[tex]\qquad \sf \dashrightarrow \: \dfrac{3 {x}^{2} y {}^{ - 1}}{3 {x}^{2} {y}^{ - 1}(9 {x}^{ - 5} {y}^{9} )} [/tex]
cancel out the common terms in numerator and denominator
[tex]\qquad \sf \dashrightarrow \: \dfrac{1}{9 x {}^{ - 5} {y}^{9} } [/tex]
[tex]\qquad \sf \dashrightarrow \: \dfrac{ {x}^{5} }{9 {}^{ } {y}^{9} } [/tex]
So, the correct choice is C
PLEASE HELP ILL MARK BRAINEST!!!
Answers
Answer:
0,5
Step-by-step explanation:
PLEASE HURRY (NEED ANSWER ASAP)
Answers
The length of the shorter diagonal is 5.241 units and the length of the longer diagonal is 14.371 units
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let p and q represent the length of the diagonals.
Hence:
[tex]p=\sqrt{9^2+6^2+2(9)(6)cos(34)}=14.371\ units\\\\q=\sqrt{9^2+6^2-2(9)(6)cos(34)}=5.241\ units[/tex]
The length of the shorter diagonal is 5.241 units and the length of the longer diagonal is 14.371 units
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Please help me asap :(
Answers
Answer:
Total surface area=
304+9pi
~= 332.3
Step-by-step explanation:
Surface area is the areas of all the parts/sides/surfaces of the shape all added together.
There is a BOTTOM, 4 SIDES, a flat TOP, and a DOME shape.
The BOTTOM and SIDES are rectangles, so you can get the areas by multiplying length × width (or b•h)
BOTTOM: 8×10 =80
SIDES: There are 4×8 sides. 4×8 = 32. There are two of them 2×32=64.
There are 4×10 sides. 4×10 = 40. There are two of them, 2×40 = 80
For the flat TOP, it is also 8×10=80, but it has a circle cut out of it. Or, well, the circle that's under the dome doesn't count bc of the dome. So we'll take it away.
CIRCLE (under the dome):
Area of a circle is A=pi•r^2= pi•3^2
A = 9pi
So the flat TOP is:
80 - 9pi ~= 51.7
The DOME is a hemisphere (a half ball shape). Surface Area of a sphere is 4pi•r^2 We find that, then take half.
DOME =
4pi•3^2•(1/2)
= 4pi•9•(1/2)
= 18pi
~= 56.5
Now add up all the pieces:
80+64+80+80-9pi+18pi
= 304+9pi
~= 304 +28.3
= 332.3
Phillipa rode her bicycle every day over the weekend. Phillipa rode [ ( 13 . 5 + 8 . 5 ) ÷ 2 ] miles on Friday, [ 18 − ( 2 × 4 ) ] miles on Saturday and [ 20 − ( 5 − 3 ) ] miles on Sunday. On which day did Phillipa ride her bicycle the most? She rode her bicycle the most on .
Answers
Answer: Use pemdas to solve
Friday:
(13.5 + 18.5) ÷ 2
= 16
Saturday:
18 - (2 x 4)
= 10
Sunday:
20 - (5 - 3)
= 18
Step-by-step explanation:
Phillipa rode her bicycle the most on Sunday.
Hope this helps.
Which equation represents the relationship between the Cost in dollars, C, and the pounds of apples, a, bought?
Answers
C = 3a
Denver is growing at a rate of 1.8% per year and has a population of 700 thousand people. Write a recursive formula to represent the Denver scenario.
Answers
7000_1.8%=61.2%this is the answer
A pizza has a diameter of 12in what is the Circumference
Answers
I need help on this problem
Answers
Answer:
45, 135
Step-by-step explanation:
9x + 12x + 75 = 180
21x + 75 = 180
21x = 180 - 75
21x = 105
x = 105 / 21
x = 5
9 x 5 = 45
12 x 5 + 75 = 135
joan has a square flower bed with a side length of 5 meters filled with tulips. there are a total of 375 tulips in the bed. find the density of tulips
for the area of the bed. round to the nearest tenth if necessary.
Answers
Answer:
the answer is 15
Step-by-step explanation:
density= total population/surface area
density= 375/5^2
density=375/25=15
Awnser the Question For 10 Pts!
rest of awnser: d: she didnt make a mistake
Answers
Answer:
Jace did not make a mistake, because the answers are the same. Jace just did the problem in a unique way.
Which of Talia’s steps is incorrect?
Step 1 is incorrect because it uses a point that is not on the line.
Step 2 is incorrect because it uses a point that is not on the line.
Step 3 is incorrect because it shows an incorrect ratio for the slope.
Step 4 is incorrect because it shows an incorrect substitution of (1, 3) into the point-slope form
Answers
Answer: Step 3 is incorrect because it shows an incorrect ratio for the slope.
Answer:
Step 3 is incorrect because it shows an incorrect ratio for the slope.
Step-by-step explanation:
The correct question is:
Talia wants to write the equation of the graphed line in point-slope form. These are the steps she plans to use:
Step 1: Choose a point on the line, such as (2, 5).
Step 2: Choose another point on the line, such as (1, 3).
Step 3: Count units to determine the slope ratio. The line runs 1 unit to the right and rises 2 units up, so the slope is .
Step 4: Substitute those values into the point-slope form.
y – y1 = m(x – x1)
y – 3 = (x – 1)
Which of Talia’s steps is incorrect?
Step 1 is incorrect because it uses a point that is not on the line.
Step 2 is incorrect because it uses a point that is not on the line.
Step 3 is incorrect because it shows an incorrect ratio for the slope.
Step 4 is incorrect because it shows an incorrect substitution of (1, 3) into the point-slope form.
Answer:
Step 1 is correct because from the graph, points (1,3) and (2,5) lies on the line so the points can be used to find the slope.
Step 2 is also correct.
Step 3 is incorrect. Slope of a graph is the ratio of vertical change to horizontal change. The vertical change is the rise while the horizontal change is the run, hence slope is the ratio of rise to run.
Since the line runs 1 unit to the right and rises 2 units up, so the slope is 2/1 = 2
Therefore the correct point-slope form is:
y – y1 = m(x – x1)
y – 3 = 2(x – 1)
Step 4 is correct, because i t shows an incorrect substitution of (1, 3) into the point-slope form.
How to evaluate this question
Answers
Refer image for working :-
Drop comments if any doubt arises.
Answer:
[tex] {2x}^{3} - 3yz[/tex]
x=-1; y=-2 and z=3[tex]2 {( - 1)}^{3} - 3( - 2)(3)[/tex]
[tex] - 2 +6(3)[/tex]
[tex] - 2 +18[/tex]
(-)+(+)=(-)
[tex]-16[/tex]
F(3) = 2x - 4 help me please
Answers
Answer:
f(3) = 2
Step-by-step explanation:
Remark
The formula starts out as
f(x)= 2x - 4
So what is telling you is that were ever you see a variable on the right, it can from the x on the left.
If you change the variable on the left, you must also do it on the right.
f(3) = 2*3 -4
f(3) = 6-4
f(3) = 2
GIVING BRAINLIEST!!!!!
Answers
Answer:
segment AD is right one.
Answer:
Segment AD
Step-by-step explanation:
The only edge which lies on both planes and is shared by both is, Plane OAD and Plane BCD, is AD
Need help asap!!!!!??????
Answers
Answer:
x=8
Step-by-step explanation:
the geometric mean(√(a*b)) of the segments of the hypotenuse is equal to the altitude of the triangle.
4^2 = 2x
16=2x
16/2 =x
8=x
4 meters to 100 centimeters
Answers
Answer:
This is incorrect because 1 meter is 100 centimeters. But then when you keep going and when you get to 4 meters, you would get 400.
For example:
1 meter - 100 centimeters
2 meters - 200 centimeters
3 meters - 300 centimeters
4 meters - 400 centimeters
Hope this helps!