Answer:
3x=152
Step-by-step explanation:
You know that there are 152 animals intotal so that goes at the end. if we say that the dogs are x because we dont know how many there are, then there are 3 times more cats then there are x.
a. Find the amplitude.
b. Find the period.
c. Find the vertical shift.
d. Find the horizontal shift.
e. Find the number of cycles between 0 and 2π.
f. Find the equation of the graph.
You must show all of your work to receive credit.
Answers:
a) Amplitude = 2b) Period = pic) Vertical shift = -2, which means it has been shifted down 2 units.d) Horizontal shift = 3pi/8, this shifting is to the right.e) There is one cycle between 0 and 2pi.f) The equation of the graph is y = 2*sin(2(x-3pi/8))-2========================================================
Explanations:
Part (a)
The highest point is when y = 0 and the lowest point is when y = -4. The vertical distance between the peak and valley is 4 units, which cuts in half to 2. This is the amplitude. It's the vertical distance from the center to either the peak or valley.
Note: Amplitude is always positive as it measures a distance.
---------------------
Part (b)
For x > 0, the first valley or lowest point occurs between 0 and pi/4. It appears to be the midpoint of the two values. So that would be (0+pi/4)/2 = pi/8.
The next valley occurs between pi and 5pi/4. Compute the midpoint to get (pi+5pi/4)/2 = (4pi/4+5pi/4)/2 = (9pi/4)/2 = 9pi/8
So we have the graph go from one valley x = pi/8 to the next valley over x = 9pi/8. This is a distance of pi units because 9pi/8-pi/8 = 8pi/8 = pi
The graph repeats itself every pi units, so the period is pi.
---------------------
Part (c)
The midline is normally through y = 0, aka the x axis. However, the graph shows the midline is through y = -2. This means the graph has been shifted down 2 units.
---------------------
Part (d)
This will depend on whether you use sine or cosine. This is entirely because cosine is a phase-shifted version of sine, and vice versa. I'll go with sine.
The parent sine function y = sin(x) goes through the origin (0,0)
However, as part (c) mentioned, we shifted the graph 2 units down. So we have y = sin(x)-2. But plugging x = 0 into this leads to the point (0,-2)
This doesn't match what the graph says. The graph shows the point (3pi/8, -2) on the red curve. The x coordinate 3pi/8 is the midpoint of pi/4 and pi/2
This must mean we need to shift the sine graph 3pi/8 units to the right.
---------------------
Part (e)
Start at the lowest point when x = pi/8. If you start the cycle here, then it ends when x = 9pi/8. See part (b).
So far we've completed one cycle. If we start at x = 9pi/8, then the next valley or lowest point is slightly beyond or to the right of x = 2pi. This means we run out of room and we haven't completed a full cycle.
Overall, one full cycle is between 0 and 2pi.
---------------------
Part (f)
Again I'm going to use sine instead of cosine. Refer back to part (d).
The general sine curve equation is
y = A*sin(B(x-C))+D
where
|A| = amplitudeB handles the period, specifically T = 2pi/B where T is the period. We can solve for B to get B = 2pi/TC = horizontal phase shiftD = vertical shift, and ties together with the midline equationIn this case, we found that
|A| = 2T = pi leads to B = 2pi/T = 2pi/pi = 2C = 3pi/8D = -2So,
y = A*sin(B(x-C))+D
will update to
y = 2*sin(2(x-3pi/8))-2
which is one way to express the equation of the red curve. Optionally you can distribute the 2 through to (x-3pi/8).
PLEASE HELP!! GIVING BRAINLIST TO WHOEVER ANSWERS
Which of the following equations has a solution that is negative?
a. – 0.4x + 4 = – 1.6
b. – 0.4(x + 1.6) = 1.6
c. – 0.4(– x + 1.6) = 1.6
d. – 0.4x – 4 + 1.6x = – 1.6
Answer:
b. – 0.4(x + 1.6) = 1.6
Step-by-step explanation:
The equation with negative solution is -
- 0.4(x + 1.6) = 1.6
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given are the equations as shown in the question.
The equation with the negative solution are -
- 0.4(x + 1.6) = 1.6
- 0.4x - 0.64 = 1.6
- 0.4x = 1.6 + 0.64
- 0.4x = 2.24
x = - (2.24/0.4)
Therefore, the equation with negative solution is -
- 0.4(x + 1.6) = 1.6.
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OH MY GOD HELPPPPPPPPPPPPPP
Answer:
? = -36
Step-by-step explanation:
When you raise an exponent to an exponent, the resulting power is a product of the two exponents.
For this problem, you can solve for the missing value by writing:
[tex]?*1/3=-12[/tex]
Divide both sides by 1/3 to isolate the missing value.
[tex]?=\frac{-12}{1/3}[/tex]
Solve for ?.
[tex]?=-36[/tex]
8 feet in 15 seconds; 16 feet in 40 seconds
does this rate form a proportion?
Answer:
no
Step-by-step explanation:
8 ft in 15 sec
16 ft in 40 sec
8 is obviuosly half of 16, so to make it proportional it would have to be 16 ft 30secs
8 numbers have a sum of 90. Whats the average number?
Answer:
[tex]\huge\boxed{11.25}[/tex]
Step-by-step explanation:
When finding the average of a set of numbers, we
A) Add up all the numbers B) Divide that sum by the total number of numbers in the data setLet's represent this with a formula, s being the sum of all numbers, n being the total number of numbers.
[tex]\frac{s}{n}[/tex]
Since we already know the sum and we know how many numbers there are (8), we can substitute inside our expression [tex]\frac{s}{n}[/tex] to find the average.
[tex]\frac{90}{8}[/tex] [tex]11.25[/tex]Therefore, the average of all these numbers is 11.25.
Hope this helped!
What is true about 3×9, guys can you help I a little confused
Answer:
27
Step-by-step explanation
have a great day
Answer:
3*9=27
Step-by-step explanation:
The thing that is true about 3*9 is that it is also equal to 9*3.
Hope this helped!! :)
Shinji is considering two different layouts for a new garden. He needs to put a length of fence around whichever
layout he chooses.
The following diagram shows both layouts on a coordinate grid.
B
Coordinate values are in meters.
Which layout needs more fencing, and how much more?
Answer:
Layout A needs 4.8 m more fencing
Step-by-step explanation:
Khan academy answer
find the value of x and y
Answer: y is 40 x is 60
Step-by-step explanation:
Answer:
x=40 and y =5
Step-by-step explanation:
Make x the subject of the formula 3 b ( 2 x − a 2 ) = 5 d − 7 g x
Answer:
[tex]x=\frac{5d+6ba}{6b+7g}[/tex]Step-by-step explanation:
Answer:
x = (3a²b + 5d) / (6b + 7g)Step-by-step explanation:
Given:
3b( 2x − a² ) = 5d − 7gxSolving for x:
6bx - 3a²b = 5d - 7gx6bx + 7gx = 3a²b + 5d(6b + 7g)x = 3a²b + 5dx = (3a²b + 5d) / (6b + 7g)Suppose a classroom where a debate is being held has an area of 252 square feet. If the classroom is 14 feet wide, how long is the classroom?
Answer:
18 feet long
Step-by-step explanation:
252 ÷ 14 = 18
:)
Jessica borrows $1500 at 7% simple interest per week. If she ends up owing $2235, how may weeks did it take her to pay back the loan?
a. 6
b. 7
c. 8
d. 9
e. 10
Answer:
7 Weeks
Step-by-step explanation:
Each week is 105 because 1500*.07=105
Then through the process of elimination I found it would take 7 weeks.
У
(6, 10),
(а, 8)
(4, b)
(2, 2)
Х
Answer:
(2,2)=x1,y1
(4,b)=x,y
(6,10)=x2,y2
using midpoint formula,
y=(y1+y2)/2
y=(2+10+)/2
y=6
which makes (4,b)=(4,6)
again,
(4,6)=x1,y1
(6,10)=x2,y2
(a,8)=x,y
using midpoint formulax=(x1+x2)/2
x=(4+6)/2
x=5
which makes (a,8)=(5,8)
Triangles A B C and N M L are shown. Angles B A C and L N M are right angles.
What additional information could be used to prove that △ABC ~ △NML? Check all that apply.
∠B ≅ ∠M
△ABC is a right triangle.
△ABC was rotated and dilated by a scale factor between 0 and 1.
△ABC was translated right and down.
∠C ≅ ∠L
Answer:
A. Angle B is congruent to angle M
C. Triangle ABC was rotated and dilated by a scale factor between 0 and 1
E. Angle C is congruent to angle L
How Do I Know?
Because I literally just did it just now and that's what it said that the answers were. January 9th, 2021- Edge :)
A. Angle B is congruent to angle M
C. Triangle ABC was rotated and dilated by a scale factor between 0 and 1
E. Angle C is congruent to angle L
What is similarity in triangles?Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles.
Given:
To prove that triangle ABC is similar to triangle NML.
The following points are considered:
∠B ≅ ∠M
△ABC was rotated and dilated by a scale factor between 0 and 1.
∠C ≅ ∠L.
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10/9 in simplest form pls
[tex]1\frac{1}{9}[/tex]
For khan academy. Need help . Explain if you can
Answer:
y = 2/3x + 1.5
Step-by-step explanation:
The Formula for that is
y = mx + b
m = slope
b = y -intercept
so to find the slope I would do y/x or rise over run
So your slope is 2/3 ( it goes up 2 and right 3 times)
Since the line is going up and not down, it is a positive slope
y = 2/3x + b
we need to find where the line crosses the vertical / y-axis and it's at the point.... (0,1.5)
y = 2/3x + 1.5
Hope this helped a little!
The Cowboys High School Band Boosters are selling candy bars and chips at the basketball tournament to raise money for their band competition. The candy bars sell for $1.00 and the chips sell for $0.50. They have 575 items ready to sell and expect to make $500 on the sale of all the items. How many candy bars do they have ready to sell?
Answer:
They have 425 candy bars ready to sell.
Step-by-step explanation:
Let,
x be the number of candy bars ready to sell
y be the number of chips ready to sell
According to given statement;
x+y=575 Eqn 1
x+0.5y= 500 Eqn 2
Subtracting Eqn 2 from Eqn 1
(x+y)-(x+0.5y)=575-500
x+y-x-0.5y=75
0.5y = 75
Dividing both sides by 0.5
[tex]\frac{0.5y}{0.5}=\frac{75}{0.5}\\y=150[/tex]
Putting y=150 in Eqn 1
x+150 = 575
x = 575-150
x = 425
Hence,
They have 425 candy bars ready to sell.
How many cubic centimers of water can this paper cone cup hold?
Answer:
B: 48π cubic centimeters
Step-by-step explanation:
A: 216π cubic centimeters
B: 48π cubic centimeters
C: 144π cubic centimeters
D: 192π cubic centimeters
Volume of the paper cone cup = 1/3πr²h
Diameter = 8 cm
Radius, r = diameter / 2
= 8 cm / 2
= 4 cm
Height, h = 9 cm
Volume of the paper cone cup = 1/3πr²h
= 1/3 × π × 4² × 9
= 1/3 × π × 16 × 9
= (1 × π × 16 × 9) / 3
= 144π / 3
= 48π cm³
Volume of the paper cone cup = 48π cm³
What is 8/9 of 360 degree ?
Answer:
320 degrees.
Step-by-step explanation:
can you help me with this
Answer:
C.
Step-by-step explanation:
Diego is on a diet. He has lost 10% of his weight this month. If he started with 75 kg (THAT'S THE 100%), how much weight did he lose?
Step-by-step explanation:
10% of 75 is the total kg he lost this month
So 10/100 x 75 = 7.5
So Diego lost 7.5 kg this month
2x - 3y = 3 solve y
Answer:
Y=-1+2x/3
Step-by-step explanation:
Move all the terms that don't contain y to the right side and solve. Hope this helps!
True or False, The value pi/12 is a solution for the equation 4 cos^2(4x)-3=0
Please explain
Answer:
Yes, π/12 is a solution.
Step-by-step explanation:
Calculator --> sin(π12)=sin15∘=0.26 . √2−√32=√0.272=0.522=0.26 . Uhmm... i dont rlly know how to explain it.. its complicated for me to word it without making it non confusing.
The statement 'The value [tex]\frac{\pi}{12}[/tex] is a solution for the equation [tex]4~cos^2(4x)-3=0[/tex] ' is True.
What is an equation?"It is a mathematical statement which consists of equal symbol between two algebraic expressions."
For given question,
We have been given an equation [tex]4~cos^2(4x)-3=0[/tex]
We need to check whether [tex]\frac{\pi}{12}[/tex] is a solution for the equation.
Substitute [tex]x=\frac{\pi}{12}[/tex] in equation [tex]4~cos^2(4x)-3=0[/tex]
[tex]\Rightarrow 4~cos^2(4\frac{\pi}{12} )-3=0\\\\\Rightarrow 4~cos^2(\frac{\pi}{3} )-3=0\\\\\Rightarrow 4~cos^2(\frac{\sqrt{3} }{4} )-3=0\\\\\Rightarrow 4~\frac{3}{4}-3=0\\\\ \Rightarrow 3-3=0\\\\\Rightarrow 0=0[/tex]
This means, [tex]\frac{\pi}{12}[/tex] is a solution of the equation [tex]4~cos^2(4x)-3=0[/tex]
Therefore, the statement 'The value [tex]\frac{\pi}{12}[/tex] is a solution for the equation [tex]4~cos^2(4x)-3=0[/tex] ' is True.
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write 103 as a series of products
Answer:
10*10*10
Step-by-step explanation:
Given the expression 10^3
We are to write this as a series of products as as shown;
10^3 means the product of 10 in 3 places. Multiplying 10 in 3 places will give the required series of product.
10^3 = 10 * 10 * 10
Hence the series of product of 10^3 is 10*10*10
Please help me answer this
Answer: 7/8
10-2/12-4= 7/8
Step-by-step explanation:
Answer:
the answer might be number 3
The dance committee at Jefferson High School decides to charge students different prices for dance tickets depending on whether they are a student at Jefferson or at another school. A student attending Jefferson pays $5, whereas a student attending a different school pays $10. The dance committee didn't make different kinds of tickets, and they lost track of how many of each kind of ticket they sold. They know they sold a total of 500 tickets and they brought in $3,135. How many Jefferson and non-Jefferson students came to the dance?
Answer:
30
Step-by-step explanation:
The number of Jefferson students and the number of non-Jefferson students if A student attending Jefferson pays $5, A student attending a different school pays $10 is 373 and 127 respectively.
What is the equation?Equation: A declaration that two expressions with variables or integers are equal. In essence, equations are questions and attempts to systematically identify the solutions to these questions have been the driving forces behind the creation of mathematics.
Given:
A student attending Jefferson pays $5,
A student attending a different school pays $10,
The total number of tickets = 500,
The total money earned = $3135,
Write the equation of the given statement as shown below,
x + y = 500
5x + 10y = 3135
Here, x is the number of Jefferson students and y is the number of non-Jefferson students,
Solve the equation by elimination method as shown below,
y = 127,
x = 500 - 127 = 373
Thus, the number of Jefferson students is 373 and the number of non-Jefferson students is 127.
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Given a triangle ABC has angles of A = 30 and B = 70, what is the smallest side?
Answer:
A=30 is the smallest side
Step-by-step explanation:
A+B+C= 180
30+70+C=180
100+C=180
C=180-100
C=80
Therefore, A=30 is the smallest side of the triangle...
Jesse drank 3/4 of liter of water Monday before going jogging. He drank 3/5 of a liter of water after his jog. How much water did Jesse drink altogether? Write your answer as a mixed number.
Answer:
[tex]1\frac{7}{20}[/tex]
Step-by-step explanation:
Step one
Given data
On Monday, Jesse drank 3/4 of liter of water before jogging
and drank 3/5 of liter after jogging
In all, Jesse drank 3/4 and 3/5 liters of water
= 3/4+3/5
the lcm is 20
=15+12/20
=27/20
in mixed numbers(i.e a whole and a fraction together we have) we have
[tex]1\frac{7}{20}[/tex]
Translate the following into an algebraic expression: "five less than the product of 7 and
the square root of a number" can be written as:
05-713
o 5 - 70
O TX-15
073-5
Answer:
7√x - 5
Step-by-step explanation:
Let the number be x
The product of 7 and the square root of a number is expressed as;
7 * √x
= 7√x
five less than the product of 7 and the square root of a number will be expressed as;
7√x - 5
Hence the required expression is 7√x - 5
CAN SOMEONE HELP ME ASAP THISS IS DUE AT 11:59 tonight