Answer:
[tex]y = 2x^4[/tex]
Step-by-step explanation:
The given statement can be represented as:
[tex]y\ \alpha\ x^4[/tex]
[tex]x =3; y = 162[/tex]
Given
Represent this as an equation
[tex]y\ \alpha\ x^4[/tex]
Convert variation to equation
[tex]y = kx^4[/tex]
Where k is a constant of variation.
Substitute [tex]x =3; y = 162[/tex]
[tex]162 = k * 3^4[/tex]
[tex]162 = k * 81[/tex]
Solve for k
[tex]k = 162/81[/tex]
[tex]k =2[/tex]
To get the equation, we have:
[tex]y = kx^4[/tex]
Substitute 2 for k
[tex]y = 2x^4[/tex]
The equation describing the relationship of the given variables is [tex]y=\frac{81}{162}x^4[/tex]
If y varies directly to the fourth power of x, this can be expressed as:
[tex]y \alpha x^4\\y=kx^4\\[/tex]
Given that x = 3 and y = 162, the equation becomes;
[tex]162 = k(3^4)\\162 = 81k\\k=\frac{81}{162}[/tex]
Substitute the value of k into the expression above to have:
[tex]y=kx^4\\y=\frac{81}{162}x^4[/tex]
Hence the equation describing the relationship of the given variables is [tex]y=\frac{81}{162}x^4[/tex]
Learn more on direct variation here: https://brainly.com/question/6499629
jenny's MP3 player has 97 songs on it. if each song cost $1.25, how much did it cost for all the songs on her MP3 player?
Answer:
$121.25
Step-by-step explanation:
97 X 1.25 = 121.25
Please answer if you know how to do this, thank you
9514 1404 393
Answer:
vertex: (-2, -1)dashed line, shaded inside, parabola is positive (opens up)Step-by-step explanation:
The given inequality is in vertex form:
y = a(x -h)^2 +k . . . . . . has vertex (h, k)
so the vertex can be read from the given expression.
y > (x +2)^2 -1 ⇒ (h, k) = (-2, -1) . . . the vertex
The leading coefficient (+1) is positive so the parabola opens upward.
__
The y > ( ) tells you the boundary line is dashed (is not part of the solution). It also tells you the shading is above the curve, hence inside the parabola.
The two offered points (0, 0), (2, -3) are NOT part of the solution set.
Help!
What is the answer to this question?
Answer:
Its perimeter is 23 units
Step-by-step explanation:
The perimeter of any figure is the sum of the lengths of its outline sides
The rule of the distance between two points is:
[tex]d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}[/tex]In the given figure ABCD:
Its perimeter = AB + BC + CD + DE + EA
→ Find the length of each side using the rule above
A = (-4, -2), B = (-1, 2), C = (2, 2), D = (5, -1), E = (2, -4)
→ Substitute them in the rule above to find the lengths of its sides
[tex]AB=\sqrt{(-1--4)^{2}+(2--2)^{2}}=\sqrt{(-1+4)^{2}+(2+2)^{2}}\\\\=\sqrt{(3)^{2}+(4)^{2}}=\sqrt{9+16}=\sqrt{25}[/tex]
∴ AB = 5
[tex]BC=\sqrt{(2--1)^{2}+(2-2)^{2}}=\sqrt{(2+1)^{2}+(0)^{2}}\\\\=\sqrt{(3)^{2}+0}=\sqrt{9+0}=\sqrt{9}[/tex]
∴ BC = 3
[tex]CD=\sqrt{(5-2)^{2}+(-1-2)^{2}}=\sqrt{(3)^{2}+(-3)^{2}}\\\\=\sqrt{9+9}=\sqrt{18}[/tex]
∴ CD = [tex]\sqrt{18}[/tex]
[tex]DE=\sqrt{(2-5)^{2}+(-4--1)^{2}}=\sqrt{(-3)^{2}+(-4+1)^{2}}\\\\=\sqrt{(-3)^{2}+(-3)^{2}}=\sqrt{9+9}=\sqrt{18}[/tex]
∴ DE = [tex]\sqrt{18}[/tex]
[tex]EA=\sqrt{(-4-2)^{2}+(-2--4)^{2}}=\sqrt{(-6)^{2}+(-2+4)^{2}}\\\\=\sqrt{(-6)^{2}+(2)^{2}}=\sqrt{36+4}=\sqrt{40}[/tex]
∴ EA = [tex]\sqrt{40}[/tex]
→ Add them to find the perimeter of the figure ABCDE
∴ Its perimeter = 5 + 3 + [tex]\sqrt{18}[/tex] + [tex]\sqrt{18}[/tex] +[tex]\sqrt{40}[/tex] ≅ 22.8098
→ Round it to the whole number
∴ Its perimeter = 23 units
3c. For each differential equation, find the Laplace transform of the solution y:
y'' + 3y' + 2y = 5 sin(πx), y(0) = y'(0) = 0.
Answer:
[tex]y(x)=\frac{5}{3\pi}-\frac{5\pi}{27+3\pi^2}e^{-3x}-\frac{15}{9\pi+\pi^3}cos(\pi x)-\frac{5}{9+\pi^2}sin(\pi x)[/tex]
Step-by-step explanation:
[tex]y''+3y'+2y=5sin(\pi x),\: y(0)=y'(0)=0\\\\\mathcal{L}\{y''\}+3\mathcal{L}\{y'\}+2\mathcal{L}\{y\}=\mathcal{L}\{5sin(\pi x)\}\\\\s^2Y(s)-sy(0)-y'(0)+3[sY(s)-y(0)]+2Y(s)=\frac{5\pi}{s^2+\pi^2}\\\\s^2Y(s)+3sY(s)=\frac{5\pi}{s^2+\pi^2}\\ \\(s^2+3s)Y(s)=\frac{5\pi}{s^2+\pi^2}\\ \\Y(s)=\frac{5\pi}{(s^2+\pi^2)(s^2+3s)}\\ \\Y(s)=\frac{5\pi}{s(s+3)(s^2+\pi^2)}[/tex]
Perform the partial fraction decomposition
[tex]\frac{5 \pi}{s \left(s + 3\right) \left(s^{2} + \pi^{2}\right)}=\frac{A}{s}+\frac{B}{s + 3}+\frac{C s + D}{s^{2} + \pi^{2}}\\5\pi=s \left(s + 3\right) \left(C s + D\right) + s \left(s^{2} + \pi^{2}\right) B + \left(s + 3\right) \left(s^{2} + \pi^{2}\right) A\\\\5 \pi=s^{3} A + s^{3} B + s^{3} C + 3 s^{2} A + 3 s^{2} C + s^{2} D + \pi^{2} s A + \pi^{2} s B + 3 s D + 3 \pi^{2} A\\\\5\pi=s^3(A+B+C)+s^2(3A+3C+D)+s(\pi^2A+\pi^2B+3D)+3\pi^2A[/tex]
Solve for each constant
[tex]\begin{cases} A + B + C = 0\\3 A + 3 C + D = 0\\\pi^{2} A + \pi^{2} B + 3 D = 0\\3 \pi^{2} A = 5 \pi \end{cases}[/tex]
[tex]3\pi^2A=5\pi\\A=\frac{5}{3\pi}[/tex]
[tex]A+B+C=0\\3A+3B+3C=0\\(3A+3B+3C=0)-(3A+3C+D=0)\\3B-D=0\\3B=D[/tex]
[tex]\pi^2A+\pi^2B+3D=0\\\pi^2(\frac{5}{3\pi})+\pi^2B+3(3B)=0\\\frac{5\pi}{3}+\pi^2B+9B=0\\ B(\pi^2+9)=-\frac{5\pi}{3}\\B=-\frac{5\pi}{3(\pi^2+9)}\\B=-\frac{5\pi}{3\pi^2+27}[/tex]
[tex]3B=D\\3(-\frac{5\pi}{3\pi^2+27})=D\\-\frac{5\pi}{\pi^2+9}=D[/tex]
[tex]A+B+C=0\\\frac{5}{3\pi}-\frac{5\pi}{3\pi^2+27}+C=0\\\frac{15\pi^2+135}{3\pi(3\pi^2+27)}-\frac{15\pi^2}{(3\pi)(3\pi^2+27)}+C=0\\\frac{135}{9\pi^3+81\pi}+C=0\\\frac{15}{\pi^3+9\pi}+C=0\\C=-\frac{15}{\pi^3+9\pi}[/tex]
Take the inverse transform and solve for the IVP
[tex]Y(s)=\frac{\frac{5}{3 \pi}}{s}+\frac{- \frac{5 \pi}{27 + 3 \pi^{2}}}{s + 3}+\frac{- \frac{15 s}{9 \pi + \pi^{3}} - \frac{5 \pi}{9 + \pi^{2}}}{s^{2} + \pi^{2}}\\\\Y(s)=\frac{\frac{5}{3 \pi}}{s}-\frac{\frac{5 \pi}{27 + 3 \pi^{2}}}{s + 3}-\frac{ \frac{15 s}{9 \pi + \pi^{3}}}{s^{2} + \pi^{2}}-\frac{\frac{5\pi}{9+\pi^2} }{s^2+\pi^2}\\ \\y(x)=\frac{5}{3\pi}-\frac{5\pi}{27+3\pi^2}e^{-3x}-\frac{15}{9\pi+\pi^3}cos(\pi x)-\frac{5}{9+\pi^2}sin(\pi x)[/tex]
answer pls 1+2.1y-0.9y+4
Answer: 1.2y+5
If 1+4 =5 and 2.1y-0.9y=1.2y then 1+2.1y-0.9y+4 = 1.2y+5
( 1 + 1 ) + 1 in standard form
Answer:
(1+1)+1=3 therefore 3×10¹
Answer: 3 times 10 to the power of just 0
Step-by-step explanation:
(1+1) + 1 is 3
So now we must put the number 3 in standard form...
The answer for this would be 3 times 10 to the power of 0
.Which statement describes a sequence of transformations that can be used to verify that rectangle H J K L is similar to rectangle H ′ J ′ K ′ L ′ ? Dilate rectangle H J K L by a scale factor of 2 about the origin, then translate it 12 units down. Dilate rectangle H J K L by a scale factor of 2 about the origin, then translate it 12 units down. Dilate rectangle H J K L by a scale factor of 2 about the origin, then reflect it across the x -axis. Dilate rectangle H J K L by a scale factor of 2 about the origin, then reflect it across the x -axis. Dilate rectangle H J K L by a scale factor of 1 2 about the origin, then translate it 12 units down. Dilate rectangle H J K L by a scale factor of 1 2 about the origin, then translate it 12 units down. Dilate rectangle H J K L by a scale factor of 1 2 about the origin, then reflect it across the x -axis.
The sequence of transformations involves reflection, translation, dilation and reflection
How to determine the sequence of transformations?The question is incomplete;
So, I will give a general explanation
For the two rectangles are similar shapes, then the corresponding sides of the shapes must be similar.
If the rectangles do not have the same size, then the scale ratio of the sides of the rectangles must be the same
if the rectangles have the same size, then the rectangles must fit perfectly on one another
Read more about transformation at:
https://brainly.com/question/4289712
CERTAIN ANSWERS ONLY! I apologize if it may be difficult, thank you in advance. I will GIVE BRAIN CROWN!!! THERE SHOULD BE 4 answers!
Answer:
See Below.
Step-by-step explanation:
Statements: Reasons:
1) [tex]\angle 4\cong \angle 3; c\parallel d[/tex] Given
2) [tex]\angle 1\cong \angle 3[/tex] Alternate Interior Angles Theorem
3) [tex]\bf{\angle 4 \cong \angle 1}[/tex] Transitive Property of Congruence
4) [tex]\angle 1\cong \angle 2[/tex] Vertical Angles Theorem
5) [tex]\bf{\angle 4\cong \angle 2}[/tex] Transitive Property of Congruence
And we’re done!
Can anyone help me with this question?
Answer:
option 1
Because not all of them are equal lengths
Find the sum of the average monthly rainfalls 1/8 + 1/4 + 5/8 + 7/8 + 1 1/8 + 1 5/8 + 1 7/8 + 2
Answer:
37/4
Step-by-step explanation:
1/8 + 1/4 + 5/8 + 7/8 + 1 1/8 + 1 5/8 + 1 7/8 + 2 = 3/8 + 3/2 + 13/4 + 33/8 = 37/4
A submarine was operating 234 feet below the surface of the ocean. Then, an underwater current caused the submarine to rise 112 feet.
What is the position of the submarine relative to the surface of the ocean now?
Answer: -122
Step-by-step explanation:
-234+112=-122 hope that helps!
Answer:
-122
Step-by-step explanation:
4. Find the value of x in the equation x+5=x+45
Answer: No solution
Step-by-step explanation:
Subtracting x from both sides, we get 5=45, which is false.
Multiply with decimal numbers:
6.0 x 74 = ? 4.5 x 80 = ? 5.1 x 78 = ? 1.9 x 70 = ?
The complete process of multiplication please :)
6.0x74=444
4.5x80=360
5.1 x 78 = 397.8
1.9 x 70=133
Can someone help answer this 6th grade question?
Answer:
Club A charges $4 per car and club B charges $4 also
Step-by-step explanation:
Answer:
Yes,
Step-by-step explanation:
Club A charges $4 per car and club B charges $4 also
Here is a set of data showing the test scores for US History class:
56, 88, 70, 72, 90, 85, 99, 65, 66, 54, 74, 85, 91, 92, 72, 88, 97, 62, 88 Create a stem and leaf plot to show this data. Hint: Decide how many stems you will need.
can somebody help me ?
Answer:
Stem Leaf
5 4 6
6 2 5 6
7 0 2 2 4
8 5 5 8 8 8
9 0 1 2 7 9
Step-by-step explanation:
That is how the stem and leaf plot will look like
Hope this helps
dounuts or snacks or chips
Answer:
snacks, the reason being that it can be anything
Step-by-step explanation:
Answer:
Donuts
Step-by-step explanation:
The donuts are specifically tastier than the options mentioned
Solve the proportion:
5/X=12.5/20
A X=8
B X=9
C X=10
Answer:
A. X =8
Step-by-step explanation:
5/X=12.5/20
cross multiply
12.5X = 20*5
12.5X=100
X=100/12.5
X=8
30 points I need an answer asap please
Answer:
D. 0.05
Step-by-step explanation:
5 x 10 = 50
50 as a decimal
0.5
Hope it helps!!!Brainliest pls!!!Flying agaist the wind, an airplane travels 6300 kilometers in7 hours. Flying with the wind, the same plane travels 8400 in 6 hours. What is the rate of the plane is still air and what is the rate of the wind?
Answer:
plane: 1150 kphwind: 250 kphStep-by-step explanation:
The given relationships allow us to write a system of equations in the speeds of the wind and plane.
Let w and p represent the speeds of the wind and the plane, respectively. We know speed is the ratio of distance to time, so ...
p -w = 6300 km/(7 h) = 900 km/h
p +w = 8400 km/(6 h) = 1400 km/h
__
Adding these two equations gives ...
2p = 2300 km/h
p = 1150 km/h . . . . . . divide by 2
Subtracting the first equation from the second gives ...
2w = 500 km/h
w = 250 km/h
The speed of the plane in still air is 1150 km per hour; the speed of the wind is 250 km per hour.
PLS HELP ME. Been on the same question for a while now.
Answer:
1050
Step-by-step explanation:
So, we know 4/5 of a gallon can paint 280ft^2, but we don't know how much each gallon can paint, so to find x, do this
4/5x=280ft^2, next multiply both sides by 5/4 to get x by itself
x=350
Now multiply x by 3 to get your new answer.
350*3=1050
Hope this helps, feel free to leave any questions.
brainliest 5. Using the Straightedge and the black pencil, connect each of the endpoints of the perpendicular diameters to the endpoints on either side of it. Sketch the result below. (4 points: 1 point for each diagonal)
The perpendicular bisector of the diameter divides the diameter into two equal parts i.e. the radius
How to sketch the resultFrom the diagram of the circle, we have two diameters, each of which have two endpoints.
This means that there are four endpoints in the figure.
Next, we connect adjacent endpoints on the diagram
When the endpoints are connected, the shape formed is a square
See attachment for the sketch
Read more about constructions at:
https://brainly.com/question/1686819
Marques made a mistake when solving this problem. On what line did he make the error?
Line 1
Line 2
Line 3
Line 4
Line 5
Answer:
line 2.
Step-by-step explanation:
the correct way is provided in the attachment (under the green line). Note, only positive value (it is the length of the side) can be considered as answer.
joanna has 45 postcards in her postcard collection, which is 180% of the number of postcards Kyle has. How many postcards does Kyle have?
Answer:
Kyle has 25 postcards
Step-by-step explanation:
Joanna has 45 postcards in her collection, which is 180% of the number of postcards of Kyle.
If the number of postcards of Kyle is K, and the number of postcards of Joanna is J, then:
J=180% K
Recall a percentage can be expressed in decimal by dividing by 100:
J=180/100*K
To find the value of K, we solve the above equation:
K=100/180*J
Since J=45:
K=100/180*45=25
Kyle has 25 postcards
Whats 1 + 1 please i need help, im taking a test
Answer:
I am sure it's 2
Step-by-step explanation:
Source: Trust me bro
Answer:
The answer is 2 because 1 plus 1 is like having 2 things
Solve for X
√5x − 7 − 3 = 8
Answer:
[tex]x=\frac{324}{5}[/tex]
Step-by-step explanation:
Given the following question:
[tex]\sqrt{5x} -7-3=8[/tex]
To find the answer we are going to use inverse of operations to isolate the variable x, doing this we can then find the value of the variable and then have our answer.
[tex]\sqrt{5x} -7-3=8[/tex]
[tex]-7-3=-10[/tex]
[tex]\sqrt{5x} -10=8[/tex]
[tex]-10+10=0[/tex]
[tex]8+10=18[/tex]
[tex]\sqrt{5x} =18[/tex]
[tex]\sqrt{5x} =5[/tex]
[tex]18\times18=324[/tex]
[tex]5x=324[/tex]
[tex]5x\div5=x[/tex]
[tex]324\div5=x=\frac{324}{5}[/tex]
[tex]x=\frac{324}{5}[/tex]
Your answer is "x = 324/5."
Hope this helps.
Help I Dont understand
Answer:
Q4 part d
Q5 part c
Step-by-step explanation:
y= 1.1x + 7what would changing the 1.1 into a -1.1 do?
Answer: It changes the slope from positive to negative.
Step-by-step explanation:
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The graph below shows the height through which an elevator travels, y, in x seconds:
A graph is shown with x axis title as Time in seconds. The title on the y-axis is Height of Elevator Above Ground in feet. The values on the x-axis are from 0 to 5 in increments of 1 for each grid line. The values on the y-axis are from 0 to 50 in increments of 10 for each grid line. A line is shown connecting points at ordered pairs 1,10 and 2, 20 and 3, 30 and 4, 40. The title of the graph is Rate of Ascent.
What is the rate of change for the relationship represented in the graph?
fraction 1 over 40
fraction 1 over 10
10
40
Use the slope formula or rise over run to determine the slope of line A.
Format: m=-5/6
Answer:
y = (-1/3)x + 4
Step-by-step explanation:
m = rise/run = y2 - y1 3 - 4 -1
----------- = -------- = ----
x2 - x1 3 - 0 3
y = mx + b
y = (-1/3)x + b
Pick either coordinate. For this, I'll pick (0, 4)
4 = (-1/3)(0) + b
4 = b
y = (-1/3)x + 4
If you are certain about M = (-5/6), then replace (-1/3) with (-5/6)
I hope this helps!