The statement that best describes the property is a · b = b · a.
What is commutative property?The commutative property of multiplication states that if there are three numbers x, y, and z, then x × y × z = z × y × x = y × z × x or another possible arrangement can be made.
If you observe the given equation, you will find that the commutative property can be applied. If x = 131, and y = 56 and z = 72, then we know that 131 x 56 x 72 = 72 x 131 x 56.
Given statement:
5 · 2 · 9 = 2 · 5 · 9
So, we can see that only the place has been changed
So, it is commutative property
Hence, the correct statement is a · b = b · a
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What is the solution to the differential equation dydx=5y2 with the initial condition y(0) = 3?
Differential equation is a way to represents the relation between the functions and their variables. The solution to the differential equation given in the question is,
[tex]y=\dfrac{3}{15x-1}[/tex]
Given-
The equation in the question is,
[tex]{dy\times {dx}=5y^2[/tex]
What is differential equation?Differential equation is a way to represents the relation between the functions and their variables.
Rewrite the equation,
[tex]\dfrac{dy}{5y^2} =dx[/tex]
Integration both sides,
[tex]-\dfrac{1}{5y} =x+c[/tex]
Here, c is the integrating constant.
Now the given initial condition is,
[tex]y(0)=3[/tex]
Use this for the integrated function to find the value of the constant,
[tex]-\dfrac{1}{5\times 3} =c[/tex]
[tex]c=-\dfrac{1}{15}[/tex]
Put this value in equation we get,
[tex]-\dfrac{1}{5y} =x-\dfrac{1}{15}[/tex]
[tex]y=\dfrac{3}{15x-1}[/tex]
Hence the solution to the differential equation given in the question is,[tex]y=\dfrac{3}{15x-1}[/tex]
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To solve the differential equation dy/dx = 5y^2 with the initial condition y(0) = 3, use separation of variables and integration. Substitute the initial condition to find the specific solution.
Explanation:To solve the differential equation dy/dx = 5y^2 with the initial condition y(0) = 3, we can use separation of variables.
First, rewrite the equation as dy/y^2 = 5dx. Integrate both sides: ∫1/y^2 dy = ∫5 dx. This simplifies to -1/y = 5x + C.
Next, apply the initial condition y(0) = 3: -1/3 = 0 + C. Therefore, C = -1/3.
Substitute C back into the equation: -1/y = 5x -1/3. Solve for y: y = -1/(5x -1/3).
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what is the half life formula
N = N₀* [tex](\frac{1}{2} )^{\frac{t}{h} }[/tex]
where N is how much you currently have
N₀ is the starting amount
t is the time
and h is the half life of the substance.
The half-life formula for a radioactive isotope is amount remaining = (amount initial) × e^(-t/t1/2), where e is the base of natural logarithms, t is the elapsed time, and t1/2 is the half-life of the isotope. The variables t and t1/2 must have the same units of time. The formula can be used to calculate how much of a radioactive isotope remains after a certain amount of time.
Explanation:The half-life formula for a radioactive isotope is given by:
amount remaining = (amount initial) × e^(-t/t1/2)
Here, e is the base of natural logarithms (approximately 2.71828182), t is the elapsed time, and t1/2 is the half-life of the isotope. The variables t and t1/2 must have the same units of time. To evaluate the exponential function, you may need to use a calculator or an inverse logarithm function. It is important to note that the length of time t does not need to be an exact multiple of half-lives.
0.45 plus 9x equals 27
Answer:
x = 2.95
Step-by-step explanation:
Step 1: Convert words into an expression
0.45 plus 9x equals 27
0.45 + 9x = 27
Step 2: Solve for x
0.45 + 9x - 0.45 = 27 - 0.45
9x / 9 = 26.55 / 9
x = 2.95
Answer: x = 2.95
.find the distance between the points (4, 3) and (0, 3).
a) 2
b) 4
c) 10
d) 12
Answer:The answer is 4
Step-by-step explanation:
Write the equation of a line in y =mx+b
form that has a slope of 3/4 and a y-intercept of 0.
Answer:
y = ¾x
Step-by-step explanation:
y = mx + b, where
m = slope and
b = y-intercept
If slope = ¾ and y-intercept =0, the equation is
y = ¾x
Please Answer both with Solution and Explanation. Will give Brainliest
1. What are the roots of [tex]x^{2}[/tex] - 2x + 2?
2. The number 16 has four fourth roots. In other words, there are four complex numbers that can be entered in the square in the equation below:[tex]\[\square^4=16.\][/tex]Find them. Please
Step-by-step explanation:
1) Given quadratic expression is [tex]x^2-2x+2[/tex]
First equate the given expression to zero then we will find the roots.
Since the given equation is quadratic hence it has two roots.
To find the roots of the given quadratic equation :For the quadratic equation we have that [tex]ax^2+bx+c=0[/tex]
Therefore roots [tex]x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex] here a and b are coefficients of [tex]x^2andx[/tex] respectively and c is a constant
[tex]x^2-2x+2=0[/tex] here a=1 ,b=-2 and c=2
Now Substitute the values in [tex]x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex] we get
[tex]x=\frac{-(-2)\pm \sqrt{(-2)^2-4(1)(2)}}{2(1)}[/tex]
[tex]=\frac{2\pm \sqrt{4-8}}{2}[/tex]
[tex]=\frac{2\pm \sqrt{-4}}{2}[/tex]
[tex]=\frac{2\pm \sqrt{4i^2}}{2}[/tex]
[tex]=\frac{2\pm2i}{2}[/tex]
[tex]=2(\frac{1\pm i}{2})[/tex]
[tex]x=1\pm i[/tex]
Therefore [tex]x=1+i[/tex] and [tex]x=1-i[/tex] are the roots of the given quadratic equation.
2) Given that the number 16 has four roots.In other words, there are four complex numbers that can be entered in the square .
Let x be the given number 16
i.e., x=16
From the given we can write [tex]x^4=16[/tex]Since the number has complex number as its rootsTherefore we can write [tex]x^4=(2i)^4[/tex] as below[tex]=2^4i^4[/tex] ( by using the formula [tex](ab)^m=a^mb^m[/tex] )
[tex]=16(1)[/tex] ( by [tex]i^2=-1[/tex] and [tex]i^4=(i^2)^2=(-1)^2=1[/tex] )
[tex]x^4=16=(2i)^4[/tex]
Therefore [tex]x^4=(2i)^4[/tex]
Since powers are same we can equate the bases ( bases are equal )
Therefore x=2i,2i,2i,2i are the roots of the given number 16 and they are complex numbers too
Write the quadratic equation whose roots are −2 and 4, and whose leading coefficient is 5.
Answer:
10x2 + 30x - 40
Step-by-step explanation:
If the two roots are -2 and 4 then the factors shall be;
5(x+2)(x-4)
5 is the leading coefficient.
FOIL:
f(x) = 5(x2+4x+2x-8) =
f(x) = 5(x2+6x-8) =
f(x) = 10x2 + 30x - 40
Answer:5x^2-10x-40=0
Step-by-step explanation:
x=-2 or x=4
x+2=0 or x-4=0
(x+2)(x-4)=0
x^2-4x+2x-8=0
x^2-2x-8=0
Multiply the equation by 5
5x^2-10x-40=0
Select Statistical or Not statistical to classify each question.
Question Statistical Not statistical
Which radio station does each of my friends prefer?
How far can each radio station broadcast its signal?
Which radio station is located on the west side of town?
Answer:1 yes. 2 yes. 3 no.
Step-by-step explanation:
i did it in the oms
e:-6=3:9 what is the blank
Answer:
e=-2
Step-by-step explanation:
3*x=9
3*3=9
x=3
e*x=-6
e*3=-6
e=-6/3
e=-2
Could a right triangle ever be an equilateral triangle?
Answer: An equilateral triangle can NOT be a right triangle.
Step-by-step explanation:
In a right triangle, however, the 3 angles can NOT be congruent. This is because in a right triangle, one angle equals 90 degrees. Therefore, you can't have 3 angles equal 90 degrees.
Answer:
n equilateral triangle can not be a right triangle. ... In a right triangle, however, the 3 angles can NOT be congruent. This is because in a right triangle, one angle equals 90 degrees. Therefore, you can't have 3 angles equal 90 degrees.
Step-by-step explanation:
Please mark me as brainliest... I really would appreciate that
A rectangular prism has a base that is 6 meters by 3.5 meters, and the prism is 9 meters high. What is the surface area of the prism?
Answer:
213 m^2
Step-by-step explanation:
The surface area for a rectangle prism is given by
A=2(wl+hl+hw)
We know the base is 6 meters by 3.5 m so l = 6 and width =3.5
The heigth is 9 m
A = 2 ( 6*3.5 + 9* 6 + 9* 3.5)
= 2 * (21 +54 +31.5)
= 2*(106.5)
=213 m^2
Answer:
213 square meters
Step-by-step explanation:
The surface area for a rectangle prism is given by
A=2(wl+hl+hw)
We know the base is 6 meters by 3.5 m so 6 * 3.5
The height is 9 m
A = 2 ( 6*3.5 + 9* 6 + 9* 3.5)
= 2 * (21 +54 +31.5)
= 2*(106.5)
=213 m^2
do these measurements represent the side lengths of a right triangle 12ft 20ft and 24ft
A. yes
B. No
Answer:
B. No
Step-by-step explanation:
We can test this theory using Pythagorean's theorem:
a² + b² = c²
12² + 20² = 24²
144 + 400 = 576
544 ≠ 576
So you can conclude that this is not a right triangle.
Graph a line that contains the point (-5,6) and has a slope of 2/3
Answer:
y= 2/3x + 28/3
Step-by-step explanation:
First, write your equation as y=2/3x+b. Plug in your coordinate into the equation, it should look like this: 6=2/3(-5)+b. Multiply 2/3 by -5 to get -10/3. It should look like this: 6= -10/3+b. Add 10/3 to both sides to get your y-intercept of 28/3. Go back to your original equation and plug 28/3 into b. This is your final equation: y= 2/3x + 28/3. Hope this helped!
6/8=y/16 how do you find the proportion of value y
Hi, I need help with my math please
Answer:
Answer:
A-H are all true facts except for C which is false. that you have to show and prove are true and false.
Rate of change Purr Island (5 questions name the letter to the workings answer and matched it) Show constant = 4 cats per year also seen as 40% rate of change. The common factor of 3 is only seen up on year 1 and year 4. as year 0 shows 2 and 4 does not fit into 2. Explain year 2 that 4 does not fit into 10 on year 2 does not as 2p-6p-10p-14p-18p may change 10p over the last 3 years and CF 3 does not fit into that or any individual (adjacent) proceeding years.
Step-by-step explanation:
The rate of change Meow Island : 3 of the 8 questions is asked to say true to all of them (name the letter to the answer the workings after you wrote this and matched it) Shows it triples = and yes they have common factors of 3 show 2, 6, 18, 54, 162 each share a common factor of 3, draw tree diagrams or show common factors of 3 and state you compare them to factors of 2 162>2x81 162> 3x27 54>2x27 54>3x18 18>2x9
18>3x6 6>2x3 6>3x2 2>2 population start number this doesnt have a common factor until it is factored into 6 ro show a common factor for 6. This also proves linear change occurs over the 4 years as population 2-156 is a series of 4 changes and underline the >3x numbers.
Help with this question
Answer:
158
Step-by-step explanation:
20 + 60 + 40 = 120 + 38 = 158
I think this is right. (I tired)
Find the slope of the line that passes through (9,3) and (6,3)
Answer:
0
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(3-3)/(6-9)
m=0/-3
m=0
find x when - 1/2 + x = - 21/4
Step-by-step explanation:
-1 / 2 + x = -21 /4
x = -21/4 + 1/2
x = (-21 + 2)/4
x = -19/4
A wise man once said,
“400 reduced by 3 times
my age is 244." How old is
the wise man?
The wise man's age can be calculated by solving the equation 400 - 3x= 244, leading to the solution that he is 52 years old.
To determine the wise man's age, we need to set up an equation based on the given statement:
Let's call the wise man's age x
The statement says, "400 reduced by 3 times my age is 244." This can be written as:
400 - 3x = 244
To find x, follow these steps
400 - 3x = 244
3x = 400 - 244
3x = 156
x = 156 / 3
x = 52
So, the wise man is 52 years old.
Greg's ceiling fan rotates 30 degrees and then stops. How many more times does it need to rotate to make a full rotation?
Answer:
330 degrees
Step-by-step explanation:
a full rotation is 360 degrees and if you subtract 30 from 360 its 330
Final answer:
To complete a full rotation, Greg's ceiling fan, which has already rotated 30 degrees, needs to rotate one more time, as there are 330 degrees left to reach 360 degrees, which is a full rotation.
Explanation:
Greg's ceiling fan rotates 30 degrees and stops. To determine how many more times the fan needs to rotate to complete a full rotation, first, we need to know that one full rotation is equal to 360 degrees. As the fan has already rotated 30 degrees, we subtract this from 360 degrees:
360 degrees - 30 degrees = 330 degrees.
Now, because one full rotation is 360 degrees, we divide the remaining degrees by 360 to find the number of additional rotations needed:
330 degrees / 360 degrees per rotation = 0.9167 rotations.
Since a fan cannot complete a fraction of a rotation in terms of action, Greg's ceiling fan would need to rotate one more time to make it a complete rotation.
what is the third angle of a triangle if two of the angles measure 29 ° and 87 °.
Answer:
64°
180°-29°-87°=64°
Edmond is on the third day of his hike up Glacier Peak. The graph below shows his hiking time and altitude for the third day only.
What was his altitude at the beginning of the third day?
A. 5,000 feet
B.
3,500 feet
C. 3,000 feet
D 4,000 feet
Answer: 3,500 feet
Step-by-step explanation:
To determine the original altitude for the third day, identify the y-intercept of the graph.
Therefore, the original altitude was 3,500 feet.
Answer: my question was a little different but i posted an image of the correct answer.
Step-by-step explanation:
To determine the original altitude for the third day, identify the y-intercept of the graph.
Therefore, the original altitude was 4,000 feet.
find the dimensions of the sports field at the right if the width is at least 60 yards AREA = 240 - 400X SQUARE YARDS
Answer:
The dimensions of the sports field are 80 yards and 3 - 5x yards
Step-by-step explanation:
1. Let's review the information provided to us to answer the question correctly:
Width of the sports field = At least 60 yards
Area of the sports field = 240 - 400x square yards
We can conclude the shape of the sports field is rectangular.
2. Find the dimensions of the sports field.
A. We need to find the Greatest Common factor between 240 and 400, this way:
The factors of 240 are: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240 .
The factors of 400 are: 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400 .
Then the greatest common factor is 80.
This GCF is also higher than 60, therefore it's one of the dimensions of the sports field.
Now, we calculate the other side of the sports, this way:
Second dimension of the sports field = (240 - 400x)/80
Second dimension of the sports field = 3 -5x
The dimensions of the sports field are 80 yards and 3 - 5x yards
Answer:
80(3-5x)
Step-by-step explanation:
240-400x
GCF: 80
Factored expression: 80(3-5x)
Janet has three coins.
One coin has a value
that is 5 times another
coin. The third coin has
a value that is 2 times
another coin. She has
404 altogether. What
coins does she have?
Write an equation to
represent your work and
solve.
Answer:
Janet has coins worth 252.5, 101, and 50.5.
Step-by-step explanation:
Let us call the three coins [tex]a,b[/tex], and [tex]c[/tex].
The first coin [tex]a[/tex] is 5 times another coin (let's say [tex]b[/tex]); therefore,
[tex]a = 5b[/tex],
and the third coin is 2 times the value of another coin (it's coin [tex]b[/tex]):
[tex]c =2b[/tex].
The total worth of all coins is 404; therefore,
[tex]a+b+c =404[/tex]
or
[tex]5b+b+2b =404[/tex]
[tex]8b =404[/tex]
[tex]\boxed{b = 50.5}[/tex]
with the value of [tex]b[/tex] in hand, we find [tex]a[/tex] and [tex]c[/tex]:
[tex]a = 5b = 5(50.5)[/tex]
[tex]\boxed{a = 252.5}[/tex]
and for [tex]c:[/tex]
[tex]c = 2 b = 2 (50.5)[/tex]
[tex]\boxed{c = 101}[/tex]
Thus, Janet has 3 coins worth 252.5, 101, and 50.5.
The formula f(x + 1) = Two-thirds(f(x)) defines a geometric sequence where f(1) = 18. Which explicit formula can be used to model the same sequence?
C. f (x) = 18 (2/3)x-1
Step-by-step explanation:
I got it right on edge. please mark brainliest!!
Use the dot plot to answer questions.
Deanna's mean score is approximately
90
90.93
92
92.4
Amy's mean score is approximately
88.5
90
90.27
92.4
Answer:
90.93 and 90.27
Step-by-step explanation:
Solve the system of linear equations using elimination.
−2x − y = 3
−9x − y = 17
A)
(2, 1)
B)
(2, −1)
C)
(−2, 1)
D)
(−2, −1)
PLEASE HELP I NEED IT BY TODAY
Answer:
C (-2,1)
Step-by-step explanation:
−2x − y = 3 (1)
−9x − y = 17 (2)
(1) y = -2x - 3
(2) y = -9x - 17
-2x - 3 = -9x - 17
7x = -14
x = -2
y = -2(-2) - 3
y = 4 - 3
y = 1
Evaluate the expression. 33 + 6( 2 + 36 )
Answer: 261
Step-by-step explanation:
You use PEMDAS to solve this problem
you first do the Parenthesis (p)
33+6(2+36)
33+6 (38)
We then multiply first (M)
33 + 6(38) - we know that 8 times 6 is 48 ; 6 times 3 is 18 +4 because we brought down the 4 from 48 to 3. which will be equal to 228
33 + 228
261
The equation 4 + 9 = 4 + 9 is an example of which property of equality? *
Transitive
Symmetric
Substitution
Reflexive
Answer:
Reflexive
Step-by-step explanation:
The reflexive property of equality says that a given real number is always equal to itself.
For example :
[tex]y = y[/tex]
[tex]a = a[/tex]
[tex]b = b[/tex]
[tex]5 = 5[/tex]
are all examples of reflexive properties of equality.
[tex]4 + 9 = 4 + 9[/tex]
can be simplified to
[tex]13 = 13[/tex]
Which is explains why it is the reflexive property.
A wagon is on sale for 20% off. The sale price of the wagon is $114. What was the original price of the wagon assuming no sales tax is paid on the item? Report your answer to two decimal places. Do not include the dollar sign, $, in the answer box below.
To calculate the original price of a wagon on sale at 20% off, divide the sale price of $114 by 0.80, resulting in the original price of $142.50.
To find the original price of the wagon before the 20% sale, we have to determine what $114 represents after the discount has been applied. If $114 is 80% of the original price (100% - 20% = 80%), we need to find 100% by dividing $114 by 0.80:
Original Price = Sale Price / (1 - Discount Percentage)
Original Price = $114 / 0.80
Original Price = $142.50
So, the original price of the wagon before the sale was $142.50.