A perfect square is a number that you get by multiplying a number by itself e.g., 3 x 3 = 9. The following is a pattern of perfect squares: 1, 4, 9, 16, 25. Draw arrays on a grid that might help someone predict the next four terms of the pattern 1, 4, 9, 16....
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Step-by-step explanation:

Given

Area of rectangle (A) = 243.9 m²

Length (L) = 15 m

first calculating the breadth (b)

We know

L * b = A

15 * b = 243.9

b = 243.9/ 15

b = 16.26 m

Now

Perimeter (p)

= 2 ( L + b)

= 2 ( 15 + 16.29)

= 62.58 m

Hope it will help

If area of a rectangle is 243.9 m2. If the length is 15 m, then  perimeter of the rectangle is 62.58 m.

The area of Rectangle is length times of width.

Given,

Area of rectangle (A) = 243.9 m²

Length (L) = 15 m

To find the  perimeter we need to know the breadth

Calculate the breadth (b)

Area=Length×Breatdth

243.9=15 × b

Divide both sides by 15

b = 243.9/ 15

b = 16.26 m

Perimeter= 2 ( Length + breadth)

= 2 ( 15 + 16.29)

= 62.58 m

Hence  the perimeter of the rectangle is 62.58 m.

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Answer:

line segment

Step-by-step explanation:

the answer is above

The equation of the circle centered at the origin and passing through the point (-4,0) is \(x^2+y^2=16\).

Equation of a circle

A circle may also be defined as a special kind of ellipse in which the two foci are coincident, the eccentricity is 0, and the semi-major and semi-minor axes are equal.

We know that,

Equation of the circle passing through the origin is given by:-

\(x^2+y^2=r^2\)

Where,

r is the radius of the circle, and

(x,y) are the coordinates of each point of the circle.

Hence, we can write,

The radius of the circle will be :-

\(\sqrt{(0-(-4))^2+(0-0)^2} =\sqrt{ 4^2+0^2} =\sqrt{16}=4 units\)

Hence, r = 4 units.

Hence, the equation of the circle is given by:-

\(x^2+y^2=16\)

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The solution to this puzzle is 10+3 = 13

To solve this the values at the top of the star were gotten by the addition of two values inside the stars.

Therefore the answer to this question is 13.

Another way of getting the value is by adding 15 + 16 = 31

12 + 6 = 18

31-18 = 13

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Answer:

8 rides

Step-by-step explanation:

20 + .50x = 24

-20             -20

.50x = 4

/.50    /.50

x = 8

Answer:

8

Step-by-step explanation:

If you have $24 and you buy a $20 ticket to get in, you are left with four dollars.

Since each ride is $0.50 and that is half a dollar, you can multiply four times two. This gives you eight.

Therefore, you can ride 8 rides :)

Therefore, the above sides  and angles will be the corresponding angles and sides of a similar triangle.

Triangle congruence: Two triangles are said to be congruent if all three of their corresponding sides and all three of their corresponding angles have the same measurements. These triangles can be moved around, rotated, flipped, and turned to have an identical appearance.

Here,

In the event that "CAT"

As per SSS guideline, we receive

CA=DO

AT=OG

CT=DG

The congruent triangles' corresponding angles will also be:

∠CAT = ∠DOG

∠ATC = ∠OGD

∠ACT = ∠ODG

Two triangles are similar if they are congruent with one another.

if ∆CAT≅∆DOG

Next,∆CAT~∆DOG

As a result, the angles and sides of the triangle with the same sides as those above will be the same.

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Answer:

answer is 13

Step-by-step explanation:

10+10+10=30
10+4+4=18
4-2=2
(-1)+4+10= 13

Answer:

Step-by-step explanation:

10 + 10 + 10 = 30

10 + 4 + 4 = 18

4 - 1 - 1 = 2

1 + 4 + 10 = 15

Answer:

I'm not sure what your choices are or if you have any choices. Try y+ 1/2 = 3(x-2)

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

on edg2021

Answer:

9 gallons were used

Step-by-step explanation:

There are 8 pints to 1 gallon

72 jars holding 1 pint each means 72 pints total

72/8=9

Beth used 9 gallons

P.S. Can I get brainlist

The solution to the given differential equation is \(y(x) = -x^4/25 + x^2/15 - (3/25)e^(-3x) + (1/2)x^4cos(x) + (1/2)x^2sin(x) + C1e^(-3x) + C2\), where C1 and C2 are arbitrary constants.

To solve the given differential equation using the method of undetermined coefficients, we assume a particular solution of the form \(y_p = A(x^4 + Bx^2e^(-3x) + Csin(x))\), where A, B, and C are undetermined coefficients.

Step 1:

Differentiating y_p with respect to x, we obtain \(y_p' = 4Ax^3 + 2Bx(e^(-3x) - 3xe^(-3x)) + Ccos(x).\)

Taking the second derivative, we have \(y_p" = 12Ax^2 + 2B(e^(-3x) - 3xe^(-3x)) + 2Bx(-3e^(-3x) + 9xe^(-3x)) - Csin(x).\)

Step 2:

Substituting y_p, y_p', and y_p" into the given differential equation, we get:

\((12Ax^2 + 2B(e^(-3x) - 3xe^(-3x)) + 2Bx(-3e^(-3x) + 9xe^(-3x)) - Csin(x)) + 5(4Ax^3 + 2Bx(e^(-3x) - 3xe^(-3x)) + Ccos(x)) = 2x^4 + x^2e^(-3x) + sin(x).\)

Simplifying the equation and grouping the like terms, we have:

\((12A + 20Ax^3) + (-6B + 10Bx)e^(-3x) + (-15Bx^2 + 9Bx^3) + (12A + 10C)cos(x) + (-C + 2Bx)sin(x) = 2x^4 + x^2e^(-3x) + sin(x).\)

Comparing the coefficients of the terms on both sides, we can determine the values of A, B, and C. Equating the coefficients of each term, we obtain:

\(12A + 20Ax^3 = 2x^4,\)

\(-6B + 10Bx = x^2e^(-3x),\)

\(-15Bx^2 + 9Bx^3 = 0,\)

12A + 10C = 0,

-C + 2Bx = sin(x).

Solving these equations, we find A = -1/25, B = 1/15, and C = 0.

Therefore, the particular solution is \(y_p = (-1/25)x^4 + (1/15)x^2e^(-3x) + (1/2)x^2sin(x).\)

To obtain the general solution, we add the particular solution y_p to the complementary function y_c, where y_c is the solution of the homogeneous equation y" + 5y' = 0. The general solution is given by y(x) = y_c + y_p.

The complementary function can be found by solving the homogeneous equation:

y" + 5y' = 0.

The characteristic equation associated with the homogeneous equation is r^2 + 5r = 0. Solving this quadratic equation

, we find two distinct roots: r = 0 and r = -5.

Therefore, the complementary function is \(y_c = C1e^(-5x) + C2\), where C1 and C2 are arbitrary constants.

Finally, the general solution to the given differential equation is:

\(y(x) = C1e^(-5x) + C2 - (1/25)x^4 + (1/15)x^2e^(-3x) + (1/2)x^2sin(x).\)

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Answer:

8/12-1/5=7/15 reduce 8/12 to 2/3

Answer:

Step-by-step explanation:

Dont do it. Just take the detention

Answer:

Is it   -13/10 ?

Step-by-step explanation:

I'm really not sure

Answer:

I think 60.00 is the answer

Step-by-step explanation:

hope you like my answer

The results for systems under rotational motion are listed below:

First section:

Part A - The angular speed of the large gear is 90π radians per minute.

Part B - The linear velocity of the large gear is 27π centimeters per minute.

Part C - The linear velocity of the smaller gear is 27π centimeters per minutes.

Part D - The angular speed of the smaller gear is 27π / 8 radians per minute.

Part E - The angular speed of the smaller gear is 27 / 16 revolutions per minute.

Second section:

Part A - The angular speed of the LP is 200π / 3 radians per minute.

Part B - The angular velocity of the LP is 200π / 3 radians per minute.

In the first part of this question we find the case of rigid transmission system under rotational motion, two gears that transmits power and whose angular speed ratio is shown below:

ωL / ωS = rS / rL

Where:

And the linear velocity (v), in centimeters per minute, is calculated by this formula:

v = rL · ωL = rS · ωS

Part A - How many radians per minute is the large gear turning?

R/ The angular speed is:

ωL = 45 rev / min × 2π rad / rev

ωL = 90π rad / min

Part B - What is the linear velocity of the teeth on the large gear?

v = (0.3 cm) · (90π rad / min)

v = 27π cm / min

Part C - What is the linear velocity of the teeth on the smaller gear?

v = 27π cm / min

Part D - How many radians per minute is the smaller gear turning?

ωS = v / rS

ωS = (27π cm / min) / (8 cm)

ωS = 27π / 8 rad / min

Part E - How many revolutions per minute is the smaller gear turning?

nS = 27π / 8 rad / min × (1 / 2π rev / rad)

nS = 27 / 16 rev / min

The second part uses the same kinematic equation used in the previous part:

Part A - How many radians per minute is this:

ω = (33 + 1 / 3 rev / min) × (2π rad / rev)

ω = 200π / 3 rad / min

Part B - Find the angular velocity:

The angular velocity is independent from radius of rotation, thus:

ω = 200π / 3 rad / min

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Answer: i think x

Step-by-step explanation:

x squared is x multiplied by x so doing the square root just gets rid of the square

Answer:

It will be 72cm

Step-by-step explanation:

Volume of a rectangular prism = (length x width x height) cubic units.

9x4x2=72

The Venn Diagram for showing odd numbers and prime numbers would be :

Odd numbers :

Prime number :

Both prime and odd:

4 is not to be included in the Venn Diagram.

Prime numbers are positive integers that have exactly two distinct divisors, which are 1 and the number itself. In other words, a prime number is a number greater than 1 that is divisible only by 1 and itself.

1 is an odd number but not a prime number. 2 is a prime number but not an odd number. 3 and 5 are both odd and prime numbers.

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Answer: it = dady

Step-by-step explanation:

1 _545454 yv 4h4te

The number of times the digit '3' is needed to label the gym lockers numbered from 1 to 99 is 20 times.

We can analyze the pattern of numbers from 1 to 99 to determine the frequency of the digit '3'.

From 1 to 9, there is only one number that contains the digit '3', which is 3 itself.

Therefore, there is one occurrence of '3' in this range.

From 10 to 19, there are ten numbers, and only one of them, 13, contains the digit '3'.

From 20 to 29, there is only one number that contains the digit '3', which is 23.

From 30 to 39, there are ten numbers, and each one of them contains the digit '3'.

Following this pattern, we can see that the digit '3' appears 20 times between 1 and 99.

Hence, we need the digit '3' a total of 20 times to label all the gym lockers numbered from 1 to 99.

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Finding the Inverse of a Polynomial Function by Restricting the Domain

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The work done in propelling the lunar module from the surface of the moon to a height of 40 miles is 3,571,607,996 Joules.

This can be calculated as follows:

Weight of the lunar module on the surface of the Earth = 12 tons
converting weight to mass = weight/acceleration due to gravity
mass = 12 x 1000 / 9.81
mass = 1,224.6 kg

The force required to lift the module off the surface of the moon is equal to its weight, which is given by the formula:
force = mass x acceleration due to gravity
force = 1,224.6 x 1.62
force = 1,982.8 N

Calculating the total distance traveled:
distance = 1,737.1 + 64.37
distance = 1,801.47 km

Calculating the work done:
work = force x distance
work = 1,982.8 x 1,801,470
work = 3,571,607,996 J

Therefore, the work done in propelling the lunar module from the surface of the moon to a height of 40 miles is 3,571,607,996 Joules.

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The minimum weight for the prize is given as follows:

683.2 lbs.

We first must use the z-score formula, as follows:

\(Z = \frac{X - \mu}{\sigma}\)

In which:

The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, and can be positive(above the mean) or negative(below the mean).

The z-score table is used to obtain the p-value of the z-score, and it represents the percentile of the measure represented by X in the distribution.

The mean and the standard deviation for this problem are given as follows:

\(\mu = 600, \sigma = 65\)

The 90th percentile is X when Z = 1.28, hence it is given as follows:

1.28 = (X - 600)/65

X - 600 = 65 x 1.28

X = 683.2 lbs.

The mean and the standard deviation for this problem are given as follows:

\(\mu = 600, \sigma = 65\)

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When we subtract a velocity vector from another velocity vector, the result is B. another velocity.

When we subtract a velocity vector from another velocity vector, we are essentially finding the difference between the two velocities. This difference is also a velocity vector, but in a different direction and with a different magnitude. Therefore, the answer is another velocity, option B.

It is important to note that acceleration is a change in velocity, not the result of subtracting one velocity from another. Scalar refers to a quantity with only magnitude, whereas velocity is a vector quantity with both magnitude and direction. Displacement refers to the change in position of an object and is not directly related to subtracting velocity vectors.

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Answer:

Step-by-step explanation:

p(x) = 2x² - 4x

g(x) = x - 3

To find (pog)(x) replace every x in p(x) by g(x)

That's

(pog)(x) = 2(x - 3)² - 4(x - 3)

= 2( x² - 6x + 9) - 4x + 12

= 2x² - 12x + 18 - 4x + 12

Hope this helps you

Answer: -2.25

9x+4y=8

4y=-9x+8

y= -9/4x+8/4

y=-2.25x+2

I hope this is good enough:

Answer:

=6×3/4×3

Now, 3cut3

=6×4

=24

"Mathematics for the Practical Man" is a book that aims to provide a simplified and quick explanation of various mathematical concepts such as algebra, geometry, trigonometry, logarithms, coordinate geometry, and calculus.

The book is targeted towards individuals who may not have a strong background in mathematics, but need to understand these concepts for practical purposes.

The book is divided into chapters that cover each topic in depth, providing clear explanations and examples for the reader to follow. The language used in the book is simple and easy to understand, without sacrificing the accuracy and rigour of the mathematical concepts being taught. Overall, "Mathematics for the Practical Man" is a useful resource for anyone who needs to quickly and easily learn or refresh their knowledge of key mathematical concepts.

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The 4 is the number the student thought about.

To solve this problem, we will use algebraic expressions. First, let us define the unknown number, x. The problem states that "4 times my number increased by 30 equals 70 decreased by the number." This can be translated into the following equation:

4x + 30 = 70 - x

To solve for x, we need to isolate it on one side of the equation. Let's start by moving all the terms with x to the left side and all the constant terms to the right side.

4x + x = 70 - 30x + 4x + x = 40

Simplifying, we get:

10x = 40

Dividing both sides by 10:

x = 4

Therefore, the number that the student thought of is 4.

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