Find equations that enclose a region such that when rotated about the x -axis, a solid is produced with a volume of 18π cubic units.

He played 7480 minutes across three years.

The information provided, expressed in minutes per year, is as follows:

The first year is 2181 minutes, the second is 2583 minutes, and the third is 2716 minutes.

Add that now to determine the total amount of time:

The sum of the three years is 7480 minutes (2181 + 2583 + 2716).

The gamer used 7480 minutes throughout the course of three years.

The measurement of continuously occurring events is done in terms of time. In hours, seconds, and minutes, it is measured. The well accepted established formulae can be used to compute it.

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For sequence: 17,8,-1, ., the explicit formula is a(n) = 26 - 9n, the recursive formula is a(n) = a(n-1) - 9

To find the recursive and explicit formula, we need to find the common difference (d) first.

In an arithmetic sequence, the common difference is the difference between two consecutive terms.

So, in the given sequence: 17,8,-1, ..

d = a(2) - a(1) = a(3) - a(2)

d = 8 - 17 = -1 - 8 = -9

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The drawing of rectangle that has diagonal twice as long as its width is attached with this.

The equation for the length of the rectangle is l = [tex]\sqrt{3} x[/tex]

Given,

Width of rectangle, w= x

Diagonal of rectangle, d = 2x

We have to find the equation for length of rectangle.

We know that d² = l² + w²

Here,

(2x)² = l² + x²

4x² = l² + x²

l² = 4x² – x²

l² = 3x²

l = [tex]\sqrt{3}[/tex]x

That is the equation for length of rectangle is l = [tex]\sqrt{3}[/tex]x

Lets take width of rectangle, x = 3

Diagonal of rectangle, d = 2 × 3 = 6

L = [tex]\sqrt{3}[/tex] × 3 = 5.20

Here we proved that the equation is correct.

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3*3=9

4*3=12

9*12=108 sq feet

Answer:

[tex]2 \sqrt{45} [/tex]

Answer: (1) y= 2*4-1

(2) y= 2*0-1

Step-by-step explanation:(1) y=8-1

y=7

(2) y=0-1

y= -1

Answer:

Step-by-step explanation:

10² + 2(6 - 3)²

100 + 2 (3)²

100 + 2(9)

100 + 18

118

The exact length of the line segments whose endpoints are (10, 1) and (9, -4) is √37

The points are given as (10, 1) and (9, -4)

The exact length of the line segments whose endpoints are (10, 1) and (9, -4) is calculated as

d = √[(x2 - x1)^2 + (y2 - y1)^2]

So, we have

d = √[(10 - 9)^2 + (1 + 5)^2]

Evaluate

d = √37

Hence, the exact length of the line segments whose endpoints are (10, 1) and (9, -4) is √37

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The length of the third side of the right triangular flower bed is 10 feet.

A right-angled triangle is a triangle with one of its interior angles equal to 90°. The side opposite to the right angle is the largest side and is referred to as the hypotenuse. Hypotenuse is always greater than any of the other two sides.

If two of the sides of the flower bed are 7 feet long each, then these are the sides adjacent to the right angle. We are to find the length of the third side, which is the hypotenuse, using the Pythagorean theorem.

Pythagorean Theorem states that the square of the length of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the two other sides.

c^2 = a^2 + b^2

where a and b are the adjacent sides to the right angle

c is the hypotenuse

c^2 = 7^2 + 7^2

c^2 = 49 + 49

c^2 = 94

c = 9.899

Hence, he length of the third side of the right-angled triangular flower bed is 10 feet.

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The value of x for the quadratic equation is  1.099 or -9.099 .

What is completing the square?

Completing the Square is a method used to solve a quadratic equation by changing the form of the equation so that the left side is a perfect square trinomial .

To solve ax²+bx+c=0 by completing the square:

1.  Transform the equation so that the constant term, c , is alone on the right side.

2.  If a , the leading coefficient (the coefficient of the x² term), is not equal to 1 , divide both sides by a .

3.  Add the square of half the coefficient of the x -term,  to both sides of the equation.

4.  Factor the left side as the square of a binomial.

5.  Take the square root of both sides.  (Remember: (x+q)²=r is equivalent to x+q= ±√ r.)

6.  Solve for x .

According to the question

Quadratic equation by completing the square

x² + 8x = 10  

As we will try to make complete square of left side

for that

we have to add   to both sides of the equation

As

a = 1

2ab = 8

b = 4

x² + 8x + 4² = 10 + 4²

By using the identity (  )

(x + 4)² = 10 + 16

(x + 4)² = 26

x + 4 = ±

x + 4 = ± 5.099  

x = 5.099 - 4

x = 1.099

or

x = -5.099 - 4

x = -9.099

Hence, The value of x for the quadratic equation is  1.099 or -9.099 .

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It involves determining the fundamental quantities and units of measurement and tracking these dimensions while computations or comparisons are made.

Now, in that equation above, b represents the velocity of the motion. Now, the formula for velocity is;

Velocity = Distance/Time

Now, distance is also named Length and represented by L in basic parameters units while Time is represented by T.

Thus, the dimensions of b are; L/T or expressed as LT⁻¹.

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Answer:

316 or -316.

Step-by-step explanation:

x^3 - y^3 = (x - y)(x^2 + xy + y^2)

               = 4(x^2 + y^2 + 21)

x - y = 4

xy = 21

Substitute x = 4 + y in the last equation

(4 + y) y = 21

y^2 + 4y - 21 = 0

(y + 7)(y - 3) = 0

y = 3, -7.

So, x = 7, - 3.

So,  x and y are 7 and 3 or -7 and -3.

But x^2 + y^2 = 9 + 49 = 58 whichever is true,

So, x^3 - y^3

= 4(x^2 + y^2 + 21)

= 4 (58 + 21)

= 316,

If x = -3 and y = -7 , then the answer is

-316.

Answer:

Part 1: The equation has no solution

Part 2: A value of a that makes the equation false is 2, which when substituted into the equation and simplified makes the equation turn into 2=4.

Another value of a that makes the equation false is -1, which when substituted and simplified makes the equation turn into -1=1.

There are honestly a lot of possible values for x for the second part here, but let me know if this is right

Step-by-step explanation:

Give me brainliest if that helped :)

Answer: 2:3, 6:1, 4:1, 6:1

Step-by-step explanation:

The first step is by finding the GCF. For 24:36 the GCF is 12. Once you divide you get 2:3. For 12:2 the GFC is 2. For 16:4 it is 4 and you get 4:1 and finally 18:3 the GCF is 3 and you get 6:1.

The area of one of the slices is  54π square inches

The given parameters are

Diameter = 36 inches

Number of slices = 6

The pie represents take the shape of a circle

And the area (A) of a circle using the diameter (d) is

A= π(d/2)^2

Multiply the above area by 1/6 to get the area of a slice of the pie

So, we have

Area = 1/6 * π(d/2)^2

This means that the area of one of the slices is calculated by

Area = 1/6 * π(d/2)^2

Where

d represents the diameter of the pie i.e. d = 36 inches

So, we have

Area = 1/6 * π * (36/2)^2

Evaluate

Area = 54π

Hence, the area of one of the slices is  54π square inches

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After calling the parents, and explaining them the issue of smashed phone, they travelled at a speed of 2.223 m/s = 8.0028 km/hr

As per the question statement, we are given that we call our parents to explain our issue with having a smashed phone and your parents travel at 20000 meters in 2.5 hours. We are supposed to find out that how fast did the parents rush to get here. Basically we have to find their speed of travelling.

Before solving the question, we must be aware that what is speed.

[tex]speed = \frac{distance}{time}[/tex]

and distance and time should be in SI units.

Given distance = 20,000 meters

Given time = 2.5 hours

[tex]1 hour = 60 min\\2.5 hour = 2.5*60\\2.5 hour = 150 min[/tex]

[tex]1 min = 60 sec\\150 min = 150*60 sec\\150 min= 9000 sec[/tex]

Therefore given time = 9000 sec

Therefore speed = [tex]\frac{distance}{time} = \frac{20000}{9000}[/tex]

Speed= 2.223 m/sec

Hence they travelled at a speed of 2.223 meters per second

2.223 m/s = 8.0028 km/hr

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[tex]f(x) = 4x^2+3\\f(-1)=4(-1)^2+3\\f(-1)=\boxed{7}[/tex]

Answer:

(x - 1)^2 =1/2 ( y - 5) or 2x^2 - 4x - y + 7 = 0

Step-by-step explanation:

(x - 1)^2 =1/2 ( y - 5)

or

x^2 - 2x + 1 = y/2 - 5/2

2x^2 - 4x + 2 - y + 5 = 0

2x^2 - 4x - y + 7 = 0

Summit (1,5) = (h,k)

4p = 2

p = 1/2

(x - h)^2 = 1/2(y - k)

The required equation is 6x+7=331 and the no. of students traveling on each bus is 54.

A mathematical equation can be defined in a variety of ways. In its most basic form, an equation is a mathematical statement that shows that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. One or more variables are used in the most basic and simple algebraic equations in mathematics.

Given data:

Total no. of students: 331

Number of students on bus = 7

No. of buses = 6

Let the no. of the students on each bus be x.

So according to the given condition,
6x+7=331

6x=331-7

6x=324

x=324/6

x=54

Therefore, the required equation is 6x+7=331 and the no. of students travelling on each bus is 54.

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Answer:

the midpoint is (-5,1)

Step-by-step explanation:

Answer: 55 degrees

Step-by-step explanation:

a+90+35=180 ==> a straight line measures 180 degrees and the angles a, a right angle, and 35 lie on that line. A 180 degree angle is called a straight angle. Also, if there is a tiny box in between an angle, that means that the angle is a right angle.

a+125=180

a+125-125=180-125

a=180-125

a=55 degrees

The algebraic expression of the mathematical statement is given as "The sum of k and 8" is k + 8

The mathematical statement is given as:

The sum of k and 8

In algebraic expression, "Sum" means +

This means that, the interpretation of the question is that we add k and 8

So, we have the following algebraic representation:

The sum of k and 8 ⇒ k + 8

Remove the mathematical statement in the above algebraic representation

i.e. k + 8

Hence, the algebraic expression of the mathematical statement is given as "The sum of k and 8" is k + 8

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The piece of meat has a weight of 1,800g.

So, as the question says allow 30 minutes of cooking to each 450g.

Similarly,

Therefore, the piece of meat has a weight of 1,800g.

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Answer:

1800

Step-by-step-explanation:

Answer:

a < -2.

Step-by-step explanation:

14 < -2a + 6-2a

14 < -4a + 6

14 - 6 < -4a

-4a > 8

Divide both sides by -4:

a < -2.

Note that the inequality flips because we are dividing by a negative number.

-89 can be represented by using 8-bit two's compliment as 10100111.

Binary encoding can be defined as a standard technique that is designed and developed to convert data in plain text (source alphabets) to a form that is easily used by different operating systems (OS), especially through the use of a binary digit (bit) or two-symbol system.

In Computer programming, two's complement of base-10 is generally easier to implement because it has a single representation of 0 only.

First of all, we would determine the positive version of -89, which is 89:

2 | 89

2 | 44 R 1

2 | 22 R 0

2 | 11 R 0

2 | 5 R 1

2 | 2 R 1

2 | 1 R 0

2 | 0 R 1

Next, you would read the decimal number (base-2) upward and this gives:

89₂ = 01011001.

For the negative integer number representation on 8-bits, we would replace all the 0s with 1s and the 1s with 0s as follows:

01011001 = 10100110

For the 8-bit two's complement, we would add 1 to the above number:

-89 = 10100110 + 1

-89 = 10100111.

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Answer:

64

Step-by-step explanation:

2^6=2x2x2x2x2x2 which then equals to 64

The resale value is not significantly higher than the cost of remodeling a kitchen based on the computed p-value of 0.42 and 0.21.

Both the p-values of 0.42 and 0.21 are greater than the level of significance of 0.05. Hence, we fail to reject the null hypothesis. So, the resale value is not significantly higher than the cost of remodeling a kitchen based on the computed p-value of 0.42 and 0.21.

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The number of hours Aisha worked babysitting and landscaping last week is 7.9 hours and 9.9 hours respectively.

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

We have been given that Aisha is working two summer jobs, making $7 per hour babysitting and $8 per hour landscaping

Let the number of hours babysitting would be x

And the number of hours landscaping would be y

Last week Aisha worked 2 more hours babysitting than hours landscaping and earned a total of $134.

y = x + 2

7x + 8y = 134

Substitute the value of y = x + 2 in the equation,

7x + 8(x + 2) = 134

7x + 8x + 16 = 134

15x = 134 - 16

15x = 118

x = 118/15

x = 7.9

Substitute the value of x = 7.9 in the equation y = x + 2 ,

y = 7.9 + 2

y = 9.9

Therefore, the number of hours Aisha worked babysitting and landscaping last week is 7.9 hours and 9.9 hours respectively

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Answer:

(x,y)=(10,8)

Step-by-step explanation:

Let x be hours worked babysitting and y be hours worked landscaping.

We would have our first equation, 7x+8y=134.

Knowing that she worked 2 more hours babysitting than landscaping, we can determine and replace the x variable as: x=y+2

7(y+2)+8y=134

Use the distributive property to multiply 7 by y+2.

7y+14+8y=134

Combine 7y and 8y to get 15y.

15y+14=134

Subtract 14 from both sides.

15y=134−14

Subtract 14 from 134 to get 120.

15y=120

Divide both sides by 15.

y=120/15​

Divide 120 by 15 to get 8.

y=8

and since she worked 2 more hours babysitting, x=10.

Let's replace our values in the original equation:

7x+8y=134

7(10)+8(8)=134.

70+64=134.

Therefore, we can conclude that Aisha worked 10 hours babysitting and 8 hours landscaping last week.

Hope this helped!

Answer

.50x + 6

If you need a step-by-step explanation or just the explanation tell me

The equation of the line in slope-intercept form is y = (-2)x + (-3)  .

The equation of a line in slope-intercept form can be written as follows,

y = mx + c                                                       equation 1

m in the above equation represents slope of the line and c represents the intercept.

The given equation is 3y + 9 = -6x .

To get the equation of the line in slope-intercept form we need to convert the given equation in the format of equation of a straight line i.e., equation1. So, now we will rearrange the given equation as

3y + 9 = -6x

3y = -6x - 9

On dividing both sides of above equation by 3, we will get

y = (-2)x + (-3)                                                 equation 2

On equating equation 1  and equation 2, we will get

Slope of the line = m = -2

Intercept = c = -3

The equation of the line in slope-intercept form is y = (-2)x + (-3)  .      

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