Use Polya's four-step problem-solving strategy and the problem-solving procedures presented in this lesson to solve the following exercise. Find the following sums without using a calculator or a formula. Hint: Apply the procedure used by Gauss. (See the Math Matters on page 31.) (a) 1 + 2 + 3 + 4 + . . . + 397 + 398 + 399 + 400 (b) 1 + 2 + 3 + 4 + . . . + 542 + 543 + 544 + 545 (c) 2 + 4 + 6 + 8 + . . . + 72 + 74 + 76 + 78

Answer:

a = -41 +30n

52nd term is

a52 = -41 + 30(52)

a52 = -41 + 1560

a52 = 1519

-3.2(-5.6)(4)

= -3.2 - 5.6 x 4

= -3.2 - 22.4

= -25.6

Answer:

congrats you just found 118,222.36 pounds of pennies worth $134,061.9

you should buy a house or car with 59 tons of pennies

Answer: B and C

explanation: The volume of solids are expressed in cubic measurements such as cubic centimeters (cm^3) or cubic meters (m^3).

Combine the same numbers and do the opposite of either subtraction or addition.

Then, multiply or divide with the coefficient.

Answer:

see below

Step-by-step explanation:

⇒  7x - 17 = 4x + 1

combine like terms

7x - 4x = 1 + 17

3x = 18

x = 18/3

x = 6

⇒  -x + 5 = x - 11

combine like terms

- x - x = - 11 - 5

-2x = -16

x = 16 / 2

x = 8

⇒  5x + 8 = 7x + 2

combine like terms

5x - 7x = 2 - 8

- 2x = - 6

x = 6 / 2

x = 3

The answer is 1.158505

Answer:

Step-by-step explanation: 12 ur welcome

Speed is Distance traveled/time, then 12 kilometer per min is the cruising speed of airplane when airplane cruises 1 kilometer in 1 12 of a minute.

Speed=Distance traveled/time

An airplane cruises 1 kilometer in 1 12 of a minute. We need to find the speed.

Given distance=1 km

time=1/12 min

We need to find speed.

Speed=Distance traveled/time

=1/(1/12)

=1*12/1

=12kilometerperminute

Therefore 12 kilometer per meter is the speed required.

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Answer:

1461321

Step-by-step explanation:

Answer:

The radius of the volleyball is 8.3 inches

Step-by-step explanation:

Given

[tex]r = \sqrt{\frac{3v}{4\pi}}[/tex]

[tex]v = 288[/tex]

Required

Determine the value of r

To do this, we simply substitute 288 for v and 3.14 for π in the given equation.

This gives

[tex]r = \sqrt{\frac{3v}{4\pi}}[/tex]

[tex]r = \sqrt{\frac{3 * 288}{4 * 3.14}}[/tex]

[tex]r = \sqrt{\frac{864}{12.56}}[/tex]

[tex]r = \sqrt{68.7898089172}[/tex]

[tex]r = 8.29396219651[/tex]

[tex]r = 8.3\ inch[/tex] (Approximated)

Hence;

The radius of the volleyball is 8.3 inches

Answer: 4.1 inches

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

b is the answer

the range is all real number

Answer:

-10

Step-by-step explanation:

well you know that

[tex](-)(-)=(+)[/tex]

so we have

[tex]-21-(-11)\\\\=-21+11\\\\=-10[/tex]

Answer:

Week 4

Step-by-step explanation:

Ben has $250 in the beginning.  He saves $150 per week.

y = 150x + 250

Tim has $1,650 in the beginning.  He spends $200 per week.

y = 1650 - 200x

We are trying to find which x-value produces the same y-value for both equations.  You can do this by setting both equations equal to each other.

150x + 250 = 1650 - 200x

(150x + 250) + 200x = (1650 - 200x) + 200x

350x + 250 = 1650

(350x + 250) - 250 = (1650) - 250

350x = 1400

(350x)/350 = (1400)/350

x = 4

By week 4, they will have the same amount of money.

Answer:you need to multiply it by 4.

Step-by-step explanation:

If the number is multiplied by 4 it square root is effectively doubled.

Example: if you take the square root of 64, its 8.

to double the square root, you multiply 64 by 4---> 256.

And the square root of 256, is 16, double that of the square root of 64.

Answer:

the sum of 6+6 is 12

Step-by-step explanation:

so the sum of the number 6+6 is 12 plz like and rate

x=-5 ___________________

The question is an illustration of linear equation, and the solution to the linear equation is x = -5

The equation is given as:

[tex]\frac 23x - \frac 12 = \frac 13 + \frac 56x[/tex]

Multiply through by 6

4x - 3 = 2 + 5x

Collect like terms

4x - 5x = 2 + 3

Evaluate the like terms

-x = 5

Divide both sides by -1

x = -5

Hence, the solution to the linear equation is x = -5

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Answer:

a) perpendicular b) parallel c) perpendicular  d) neither

Step-by-step explanation:

Perpendicular means that the lines will intersect/cross and create a 90 degree angle

Parallel lines will never intersect/cross because they are going the same way.

Answer:

D) 60=(x+45)

Step-by-step explanation:

D.  Since the two are equal, you need to put the two on opposite sides of the equation.  The equation doesn’t involve 90 or 180 degrees, so no reason to have them.  

Solving for x this way, you’d get 15, which is correct.

Answer:

5,600

Step-by-step explanation:

i used calculator.

Answer: D

Step-by-step explanation: becasue i did it

Answer:

total no of cars =57

Cars which are not boxcars =57-23=34

23/34×57=1339/34

Answer:

y= -12x+63/4

Step-by-step explanation:

16x + 4/3 y = 21

4/3 y =21-16x

4y=3(21-16x)

4y=63-48x

y=63/4-48/4 x

y=-12x+63/4

Answer:

3.5cm

Step-by-step explanation:

[tex]C = 22cm\\r = ?\\\\C = 2\pi r\\\\r = \frac{C}{2\pi} \\\\r = \frac{22}{2(3.14)}\\ \\r = \frac{22}{6.28} \\\\r = 3.5[/tex]

Given :

A point ( 1 ,4 ,5 ).

To Find :

The projection of the point on the xy-plane .

Solution :

Now , to find projection of a point in a plane in a plane we need to replace the coordinate of that remaining axis which is not in the plane .

Here , the plane given is xy-plane . So , remaining axis is z .

So , we replace coordinate of z =0 .

Therefore ,  the projection of the point ( 1 ,4 ,5 ) on the xy-plane is ( 1 ,4 ,0 ) .

Hence , this is the required solution .

Through my trials and tribulations I have decided that the answer is.

Y E S

Answer:

B a translation 5 units to the left

Step-by-step explanation:

Edge 2021

Answer:

  d  5,15,19​

Step-by-step explanation:

The sum of the shortest two sides must be longer than the longest side. That is only the case for selection D.

__

If the sum is equal to the longest side, the segment ends will meet, but the "triangle" will look like a line segment. Many authors do not allow such a thing to be called a triangle. Hence, 'b' is not an answer to this question.

(Some authors do allow such a triangle, in which case, there would be two answers here: B and D.)

Answer:

So the way to  express a vector( [tex]v =  2i - 2j - 2k[/tex]) as a product of its length and direction is

        [tex]v  =    |v| u =  \sqrt{12} (\frac{2}{ \sqrt{12} } , -\frac{2}{ \sqrt{12} }, - \frac{2}{ \sqrt{12} })[/tex]

Step-by-step explanation:

Generally a vector  is  expressed as a product of its length and direction using the formula below  

           [tex]v  =  |v|\cdot u[/tex]

Here v is the vector

        |v| is its magnitude (length)

         u is its unit vector (direction)

Now let take an example

Let  

     [tex]v =  2i - 2j - 2k[/tex]

The magnitude is mathematically evaluated as

          [tex]|v| =  \sqrt{ 2^2  + (-2)^2 +  (-2)^2 }[/tex]

         [tex]|v| =  \sqrt{12}[/tex]

The unit vector is mathematically represented as

        [tex]u  =  \frac{v}{|v|}[/tex]

        [tex]u  =  \frac{ <2 , -2 , -2>}{\sqrt{12} }[/tex]

    [tex]u =  \frac{2}{ \sqrt{12} } , -\frac{2}{ \sqrt{12} }, - \frac{2}{ \sqrt{12} }[/tex]

So

    [tex]v  =    |v| u =  \sqrt{12} (\frac{2}{ \sqrt{12} } , -\frac{2}{ \sqrt{12} }, - \frac{2}{ \sqrt{12} })[/tex]