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6 * 2

6(2)

(6)(2)

(6)2

12

6 x 2

6 · 2         Is this what your question is asking?

if your average stride length is 2.6ft, how many strides will it take you to walk to your grandparent's home?   

My grandparents are in Oklahoma, so I calculate it would take about 1,265, 640 strides, if I didn't make any side excursions along the way.

base2   1 0 1 0 1 1 1

base3   1 0 0 2 0

I do not know what the  ⁽²⁰⁾  is  supposed to be ....

6 + 7²  = 6 + 49 = 55

The two angles with x in them are supplementary ...add to 180

7x+4  + 4x-22 = 180     then solve for x  and calculate the angles

do the same thing for the 'y' angles ....

6*4/2=12

What is an equation of the line that passes through the points (-6,5) and (6,7)

The surface area of this sphere is 615.44 square yards. What is the volume of this sphere? Use ​𝜋 ≈ 3.14 and round your answer to the nearest hundredth.   

The first thing to do is determine the radius of the sphere 

We'll just use the formula for the area of a sphere                            4 π r²  =  A

Area is 615.44 and 4 π is 12.56 so plug them in                         (12.56) r²  =  615.44  

Divide both sides by 12.56                                                                       r²  =  49  

Well.  That turned out pretty convenient.  A perfect square. 

Take the square root of both sides.                                                            r  =  7 

Actually it's +7 but we discard the negative value. 

                                                                                                           4  

Now use the formula to determine the volume of a sphere.       V  =  –– π r³    

                                                                                                           3  

Doing a little arithmetic on the calculator                                             4308.08

                                                                                                  V  =  ——–——  

                                                                                                                 3   

Once more to the calculator and ta da                                       V  =  1436.03 yd³   

_.

0.75(x + 20) = 2 + 0.5(x − 2)

.75x  + 15   = 2 + .5x -1

.25x + 15 = 1

.25x = -14

x = -56

ln 5   +   ln (2x)   =  ln (5 * 2x) = ln 10x =5      e to  each side

                                       10x = e⁵

                                         x =   e⁵ /10 = .......

6^2x = 800        log both sides

2x log 6 = log 800

x = log 800 / ( 2 log 6) = .......

2x+4 > 8            or      2x+4 > -8

x > 2                            2x > -12

                                      x < -6

Graph C

common ratio ,  r = 2

Value =  1.00 (2^n-1)

I think I found it:

hr   1       2         3        4        5        6     7  

    675 + 625 + 575 + 525 + 475 +425 +375 = 3675 ft   Not quite there....add some  more hours

hr   7        8         9       10

   3675 + 325 + 275 +225 = 4500 ft

(sometimes it is just shorter to 'brute force' it !)

A      w = f * d

         w = 5 x .5 = 2.5 j

b        w = f * d

                500 * 15 = ....... j

First one :

solve 

3x+2 = 2      or     3x+2 = -2

x = 0                          x = - 4/3

Remember      cos^2 + sin^2 = 1

                             so sin = +- sqrt (65) / 9     but since it is in Q II   it is + sqrt(65)/ 9

then:

CSC = 1/sin

Cot = cos/ sin

Use the AP formula to find number of hours.

Sum = N/2 * [2*F + D*(N - 1)]
4500 =N/2 * [2*675 + (-50*(N-1))], solve for N

Solve for N:
4500 = 1/2 N (1350 - 50 (N - 1))

4500 = 1/2 (1350 - 50 (N - 1)) N is equivalent to 1/2 (1350 - 50 (N - 1)) N = 4500:
1/2 N (1350 - 50 (N - 1)) = 4500

Multiply both sides by 2:
N (1350 - 50 (N - 1)) = 9000

Expand out terms of the left hand side:
1400 N - 50 N^2 = 9000

Divide both sides by -50:
N^2 - 28 N = -180

Add 196 to both sides:
N^2 - 28 N + 196 = 16

Write the left hand side as a square:
(N - 14)^2 = 16

Take the square root of both sides:
N - 14 = 4 or N - 14 = -4

Add 14 to both sides:
N = 18 or N - 14 = -4

Add 14 to both sides:
 
N = 10 hours      or      N = 18[discard]

What is the remainder when the base-50  integer 12345 base50   is divided by 48base10? Write your answer in base 10.

It is simply

\(12345_{50}=(5+4*50+3*50^2+2*50^3+1*50^4) _{10}\\~\\ 5+4*50+3*50^2+2*50^3+1*50^4 \quad\mod{48}\\ =5+4*(-2)+3*(-2)^2+2*(-2)^3+1(-2)^4 \quad\mod{48}\\ =5-8+12-16+16 \quad\mod{48}\\ =9 \quad\mod{48}\\ \)

The remainder will be 9

"Find all pairs (x,y) such that x^2 + y^2 - 2x + 4y + 5 = 0"

 The 5th term is \(\frac{5}{9}\) . Here's my methodology:

To find the 5th term, we have to first find the difference between each of the terms. Since adding the difference 8 times to the 1st term gives us the 9th term, we can set up the equation \(\frac{4}{9}-\frac{2}{3}=8x\).

We can then solve for x to get \(x=-\frac{1}{36}\). 

Then, all we have to do is add \(4x\)  to the 1st term to get \(\frac{2}{3}-\frac{5}{36}=\frac{24}{36}-\frac{4}{36}=\frac{20}{36}=\boxed{\frac{5}{9}}\).

I hope this helps!

–Doggo

thhhaaankkss

can you please explain more? like why would i write 5=3+2? how would i apply the binomial theorem to that?