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Solve for x over the real numbers:
4 abs(0.5 x - 2.5) = 0

4 abs(0.5 x - 2.5) = 4 abs(x/2 - 5/2):
4 abs(x/2 - 5/2) = 0

Divide both sides by 4:
abs(x/2 - 5/2) = 0

Eliminate the absolute value:
1 (x/2 - 5/2) = 0

Divide both sides by 1:
x/2 - 5/2 = 0

Bring x/2 - 5/2 together using the common denominator 2:
(x - 5)/2 = 0

Multiply both sides by 2:
x - 5 = 0

Add 5 to both sides:
Answer: | x = 5

D=(R)(T)

Distance equals rate multiplied by time.

Key step:  convert your days to hours since you are travelling in miles per hour.  Mulitply the days by 24 to get the total numbers of hours in the time.

5 : 7    means that there are 12 equal parts  of the $240

And Kate gets 7  of these....so......

(7/12) * $240   =   7 * $20   =  $140

And Janee has $100

If they each spend  $20   there is  $200  left

Jane has $80    and Kate has  $120

So

80  :  120   =

8   :  12   =

2  :  3

Take the integral:
 integral sin(2 x) sec^2(x) dx

Simplify the integrand sin(2 x) sec^2(x) to get 2 tan(x):
 = integral2 tan(x) dx

Factor out constants:
 = 2 integral tan(x) dx

Rewrite tan(x) as (sin(x))/(cos(x)):
 = 2 integral(sin(x))/(cos(x)) dx
For the integrand (sin(x))/(cos(x)), substitute u = cos(x) and du = -sin(x) dx:
 = 2 integral-1/u du

Factor out constants:
 = -2 integral1/u du

The integral of 1/u is log(u):
 = -2 log(u) + constant

Substitute back for u = cos(x):
Answer: | = -2 log(cos(x)) + constant

The lengths of the sides of a triangle are positive integers. One side has length 17cm and the perimeter of the triangle is 50cm. If the area is also an integer, then the length of the shortest side is.  

Mmmmm......this one might be tough to figure out.....

This is a "guess  and check"  answer

Let  side  a  =  17

Call the unknown sides  b and c

We know that     17  + b + c  =  50   →  b +  c  =  33

Let the other two  sides be   b  =  17  and  c  = 16

The  semi-perimeter  =  perimeter/ 2 =   50/2  = 25  = s

And by Heron's formula....we have...

Area  = sqrt  [ s  (s - a) (s - b) (s - c) ]

Area  =  sqrt [ 25 * (25 - 17) (25- 17) (25 - 16)] =

sqrt [ 25 * 8^2  * 9 ]  =

sqrt [ 25 * 64  * 9]  =

5 * 8 * 3    =    120  cm^2

So...... the two sides a and b  are  equal  = 17 cm  each  

And the remaining shortest side  = c = 16 cm

P.S.  -  there may be other possibilities ?? 

Where do you live? And where is your new school?

Because it is x² = 4 this means to get a singular x you'd square root it (√4)

and the answer will equal = 2

10 x 10 (also can be written as 10 squared)

10 (squared) shows with a small two (2) being the square sign and this means for 10 x 10 there are 2 lots of 00's

so it makes 1_ _ (100)

Here's the answer.

Look  at the image :

(a)  is untrue.....angle BAC  = 90

(b)  is untrue...the area  =  (1/2)(8)(4) =  16 u^2

(c) is obviously false

(d) false...The perimeter > 16  =  5.66*2 + 8  =  about 19.32

(e)  is true.....AB  = AC   so.....since BAC  = 90......the  two  angles opposite these two sides are = 45

Sulfuric acid is diluted with water to make, in one container, 72 ml of a 14% acid solution and, in another container, 64 ml of a 31% acid solution. The contents of the two containers are mixed together. The percentage strength of the acid in the mixture is.  

Let P  be the unknown % of acid in the final solution.......we have the following set up

Amt of 14% solution * .14   + Amt of 31% solution * .31   =  Total amount * P

72 * .14   +   64 * .31   =  (72 + 64)* P          simplify

10.08   +  19.84    =   136*P

29.92   =   136 * P      divide both sides by 136

29.92  / 136   =  P    =    22%

A 59% copper alloy is made by mixing 20 g of a 43% copper alloy with some 63% copper alloy. The number of grams of 59% copper alloy produced is. 

Let x be the amount of the 63% alloy  ...  so....

Amt of 43% copper alloy* 43%  + Amount of 63% alloy * 63%  =   Total amount * 59%

20 (.43)   +  x (.63)  =  (20 + x) (.59)     simplify

8.6   + .63x   =   11.8 + .59x         sutract  8.6, .59x   from both sides

.04x   =   3.2           divide both sides by  .04

x  = 80g  of  63% alloy

So......the total amount of 59% alloy  =    (20 + 80)  = 100 g

Consider a square and a triangle. The sides of the square are x cm long. The base length and height of the triangle are equal, and are twice as long as the sides of the square. The area of the triangle is 9cm2 larger than the area of the square.

Find the perimeter of the square

The  base and height of the triangle  =   2x

So.....

Area of the triangle  =  Area of square  +  9cm^2

(1/2)B*H   =   x^2  +  9

(1/2) (2x) (2x)   =  x^2 + 9

2x^2   =  x^2  +  9       subtract     x^2, 9   from both sides

x^2 -  9  = 0        factor

(x + 3)  ( x - 3)  = 0

The first factor produces a negative solution  [reject ]

Setting the second factor to 0 we have

x - 3  =  0     add  3  to both sides

x  = 3 cm            this is the side of the square........and its perimeter is 4 times this  = 12 cm

Check.....area of triangle  =   2x^2  = 2(3)^2   =  18 cm^2

Area of square  =  9 cm ^2      

And the triangle has an area that is 9 cm greater than that of the square

Could you post a specific problem  (or problems  ??  )

( i )

At local time in London  he arrives in LA  at   8:45

So....local time in LA will be   12:45

(ii)  11hr, 10 min  =  11 + 1/6  hrs  =   67/6  hrs

So      Distance / Time  =  Rate

8880  / ( 67/6)     ≈ 795.22 km / hr

sec(θ)=2

r/x  = 2

sqrt [ x^2 + y^2] / x  = 2

sqrt [ x^2 + y^2 ]  = 2x     square both sides

x^2 + y^2  = 4x^2

y^2  = 3x^2         take the square root of both sides

y =  ±√(3)x

Very impressive Max   

\((32k^5)^{(2/5)}\\ =((2k)^5)^{(2/5)}\\ =(2k)^{(2\cdot5/5)}\\ =(2k)^2\\ =4k^2\)

\(\sqrt\pi \approx 1.7724538509055159\)

Btw, by any chance would a teacher give you a project to find the square root of pi !?

You have at least nothing.

Exact value = \(\sqrt7\)

Right here in your question!!

You listen to what you teacher says carefully, and remember it, and you can do it!!

Btw, can you post the worksheet on here? because we would not know what problems are you going to solve if you don't do so.

A black-and-white word "all over"?

Hi Jaycat(is this you? :D), this is definitely an Oyster XD