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Pachacha [2.7K]
4 years ago
9

Which expression is equivalent to 4.8+2.2w−1.4w+2.4 ?

Mathematics
1 answer:
ASHA 777 [7]4 years ago
6 0

Answer:

7.2+0.8w

Step-by-step explanation:

You might be interested in
Express (8 - 3sqrt(2))/(4 + 3sqrt(2)) in the form of a + b * sqrt(2) where a and b are integers.​
Naya [18.7K]

Answer:   \boldsymbol{-25+18\sqrt{2}}

The expression is in the form a+b\sqrt{2} where a = -25 and b = 18

==========================================================

Work Shown:

Let x = 3\sqrt{2} and then square both sides

x = 3\sqrt{2}\\\\x^2 = \left(3\sqrt{2}\right)^2\\\\x^2 = \left(3\right)^2*\left(\sqrt{2}\right)^2\\\\x^2 = 9*2\\\\x^2 = 18\\\\

We'll use both x and x^2 later on.

---------------------

The denominator is in the form 4+x. We'll multiply top and bottom by 4-x to then use the difference of squares rule. This will allow us to eliminate the square root in the denominator.

\frac{8-3\sqrt{2}}{4+3\sqrt{2}}\\\\\frac{8-x}{4+x}\\\\\frac{(8-x)(4-x)}{(4+x)(4-x)}\\\\\frac{32-8x-4x+x^2}{16-x^2} \ \text{ difference of squares rule}\\\\\frac{32-12x+x^2}{16-x^2}\\\\

\frac{32-12*3\sqrt{2}+18}{16-18} \ \text{ plug in } x = 3\sqrt{2} \text{ and } x^2 = 18\\\\\frac{50-36\sqrt{2}}{-2}\\\\\frac{-2(-25+18\sqrt{2})}{-2}\\\\\boldsymbol{-25+18\sqrt{2}}

Therefore,

\frac{8-3\sqrt{2}}{4+3\sqrt{2}}=\boldsymbol{-25+18\sqrt{2}}

-------------------------------------

Checking the answer:

Use a calculator to find that,

\frac{8-3\sqrt{2}}{4+3\sqrt{2}} \approx 0.45584412271571 \\\\-25+18\sqrt{2} \approx 0.45584412271571

We get the same decimal approximation, which helps confirm the correct answer.

Or you could use the idea that if M = N, then M-N = 0 to subtract the original expression M and the final result N. You should get 0 or very close to it.

3 0
3 years ago
The base angle theorem is written as a conjecture,"if two sides of a triangle are congruent, then the angles opposite of them ar
diamong [38]

Step-by-step explanation:

Statement:

"If two sides of a triangle are congruent, then the angles opposite of them are congruent"

Converse:

If two angles of a triangle are congruent, then the two sides opposite them are congruent.

The converse of the statement is true and can be proven true using a two-column proof. In fact it is a theorem.

8 0
3 years ago
Lisa purchased a prepaid phone card for $30. Long distance calls cost 6 cents a minute using this card. Lisa used her card only
Reptile [31]

Answer:

My answer is 27.48 minutes

Step-by-step explanation: what i did to get this answer is i subtracted my numbers and add so i added $30 + 6 ( don't have to put the dollar sign when you add your numbers together) and i got 36 as my answer and then after i did that i subtracted $27.84 - 36 and got 27.48 as my answer.

hope it helps you

8 0
4 years ago
Justin is 10 yeas less than half his father's age.If Justin is 12 years old,how old is his father?
mario62 [17]
Lets say justin's age is 'j' and his father's age is 'f'
j = f / 2 - 10
12 = f / 2 - 10
f = j + 10 x 2
f = 12 + 10 = 22 x 2 = 44
Hope this helps :)
4 0
4 years ago
Read 2 more answers
Find the value of x and y
Alik [6]

Line EB is the mid segment of the triangle

EB and DC are parallel if angle EBA is equal to angle DCB

so

4x - 3 = 3x + 9  now solve for x

-3x          -3x

    x -3 =  + 9

       -3      -3  

    x      =   12

Now I know x and 3x +9, so sub in for x

3(8) + 9 = 32 + 9 = 41  


now we know angle EBA

and angle EBA and angle EBC are a linear pair meaning when I add them together they equal 180

so

angle EBA +  angle EBC = 180

     41         +        14y - 5   = 180 now solve for y

     36 + 14y = 180

    -36             -36

             14y = 144

              /14     /14

               y  =  10.28  


4 0
4 years ago
Read 2 more answers
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