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stellarik [79]
3 years ago
14

What's the solution to -182=2(1+2x)-2

Mathematics
2 answers:
MatroZZZ [7]3 years ago
8 0
-182=2(1+2x)-2

2*1=2
2*2x=4x

-182=4x+2-2
-182=4x
-45.5=x
AnnyKZ [126]3 years ago
4 0

Answer: x = -\frac{91}{2}

Step-by-step explanation:

If you have any questions, feel free to ask :)

Step 1: <u>Add</u> 2 <u>to both sides.</u>

-182 + 2 = 2(1 + 2x)

Step 2: <u>Simplify</u> -182 + 2 <u>to</u> -180.

-180 = 2(1 + 2x)

Step 3: <u>Divide both sides by</u> 2.

-\frac{180}{2} = 1 + 2x

Step 4: <u>Simplify</u> \frac{180}{2} <u>to</u> 90.

-90 = 1 + 2x

Step 5: <u>Subtract</u> 1 <u>from both sides.</u>

-90 - 1 = 2x

Step 6: <u>Simplify</u> -90 - 1 <u>to</u> -91.

-91 = 2x

Step 7: <u>Divide both sides by</u> 2.

-\frac{91}{2} = x

Step 8: <u>Switch sides.</u>

x = -\frac{91}{2}

~I hope I helped you :)~

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2 years ago
Solve the matrix equation for a, b, c, and d. [1 2] [a b] [6 5][3 4] [c d]= [19 8]
Anit [1.1K]

Answer:

The answer is "\bold{\left[\begin{array}{cc}a&b\\c&d\end{array}\right] = \left[\begin{array}{cc}7&-2\\ -\frac{1}{2}&\frac{7}{2}\end{array}\right]}".

Step-by-step explanation:

\bold{\left[\begin{array}{cc}1&2\\3&4\end{array}\right] \left[\begin{array}{cc}a&b\\c&d\end{array}\right] = \left[\begin{array}{cc}6&5\\ 19&8\end{array}\right]}

Solve the L.H.S part:

\left[\begin{array}{cc}1&2\\3&4\end{array}\right] \left[\begin{array}{cc}a&b\\c&d\end{array}\right]\\\\\\\left[\begin{array}{cc}a+2c&b+2d\\3a+4c&3b+4d\end{array}\right]

After calculating the L.H.S part compare the value with R.H.S:

\left[\begin{array}{cc}a+2c&b+2d\\3a+4c&3b+4d\end{array}\right]= \left[\begin{array}{cc}6&5\\ 19&8\end{array}\right]} \\\\

\to a+2c =6....(i)\\\\\to b+2d =5....(ii)\\\\\to 3a+4c =19....(iii)\\\\\to 3b+4d = 8 ....(iv)\\\\

In equation (i) multiply by 3 and subtract by equation (iii):

\to 3a+6c=18\\\to 3a+4c=19\\\\\text{subtract}... \\\\\to 2c = -1\\\\\to  c= - \frac{1}{2}

put the value of c in equation (i):

\to a+ 2 (- \frac{1}{2})=6\\\\\to a- 2 \times \frac{1}{2}=6\\\\\to a- 1=6\\\\\to a =6 +1\\\\\to a = 7\\

In equation (ii) multiply by 3 then subtract by equation (iv):

\to 3b+6d=15\\\to 3b+4d=8\\\\\text{subtract...}\\\\\to 2d = 7\\\\\to d= \frac{7}{2}\\

put the value of d in equation (iv):

\to 3b+4 (\frac{7}{2})=8\\\\\to 3b+4 \times \frac{7}{2}=8\\\\\to 3b+14=8\\\\\to 3b =8-14\\\\\to 3b = -6\\\\\to b= \frac{-6}{3}\\\\\to b= -2

The final answer is "\bold{\left[\begin{array}{cc}a&b\\c&d\end{array}\right] = \left[\begin{array}{cc}7&-2\\ -\frac{1}{2}&\frac{7}{2}\end{array}\right]}".

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Jayden sells snow cones for $3.75 each. He started the day with a total of 300 snow cones to sell. If he made a total of $843.75
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Number of cone left is 75 cone

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Cost of each cone = $3.75 each

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<u>Find:</u>

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<u>Computation:</u>

Number of cone sale = Total amount earn / Cost of each cone

Number of cone sale = 843.75 / 3.75

Number of cone sale = 225 cone

Number of cone left = Starting number of cone - Number of cone sale

Number of cone left = 300 - 225

Number of cone left = 75 cone

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