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3 years ago

Identify whether each equation has no solution, one solution, or infinitely many solutions.

Mathematics

1 answer:

butalik [34]3 years ago

5 0

Answer:

infinitely many
one solution
no solution
one solution

Step-by-step explanation:

1. 4x−x=2x+x

Simplifies to 3x = 3x, which is true for all values of x. Hence there are infinitely many solutions.

___

2. 2x+1=5

True only for x=2; one solution.

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3. 4x+2=5x−x+4

Simplifies to ...

4x +2 = 4x +4

2 = 4 . . . . . . . not true for any value of x; no solution.

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4. 2(x+4)=4(x+2)

Simplifies to ...

2x +8 = 4x +8

0= 2x . . . . . . . . . subtract 2x+8

True only for x=0; one solution.

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Simplify (4x-6)-(3x+6)

DaniilM [7]

Answer:

$x-12$

Step-by-step explanation:

First open the brackets

$=(4x-6)-(3x+6)\\\\\\=4x-6-3x-6$

Then collect the like terms

$4x-3x-6-6$

Solve the like terms

$4x-3x=x\\\\\\-6-6=-12\\\\\\=x-12$

The simplified form is

$x-12$

3 0

2 years ago

the price of a gallon of unleaded gas was $2.86 yesterday. today, the price fell to $2.79. find the percent decrease. round answ

soldier1979 [14.2K]

So.. 2.86 - 2.79 is the amount in decrease or 0.07

so.. if we take 2.86 as the 100%, how much is 0.07 of that in percentage?

well $\bf \begin{array}{ccllll}
amount&\%\\
\textendash\textendash\textendash\textendash\textendash\textendash&\textendash\textendash\textendash\textendash\textendash\textendash\\
2.86&100\\
0.07&x
\end{array}\implies \cfrac{2.86}{0.07}=\cfrac{100}{x}$

solve for "x"

3 0

2 years ago

Evaluate the surface integral. s y ds, s is the helicoid with vector equation r(u, v) = u cos(v), u sin(v), v , 0 ≤ u ≤ 6, 0 ≤ v

Juliette [100K]

Compute the surface element:

$\mathrm dS=\|\vec r_u\times\vec r_v\|\,\mathrm du\,\mathrm dv$

$\vec r(u,v)=(u\cos v,u\sin v,v)\implies\begin{cases}\vec r_u=(\cos v,\sin v,0)\\\vec r_v=(-u\sin v,u\cos v,1)\end{cases}$

$\|\vec r_u\times\vec r_v\|=\sqrt{\sin^2v+(-\cos v)^2+u^2}=\sqrt{1+u^2}$

So the integral is

$\displaystyle\iint_Sy\,\mathrm dS=\int_0^\pi\int_0^6u\sin v\sqrt{1+u^2}\,\mathrm du\,\mathrm dv$

$=\displaystyle\left(\int_0^\pi\sin v\,\mathrm dv\right)\left(\int_0^6u\sqrt{1+u^2}\,\mathrm du\right)$

$=\dfrac23(37^{3/2}-1)$

4 0

3 years ago

What are the least amount of lines needed to link all 9 dots set out in a square - three up and three across?https://www..com/fi

Sedaia [141]

You only need one if you follow a pattern of
top left dot
top middle dot
middle middle dot
middle left dot
bottom left dot
bottom middle dot
bottom right dot
middle right dot
top right dot

7 0

2 years ago

One safe investment pays 8% per year, and a more risky investment pays 12% per year.

Mice21 [21]

Principal = 109,000

Return - 9,920

Return = (principal x rate x time)/100

X = the amount invested at 12%

Then 102000- x = the amount invested at 8%

9920 = (x*12)/100 + (109000-x*8)100

x = 30,000

a) 30,000 is invested at 12%

79,000 is invested at 8%

b) The 12% investment is riskier so if all the money was in that account the investor could lose all his money.

3 0

2 years ago