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12345 [234]
3 years ago
14

what do the following two equations represent? please help 4x+2y= 10 4x-2y= -10 a) the same line b) distance parallel lines c) p

erpendicular lines d) intersecting, but not perpendicular lines

Mathematics
1 answer:
sleet_krkn [62]3 years ago
8 0

Answer:

  d)  intersecting, but not perpendicular lines

Step-by-step explanation:

Changing the sign of one of the variable terms causes the line to be reflected across one of the axes. The slope is the opposite of what it was. Since the original slope was not 1 or -1, the resulting line is not perpendicular to it. Lines with different slopes will be intersecting.

The two lines are intersecting, but not perpendicular.

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hi, i dont undertand number 20 because i was absent in class today and i rerally need help, i will appraciate with the help, and
Mariulka [41]

Given:

The equation is,

2\log _3x-\log _3(x-2)=2

Explanation:

Simplify the equation by using logarthimic property.

\begin{gathered} 2\log _3x-\log _3(x-2)=2 \\ \log _3x^2-\log _3(x-2)=2_{}\text{      \lbrack{}log(a)-log(b) = log(a/b)\rbrack} \\ \log _3\lbrack\frac{x^2}{x-2}\rbrack=2 \end{gathered}

Simplify further.

\begin{gathered} \log _3\lbrack\frac{x^2}{x-2}\rbrack=2 \\ \frac{x^2}{x-2}=3^2 \\ x^2=9(x-2) \\ x^2-9x+18=0 \end{gathered}

Solve the quadratic equation for x.

\begin{gathered} x^2-6x-3x+18=0 \\ x(x-6)-3(x-6)=0 \\ (x-6)(x-3)=0 \end{gathered}

From the above equation (x - 6) = 0 or (x - 3) = 0.

For (x - 6) = 0,

\begin{gathered} x-6=0 \\ x=6 \end{gathered}

For (x - 3) = 0,

\begin{gathered} x-3=0 \\ x=3 \end{gathered}

The values of x from solving the equations are x = 3 and x = 6.

Substitute the values of x in the equation to check answers are valid or not.

For x = 3,

\begin{gathered} 2\log _3(3^{})-\log _3(3-2)=2 \\ 2\log _33-\log _31=2 \\ 2\cdot1-0=2 \\ 2=2 \end{gathered}

Equation satisfy for x = 3. So x = 3 is valid value of x.

For x = 6,

\begin{gathered} 2\log _36-\log _3(6-2)=2 \\ 2\log _36-\log _34=2 \\ \log _3(6^2)-\log _34=2 \\ \log _3(\frac{36}{4})=2 \\ \log _39=2 \\ \log _3(3^2)=2 \\ 2\log _33=2 \\ 2=2 \end{gathered}

Equation satifies for x = 6.

Thus values of x for equation are x = 3 and x = 6.

6 0
1 year ago
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3 years ago
Find the value of <br>Sin (60° +45°)​
horrorfan [7]

Answer:

Step-by-step explanation:

The exact value of sin(45) sin ( 45 ) is √22 2 2 . The exact value of cos(60) cos ( 60 ) is 12 1 2 . The exact value of cos(45) cos ( 45 ) is √22 2 2 . The exact value of sin(60) sin ( 60 ) is √32 3 2 .

8 0
3 years ago
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Find the perimeter and area of a rectangle of cardboard measuring 17.8 cm by 13.4 cm​
klasskru [66]

Step-by-step explanation:

perimeter \: of \: rectangle \\  = 2(17.8 + 13.4) \\  = 2 \times 31.2 \\  = 62.4 \: cm \\  \\ area \: of \: rectangle \\  =17.8 \times 13.4 \\  = 238.52 \:  {cm}^{2}  \\

8 0
3 years ago
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(Please please, actually type the answer and dont send it in a file because it wont work)
NNADVOKAT [17]

Answer: like 36 i think

Step-by-step explanation:

6 0
3 years ago
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