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rosijanka [135]
3 years ago
8

Solve for x: 3 - (2x - 5) < -4(x + 2)

Mathematics
2 answers:
sattari [20]3 years ago
5 0

x < -23/2

Step-by-step explanation:

you open the bracket first

LHS

3-(2x - 5)

-6x+15

RHS

-4(x+2)

=-4x-8

therefore:

-6x+15 < -4x-8

By collecting the like terms

-6x+4x < -8-15

=-2x<-23

Divide both side by -2x

-2x/-2 < -23/-2

x < -23/2

nata0808 [166]3 years ago
3 0

Step-by-step explanation:

3-(2x-5) <-4(x+2)

=> 3- 2x +5 +4x +8<0

=> 16 + 2x <0

=> 2x < -16

=> x < -8

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The system of equations may have a unique solution, an infinite number of solutions, or no solution. Use matrices to find the ge
Leno4ka [110]

Answer:

Infinite number of solutions.

Step-by-step explanation:

We are given system of equations

5x+4y+5z=-1

x+y+2z=1

2x+y-z=-3

Firs we find determinant of system of equations

Let a matrix A=\left[\begin{array}{ccc}5&4&5\\1&1&2\\2&1&-1\end{array}\right] and B=\left[\begin{array}{ccc}-1\\1\\-3\end{array}\right]

\mid A\mid=\begin{vmatrix}5&4&5\\1&1&2\\2&1&-1\end{vmatrix}

\mid A\mid=5(-1-2)-4(-1-4)+5(1-2)=-15+20-5=0

Determinant of given system of equation is zero therefore, the general solution of system of equation is many solution or no solution.

We are finding rank of matrix

Apply R_1\rightarrow R_1-4R_2 and R_3\rightarrow R_3-2R_2

\left[\begin{array}{ccc}1&0&1\\1&1&2\\0&-1&-3\end{array}\right]:\left[\begin{array}{ccc}-5\\1\\-5\end{array}\right]

ApplyR_2\rightarrow R_2-R_1

\left[\begin{array}{ccc}1&0&1\\0&1&1\\0&-1&-3\end{array}\right]:\left[\begin{array}{ccc}-5\\6\\-5\end{array}\right]

Apply R_3\rightarrow R_3+R_2

\left[\begin{array}{ccc}1&0&1\\0&1&1\\0&0&-2\end{array}\right]:\left[\begin{array}{ccc}-5\\6\\1\end{array}\right]

Apply R_3\rightarrow- \frac{1}{2} and R_2\rightarrow R_2-R_3

\left[\begin{array}{ccc}1&0&1\\0&1&0\\0&0&1\end{array}\right]:\left[\begin{array}{ccc}-5\\\frac{13}{2}\\-\frac{1}{2}\end{array}\right]

Apply R_1\rightarrow R_1-R_3

\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right]:\left[\begin{array}{ccc}-\frac{9}{2}\\\frac{13}{2}\\-\frac{1}{2}\end{array}\right]

Rank of matrix A and B are equal.Therefore, matrix A has infinite number of solutions.

Therefore, rank of matrix is equal to rank of B.

4 0
3 years ago
Find the midpoint of points A(8,-7) and B(3,-1) graphically
sukhopar [10]

Answer: (5.5, -4)

Step-by-step explanation:

You can use the midpoint formula to find the midpoint of point A and point B.

M(\frac{x_{1}+x_{2} }{2}, \frac{y_{1} + y_{2} }{2})

x₁ = 8

x₂ = 3

y₁ = -7

y₂ = -1

M(\frac{x_{1}+x_{2} }{2}, \frac{y_{1} + y_{2} }{2})

M(\frac{8+3 }{2},  \frac{-7 +-1}{2} )

M(\frac{8+3 }{2},  \frac{-7 -1}{2} )

M(\frac{11 }{2},  \frac{-8}{2} )

M(5.5, -4 )

Midpoint = (5.5, -4)

Hope this helps!

3 0
2 years ago
Due in 20 mins help pls
kodGreya [7K]

Answer: ....

P/s:

  • 2 × 3/12 = 3 × 2/12 = 6 × 1/12 (= 1/2)
  • 4 × 3/12 = 1

ok done. Thank to me :>

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Answer:

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30,050,000 in scientific notation
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