Select the correct answer. Solve this inequality for x: -46 − 8x > 22.

Mathematics

1 answer:

Dmitry [639]3 years ago

5 0

Answer: x < - 8.5

Step-by-step explanation:

-46 - 8X > 22

+46. +46

-8x > 68

x < - 8.5

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Use substitution to solve the following system of equations. What is the value of y? {3x+2y=12{5x−y=7 A) y = -3B) y = 3C) y = -2

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Given the system of equations:

$\begin{gathered} 3x+2y=12\text{ \lparen eq. 1\rparen} \\ 5x-y=7\text{ \lparen eq. 2\rparen} \end{gathered}$

Isolating x from equation 1:

$\begin{gathered} 3x+2y-2y=12-2y \\ 3x=12-2y \\ \frac{3x}{3}=\frac{12-2y}{3} \\ x=\frac{12}{3}-\frac{2}{3}y \\ x=4-\frac{2}{3}y\text{ \lparen eq. 3\rparen} \end{gathered}$

Substituting equation 3 into equation 2 and solving for y:

$\begin{gathered} 5(4-\frac{2}{3}y)-y=7 \\ 5\cdot4-5\cdot\frac{2}{3}y-y=7 \\ 20-\frac{10}{3}y-y=7 \\ 20-\frac{13}{3}y=7 \\ 20-\frac{13}{3}y-20=7-20 \\ -\frac{13}{3}y=-13 \\ (-\frac{3}{13})\cdot-\frac{13}{3}y=(-\frac{3}{13})\cdot-13 \\ y=3 \end{gathered}$

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A point Q on a segment with endpoints A (2, −1) and C (4, 2) partitions the segment in a 4:1 ratio. Find Q.

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The point Q on a line segment with end points(2,1) and (4,2) is Q(12/5, -2/5)

<h3>What is a line segment?</h3>

A line segment is a straight line that passes through two given points.

The end points of the line determine how long or short a given line segment would be.

Analysis:

point Q(x, y )

x = $\frac{MX1 + NX2}{M+N}$