Mathematics, 20.10.2020 05:01 Onlytrillest

* ABS 2 A 10. Given Te is the segment bisector of ab,
AD 24, AZ - 244, and MZIZAS
Find the value of x and y
Z

Answers: 2

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Answer from: Quest

infinitely many solutions

step-by-step explanation:

we have been given the equation;

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

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions

Answer from: Quest

$y> \frac{1}{3}x$ and y≤ -x +4 .

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be = $\frac{1-0}{3-0} = \frac{1}{3}$ .

y-intercept of dotted line is y=0 only.

plugging slope m= $\frac{1}{3}$ and b=0 in slope-intercept form y=mx+b, we get

$y=\frac{1}{3}x$ .

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

$y> \frac{1}{3}x$ .

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be = $\frac{4-1}{0-3} = \frac{3}{-3}=-1$ .

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be

y≤ -x +4 .
Write a system of inequalities to represent the shaded portion of the graph.

Answer from: Quest

the simplified form is

$\frac{x^2(2x+3)}{2(4x-3)}$

step-by-step explanation:

we want to simplify the expression,

$\frac{\frac{6x+9}{15x^2} }{\frac{16x-12}{10x^4} }$

let us change the middle bar to a normal division sign to obtain,

$\frac{6x+9}{15x^2}\div\frac{16x-12}{10x^4}$

we multiply the first fraction by the reciprocal of the second fraction to obtain,

$\frac{6x+9}{15x^2}\times \frac{10x^4}{16x-12}$

we factor to obtain,

$\frac{3(2x+3)}{3\times5\times x^2}\times \frac{2\times5\times x^2\times x^2}{4(4x-3)}$

we cancel the common factors to get,

$\frac{(2x+3)}{1}\times \frac{ x^2}{2(4x-3)}$

we simplify to get,

$\frac{x^2(2x+3)}{2(4x-3)}$

the correct answer is b

Answer from: Quest

∠cbe and ∠deb are same-side interior angles.

i took the test

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