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denis23 [38]
3 years ago
14

1/3(z+4)-6=2/3(5-z) solve for z and check solution

Mathematics
2 answers:
Marat540 [252]3 years ago
7 0

Answer:

z = 8

Step-by-step explanation:

Solve for z:

(z + 4)/3 - 6 = (2 (5 - z))/3

Put each term in (z + 4)/3 - 6 over the common denominator 3: (z + 4)/3 - 6 = (z + 4)/3 - 18/3:

(z + 4)/3 - 18/3 = (2 (5 - z))/3

(z + 4)/3 - 18/3 = ((z + 4) - 18)/3:

(z - 18 + 4)/3 = (2 (5 - z))/3

Add like terms. 4 - 18 = -14:

(z - 14)/3 = (2 (5 - z))/3

Multiply both sides by 3:

(3 (z - 14))/3 = (3×2 (5 - z))/3

(3 (z - 14))/3 = 3/3×(z - 14) = z - 14:

z - 14 = (3×2 (5 - z))/3

(3×2 (5 - z))/3 = 3/3×2 (5 - z) = 2 (5 - z):

z - 14 = 2 (5 - z)

Expand out terms of the right hand side:

z - 14 = 10 - 2 z

Add 2 z to both sides:

2 z + z - 14 = (2 z - 2 z) + 10

2 z - 2 z = 0:

2 z + z - 14 = 10

z + 2 z = 3 z:

3 z - 14 = 10

Add 14 to both sides:

3 z + (14 - 14) = 14 + 10

14 - 14 = 0:

3 z = 10 + 14

10 + 14 = 24:

3 z = 24

Divide both sides of 3 z = 24 by 3:

(3 z)/3 = 24/3

3/3 = 1:

z = 24/3

The gcd of 24 and 3 is 3, so 24/3 = (3×8)/(3×1) = 3/3×8 = 8:

Answer:  z = 8

suter [353]3 years ago
4 0

\dfrac{1}{3}(z+4)-6=\dfrac{2}{3}(5-z)\qquad\text{multiply both sides by 3}\\\\\not3^1\cdot\dfrac{1}{\not3_1}(z+4)-3\cdot6=\not3^1\cdot\dfrac{2}{\not3_1}(5-z)\\\\1(z+4)-18=2(5-z)\qquad\text{use distributive property}\\\\z+4-18=(2)(5)-(2)(z)\\\\z-14=10-2z\qquad\text{add 14 to both sides}\\\\z=24-2z\qquad\text{add 2z to both sides}\\\\3z=24\qquad\text{divide both sides by 3}\\\\\boxed{z=8}

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Answer:

The required equation is:

y = -\frac{3}{2}x+9

Step-by-step explanation:

To find the equation of a line, the slope and y-intercept is required.

The slope can be found by finding the slope of given line segment. A the perpendicular bisector of a line is perpendicular to the given line, the product of their slopes will be -1 and it will pass through the mid-point of given line segment.

Given points are:

(x_1,y_1) = (8,10)\\(x_2,y_2) = (-4,2)

We will find the slope of given line segment first

m = \frac{y_2-y_1}{x_2-x_1}\\= \frac{2-10}{-4-8}\\=\frac{-8}{-12}\\=\frac{2}{3}

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Now the mid-point

(x,y) = (\frac{x_1+x_2}{2} , \frac{y_1+y_2}{2})\\= (\frac{8-4}{2} , \frac{10+2}{2})\\=(\frac{4}{2}, \frac{12}{2})\\=(2,6)

We have to find equation of a line with slope -3/2 passing through (2,6)

The equation of line in slope-intercept form is given by:

y = m_1x+b

Putting the value of slope

y= -\frac{3}{2}x+b

Putting the point (2,6) to find the y-intercept

6 = -\frac{3}{2}(2)+b\\6 = -3+b\\b = 6+3 =9

The equation is:

y = -\frac{3}{2}x+9

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Answer:

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Step-by-step explanation:

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f(g(h(x)))=f(g(\sqrt x))=f(\sqrt x-1)=\boxed{(\sqrt x-1)^4+4}

This is because

h(x)=\sqrt x

g(x)=x-1

\implies g(h(x))=\sqrt x-1

(that is, replace any instance of <em>x</em> in the definition of <em>g</em> with √<em>x</em> )

and

f(x)=x^4+4

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