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3 years ago

11

In the poportion 1/z =4/5/8 which number is equal to z in the proportion

1 answer:

Nady [450]3 years ago

8 0

Answer:

case 1) $z=10$

case 2) $z=5/32$

Step-by-step explanation:

case 1) we know that

Using proportion

$\frac{1}{z}=\frac{(4/5)}{8}$

solve for z

$\frac{1}{z}=\frac{(4/5)}{8}\\ \\z(4/5)=8\\ \\z=8*5/4\\ \\z=10$

case 2) we know that

Using proportion

$\frac{1}{z}=\frac{4}{5/8}$

solve for z

$\frac{1}{z}=\frac{4}{5/8}\\ \\4z=5/8\\ \\z=5/32$

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In mathematics, a limit is the value that a function or sequence "approaches" as the input or index approaches some value.

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For this case we have that by definition, the roots, or also called zeros, of the quadratic function are those values of x for which the expression is 0.

Then, we must find the roots of:

$2x ^ 2-4x + 5 = 0$

Where:

$a = 2\\b = -4\\c = 5$

We have to: $x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2 (a)}$

Substituting we have:

$x = \frac {- (- 4) \pm \sqrt {(- 4) ^ 2-4 (2) (5)}} {2 (2)}\\x = \frac {4 \pm \sqrt {16-40}} {4}\\x = \frac {4 \pm \sqrt {-24}} {4}$

By definition we have to:

$i ^ 2 = -1$

So:

$x = \frac {4 \pm \sqrt {24i ^ 2}} {4}\\x = \frac {4 \pm i \sqrt {24}} {4}\\x = \frac {4 \pm i \sqrt {2 ^ 2 * 6}} {4}\\x = \frac {4 \pm 2i \sqrt {6}} {4}\\x = \frac {2 \pm i \sqrt {6}} {2}$

Thus, we have two roots:

$x_ {1} = \frac {2 + i \sqrt {6}} {2}\\x_ {2} = \frac {2-i \sqrt {6}} {2}$

Answer:

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3 years ago

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For this case we have that by definition, the equation of a line in the point-slope form is given by:

$y-y_ {0} = m (x-x_ {0})$

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We have the following equation of the slope-intersection form:

$y = 4x + 1$

Where the slope is $m = 4$

By definition, if two lines are perpendicular then the product of their slopes is -1.

Thus, a perpendicular line will have a slope:

$m_ {2} = \frac {-1} {m_ {1}}\\m_ {2} = \frac {-1} {4}\\m_ {2} = - \frac {1} {4}$

Thus, the equation will be of the form:

$y-y_ {0} = - \frac {1} {4} (x-x_ {0})$

Finally we substitute the given point and we have:

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Option B

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3 years ago

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avanturin [10]

The area shaded in green is 864 cm²

<h3>Similar figures</h3>

Similar figures, corresponding angles are congruent and the sides are ratio of each other. Therefore,

AB / PQ = CD / RS

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RS = 240 / 30

RS = 8 cm

let find the height of trapezium PQRS.

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30h = 360

h = 360 / 30

h = 12 cm

Therefore,

area of the green portion = area of ABCD - area of PQRS

<h3>Area of a trapezium</h3>

area = 1 / 2(a + b)h

Therefore,

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Area of the green portion = 972 - 108 = 864 cm²

learn more on trapezium here: brainly.com/question/11961445

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