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4 years ago

If y varies directly as x, and y is 180 when x is n and y is n when x is 5, what is the value of n?

Mathematics

1 answer:

Murrr4er [49]4 years ago

5 0

Answer:

n = 30

Step-by-step explanation:

Given that y varies directly as x then the equation relating them is

y = kx ← k is the constant of variation

To find k use the condition y = 180 when x = n, then

180 = kn ( divide both sides by n )

k = $\frac{180}{n}$

y = $\frac{180}{n}$ x ← equation of variation

y = n when x = 5, thus

n = $\frac{180}{n}$ × 5 = $\frac{900}{n}$ ( multiply both sides by n )

n² = 900 ( take the square root of both sides )

n = $\sqrt{900}$ = 30

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Figure I and Figure II are similar figures,

ELEN [110]

The ratio of corresponding sides is same for all the sides for similar polygon. the correct proportion is,

$\frac{ST}{EF}=\frac{WR}{CD}$

Thus the option H is the correct option.

To find the correct proportion we need to know about the properties of slimier polygon.

<h3>What are the properties of similar polygon?</h3>

Two polygons are said to be similar or congruent pentagon-

The corresponding angle of two pentagons are congruent.

The ratio of corresponding sides is same for all the sides.

The figure given in the problem of similar two polygons with six sides.

Rearrange the second figure as shown in figure.

As for the similar polygons, the ratio of corresponding sides is same for all the sides.

Thus the sides shown in the two rearranged figure must be same. Therefore,

$\frac{ST}{EF}=\frac{WR}{CD}$

Hence the correct proportion is,

$\frac{ST}{EF}=\frac{WR}{CD}$

Thus the option H is the correct option.

Learn more about the similar polygon here;

brainly.com/question/771807

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2 years ago

Solve. 10x^2 = 6 + 9x10x 2 =6+9x10, x, start superscript, 2, end superscript, equals, 6, plus, 9, x Choose 1 answer: Choose 1 an

yulyashka [42]

Answer:

Option B.

Step-by-step explanation:

If a quadratic equation is defined as

$ax^2+bx+c=0$ .... (1)

then the quadratic formula is

$x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}$

The given equation is

$10x^2=6+9x$

It can rewritten as

$10x^2-9x-6=0$ .... (2)

On comparing (1) and (2) we get

$a=10,b=-9,c=-6$

Using quadratic formula we get

$x=\dfrac{-(-9)\pm \sqrt{(-9)^2-4(10)(-6)}}{2(10)}$

$x=\dfrac{9\pm \sqrt{81+240}}{20}$

$x=\dfrac{9\pm \sqrt{321}}{20}$

Therefore, the correct option is B.

6 0

4 years ago

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Solve for x in the literal equation -20=xy +z.

erastovalidia [21]

Answer:

-(20+z)/y = x

Step-by-step explanation:

-20=xy +z

Subtract z from each side

-20 -z = xy+z-z

-20 -z = xy

Divide each side by y

(-20 -z)/y = xy/y

Factor out a negative

-(20+z)/y = x

5 0

3 years ago

Determine whether f(x) = –5x^2 – 10x + 6 has a maximum or a minimum value.

Blizzard [7]

First,

We are dealing with parabola since the equation has a form of,

$y=ax^2+bx+c$

Here the vertex of an up - down facing parabola has a form of,

$x_v=-\dfrac{b}{2a}$

The parameters we have are,

$a=-5,b=-10, c=6$

Plug them in vertex formula,

$x_v=-\dfrac{-10}{2(-5)}=-1$

Plug in the $x_v$ into the equation,

$y_v=-5(-1)^2-10(-1)+6=11$

We now got a point parabola vertex with coordinates,

$(x_v, y_v)\Longrightarrow(-1,11)$

From here we emerge two rules:

If $a$ then vertex is max value
If $a>0$ then vertex is min value

So our vertex is minimum value since,

$a=-5\Longleftrightarrow a$

Hope this helps.

r3t40

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3 years ago

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weqwewe [10]

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EX: 75/100
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25 goes into 75 3 times. So that is your numerator or the number on top.
25 goes into 100 4 times. This will be your denominator or the number on the bottom.
Your answer should be 3/4! Make sure to show your work! good luck!

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3 years ago

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