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3 years ago

How can you use similar triangles to find a missing measurement?

Mathematics

1 answer:

Vlad1618 [11]3 years ago

8 0

Answer:

By comparison of the sides.

Step-by-step explanation:

If triangles are similar, that means their angles are equal and sides are proportional.

If you already have a proportion of two corresponding sides between triangles, then use that proportion and set it equal to a side you already know the measurement to. Hopefully that side is corresponding to your missing measurement, and you can then solve it.

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Help with bonus question please

Sedbober [7]

Bonus #1) June 30 is equivalent to the 91st day of April or the 61st day of May.

Hilda's deposit of 4520 earned interest for 91-1 = 90 days.

Hilda's deposit of 580 earned interest for 61-10 = 51 days.

Hilda's deposit of 590 earned interest for 61-23 = 38 days.

Balance = $4520·(1 +.035/365)⁹⁰ + 580·(1 +.035/365)⁵¹ + 590·(1 +.035/365)³⁸

... = $4559.175 +582.843 +592.154

... ≈ $5734.17

Deposits total 4520 +580 +590 = 5690, so interest earned is

... $5734.17 -5690.00 = $44.17

Bonus #2) This problem can be worked the same way, except that withdrawals are subtracted from the final balance.

Owner's deposit of $12,300 earned interest for 91 days.

Owner's withdrawal of $3600 reduced the balance for 53 days.

Owner's withdrawal of $1200 reduced the balance for 10 days.

Balance = $12300·(1 +.035/365)⁹¹ -3600·(1 +.035/365)⁵³ -1200·(1 +.035/365)¹⁰

... = $12,407.795 -3618.342 -1201.151

... ≈ $7588.30

Interest earned = $7588.30 - (12300 -3600 -1200) = $88.30

6 0

2 years ago

You have 600 feet of fencing to enclose a rectangular plot that borders on a river. If you do not fence the side along the river

inn [45]

Answer:

The length and width of plot is $L=300\:ft$ , $W=150\:ft$

Largest area of the plot is $A=45000 ft^{2}$

Step-by-step explanation:

Assume width as x and length as y. Given that length of fencing is 600 feet and fencing is enclosed on 3 sides. So perimeter is given as,

Perimeter = width + length + width

Substituting the value,

$600=x+y+x$

$600= 2x+y$ ….1

Now area of fence of rectangular box is given as follows,

$A=xy$ ….2

Solving equation 1 for y, subtracting 2x from both sides,

$600-2x= y$

Substituting the value in equation 2,

$A=x\left (600-2x \right )$

Simplifying

$A=600x-2x^{2}$

Rewriting,

$A=-2x^{2}+600x$

Above equation looks like quadratic equation $f\left ( x \right )=ax^{2}+bx+c$ whose graph looks like parabola.

Comparing equation f(x) and A values of a, b and c are, $a=-2,b=600$ and $c=0$ .

Now maximum of $f\left ( x \right )$ occurs at vertex.

The x coordinate of the vertex is given as $-\dfrac{b}{2a}$

Substituting the values,

$x=-\dfrac{600}{2\left (-2 \right )}$

Simplifying,

$x=\dfrac{600}{4}$

$x=150$

So width of plot is 150 feet.

Now to calculate value of length by using equation 1,

$600= 2x+y$

Substituting the values,

$600= 2\left (150 \right )+y$

$600= 300+y$

Subtracting 300 from both sides,

$300= y$

So length of plot is 300 ft.

The y coordinate of the vertex is given as $y=f\left ( -\dfrac{b}{2a} \right )$ which also means, $y=f\left ( 150 \right )$

$\therefore A=-2\left (150 \right )^{2}+600\left (150 \right )$

Simplifying,

$\therefore A=-2\left (22500 \right )^{2}+600\left (150 \right )$

$\therefore A=-45000+90000$

$\therefore A=45000$

So, area of the plot will be $A=45000 ft^{2}$

7 0

3 years ago

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g100num [7]

The answer is D........

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3 years ago

Simplest form of 14/63

kupik [55]

Answer:

2/9

Step-by-step explanation:

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Whitepunk [10]

I would believe it to be 22

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