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malfutka [58]
3 years ago
13

The two shortest sides of a right triangle are 10 in. And 24 in. long. What is the length of the shortest side of a similar righ

t triangle whose two longest sides are 36 in. And 39 in?
Mathematics
2 answers:
mel-nik [20]3 years ago
7 0
Draw two triangles. label the legs 10 in and 24 in on the first.
On the second note that the longest side of a right triangle is the hypotenuse, and label the hypotenuse 39, and a leg 36 in.

Since the triangle are similar, all the sides will be in direct proportion to each other.

36/24 = 1.5  so the second triangle has side lengths that are 1.5 times longer than the first. 1.5 x 10 = 15

the shortest side of the second right triangle is 15 in.
ivanzaharov [21]3 years ago
5 0
If the two shortest sides of the triangle are 10in and 24in, then using Pythagoras' theorem, the longest side =
\sqrt{10^2 + 24^2} 
= \sqrt{676}
= 26

Now we know the two longest sides of the first triangle (24in and 26in) we can compare them with the two longest sides of the second triangle.
If x = the scale factor the first triangle is enlarged by then
26x = 39 and 24x = 36 
⇒ x = 1.5

Finally, we need to multiply the smallest side of the first triangle by the scale factor to find the shortest side of the second triangle.
10(1.5) = 15
So the length of the shortest side of the other triangle is 15in.

You could, instead, calculate the length of the shortest side of the second triangle by using Pythagoras' theorem and ignoring the first triangle completely.
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3x+4x+7

Step-by-step explanation:

First, a Trinomial consists of three terms.

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<u>3</u>+<u>4</u>+<u>blank</u>

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And lastly, add the constant.

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8 0
3 years ago
Which inequality represents all values of x for which the quotient below is O A. 1 O B. XS -1 O c. x 1 O D. x -1
Olegator [25]
We have to solve two inequations:
Equation 1:
30(x-1)≥0
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The solution is: solution1 <span>∩ solution2

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6 0
3 years ago
76. Currently, your savings for each month is capped at $400. If you start investing all of this into a savings plan earning 1%
Alexxandr [17]

Answer:

10 years and 10 months.

Step-by-step explanation:

The annually interest rate (ia) can be converted by monthly (im) by the equation:

(1 + im)¹² = 1 + ia

(1 + im)¹² = 1 +0.01

(1 + im)¹² = 1.001 (putting ln in both sides)

ln(1 + im)¹² = ln1.001

12*ln(1 + im) = 1.0x10⁻³

ln(1 + im) = 8.33x10⁻⁵(applying "e in both sides)

e^{ln(1 + im)} = e^{8.33x10^{-5}}

1 + im = 1.00083

im = 0.00083 = 0.083%

For a investimenting, the final amount (A) can be calculated by:

A = R*(\frac{(1+i)^n-1}{i} )

Where R is the amount invested per month, i is the interest, and n the number of months:

160000 = 400 *\frac{(1 +0.00083)^n - 1}{0.00083}

\frac{(1 +0.00083)^n - 1}{0.00083} = 400

1.00083ⁿ - 1 = 0.332

1.00083ⁿ = 1.332 (applying ln in both sides)

n*ln1.00083 = ln1.332

8.3x10⁻⁴n = 0.2867

n = 345.4 months

345.4 months *1 yea12 months = 10 years and 10 months.

7 0
3 years ago
Read 2 more answers
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Zigmanuir [339]

Answer:

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Step-by-step explanation:

5 0
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