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Reil [10]
2 years ago
14

The right triangle on the right is a scaled copy of the right triangle on the left. Identify

Mathematics
2 answers:
AlekseyPX2 years ago
5 0

Answer:

scale factor is 1:3.5

Step-by-step explanation:

56/16 = 3.5

Marat540 [252]2 years ago
4 0

Answer:

The scale factor expressed as a fraction is 4/5

Since the right triangle on the right is a scaled copy of the right triangle on the left, then the ratio of their similar sides is equal to the scale factor.

This is expressed as:

Taking the ratio of the fractions

\frac{20}{25} = \frac{4}{5}

25

20

=

5

4

Similarly for \frac{12}{15}

15

12

\frac{12}{15} =\frac{4}{5}

15

12

=

5

4

This shows that \frac{20}{25} = \frac{12}{15} = \frac{4}{5}

25

20

=

15

12

=

5

4

Hence the scale factor expressed as a fraction is 4/5

Learn more here: brainly.com/question/9386516

Step-by-step explanation:

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Use the function f(x)=2^x/x to answer the question. Which combination could result in the function f(x)?
KonstantinChe [14]

Answer:

A function is shown where b is a real number. f(x)=x^2+bx+144 The minimum value of the function is 80. Create an equation for an equivalent function in the form f(x)=(x-h)^2+k.

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3 years ago
A piece of wire of length 6363 is​ cut, and the resulting two pieces are formed to make a circle and a square. Where should the
Lerok [7]

Answer:

a.

35.2792 cm from one end (The square)

And 27.7208 cm from the other end (The circle)

b. See (b) explanation below

Step-by-step explanation:

Given

Length of Wire ,= 63cm

Let L be the length of one side of the square

Circumference of a circle = 2πr

Perimeter of a square = 4L

a. To minimise

4L + 2πr = 63 ----- make r the subject of formula

2πr = 63 - 4L

r = (63 - 4L)/2π

r = (31.5 - 2L)/π

Let X = Area of the Square. + Area of the circle

X = L² + πr²

Substitute (31.5 - 2L)/π for r

So,

X² = L² + π((31.5 - 2L)/π)²

X² = L² + π(31.5 - 2L)²/π²

X² = L² + (31.5 - 2L)²/π

X² = L² + (992.25 - 126L + 4L²)/π

X² = L² + 992.25/π - 126L/π +4L²/π ------ Collect Like Terms

X² = 992.25/π - 126L/π + 4L²/π + L²

X² = 992.25/π - 126L/π (4/π + 1)L² ---- Arrange in descending order of power

X² = (4/π + 1)L² - 126L/π + 992.25/π

The coefficient of L² is positive so this represents a parabola that opens upward, so its vertex will be at a minimum

To find the x-cordinate of the vertex, we use the vertex formula

i.e

L = -b/2a

L = - (-126/π) / (2 * (4/π + 1)

L = (126/π) / ( 2 * (4 + π)/π)

L = (126/π) /( (8 + 2π)/π)

L = 126/π * π/(8 + 2π)

L = (126)/(8 + 2π)

L = 63/(4 + π)

So, for the minimum area, the side of a square will be 63/(4 + π)

= 8.8198 cm ---- Approximated

We will need to cut the wire at 4 times the side of the square. (i.e. the four sides of the square)

I.e.

4 * (63/(4 + π)) cm

Or

35.2792 cm from one end.

Subtract this result from 63, we'll get the other end.

i.e. 63 - 35.2792

= 27.7208 cm from the other end

b. To maximize

Now for the maximum area.

The problem is only defined for 0 ≤ L ≤ 63/4 which gives

0 ≤ L ≤ 15.75

When L=0, the square shrinks to 0 and the whole 63 cm wire is made into a circle.

Similarly, when L =15.75 cm, the whole 63 cm wire is made into a square, the circle shrinks to 0.

Since the parabola opens upward, the maximum value is at one endpoint of the interval, either when

L=0 or when L = 15.75.

It is well known that if a piece of wire is bent into a circle or a square, the circle will have more area, so we will assume that the maximum area would be when we "cut" the wire 0, or no, centimeters from the

end, and bend the whole wire into a circle. That is we don't cut the wire at

all.

7 0
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Kelly rows a boat at the rate of 7040 yards per hour. How fast did Kelly row in miles?
irakobra [83]

Answer:

4 mph

Step-by-step explanation:

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6 0
3 years ago
Please can someone help?
alexandr402 [8]

Hey there! :)

Answer:

(5, -2), or x = 5 and y = -2.

Step-by-step explanation:

We can solve the two equations algebraically by eliminating a variable:

2x + 5y = 0

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Eliminate the x variable by finding the least common multiple and multiplying both equations:

3(2x + 5y = 0)

2(3x - 4y = 23)

Distribute and subtract the bottom equation from the top:

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6x - 8y = 46

------------------

0x + 23y = -46

23y = -46

y = -2.

Plug in y into an equation to solve for x:

2x + 5(-2) = 0

2x - 10 = 0

2x = 10

x = 5. Therefore:

The solution to this equation is (5, -2), or x = 5 and y = -2.

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3 years ago
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