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Ad libitum [116K]
3 years ago
6

A golden rectangle has a length of 5 cm. Find the area of the rectangle to the nearest square centimeter.

Mathematics
1 answer:
MatroZZZ [7]3 years ago
4 0

Answer: is it 25? i am bad at math but i am guessign

Step-by-step explanation:

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Which of these intervals has an average rate of change that is less than 1/4
RideAnS [48]

Answer:

Interval [b,c] and interval [c,d]

Step-by-step explanation:

a(-5,0)

b(-1,2)

c(4,3)

d(11,4)

The average rate of change is the the total rise over the total run.

The Rise means the vertical increase and the Run means horizontal incease.

For interval [a,b]

rate of change is \dfrac{2-0}{-1-(-5)}=\dfrac{2}{4}=\dfrac{1}{2}

For [b,c]

\frac{3-2}{4-(-1)}=\frac{1}{5}

For [c,d]

\dfrac{4-3}{11-4}=\dfrac{1}{7}

8 0
2 years ago
Which statement best explains how Italian society was affected by the Renaissance?
Tresset [83]

italian society entered a new era of artistic and academic achievement

4 0
2 years ago
HELP PLEASE ITS JUST ONE QUESTION
Nady [450]

Answer:

y = 2x - 1

Step-by-step explanation:

The given line is y = 2x - 6.

It is in the y = mx + b form, where m is the slope, so its slope is 2.

We need a line that passes through point P(3, 5) and has slope 2.

y = mx + b

Put the slope in m.

y = 2x + b

Use the given point with x = 3 and y = 5 and solve for b.

5 = 2(3) + b

b + 6 = 5

b = -1

The equation is

y = 2x - 1

4 0
3 years ago
Shameeka sold her hamsters to a pet store. This doubled the number of hamsters in the store. Then the store got six more hamster
nalin [4]

Answer: shameeka sold 20 hamsters to the store.

Step-by-step explanation:

Let x represent the number of hamsters that shameeka sold to the store.

Let y represent the number of hamsters that the pet store had initially.

Shameeka sold her hamsters to a pet store. This doubled the number of hamsters in the store. It means that

x + y = 2y

x = 2y - y

x = y

Then the store got six more hamsters. If the pet store has 46 hamsters now, it means that

2y + 6 = 46

2y = 46 - 6

2y = 40

y = 40/2

y = 20

Since x = y, then

x = 20

5 0
3 years ago
A 11 inch by 8 inch piece of cardboard squares cut out of the corners and is folded up to make up an open-top-box. If the volume
Arada [10]
<h3>Answer:  b. either 2.5 inches or about .716 inches</h3>

=====================================================

Work Shown:

I have attached two images below. The first shows figures 1 through 4. The second image shows figure 5.

Start with figure 1. Work your way left to right, top to bottom til you get to figure 4. This is the basic process to turn a flat piece of cardboard into a 3D folded box.

The dashed lines in figure 1 are x inches long.

Figure 2 is the result of cutting out the dashed lines you see in figure 1.

When you fold along the dashed lines in figure 2, you'll end up with something similar to figure 3.

Figure 4 is the completed open-top-box. In other words, this box does not have a lid.

The green portions in figures 3 and 4 indicate where the flaps used to be in reference to figure 2.

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

Since those dashed lines in figure 1 were x inches long, this means that the distance from A to B is 11-x-x = 11-2x inches long.

This makes segment BD to be 8-2x inches long. We are subtracting off 2 copies of x each time for each dimension.

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

length = AB = 11-2x

width = BD = 8-2x

Since we want the length to be positive, this means 11-2x > 0 which solves to x < 5.5

Since we want the width to be positive, this means 8-2x > 0 which solves to x < 4

Overall, we must make x < 4 to make both inequalities 11-2x > 0 and 8-2x > 0 to be true at the same time.

Furthermore, x is some length itself, so it cannot be negative either. Therefore x > 0 or 0 < x

Combine 0 < x and x < 4 to get 0 < x < 4

The restriction 0 < x < 4 will be used later.

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

For now, let's compute the volume.

Volume = Length*Width*Height

Volume = (AB)*(BD)*x

Volume = (11-2x)*(8-2x)*x

Volume = (88-22x-16x+4x^2)*x

Volume = (88-38x+4x^2)*x

Volume = 88x-38x^2+4x^3

This is the algebraic way of representing the volume in terms of the cut length x

We want this volume to be 45 cubic inches. We set  88x-38x^2+4x^3 equal to 45 and solve for x

88x-38x^2+4x^3 = 45

4x^3-38x^2+88x-45 = 0

At this point we try to factor by grouping or we turn to a calculator. Cubics are often very difficult to solve by hand, so I recommend using a calculator (unless you can quickly spot how to factor by grouping, but I don't see a quick way of doing that). Note: based on the answer choices that aren't whole numbers (assuming choice C is a non-answer), this heavily implies we do not have rational roots, and therefore factoring over the rationals will be impossible. In other words, the answer choices tell us to immediately use a graphing calculator to find the roots.

Using geogebra (see figure 5), I find the three approximate roots to be

x = 0.716 (shown as point A)

x = 2.5 (point B)

x = 6.284 (point C)

Recall that earlier we made 0 < x < 4. The first two roots satisfy this inequality, but x = 6.284 is outside this range. So we ignore it. It looks like your teacher put 6.284 as a trick answer in choice A.

5 0
3 years ago
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