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Gwar [14]
3 years ago
15

A rectangle has a height to width ratio of 3:4.5. Give two examples of dimensions for rectangles that could be scaled versions o

f this rectangle.
Mathematics
1 answer:
OlgaM077 [116]3 years ago
6 0

We have been given that a rectangle has a height to width ratio of 3:4.5.

Let h be height and w be width of rectangle.

We can set our given information in an equation as:

\frac{h}{w} =\frac{3}{4.5}

h=\frac{3}{4.5} *w

Now we will substitute h=1 in this equation.

1=\frac{3}{4.5} *w

3w=4.5

w=\frac{4.5}{3} =1.5

We can see that width of rectangle is 1.5 times height of rectangle.

Our one set of dimensions of rectangle will be: height=1 and width=1.5.

We can get many set of dimensions for our rectangle by multiplying both height and width of rectangle by same number.

Multiplying by 5 we will get our dimensions as: height 5 and width 7.5.  

Therefore, (1 and 1.5) and (5 and 7.5) dimensions for rectangle will be scaled version of our rectangle.

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Use the number line below, where RS = 7y +5. ST = 3y +5, and RT = 70.<br> a. What is the value of y?
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Step-by-step explanation:

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How many pennies are in 1 months lion dollars?
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A detective has interviewed four witnesses to a crime. From the stories of the witnesses the detective has concluded
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Answer:

Step-by-step explanation:

Step 1:we should turn the “facts” into logical expressions.

Step 2:Assign variables

Our variables are: b (for butler), c (for cook), g (for gardener), h (for handyman)

Step 3 . Let the value of true indicate that the person is telling the truth. For example, b = T means the butler is telling the truth. Then we can translate the statements as follows:

Check attachment

Step 4

We know all of these must hold. So we really want to know when (b→c)∧¬(c∧g)∧¬(¬g∧¬h)∧(h → ¬c) is true.

Step 5

Behold, another truth table task! If you work out the truth table, you see that this statement is only true when:

Check attachment

Step 6

Therefore we can say the butler and cook are definitely lying, but we can not determine if the gardener or handyman are lying. However, there are four variables in this problem. Instead, we can do this with some straight reasoning. Notice that:

If the butler is telling the truth, then by (a) the cook is telling the truth.

If the cook is telling the truth, then by (b) the gardener is lying.

If the gardener is lying, then by (c) the handyman is telling the truth.

If the handyman is telling the truth, they by (d) the cook is lying.

This leads to a contradiction (the cook can not be both telling the truth and lying)! Therefore the butler and cook must be lying. What about the gardener and the handyman? We don’t have enough information to figure out if they are lying. Since the cook is lying, we can’t use (b) to come to any conclusions about the gardener. Even if we are able to conclude that the gardener is telling the truth, we can’t use (c) to come to any conclusions about the handyman.

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