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Olenka [21]
3 years ago
13

A 2.7 meter ladder leans against a house forming

Mathematics
1 answer:
mrs_skeptik [129]3 years ago
3 0

Answer:

1.35m

Step-by-step explanation:

A 2.7 meter ladder leans against a house forming a 30° angle with the house. Exactly how far is the base of the ladder from the house?

We solve the above question using the Trigonometric function of Sine

cos theta = Opposite/Hypotenuse

From the question

Opposite = Distance of base of the ladder from the house = x

Hypotenuse = Length of the ladder = 2.7m

Theta = 30°

Hence,

sin 30 = x/2.7 m

Cross Multiply

x = sin 30 × 2.7m

x = 1.35m

Option b is correct.

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Write an equation to describe the proportional relationship in this table. Explain your thinking and how you got your answer.
creativ13 [48]

Focus on the values in red outside the table (on the left and right sides). As the output increases by 4, the input increases by 1. This leads to the slope being rise/run = 4/1 = 4. The slope is the number just to the left of the x variable. So that's how they ended up with the equation y = 4x.

You can think of it as y = 4x+0, and note how it's in the form y = mx+b

m = 4 = slope

b = 0 = y intercept

The y intercept is the value of y when x = 0.

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Now because x = 0 and y = 0 pair up together, we can find the slope a different way: Pick any row other than the first row. Divide the y value over its paired x value. So let's say we pick on row two and we'd get a slope of y/x = 4/1 = 4.

Or we could pick on row three and get y/x = 8/2 = 4.

Picking on the fourth row gets us the slope to be y/x = 12/3 = 4. We end up with the same slope value each time. Again, this trick only works if (x,y) = (0,0) is on the line. Otherwise, you'll need to use the first method or use the slope formula.

For equations like this, we consider them a direct proportion. As x increases, so does y. As x increases by 1, y increases by 4. This is the same throughout the table.

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A real world example of this could be that x represents the number of sodas you buy, and if each soda is $4, then y = 4x represents the total cost of buying x number of sodas.

For instance, if you bought x = 10 sodas, then y = 4*x = 4*10 = 40 dollars is what you spend overall.

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3 years ago
X - 2y = -3<br> 2x + y = -1
bezimeni [28]

Answer:

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3 0
2 years ago
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never [62]

Number of days Val rented the bicycle is 8

<h3><u>Solution:</u></h3>

Given that val paid a flat rental fee of $55.00 plus $8.50 each day

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Let "a" be the number of days she rented the bicycle

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4 0
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