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swat32
3 years ago
12

The function C(x) = 29x + 54.5 represents the cost (in dollars) of cable for x months, including $54.50 installation fee. How ma

ny months of cable service can you have for $344.50?
c(x) = 29x + 54.5
Mathematics
1 answer:
Ratling [72]3 years ago
8 0

Hey there!!

Given equation :

... c(x) = 29x + 54.5

<em>In this equation $54.50 is installation fee and this would remain as a constant. ( This value wouldn't change ). </em>

<em>'x' is represented as the number of months. </em>

The total cost or c(x) is given as $344.50

Getting this into equations :

... 344.50 = 29x + 54.5

Subtracting 54.5 on both sides :

... 29x = 290

Dividing by 29 on both sides :

... x = 10

<u><em>Hence, the number of months is 10. </em></u>

Hope my answer helps!!

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d=3\sqrt{2}\ units

Step-by-step explanation:

<u><em>The complete question is</em></u>

Line L contains points (3, 5) and (7, 9). Points P has coordinates (2, 10). Find the distance from P to L

step 1

Find the equation of the line L contains points (3,5) and (7,9)

<em>Find the slope</em>

The formula to calculate the slope between two points is equal to

m=\frac{y2-y1}{x2-x1}

substitute the given values

m=\frac{9-5}{7-3}

m=\frac{4}{4}=1

<em>Find the equation of the line in point slope form</em>

y-y1=m(x-x1)

we have

m=1\\point\ (3,5)

substitute

y-5=(1)(x-3)

isolate the variable y

y=x-3+5

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step 2

Find the equation of the perpendicular line to the given line L  that passes through the point P

Remember that

If two lines are perpendicular, then their slopes are opposite reciprocal

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The slope of the given line L  is m=1

The slope of the line perpendicular to the given line L  is

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step 3

Find the intersection point equation A and equation B

y=x+2 -----> equation A

y=-x+12 ----> equation B

solve the system by graphing

The intersection point is (5.7)

see the attached figure

step 4

we know that

The distance from point P to the the line L is equal to the distance between the point P and point (5,7)

the formula to calculate the distance between two points is equal to

d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}

we have

(2,10) and (5,7)

substitute

d=\sqrt{(7-10)^{2}+(5-2)^{2}}

d=\sqrt{(-3)^{2}+(3)^{2}}

d=\sqrt{18}\ units

simplify

d=3\sqrt{2}\ units

see the attached figure to better understand the problem

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A television screen's width is 1.778 times its height. If its
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Answer:

Let a, b, and c be the height, width, and the diagonal of the screen respectively

Since they form a triangle and the angle between a and b is 90 degrees, according to the Pythagorean Theorem a^2 + b^2 = c^2

Let's assume that the aspect ratio is 16:9. Therefore b/a = 16/9

Now we have a system of two equations with two unknowns. We need to express everything in terms of a single unknown, so let's express a in terms of b.

Since, b/a = 16/9, by cross multiplying 16a = 9b. Therefore a=9b/16.

Now we can subsitute 9b/16 for a in the first equation

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Squaring the nominator and the denominator of the fraction yields

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To perform the addition, we need to express b^2 as a fraction with denominator 256 which is 256b^2/256, Now we have

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TLDR; just multiply the diagonal by the following two coefficients, and add the bezel width, to get the width and height:

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Thats all you need to know to do this.

Now here’s the Teig behind it:

First, calculate the angle of the diagonal relative to the base, using tangent, which yields ::

a = tan(9/16)

This will give you an angle of 0.512 radians (or roughly 30 degrees).

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The result will be roughly h = 0.49, or 49% of the diagonal.

Finally, get the ratio of eidth to hypotenuse using arc-cosine:

w = acos(0.512)

The result is roughly w = 0.872, or 87.2% of the diagonal.

that’s all the math! Enjoy!

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