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kozerog [31]
3 years ago
10

A rectangular room has an area of 131 1/4 square feet. The length of the room is 12 1/2 feet. What is the width, in feet, of the

room.
Mathematics
2 answers:
Vsevolod [243]3 years ago
4 0
Before we try to solve anything, let's convert our fractions into decimals, this so if we use a calculator (or writing on paper), it will be much easier to put it.
131 1/4 = 131.25 (divide 100 by the denominator to know each 1/x value).
12 1/2 = 12.50
The formula for the area of a rectangle is L x W, or Length x Width.
Since we are looking for our width, w, we need to divide by the length.
131.25 / 12.5 = 10.5.
Our width is 10 1/2 ft.
I hope this helps!
Darina [25.2K]3 years ago
4 0
The answer for the question 10.5. Good luck
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Line with a slope 6 passes through the points (2,-10) and (5,g)
Irina-Kira [14]

Answer:

8 =g

Step-by-step explanation:

We have two points so we can use the slope formula

m = ( y2 -y1)/(x2-x1)

6 = ( g - -10)/(5-2)

6 = (g+10)/(5-2)

6 = (g+10)/3

Multiply each side by 3

6*3 = g+10

18 = g+10

Subtract 10

18-10 =g

8 =g

4 0
3 years ago
Show that every triangle formed by the coordinate axes and a tangent line to y = 1/x ( for x > 0)
vfiekz [6]

Answer:

Step-by-step explanation:

given a point (x_0,y_0) the equation of a line with slope m that passes through the  given point is

y-y_0 = m(x-x_0) or equivalently

y = mx+(y_0-mx_0).

Recall that a line of the form y=mx+b, the y intercept is b and the x intercept is \frac{-b}{m}.

So, in our case, the y intercept is (y_0-mx_0) and the x  intercept is \frac{mx_0-y_0}{m}.

In our case, we know that the line is tangent to the graph of 1/x. So consider a point over the graph (x_0,\frac{1}{x_0}). Which means that y_0=\frac{1}{x_0}

The slope of the tangent line is given by the derivative of the function evaluated at x_0. Using the properties of derivatives, we get

y' = \frac{-1}{x^2}. So evaluated at x_0 we get m = \frac{-1}{x_0^2}

Replacing the values in our previous findings we get that the y intercept is

(y_0-mx_0) = (\frac{1}{x_0}-(\frac{-1}{x_0^2}x_0)) = \frac{2}{x_0}

The x intercept is

\frac{mx_0-y_0}{m} = \frac{\frac{-1}{x_0^2}x_0-\frac{1}{x_0}}{\frac{-1}{x_0^2}} = 2x_0

The triangle in consideration has height \frac{2}{x_0} and base 2x_0. So the area is

\frac{1}{2}\frac{2}{x_0}\cdot 2x_0=2

So regardless of the point we take on the graph, the area of the triangle is always 2.

6 0
3 years ago
Write this number in expanded form 382,706
77julia77 [94]

Answer:

Expanded form : 300,000 +80,000 +2000 +700 +6.

Step-by-step explanation:

Given  : 382,706.

To find : Write this number in expanded form.

Solution : We have given  382,706.

We can  see 3 is at hundred thousand place = 300,000

8 is at ten thousand place = 80,000.

2 is at thousand place  = 2000.

7 is at hundred place  = 700.

6 is at ones place = 6

Then

Expanded form : 300,000 +80,000 +2000 +700 +6.

Therefore, Expanded form : 300,000 +80,000 +2000 +700 +6.

5 0
3 years ago
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Need help with Algebra 2! Thank you! :)
Olin [163]

Answer:

Consider the parent logarithm function f(x) = log(x)

Now,

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•Now, shrinking the graph of y = 3log(x) horizontally by a fctor of 2 to get the grpah of y = 3log(x/2) i.e the graph of g(x)

Hence, the function g(x) after the parent function f(x) = log(x) undergoes a vertical stretch by a factor of 3, and a horizontal shrink by a factor of 2 is

g(x) = 3 log(x/2) (Option-B).

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What is the completely factored form of f(x) = 6x<br>x2 - 4x + 15?​
maria [59]

Answer:

(x+1)(2x-3)(3x-5)

Step-by-step explanation:

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