Solve for x: 7(2x - 4) = 42
1 answer:
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Please see the attached figure. This is how you draw a hyperbola. Its general formula is:
(x-h)²/a² - (y-k)²/b² = 1, where
(h,k) is the center
a is the semi-major axis
b is the semi-minor axis
The given equation is
(x+4)²/16 - (y+3)²/25 = 1
So, from the general form we can deduce that,
Center(-4,-3)
a = 4
b = 5
So, the first point we can plot is the centerpoint. Next, you draw the two intersecting lines. Their slopes are +/- b/a. Thus, it corresponds to +/- 5/4. Using this slope, we can find the equation of the two lines by using the slope and the center.
-3 = +5/4 (-4) + b ---> b= 2
-3 = -5/4 (-4) + b ---> b= -8
So, you plot the equations y=5/4x + 2 and y = -5/4 x -8 by assigning values of x and plotting them against y. Then, the vertex of the hyperbolas are 4 units from the center, denoted by the green dots. The hyperbola is shown in the next picture.
(x-h)²/a² - (y-k)²/b² = 1, where
(h,k) is the center
a is the semi-major axis
b is the semi-minor axis
The given equation is
(x+4)²/16 - (y+3)²/25 = 1
So, from the general form we can deduce that,
Center(-4,-3)
a = 4
b = 5
So, the first point we can plot is the centerpoint. Next, you draw the two intersecting lines. Their slopes are +/- b/a. Thus, it corresponds to +/- 5/4. Using this slope, we can find the equation of the two lines by using the slope and the center.
-3 = +5/4 (-4) + b ---> b= 2
-3 = -5/4 (-4) + b ---> b= -8
So, you plot the equations y=5/4x + 2 and y = -5/4 x -8 by assigning values of x and plotting them against y. Then, the vertex of the hyperbolas are 4 units from the center, denoted by the green dots. The hyperbola is shown in the next picture.
Hi!
I've included an image showing the shape divided into 3 rectangles. We're going to find the area of each rectangle.
To find the area of a rectangle, multiply the length times the width.
The red rectangle:
8 · 9 = 72
The area of the red rectangle is 72in.
The orange rectangles:
The orange rectangles have the same area.
10 · 3 = 30
30 + 30 = 60
The area of both orange rectangles is 60in.
72 + 60 = 132
The answer is 132 square inches.
Hope this helps! :)
I've included an image showing the shape divided into 3 rectangles. We're going to find the area of each rectangle.
To find the area of a rectangle, multiply the length times the width.
The red rectangle:
8 · 9 = 72
The area of the red rectangle is 72in.
The orange rectangles:
The orange rectangles have the same area.
10 · 3 = 30
30 + 30 = 60
The area of both orange rectangles is 60in.
72 + 60 = 132
The answer is 132 square inches.
Hope this helps! :)