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3 years ago

If (5^4)m = 5^12, what is the value of m? A.)2 B.)3 C.) 5 D.)8

Mathematics

1 answer:

Sauron [17]3 years ago

8 0

Answer:

B.) 3

Step-by-step explanation:

Exponent rule: $(b^m)^n = b^{mn}$

(5⁴)ⁿ = 5¹²

4n = 12

n = 3

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Find the measure of unknown angle

Bumek [7]

Answer:

The angle in the upper right quadrilateral corner = 68 degrees because vertical angles are equal.

Angle Y = 68 (opposite quadrilateral angles are equal).

All quadrilateral angles add to 360 so:

68 + 68 + x + z = 360 = 292

angle X + Z = 292

Therefore angle x = angle z = 146

Step-by-step explanation:

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2 years ago

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A Norman window has the shape of a semicircle atop a rectangle so that the diameter of the semicircle is equal to the width of t

Makovka662 [10]

Answer:

132.233 ft2

Step-by-step explanation:

Let's call the width of the rectangle 'w' and the length 'x'. So the area of the semicircle is:

$A_1 = \pi*radius^2/2$

$A_1 = \pi*(w/2)^2/2$

$A_1 = \pi/8*w^2$

And the area of the rectangle is:

$A_2 = w*x$

If the perimeter of the window is 41 feet, we have:

$Perimeter = length + 2*width + \pi*radius$

$41 = x + 2*w + \pi*w/2$

$x = 41 - w(2 + \pi/2)$

Now, the equation for the total area of the window is:

$A = A_1 + A_2 = \pi/8*w^2 + w*x$

$A = \pi/8*w^2 + w*(41 - w(2 + \pi/2))$

$A = (\pi/8-2 - \pi/2)*w^2 + 41w = -3.1781w^2 + 41w$

To find the maximum area, we can find the x-coordinate of the vertex of the quadratic equation:

$x\_vertex = -b / 2a = -41 / (-3.1781*2) = 6.45$

So the width that gives us the maximum area of the window is 6.45 feet, and the area will be:

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3 years ago

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balandron [24]

Answer:

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Step-by-step explanation:

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2 years ago

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Sedbober [7]

Answer:

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3 years ago

What is the equation of the line that passes through the point (-2 0) and has a slope of 2

podryga [215]

The equation of the line will be y = 2x - 2.

<h3>What is an equation of the line?</h3>

A linear equation with a degree of one is referred to as a line equation. Two variables, x, and y are present in the equation of the line. The third parameter is the line's slope, which indicates the line's elevation.

The general form of the equation of the line is given as:-

y = mx + c

Given that the equation of the line is passing through the point ( -2,0) and the slope of the line is 2.

The equation of the line will be calculated as:-

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Therefore, the equation of the line will be y = 2x - 2.

To know more about an equation of the line follow

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1 year ago