What are the steps to this equation?

Mathematics

1 answer:

Gala2k [10]3 years ago

3 0

Answer:

1. Add 1 to both sides

2. Multiply both sides by 4

3. Take the square root of both sides

4. Subtract 5 from both sides

Step-by-step explanation:

$\frac{1}{4} (x+5)^{2} -1=3$

Add 1 to both sides

$\frac{1}{4} (x+5)^{2}=4$

Multiply both sides by 4

$(x+5)^{2}=16$

Square root both sides

$x+5=4$

Subtract 5 from both sides

$x=-1$

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2. The height of one square pyramid is 24 m. A similar pyramid has a height of 8 m. The volume of the larger pyramid is 648 m3.

Dmitrij [34]

Larger PyramidHeight 24 Volume 648

Pyramid Volume = (Area of the Base * Height) ÷ 3648 = Base Area * 24 / 3Base Area = 648 * 3 / 24Base Area = 648 / 8Base Area = 81Base Length = 9
a) The Scale Factor between the Small & Large PyramidLength - 3LATERAL Area - 9Volume - 27

Slant Height^2 = 4.5^2 + 24^2Slant Height^2 = 596.25 Slant Height^2 = 24.4182308941 
b)
Large Pyramid Area = (½ * Perimeter of Base * Slant Height) + Base AreaLarge Pyramid Area = (.5 * 36 * 24.4182308941) + 81
Large Pyramid Area = 439.5281560938 + 81
Large Pyramid TOTAL Area = 520.5281560938 Large Pyramid LATERAL Area = 439.5281560938 

**********************************************************************************c)
Smaller PyramidHeight 8Surface Area = 124
This pyramid has dimensions that are one third of the larger pyramid.Therefore, it has a base length of 3.Base Area = 9.
Its base perimeter would be 12.
Small Pyramid Volume = (Area of the Base * Height) ÷ 3Small Pyramid Volume = ( 9 * 8 ) / 3Small Pyramid Volume = 72 / 3
c) Small Pyramid Volume =24 cubic meters

d) Ratio of larger pyramid volume to smaller pyramid volume648 / 24 = 27The reason? Volume is a 3 dimensional quantity. The Larger pyramid is 3 times larger in terms of the base measurement.9 meters vs 3 meters - a factor of 3When we compare volumes, we have to cube this factor.3^3 = 27

Source : http://www.1728.org/volpyrmd.htm

3 0

3 years ago

How to write y-2=-1/3 (x+6) in standard form and why PLZ HELP

stich3 [128]

$y-2=-\frac{1}{3}(x+6)\\y=-\frac{1}{3}(x+6)+2$