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3 years ago

Write the equation of the line that passes through the points (1, -7) and (-6, -9).

Mathematics

1 answer:

jek_recluse [69]3 years ago

3 0

Answer:

y = 2/7 x - 51/7

Step-by-step explanation:

Equation of the line

(y-y1)/(y2-y1) = (x-x1)/(x2-x1)

(y-(-7)/(-9-(-7) = (x-1)/(-6-1)

(y+7)/-2 = (x-1)/-7

(-y-7)/2 = (-x+1)/7

-y-7 = -2/7 x + 2/7

-y = -2/7x +2/7 + 7

y = 2/7 x - 2/7 - 7

y = 2/7 x + (-2-49)/7

y = 2/7 x - 51/7

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A square pyramid has a base area of 64 ft2. The pyramid’s total surface area is 224 ft2.

borishaifa [10]

The area of each triangular face is 40 square feet

Solution:

Given that,

Square pyramid has a base area of 64 square feet

The pyramid’s total surface area is 224 square feet

The total surface area of a regular pyramid is the sum of the areas of its lateral faces and its base

Therefore, total surface area of square pyramid is given as,

Total surface area = base area + 4(Area of traingular face)

Let "x" be the area of each traingular face

$224 = 64 + 4(x)\\\\224 - 64 = 4x\\\\4x = 160\\\\x = 40$

Thus area of each triangular face is 40 square feet

5 0

3 years ago

The sides of two regular octagons are 3 in. And 6 in. respectively. Find the ratio of their perimeters and their areas

photoshop1234 [79]

The ratio of their perimeters is $\frac{1}{2}$ and the ratio of their areas is $\frac{1}{4}$

Step-by-step explanation:

A regular n-side polygon has

n equal sides
n equal angles
The measure of each interior angle = $\frac{(n-2).180}{n}$
Its perimeter = n × a, where a is the length of its side

V.I.Note: all regular polygons have same number of sides are similar, because their interior angles are equal in measures and their sides are proportion

∵ There are to regular octagons

- Regular octagon has 8 equal sides and 8 equal angles

∴ The two octagon are similar

∵ Their sides are 3 inches and 6 inches

∴ The constant ratio between their sides = $\frac{3}{6}$

- Divide the two terms of the ratio by 3 to simplify it

∴ The constant ratio between their sides = $\frac{1}{2}$

In similar figures the ratio between their perimeters is equal to the constant ratio between their sides, and the ratio between their areas is equal to square the constant ratio between their sides

∵ The two octagons are similar

∵ The constant ratio between their sides = $\frac{1}{2}$

∵ The ratio between their perimeters = the constant ratio between

their sides

∴ The ratio between their perimeters = $\frac{1}{2}$

∵ The ratio between their areas = (constant ratio)²

∴ The ratio between their areas = $(\frac{1}{2})^{2}=\frac{1}{4}$