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3 years ago

What is the answer. I can’t figure out the formula

Mathematics

1 answer:

kotegsom [21]3 years ago

7 0

9514 1404 393

Answer:

Angles 4, 5, 6, 7, 8, 9 are 82°
Angles 1, 2, 3, 10, 11, 12 are 98°

Step-by-step explanation:

Angles are related in this geometry by being either congruent or supplementary. Corresponding and vertical angles are congruent; any linear pair of angles is supplementary.

The given angle 5 is on the southwest corner of the intersection of the parallel line with the transversal. All southwest and northeast angles are congruent to that. That is, angles 4, 5, 6, 7, 8, 9 will all have the same measure. The remaining angles will have the supplementary measure.

Angles 4, 5, 6, 7, 8, 9 are 82°

Angles 1, 2, 3, 10, 11, 12 are 98°

_____

As you know, supplementary angles total 180°, so each is found by subtracting the other from 180°: 180° -82° = 98°.

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Liula [17]

Answer:

volume = 140 cubic units

area = 183.3 square units

Step-by-step explanation:

I am going to assume we are dealing with a pyramid with a rectangular base. The rectangular base has length 7 units, width 5 units, and height 12 units.

Let's do the volume first since it's simpler.

Volume:

volume of pyramid = (1/3) * (area of base) * height

volume = (1/3) * 7 units * 5 units * 12 units

volume = 140 cubic units

Now we deal with the surface area.

The total surface area of a rectangular pyramid is the sum of the lateral area and the area of the base. The area of the base is the area of a rectangle. The lateral area is the sum of the areas of the 4 triangular sides. Each two opposite sides are congruent. For the base, we have the length and width of the rectangular base, so we can find the area easily.

For the 4 triangular sides, we need to find the the height of the triangles. Since each pair of opposite faces is congruent, we have two triangles we need to find the heights for. I'll call the heights "p" and "q". We use the Pythagorean theorem to find the heights of the triangular faces.

a^2 + b^2 = c^2

(3.5)^2 + (12)^2 = p^2

p^2 = 156.25

p = 12.5

(2.5)^2 + (12)^2 = q^2

q^2 = 150.25

q = 12.25765

Area of triangle = (1/2) * base * height

For two of the triangles, the base is 5 and the height is 12.5.

For the other two of the triangles, the base is 7 and the height is 12.25765.

total surface area = area of base + 2(area of triangle with base 5) + 2(area of triangle with base 7)

A = LW + 2(1/2)(base)(height) + 2(1/2)(base)(height)

A = 7(5) + 2(1/2)(5)(12.5) + 2(1/2)(7)(12.25765)

A = 183.3 square units

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3 years ago

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Simplify<br><br><img src="https://tex.z-dn.net/?f=%20%7B3%7D%5E%7B7y%7D%20%20%5Ctimes%20%20%7B81%7D%5E%7B8y%7D%20%5Ctimes%20%20%

Papessa [141]

Answer

$3^{7y} * 81^{8y} * 3^9 * 27^{-9y} = 3^{7y} * (3^4)^{8y} * 3^9 *(3^3)^{-9y}$

$=3^{7y} * (3)^{32y} * 3^9 *(3)^{-27y}\\\\=3^{7y +32y +9 -27y}\\\\=3^{12y+9}$

Tip :

$\frac{1}{27^{9y}} = 27^{-9y} = (3^3)^{-9y} = 3^{-27y}$

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6m - 3p + 10 when m = 6, p = 4

asambeis [7]

Answer:

The answer is 58.

Step-by-step explanation:

Plug in and Solve.

$6m - 3p + 10 \\ 6(6) + 3(4) + 10 \\ 36 + 12 + 10 \\ 48 + 10 \\ 58$

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Part 3: Write the equation of and graph an ellipse.

tensa zangetsu [6.8K]

Answer:

Step-by-step explanation:

The center is halfway between vertices, at (4, -6).

It is also halfway between foci.

:::::

The vertices are vertically aligned, so the parabola is vertical.

General equation for a vertical ellipse:

(y-k)²/a² + (x-h)²/b² = 1

with

center (h,k)

vertices (h,k±a)

co-vertices (h±b,k)

foci (h,k±c), c² = a²-b²

Apply your data and solve for h, k, a, and b.

center (h,k) = (4, -6)

h = 4

k = -6

vertices (4,-6±a) = (4,-6±9)

a = 9

foci (4,-6±c) = (4,-6±5√2)

b² = a² - c² = 9² - (5√2)² = 31

b = √31

The equation becomes

(y+6)²/81 + (x-4)²/31 = 1

:::::

length of major axis = 2a = 18

length of minor axis = 2b = 2√31

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3 years ago