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Stels [109]
3 years ago
9

Find two integers whose sum is -8 and product is -48

Mathematics
1 answer:
fomenos3 years ago
5 0

Answer:

-12 and 4

Step-by-step explanation:

-12+4=-8

(-12)*4= -48

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Find the volume of the parallelepiped with adjacent edges t = 3j – 4j – 6k, u = 3i – 7j – 7k and v = 5i + j + 3k.
Assoli18 [71]

Answer:

94 cubic units

Step-by-step explanation:

The volume of this parallelepiped (the product of area of its base and height) is equal to the absolute value of the scalar triple product |\vec{t}\cdot (\vec{u}\times \vec{v})|

Since

\vec{t}=3\vec{i}-4\vec{j}-6\vec{k}=(3,-4,-6)\\ \\\vec{u}=3\vec{i}-7\vec{j}-7\vec{k}=(3,-7,-7)\\ \\\vec{v}=5\vec{i}+\vec{j}+3\vec{k}=(5,1,3)

we have

|\vec{t}\cdot (\vec{u}\times \vec{v})|=\left|\left|\begin{array}{ccc}3&-4&-6\\3&-7&-7\\5&1&3\end{array}\right|\right|=|3\cdot (-7)\cdot 3+(-4)\cdot (-7)\cdot 5+3\cdot 1\cdot (-6)-5\cdot (-7)\cdot (-6)-3\cdot (-7)\cdot 1-3\cdot (-4)\cdot 3|=|-63+140-18-210+21+36|=|-94|=94\ un^3.

4 0
3 years ago
Triangle ABC is similar to triangle LMN by the AA Similarity Postulate.
chubhunter [2.5K]
Well looking at the information in triangle ABC you know 

Angle B + Angle C = 180 - 144

so Angle B + Angle C = 36

since the triangles are similar let angle M = x   

then Angle C = 2x        and angle B = angle M but the similarity postulate

so form an equation 

2x + x = 36 

solve for x 

Hope it helps
8 0
3 years ago
Read 2 more answers
Explain why a square must be a rectangle but a rectangle does not have to be a square
Sergio [31]

Answer:

A rectangle is any four sided shape that has four right angles; Therefore, since a square is a four sided shape that has four right angles and congruent (equal) sides, it always has to be a rectangle. However a rectangle does not always have congruent sides, so it is not necessarily a square.

7 0
3 years ago
Read 2 more answers
Find the area of the shaded portion in the equilateral triangle with sides 6. Show all work for full credit. (Hint: Assume that
Vadim26 [7]
So... if you notice the picture below

each circle, has their central angle at the vertex of the triangle
that simply means, 3 circles with a radius of 3, overlapping the triangle

now, the area in the middle, the shaded one, will be, the whole area of the triangle MINUS those 3 circle sectors

hmmmm each sector has 60°, that means, all three of them will then be 60+60+60 or 180°, so the area of those three sectors, can be combined into a 180° sector, well, hell, 180° is really half a circle

so.... the area of those three sectors of 60° each, all three combined, is the same area of half a circle with a radius of 3

so    \bf \textit{area of an equilateral triangle}\\\\
A=\cfrac{s^2\sqrt{3}}{4}\qquad s=\textit{length of one side}\\\\
-----------------------------\\\\
\textit{area of a circle}\\\\
A=\pi r^2\qquad r=radius\\\\
\textit{area of half a circle}\\\\
A=\cfrac{\pi r^2}{2}\\\\
-----------------------------\\\\

\bf \textit{now, let us use the side of 6, and radius of 3}
\\\\\\

\begin{array}{clclll}
\cfrac{6^2\sqrt{3}}{4}&-&\cfrac{\pi 3^2}{2}\\
\uparrow &&\uparrow \\
triangle's&&semi-circle's
\end{array}\impliedby \textit{area of shaded area}\\\\
-----------------------------\\\\
\boxed{\cfrac{36\sqrt{3}}{4}-\cfrac{9\pi }{2}}

you can, add the fractions if you want, or leave them like that, or get their difference by using their decimal format

8 0
3 years ago
Read 2 more answers
If a2= 18 and a4= 8, find two possible common ratios. Then, write two sequences lhaving five terms each.
Marizza181 [45]

common ratio = a4/a3 = a3/a2

8/a3 = a3/18

(a3)^2 = 8 * 18

(a3)^2 = 144

a3 = 12 or a3 = -12

common ratio = 8/12 or common ratio = 8/(-12)

common ratio = 2/3 or common ratio = -2/3

Answer: 12 or -12

3 0
3 years ago
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