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solmaris [256]
3 years ago
12

The sum of three consecutive odd integers is –15. What are the numbers?

Mathematics
1 answer:
liberstina [14]3 years ago
3 0
Odd numbers are represented as 2n+1 where 2 is a natural number ( negative and possitive whole numbers)

consecutive odd numbers are 2 away from each other so 3 consecutive odd numbers would be
(2n+1),(2n+1+2),(2n+1+2+2)
the all add to -15 so they must all be negative
2n+1+2n+1+2+2n+1+2+2=-15
add like terms
6n+9=-15
subtract 9 from both sides
6n=-24
divide both sides by 6
n=-4
subsitute
first number=2n+1=2(-4)+1=-8+1=-7
second number=2n+1+2=2(-4)+3=-8+3=-5
third number=2n+1+2+2=-8+5=-3

the numbers are -7,-5, -3
the answe ris B
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2.34 x 10^65   + 9.2 x10^66  
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Answer:

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Step-by-step explanation:

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We can say that 2.34 X 10^65 = 0.234 X 10^66

Now that the indexes are equivalent, we can proceed to add the two bases together.

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Here is a triangular pyramid and its net.
bazaltina [42]

Answer:

a) Area of the base of the pyramid = 15.6\ mm^{2}

b) Area of one lateral face = 24\ mm^{2}

c) Lateral Surface Area = 72\ mm^{2}

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Step-by-step explanation:

We are given the following dimensions of the triangular pyramid:

Side of triangular base = 6mm

Height of triangular base = 5.2mm

Base of lateral face (triangular) = 6mm

Height of lateral face (triangular) = 8mm

a) To find Area of base of pyramid:

We know that it is a triangular pyramid and the base is a equilateral triangle. \text{Area of triangle = } \dfrac{1}{2} \times \text{Base} \times \text{Height} ..... (1)\\

{\Rightarrow \text{Area of pyramid's base = }\dfrac{1}{2} \times 6 \times 5.2\\\Rightarrow 15.6\ mm^{2}

b) To find area of one lateral surface:

Base = 6mm

Height = 8mm

Using equation (1) to find the area:

\Rightarrow \dfrac{1}{2} \times 8 \times 6\\\Rightarrow 24\ mm^{2}

c) To find the lateral surface area:

We know that there are 3 lateral surfaces with equal height and equal base.

Hence, their areas will also be same. So,

\text{Lateral Surface Area = }3 \times \text{ Area of one lateral surface}\\\Rightarrow 3 \times 24 = 72 mm^{2}

d) To find total surface area:

Total Surface area of the given triangular pyramid will be equal to <em>Lateral Surface Area + Area of base</em>

\Rightarrow 72 + 15.6 \\\Rightarrow 87.6\  mm^{2}

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b) Area of one lateral face = 24\ mm^{2}

c) Lateral Surface Area = 72\ mm^{2}

d) Total Surface Area = 87.6\ mm^{2}

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