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solmaris [256]
2 years ago
12

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

Mathematics
1 answer:
liberstina [14]2 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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The sum of the diagonals of a rhombus is 5√2.
Alex
Greetings!
Let ABCD be a rhombus
AC + BD = 5√2 cm

Area of ABCD = Ar△ABD + Ar △BCD
= \frac{1}{2} \times BD \times AO + \frac{1}{2} \times BD \times OC
= \frac{1}{2} BD (AO + OC)
\frac{1}{2} BD \times AC

So, \frac{ BD \times AC}{2} = 4 \: cm {}^{2}
BD \times AC = 8
Now, AC + \: BD = 5 \sqrt{2}

Squaring both sides, we get
AC {}^{2} + BD {}^{2} + 2 AC.BD =50
AC {}^{2} + BD {}^{2} + 2 \times 8 = 50
AC {}^{2} + BD {}^{2} = 50 - 16
AC {}^{2} + BD {}^{2} = 34

In △AOB, we have
OA {}^{2} + OB {}^{2} =AB {}^{2}
( \frac{ AC }{2} ) {}^{2} + ( \frac{ BD}{2} ) {}^{2} = AB {}^{2}
\frac{ AC {}^{2} } {4} + \frac{ BD {}^{2} }{4} = AB {}^{2}
AC {}^{2} + BD {}^{2} = 4 AB {}^{2}
34 = 4 AB {}^{2}

Square rooting both sides
\sqrt{34} = 2 AB
Perimeter = 4 \: AB \\ = 2 \times 2 \: AB \\ = 2 \: \times \sqrt{34 } \\ = 2 \sqrt{34 \: } units.

Hope it helps!

7 0
3 years ago
A football team recieved 3 penalties for 15 yeards each 1 for 5 yards and 1 for half the distance to tge goal from the 34-yard l
Oksanka [162]
He w has 59 penalties
6 0
2 years ago
What is the common difference between successive terms in the sequence 2,8,14,20,26
artcher [175]
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4 0
3 years ago
Brad walked 2.5 miles in 5/6 of an hour.how fast does he walk per hour
Lelu [443]

Answer:

Rate or speed=3 Miles per hour

Step-by-step explanation:

Brad walked 2.5 miles in 5/6 of an hour.

Distance covered by Brad = 2.5 miles

Distance covered by Brad= 2 1/2 miles

Distance covered by Brad= 5/2 miles

Time taken to cover the distance = 5/6 of an hour

His rate of walking or how fast he walks is determined by the formula

Rate or speed= distance/time

Rate or speed=( 5/2)/(5/6)

Rate or speed= (5/2)*(6/5)

Rate or speed=6/2

Rate or speed=3 Miles per hour

6 0
3 years ago
3/5 of a number is 21 find the number​
DedPeter [7]

Answer:

35

Step-by-step explanation:

To find the original number multiply by the reciprocal of \frac{3}{5} , that is

number = \frac{5}{3} × 21 = \frac{105}{3} = 35

7 0
2 years ago
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