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Natasha2012 [34]
3 years ago
10

Find 4 consecutive odd integers where the product of the two smaller numbers is 64 less than the product of the two larger numbe

rs.
Mathematics
2 answers:
Galina-37 [17]3 years ago
8 0
Odd number is: (2n-1), (2n+1), (2n+3), (2n+x),... where x x changes every two
(2n-1)(2n+1)=(2n+3)(2n+5)-64
4n^2-1=4n^2+10n+6n+15-64
16n=48|:16
n=3
Now we substitute to (2n-1), (2n+1), (2n+3), (2n+5):
2n-1 = 2*3-1=5
2n+1 = 2*3+1=7
2n+3 = 2*3+3=9
2n+5 = 2*3+5=11
5,7,9,11
vagabundo [1.1K]3 years ago
6 0
If there are such numbers, then they can be written as 'x', (x + 2), (x + 4), and (x + 6).

Now, the problem says that  x(x+2) + 64 = (x+4) (x+6)

Expand each side:

x² + 2x + 64 = x² + 10x + 24

Subtract (x² + 24) from each side:

2x + 40 = 10x

Subtract 2x from each side:

40 = 8x

Divide each side by 8 :

x = 5

The numbers are <u>5, 7, 9, and 11</u>.

(5 x 7) + 64 = 35 + 64 = 99  and  9 x 11 = 99 .    yay !
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PLEASE HELP IM DESPERATE WILL GIVE BRAINLIEST ONLY ANSWER IF YOU ARE HELPING
VARVARA [1.3K]

Answer:

48

Step-by-step explanation:

u • w

= (i + 6j ) • (9i - 2j )

= (1 × 9 ) + (6 × - 2 )

= 9 + (- 12)

= 9 - 12

= - 3

v • w

= (5i - 3j ) • (9i - 2j )

= (5 × 9) + (- 3 × - 2)

= 45 + 6

= 51

Then

u • w + v • w

= - 3 + 51

= 48

7 0
3 years ago
Rationalize the denominator and simplify.<br> 6<br> 15 - 3
Rzqust [24]

Answer:

a)6 =  \frac{6}{1} = 6  \:  \:  \: b)15 - 3 =  \frac{15}{3} = 5

5 0
2 years ago
What property would justify the following statement? If a = b and b = c, then a = c. Addition Property Reflexive Property Subtra
romanna [79]

Answer:

It would be the transitive property! If you look up "If a = b, and b = c, then a = c" you'd see the transitive property. I hope this helps!

6 0
3 years ago
How tall is a building that casts a ​78-ft shadow when the angle of elevation of the sun is 30 degrees​?
Marta_Voda [28]

Answer: 45.03\ ft

Step-by-step explanation:

Given

The length of the shadow is 78 ft

the angle of elevation is \theta =30^{\circ}

Suppose the height of the building is h

From the figure, we can write

\tan 30^{\circ}=\dfrac{h}{78}\\\\h=78\tan 30^{\circ}\\\\h=45.03\ ft

The height of the building is 45.03 ft

8 0
2 years ago
(⚠️⚠️HELP!⚠️⚠️)Mary bought 18 books. Mary bought 6 times as many books as Carlos. Let b be the number of books that Carlos bough
kvasek [131]

Answer:

18=6b, b=3

Because Mary has 6 times as much as Carlos does, we put the x with 6. 18 is the number that 6x equals. 6*3=18

8 0
3 years ago
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