15 POINTS Please do #53 and show work

Mathematics

2 answers:

Nitella [24]2 years ago

7 0

Answer: 511

Step-by-step explanation:

53.

For this problem simply plug in the numbers: 1 through 9 for n

the n=1 on the bottom represents the start and the 9 at the top represents the end

and the 2^n-1 represents the rule

solving for a1: plugging in one for n

a1=2^1-1

a1=1

a2=2^2-1

a2=2

a3=2^3-1

a3=4

a4=2^4-1

a4=8

a5=2^5-1

a5=16

a6=2^6-1

a6=32

a7=2^7-1

a7=64

a8=2^8-1

a8=128

a9=2^9-1

a9=256

after finding all these values add them all together and you should get your answer

1+2+4+8+16+32+64+128+256

=511

MaRussiya [10]2 years ago

3 0

Answer:

511 Is the answer

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A newspaper carrier has $5.40 in change. He has six more quarters than dimes but five times as many nickles as quarters. How man

BigorU [14]

X= number of dimes
x+6= number of quarters
5(x+6)= number of nickels
$5.40= 540 cents

Add the number of each coin and set it equal to the total in cents.

x + (x + 6) + 5(x + 6)= $5.40
multiply 5 by parentheses; change dollar total to cents

x + (x + 6) + (5 * x) + (5 * 6)= 540

x + (x + 6) + 5x + 30= 540
combine like terms

7x + 36= 540
subtract 36 from both sides

7x= 504
divide both sides by 7

x= 72 dimes

x + 6= 78 quarters

5(x + 6)= 390 nickels

CHECK
72 + 78 + 390= 540
540= 540

ANSWER: There are 72 dimes, 78 quarters and 390 nickels.

Hope this helps! :)

5 0

2 years ago

Write the quadratic equation whose roots are -3 and 2 , and whose leading coefficient is 5

KiRa [710]

Step-by-step explanation:

Since, roots are - 3 & 2

Therefore, (x + 3) & (x - 2) would be factors.

Leading coefficient is 5

Hence, required quadratic equation is:

$5(x + 3)(x - 2) = 0 \\ \therefore \: 5( {x}^{2} - 2x + 3x - 6) = 0\\ \therefore \: 5( {x}^{2} + x - 6) = 0\\ \therefore \: 5 {x}^{2} + 5x - 30 = 0\: \\ is \: the \: required \: quadratic \: equation.$