HELP WANTED ASAP PLEASE!!!!

Answers

Answer 1

Answer: 21. x^2 + 9x - 14 = 0
x^2 + 9x = 14
x^2 + 9x + (4.5)^2 = 14 + (4.5)^2
(x + 4.5)^2 = 14 + 20.25 = 34.25
x + 4.5 = + or - sqrt(34.25)
x = + or - sqrt(34.25) - 4.5
x = sqrt(34.25) - 4.5 or -sqrt(34.25) - 4.5
x = 5.85 - 4.5 or -5.85 - 4.5
x = 1.35 or -10.35

Answer: the last option.

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if we have a geometric series with u1 = 2.1 and r= 1.06, what would the least value of n be such that Sn > 5543?

Answers

Answer:

Step-by-step explanation:

Write the expression for the sum in the relation you want.

Sn = u1(r^n -1)/(r -1) = 2.1(1.06^n -1)/(1.06 -1)

Sn = (2.1/0.06)(1.06^n -1) = 35(1.06^n -1)

The relation we want is ...

Sn > 5543

35(1.06^n -1) > 5543 . . . . substitute for Sn

1.06^n -1 > 5543/35 . . . . divide by 35

1.06^n > 5578/35 . . . . . . add 1

n·log(1.06) > log(5578/35) . . . take the log

n > 87.03 . . . . . . . . . . . . . . divide by the coefficient of n

The least value of n such that Sn > 5543 is 88.

What is -3 1/3 - -5 2/3

Answers

2 1/3
because -3 1/3+5 2/3

The answer is 3 because you subtract -3 and 5 and get 2 but then u add the 3/3 and get 1 which u add to the 2 and get 3 as your answer

Devin has started a lawn care service. He will charge a mowing fee of $10 plus $3 per square yard of lawn. He also offers trimming service, at $8 plus $1 per yard of the perimeter. Using x for the length of the lawn and y for the width of the lawn which part of the expression 10+3xy+8+(2x+2y) represents the charge for the mowing?A. 8+(2x+2y)
B. (2x+2y)
C. 3xy
D. 10+3xy

Answers

Answer:

Option D is correct.

Charge for the mowing = 10 + 3xy

Step-by-step explanation:

here, x represents the length of the lawn and y represents the width of the lawn.

$\text{Area of lawn} = \text{length} * \text{width}$ = xy square yard

Perimeter of lawn = 2 (x+y) = 2x + 2y yard

As per the statement:

Devin has started a lawn care service. He will charge a mowing fee of $10 plus $3 per square yard of lawn.

then;

Charge for mowing = $10 + 3 \cdot \text{Area of lawn}$

= 10 + 3xy

Also, he offers trimming service at $8 plus $1 per yard of the perimeter.

⇒ Trimming service = $8 + 1 \cdot \text{Perimeter}$ = 8 + (2x +2y)

Therefore, from the expression: 10 + 3xy +8 + (2x+2y)

10 + 3xy represents the charge for the mowing.

Answer is D because he charge 10 $ mowing free +3 per square yard of lawn
lawn has dimensions:
x and y
Area= x*y=xy squar yard
so charge is
10 +3*Area=10+3xy

What is the sum of the infinite geometric series?.

1/2+1/4+1/8+1/16+...

Answers

Answer:

The sum of the given geometric series is, 1

Step-by-step explanation:

Geometric sequence states that a sequence of numbers that follows a pattern were the next term is found by multiplying by a constant called the common ratio (r).

The sum of the infinite terms of a geometric series is given by:

$S_\infty = (a)/(1-r)$ ......[1] ;where $0<r<1$

Given the series: $(1)/(2)+(1)/(4)+(1)/(8)+(1)/(16)+.....$

Since, this series is geometric series with constant term(r) = $(1)/(2)$

Since,

$((1)/(4))/((1)/(2) ) =(2)/(4) = (1)/(2)$ ,

$((1)/(8))/((1)/(4)) =(4)/(8) = (1)/(2)$ and so on....

Here, first term(a) = $(1)/(2)$

Substitute the values of a and r in [1] we get;

$S_\infty = ((1)/(2))/(1-(1)/(2))$ where r = $(1)/(2)< 1$

$S_\infty = ((1)/(2))/((2-1)/(2))$

$S_\infty = ((1)/(2))/((1)/(2))$

Simplify:

$S_\infty = 1$

Therefore, the sum of the infinite geometric series is, 1

$1/2+1/4+1/8+1/16+...=\sum\limits_(n=1)^\infty ((1)/(2))^n = ((1)/(2))/(1-(1)/(2))=1$

We can see that consecutive fractions are made from 1/2 to consecutive powers. Because we begin with 1/2, n=1
We will infinitely add fractions , hence Lemniscate sign.

In other words you cannot find a number which needs to be added to the geometric series to get "1", therefore the answer is 1. I remember the teacher explaining it this way :)

I NEED HELP on this

Answers

the third choice is the correct one

Alan has 80% more stamps than Billy. Billy has 3/5 of the number of Charlies stamps. If Billy gave 150 stamps to Charlie, then Charlie would now have three times the number of Billys remaining stamps. What is the total number of stamps they have altogether?

Answers

a=alan
b=billy
c=charlie

a is 80% more than charlie means that a is 100% and billy=20%, so 20% of alan=billy
0.2a=c

b has 3/5 of c
b=3/5c

if b-150 and c+150, (c+150)=3 times (b-150)
luckily we can related c and b
b=3/5c
c+150=3(3/5c-150)
distribute
c+150=9/5c-450
add 450 both sides
c+600=9/5c
minus c both sides
600=4/5c
times 5/4 both sides
750=c

charlie has 750 stamps
billy=3/5 times c
b=3/5 times 750
b=450
allan has 80% more than billy
0.2a=b
0.2a=450
divide both sides by 0.2
a=2250

b=450
a=2250
c=750
add them
a+b+c=2250+450+750=3450 stamps

a=alan

b=billy

c=charlie

a is 80% more than charlie means that a is 100% and billy=20%, so 20% of alan=billy

0.2a=c

b has 3/5 of c

b=3/5c

if b-150 and c+150, (c+150)=3 times (b-150)

luckily we can related c and b

b=3/5c

c+150=3(3/5c-150)

distribute

c+150=9/5c-450

add 450 both sides

c+600=9/5c

minus c both sides

600=4/5c

times 5/4 both sides

750=c

charlie has 750 stamps

billy=3/5 times c

b=3/5 times 750

b=450

allan has 80% more than billy

0.2a=b

0.2a=450

divide both sides by 0.2

a=2250

b=450

a=2250

c=750

add them

a+b+c=2250+450+750=3450 stamps