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4 years ago

2loge3 + loge x - loge2 = loge3 Solve for x

1 answer:

7 0

$2\ln 3+\ln x-\ln 2=\ln 3\\
\ln x=-\ln 3+\ln 2\\
\ln x=\ln \dfrac{1}{3}+\ln 2\\
\ln x=\ln \dfrac{2}{3}\\
x=\dfrac{2}{3}$

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A storekeeper has two kinds of flour, one selling for 65 cents per pound, and the other selling for 95 cents per pound. How many

Murrr4er [49]

Answer:

The amount of 65 cents per pound flour to use is 40 pounds and the amount of 95 cents per pound flour to use is 60 pounds

Step-by-step explanation:

Let

x ----> amount of 65 cents per pound flour to use

y----> amount of 95 cents per pound flour to use

we know that

$x+y=100$ ----> $y=100-x$ ----> equation A

$0.65x+0.95y=0.83(100)$ ----> equation B

substitute equation A in equation B

$0.65x+0.95(100-x)=0.83(100)$

Solve for x

$0.65x+95-0.95x=83$

$0.95-0.65x=95-83$

$0.30x=12$

$x=40\ lb$

Find the value of y

$y=100-40=60\ lb$

therefore

The amount of 65 cents per pound flour to use is 40 pounds and the amount of 95 cents per pound flour to use is 60 pounds

4 0

3 years ago

Read 2 more answers

The line passing through point (0, 0) and parallel to the line whose equation is 3x + 2y - 6 = 0

choli [55]

Answer: y= -3/2x

Explanation:

3x+ 2y- 6

→ 2y= -3x+ 6

→ y= -3/2x+ 3

Parallel to y= ax+ b is to have the same slope (ax) and have a different y- intercept.

For this equation, y= -3/2x + 3, it is y= -3/2x because the line has to pass through point (0,0).

8 0

4 years ago

Read 2 more answers

Which number is a factor of 10 but not a multiple of 2

Llana [10]

5 maybe could be the right answer hope this helps

4 0

3 years ago

Read 2 more answers

Gianna has 2 pairs of shoes, 3 pairs of pants, and 4 shirts. How many outfits can he make

alekssr [168]

Answer:

Step-by-step explanation:

2 x 3 = 6

6 x 4 = 24

1 pair of shoes would pair with the 3 pants,

multiply that by 2 for the other pair and you get 6 different possibilties.

you multiply the 6 possibilities by 4 shirts to get 24 different combinations.

7 0

3 years ago

Chelsea took out three loans for a total of $ 78 comma 000 78,000 to start an organic orchard. Her business-equipment loan was

lianna [129]

Answer:

Business-equipment loan, A=$15000

Small-business loan, B=$24000

home-equity loan, C= $39000

Step-by-step explanation:

Let the Business-equipment loan at an interest rate of 11%=A

Let the small-business loan was at an interest rate of 5% =B

Let her home-equity loan was at an interest rate of 4.5%.=C

Since her total Loan=$78000

A+B+C=78000....(I)

Simple Interest = (P X R X T)/100

Since the Time, T=1 year

Interest on A = 0.11A

Interest on B = 0.05B

Interest on C = 0.045C

The total simple interest due on the loans in one year was $4605.

0.11A+0.05B+0.045C=4605....(II)

The annual simple interest on the home-equity loan was $105 more than the interest on the business-equipment loan.

0.045C = 0.11A +105...(III)

We proceed to solve the simultaneous equations.

A+B+C=78000....(I)

0.11A+0.05B+0.045C=4605....(II)

0.045C = 0.11A +105...(III)

From (III), 0.045C = 0.11A +105

Substitute 0.045C = 0.11A +105 into (II).

0.11A+0.05B+0.11A +105=4605

0.22A+0.05B=4500

From (III),

$C=\frac{22A}{9}+\frac{7000}{3}$

Substitute into (I)

$A+B+\frac{22A}{9}+\frac{7000}{3}=78000$

$\frac{31A}{9}+B=78000-\frac{7000}{3}$

$\frac{31A}{9}+B=\frac{227000}{3}$

$\frac{31A+9B}{9}=\frac{227000}{3}$

3(31A+9B)=9 X 227000

31A+9B=681000

0.22A+0.05B=4500 (Multiply by 9)

31A+9B=681000 (Multiply by 0.05)

1.98A+0.45B=40500

1.55A+0.45B=34050

Subtracting

0.43A=6450

A=$15000

From (III)

$C=\frac{22A}{9}+\frac{7000}{3}$

$C=\frac{22X15000}{9}+\frac{7000}{3} =39000$

C=$39000

from (I)

A+B+C=78000

15000+B+39000=78000

B=$24000

8 0

3 years ago