1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
DanielleElmas [232]
3 years ago
8

6(2c+3d)=5(4c-3d) solve for d

Mathematics
1 answer:
Arturiano [62]3 years ago
8 0

Answer:

d = \frac{8c}{33}

Step-by-step explanation:

6(2c + 3d) = 5(4c - 3d)

6(2c) + 6(3d) = 5(4c) - 5(3d) distribute out the terms

12c + 18d = 20c - 15d

18d + 15d = 20c - 12c get all like terms onto the same side

33d = 8c

d = \frac{8c}{33} divide by 33 to isolate the d variable

You might be interested in
Which of these does not represent the distance a car travels when going 55miles per hour
sveticcg [70]

Answer:

it is C

Step-by-step explanation:

if you see 160 mph doesent come from 50 times 3

4 0
3 years ago
Which is the least common multiple of 4 and 12
spayn [35]
The answer is 12. My explanations is that LCM is the smallest number that both numbers can fit into. 12 fits into 12 once, and 4 fits into 12 3 times, so 12 is the answer.
3 0
2 years ago
City A had a population of 10000 in the year 1990. City A’s population grows at a constant rate of 3% per year. City B has a pop
Georgia [21]

Answer:

City A and city B will have equal population 25years after 1990

Step-by-step explanation:

Given

Let

t \to years after 1990

A_t \to population function of city A

B_t \to population function of city B

<u>City A</u>

A_0 = 10000 ---- initial population (1990)

r_A =3\% --- rate

<u>City B</u>

B_{10} = \frac{1}{2} * A_{10} ----- t = 10 in 2000

A_{20} = B_{20} * (1 + 20\%) ---- t = 20 in 2010

Required

When they will have the same population

Both functions follow exponential function.

So, we have:

A_t = A_0 * (1 + r_A)^t

B_t = B_0 * (1 + r_B)^t

Calculate the population of city A in 2000 (t = 10)

A_t = A_0 * (1 + r_A)^t

A_{10} = 10000 * (1 + 3\%)^{10}

A_{10} = 10000 * (1 + 0.03)^{10}

A_{10} = 10000 * (1.03)^{10}

A_{10} = 13439.16

Calculate the population of city A in 2010 (t = 20)

A_t = A_0 * (1 + r_A)^t

A_{20} = 10000 * (1 + 3\%)^{20}

A_{20} = 10000 * (1 + 0.03)^{20}

A_{20} = 10000 * (1.03)^{20}

A_{20} = 18061.11

From the question, we have:

B_{10} = \frac{1}{2} * A_{10}  and  A_{20} = B_{20} * (1 + 20\%)

B_{10} = \frac{1}{2} * A_{10}

B_{10} = \frac{1}{2} * 13439.16

B_{10} = 6719.58

A_{20} = B_{20} * (1 + 20\%)

18061.11 = B_{20} * (1 + 20\%)

18061.11 = B_{20} * (1 + 0.20)

18061.11 = B_{20} * (1.20)

Solve for B20

B_{20} = \frac{18061.11}{1.20}

B_{20} = 15050.93

B_{10} = 6719.58 and B_{20} = 15050.93 can be used to determine the function of city B

B_t = B_0 * (1 + r_B)^t

For: B_{10} = 6719.58

We have:

B_{10} = B_0 * (1 + r_B)^{10}

B_0 * (1 + r_B)^{10} = 6719.58

For: B_{20} = 15050.93

We have:

B_{20} = B_0 * (1 + r_B)^{20}

B_0 * (1 + r_B)^{20} = 15050.93

Divide B_0 * (1 + r_B)^{20} = 15050.93 by B_0 * (1 + r_B)^{10} = 6719.58

\frac{B_0 * (1 + r_B)^{20}}{B_0 * (1 + r_B)^{10}} = \frac{15050.93}{6719.58}

\frac{(1 + r_B)^{20}}{(1 + r_B)^{10}} = 2.2399

Apply law of indices

(1 + r_B)^{20-10} = 2.2399

(1 + r_B)^{10} = 2.2399 --- (1)

Take 10th root of both sides

1 + r_B = \sqrt[10]{2.2399}

1 + r_B = 1.08

Subtract 1 from both sides

r_B = 0.08

To calculate B_0, we have:

B_0 * (1 + r_B)^{10} = 6719.58

Recall that: (1 + r_B)^{10} = 2.2399

So:

B_0 * 2.2399 = 6719.58

B_0  = \frac{6719.58}{2.2399}

B_0  = 3000

Hence:

B_t = B_0 * (1 + r_B)^t

B_t = 3000 * (1 + 0.08)^t

B_t = 3000 * (1.08)^t

The question requires that we solve for t when:

A_t = B_t

Where:

A_t = A_0 * (1 + r_A)^t

A_t = 10000 * (1 + 3\%)^t

A_t = 10000 * (1 + 0.03)^t

A_t = 10000 * (1.03)^t

and

B_t = 3000 * (1.08)^t

A_t = B_t becomes

10000 * (1.03)^t = 3000 * (1.08)^t

Divide both sides by 10000

(1.03)^t = 0.3 * (1.08)^t

Divide both sides by (1.08)^t

(\frac{1.03}{1.08})^t = 0.3

(0.9537)^t = 0.3

Take natural logarithm of both sides

\ln(0.9537)^t = \ln(0.3)

Rewrite as:

t\cdot\ln(0.9537) = \ln(0.3)

Solve for t

t = \frac{\ln(0.3)}{ln(0.9537)}

t = 25.397

Approximate

t = 25

7 0
3 years ago
An absolute value equation that equals 3 and -3
forsale [732]

Answer\sqrt{9}

Step-by-step explanation:

3 0
3 years ago
Triangle V P M. Angle V is 52 degrees, angle P is 78 degrees, angle M is x degrees. What is the measure of AngleM?
Phantasy [73]

Answer:

The answer is 50

Step-by-step explanation:

Got it right on edge

3 0
3 years ago
Read 2 more answers
Other questions:
  • Write decimal 3.4 as a fraction or a mixed number in simplesy form
    8·1 answer
  • 15 POINTS!!!!!!! A music store has 500 guitar picks. They order 15 boxes with 9 picks each. They sell 19 boxes that have 10 pick
    10·1 answer
  • What is the slope of a line that is parallel to the line represented by the equation x-y=8?
    13·1 answer
  • Can someone plz tell me the answer and response plz
    14·1 answer
  • 60 + $50.45 x equals $57 .95 cents x
    5·1 answer
  • 1) Find an equation of the line that passes through the point and has the indicated slope m. (Let x be the independent variable
    7·1 answer
  • 1. 8 feet to 10 feet *
    6·1 answer
  • (x+7)(x-6) Find the product.ddddddddddddd
    14·2 answers
  • X
    5·1 answer
  • The figure below has a point marked with a large dot
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!