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2 years ago

Zachery is solving the equation 3/4 (x - 8) = 12

Mathematics

1 answer:

Maru [420]2 years ago

6 0

Answer:

3/4*x - 3/4*8=12

3/4x -6=12

3/4x=12+6

3/4x=18

x=24

Step-by-step explanation:

multiply 3/4 into the content inside the brackets

have -3/4*8 cross the equal sign changing its sign from - to +

divide both sides by 3/4

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a motor boat traveled 18 miles down a river in 2 hours but took 4.5 hours to return upstream. Find the rate of the motor boat in

tangare [24]

Answer:

rate of the boat in still water = 6.5 miles / hour

rate of the current = 2.5 miles / hour.

Explanation:

1) Name the two variables:

c: rate of the current

b: rate of the boat in still water:

With that, the net rates of the boat down the river and upstrean are:

down the river: b + c

upstream: b - c

2) Now set the equations for the distance as a function of the times and the rates:

distance = rate × time

downstream: 18 miles = (b + c) × 2 hours

upstream: 18 miles = (b - c) × 4.5 hours

3) Set the system of equations:

18 = 2(b + c) ⇒ 9 = b + c . . . Equation (1)

18 = 4.5 (b - c) ⇒ 4 = b - c . . . Equation (2)

4) Solve the system by elimination:

Add equations (1) and (2): 9 + 4 = 2b

Divide both sides by 2: 13/2 = b

Simplify: b = 6.5

Replace b with 6.5 in equation (2) and solve:

4 = 6.5 - c ⇒ c = 6.5 - 4 = 2.5

5) Results:

b = rate of the boat in still water = 6.5 miles / hour

c = rate of the current = 2.5 miles / hour.

3 0

2 years ago

Read 2 more answers

Nathaniel purchased a new car in 1997 for $20,300. The value of the car has been depreciating exponentially at a constant rate.

Tems11 [23]

Answer:

Step-by-step explanation:

We would apply the formula for exponential decay which is expressed as

A = P(1 - r)^t

Where

A represents the value of the car after t years.

t represents the number of years.

P represents the initial value of the car.

r represents rate of decay.

From the information given,

A = $2700

P = $20300

n = 2004 - 1997 = 7 years

Therefore,

20300 = 2700(1 - r)^7

20300/2700 = (1 - r)^7

7.519 = (1 - r)^7

Taking log of both sides, it becomes

Log 7.519 = 7 log(1 - r)

0.876 = 7 log(1 - r)

Log (1 - r) = 0.876/7 = 0.125

Taking inverse log of both sides, it becomes

10^log1 - r = 10^0.125

1 - r = 1.33

r = 1.33 - 1 = 0.33

The expression would be

A = 20300(1 - 0.33)^t

A = 20300(0.67)^t

Therefore, in 2007,

t = 2007 - 1997 = 10 years

The value would be

A = 20300(0.67)^10

A = $370

6 0

2 years ago

Of the 400 eighth-graders at pascal middle school, 117 take algebra, 109 take advanced computer, and 114 take industrial technol

Hatshy [7]

If 164 of the 400 eighth-graders take none of these courses, then 400-164=236 students take some courses.

Let x students take all three courses, then:

1. 70-x take only both algebra and advanced computer,

2. 34-x take only both algebra and industrial technology,

3. 29-x take only both advanced computer and industrial technology.

Now let's count how many student take only one course:

1. 117-(x+34-x+70-x)=13+x take algebra,

2. 109-(x+29-x+70-x)=10+x take advanced computer,

3. 114-(x+29-x+34-x)=51+x take industrial technology.

Now count all students that take some courses:

51+x+10+x+13+x+29-x+34-x+70-x+x=236,

x=236-51-10-13-29-34-70,

x=29.

Answer: all three courses take 29 students.

6 0

2 years ago

Read 2 more answers

Suppose students' ages follow a skewed right distribution with a mean of 24 years old and a standard deviation of 3 years. If we

natta225 [31]

Answer: Option 'c' is correct.

Step-by-step explanation:

Since we have given that

Mean of students' age = 24 years

Standard deviation of students' age = 3 years

Sample size = number of students = 350

So, according to options,

a. The shape of the sampling distribution is approximately normal.

It is true as n >30, we will use normal.

b. The mean of the sampling distribution is approximately 24-years old.

It is true as it is given.

c. The standard deviation of the sampling distribution is equal to 5 years.

It is not true as it is given 3 years.

Hence, Option 'c' is correct.

8 0

2 years ago

Dimensional Analysis Method (also called conversion factor or unit analysis) (Appendix D: Dimensional Analysis, Page 397) o The

garik1379 [7]

Answer:

The dimensional analysis method uses equivalences written in fractional form. Because the numerator and denominator of the fraction are equivalent, the value of the fraction is 1. Multiplying by 1 does not change the quantity, but using an equivalence will change the units (or label). In order for units to cancel they must be in the numerator and the denominator of the fraction

Step-by-step explanation:

Dimensional analysis is a method of problem solving that takes into consideration the identity property of multiplication whereby the product of a number and 1 will always give the same number, that is 1 × n = n whereby the value "n" remains the same after the multiplication

Therefore, a fraction of two equivalent measurements but different units has a value of 1, and multiplying the equivalent fraction with another measurement with the same unit as the denominator of the fraction with a value of 1 changes the unit to that of the unit of the numerator

4 0

2 years ago