MATHEMATICS HIGH SCHOOL

A motorcycle and a car leave an intersection at the same time. the motorcycle heads north at an average speed of 20 miles per hour, while the car heads east at an average speed of 48 miles per hour. find an expression for their distance apart in miles at the end of t hours.

Answers

Answer 1

Answer:

An expression relating the distance between the car and motorcycle after t is 52t

Speed of motorcycle = 20 mph

Speed of car = 48 mph

Distance apart after, t hours :

Recall :

Distance traveled = Speed × time

Hence,

Distance traveled by car after t hours

Distance of car = 48t

Distance traveled by Motorcycle after t hours

Distance of motorcycle = 20t

Since, the direction followed by the car and motorcycle forms a right angle, the distance apart after t hours can obtained using Pythagoras :

Recall from Pythagoras :

a² = b² + c²

Where, a = hypotenus

b and c = opposite and adjacent

Therefore, distance apart :

d² = (48t)² + (20t)²

d² = 2304t² + 400t²

d² = 2704t²

Take the square root of both sides :

d = √2704t²

d = 52t

Therefore, the distance between the car and motorcycle after t hours is : 52t

Learn more : brainly.com/question/8283882

Answer 2

Answer: First, determine the distance of the motorcycle and the car from the start point. The distance could be determined using
$\boxed{d=v * t}$
d stands for distance, v stands for speed, t stands for time

The car
d = 48 × t
d = 48t

The motorcycle
d = 20 × t
d = 20t

At the end of t hours, the car is 48t miles (east) from the start point and the motorcycle is 20t miles (north) from the start point.

Second, determine the distance between 48t miles at east and 20t miles at north using pythagoras
distance = $\sqrt{(48t)^(2)+(20t)^(2)}$
distance = $\sqrt{2304t^(2)+400t^(2)}$
distance = $\sqrt{2704t^(2)}$
distance = 52t

The expression for their distance apart at the end of t hours is 52t

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The question says evaluate 2a-b/b when a=4 and b=-3.
How would I start this problem?

Answers

You would start by writing down the expression that you have to evaluate:

2a - b/b

Then, get to work:
-- Wherever you see 'a', put in 4 .
-- Wherever you see 'b', put in -3 .

2(4) - (-3/-3)

Can you handle that ?

Hint:
The thing on the right is a fraction with the same number on top and bottom.
Any fraction like that is always equal to ' 1 '.

$(2a-b)/(b)\n\nsubstitute\ a=4;\ b=-3:\n\n(2\cdot4-(-3))/(-3)=(8+3)/(-3)=-(11)/(3)=-3(2)/(3)$

$or\ if\ 2a+(b)/(b)=2a+1\ then\ for\ a=4\ and\ b=-3:\n\n2\cdot4-3=8-3=5$

What is the definition of a two-column proof

Answers

Definition of Two-Column Proof. A proof is a logical argument presented with factual statements in order to arrive at a conclusion. Writing a proof is like solving a puzzle or using legos to create a model of something. Everything needs to fit in an appropriate place.

a population of 1200 leopards decreases by 12% per year. How many leopards will there be in the population after 6 years? Round your answer to the nearest whole number.

Answers

Answer:

557

Step-by-step explanation:

We are given that a population of 1200 leopards decreases by 12% per year.

So, we will use exponential function: $a_n=a_0(1-r)^x$

Where $a_n$ is the population left.

$a_0$ is the initial population.

r = rate of decrease

x = time

Now $a_0=1200$

r =12%=0.12

x = 6 years

Substitute the values.

$a_n=1200(1-0.12)^6$

$a_n=1200(0.464404086784)$

$a_n=557.28$

Thus there will be 557 leopards in the population after 6 years.

After 6 years approximately 557 leopards would be left.

Gracie, Mary, and Nancy each have a small collection of seashells. Gracie has 5 more than times the number of shells Mary has. Nancy has 1 more than times the number of shells Mary has. Gracie and Nancy have the same number of shells. If x is the number of shells Mary has, identify the equation that represents this situation and identify its solution.

Answers

First, let's name or variables. Let us name Gracie's number of seashells as G, Nancy's number of seashells as N and Mary's number of seashells is x. The first statement would give an algebraic expression of G = x + a5. The second statement gives N = x +b1. Also, G = N hence x +a5 = x + b1. Clearly, there are lacking values noted as a and b in the equation. Given a and b we can solve for x.

Joe owned a grocery store and wanted to raise some money. He decided to sell his land and building to an investor and leased it back to himself in order to to continue running his grocery store there. Which of the following would be a tax benefit to Joe? A. All capital gains for Joe are deferred B. Joe has a new tax base for his future depreciation of the building C. Joe's rent payments to the investor will be fully deductible for income tax purposes as a business expense D. None of the above

Answers

Answer:

D none of the above. I hope it is correct

Eric's father works two part time jobs, one in the morning and one in the afternoon, and works a total of 40 hours each 5-day workweek. If his schedule is the same each day, and he works 3 hours each morning, how many hours does Eric's father work each afternoon?

Answers

Answer:

Eric's father works for 5 hours in the afternoon

Step-by-step explanation:

Eric's father works two part time jobs, one in the morning and one in the afternoon, and works a total of 40 hours each 5-day workweek.

Step 1

The number of hours he works each days is calculated as:

40 hours÷ 5days

= 8 hours per day.

Hence, he works 8 hours per day.

Step 2

We are told in the question that:

If his schedule is the same each day, and he works 3 hours each morning, how many hours does Eric's father work each afternoon?

The total number of hours in works in a day = Number of hours worked in the morning + Number of hours worked in the afternoon

Hence:

8 hours = 3 hours + x

x = 8 hours - 3 hours

x = 5 hours

Therefore, Eric's father works for 5 hours in the afternoon

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A motorcycle and a car leave an intersection at the same time. the motorcycle heads north at an average speed of 20 miles per​ hour, while the car heads east at an average speed of 48 miles per hour. find an expression for their distance apart in miles at the end of t hours.

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A motorcycle and a car leave an intersection at the same time. the motorcycle heads north at an average speed of 20 miles per hour, while the car heads east at an average speed of 48 miles per hour. find an expression for their distance apart in miles at the end of t hours.