Halfway through a bus route, 23 students have been dropped off and 48 students remain on the bus. Write an equation to determine whether there are 61 or 71 students on the bus at the begginning of the route.

Answers

Answer 1
Answer:

Answer: The required equation is

x=23+48\n\Rightarrow\ x=71

Thus, there are 71 students on the bus at the beginning of the route.

Step-by-step explanation:

Given: The number of students dropped off = 23

The number of students remain on the bus = 48

Let 'x' be the total number of students in the bus then we get the equation as

x=23+48

On adding 23 to 48, we get 71

Hence,x=71

Therefore, There are 71 students on the bus at the beginning of the route.

Answer 2
Answer: 48+23=71. So seventy one students were on the bus then 23 were dropped off leaving 48 remaining

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The weight of a package is at least 1.5 pounds. Write an inequality to represent this situation. (Show work please)

Consider the following formula:

ax-bc+y=z

What represents the formula for x?

Answers

Answer:

x = (z-y)/(a-b)

Step-by-step explanation:

Given ax-bx+y=z, we are asked to isolate x. To do so, first take common factor between the first and the second terms

ax-bx+y=z  

(a-b)*x+y = z

Then, isolate the x term by subtracting y at both sides

(a-b)*x+y-y = z-y

(a-b)*x = z-y

Finally, divide by (a-b) at both sides

(a-b)*x/(a-b) = (z-y)/(a-b)

x = (z-y)/(a-b)

Answer: z-y+bc/a

Step-by-step explanation:

ax-bc+y=z

ax-bc=z-y

ax=z-y+bc

x=z-y+bc/a

Stephen has been saving money to buy a new car. The new car costs $21,920.00. He has to pay 17.25% in taxes based off the cost of the car. If he also purchases an extended warranty for $1,200.00, what is a reasonable estimate for the total price of the car?sorry the numbers were mixed up!

Answers

The total price of the car is $26901.20

Step-by-step explanation:

It is given that,  

  • The cost of the new car = $21,920.00
  • The tax percent for the cost of the car = 17.25%
  • He also purchases an extended warranty for the car = $1,200.00

To find the total price of the car :

Total Price = cost of the car + Tax cost + warranty cost.

The cost of the car and warranty cost are already given. So, we need to calculate the Tax amount paid for the car.

Tax amount = 17.25% of $21,920.00

17.25/100 × 21,920.00

⇒ 0.1725 × 21,920

⇒ 3781.2 dollars.

Therefore, the cost of tax is $3781.2

Now, coming to the total price of the car,

Total Price ⇒ 21,920.00 + 3781.20 + 1200.00  = 26901.20  dollars.

The total price of the car is $26901.20

the ratio of the number of apples to the number of oranges is 4:6. The ratio of the number of oranges to the number of pears is 8:1. How many apples, Oranges and pears are there if there are 172 fruits.

Answers

The answer is 64 apples, 96 oranges, and 12 pears.

Let's represent the fruit as following:
a - the number of apples,
o - the number of oranges,
p - the number of pears.

a:o=4:6
⇒ (a)/(o)= (4)/(6)
⇒ a= (4)/(6)o

o:p=8:1
⇒ (o)/(p)= (8)/(1)
⇒ o= 8p

Therefore:
a= (4)/(6)*8p =16/3p

Now, if a+o+p=172, then:
(16)/(3)p +8p+p=172
(16)/(3)p +9p172

Since 9= (9)/(1) = (27)/(3), 9p can be expressed as 27/3p:
(16)/(3)p+ (27)/(3)p=172
(43)/(3)p =172
p =172* (3)/(43)
⇒ p = 12
There are 12 pears.

Since o = 8p, o = 96:
o = 8 × 12 = 96
There are 96 oranges.

Since a= (16)/(3)p, a = 64:
a= (16)/(3) *12=16*4=64
There are 64 apples.

Therefore, there are 64 apples, 96 oranges, and 12 pears.

Identify the correct ways to classify ∠1 and ∠4 in the figure shown below.

Answers

Answer:

adjacent and complementary angles

Step-by-step explanation:

we know that

If the sum of two angles is equal to 90\° then, the angles are Complementary

and

Two angles are Adjacent when they have a common side and a common vertex

In this problem we have

m<1+m<4=90\° -----> by complementary angles

and

m<1 and m<4 have a common side and a common vertex

therefore

m<1 and m<4 are adjacent and complementary angles

They are adjacent and complementary.
Next to each other and add up to 90 degrees.

Is y=4x-5 proportional

Answers

Answer: A proportional relation between two numbers, x and y is when:

y= k*x, where k is a real number.

this is read as "the number y is k times the number x" so y is proportional to x, and the constant of proportionality is k.

The equation in the problem is: y = 4x - 5, here you have an x-intercept equal to -5, this quantity breaks the proportionality relation. So in this case y is not proportional to x.

No it's not proportional because it would be like y=4x. And proportional relationship doesn't have any operation between the “k” and “x” where K is the unit rate or the constant of proportionality!

Find the greatest common factor of
21
and
49
.

Answers

The greatest common factor (GCF) is 7.