MATHEMATICS HIGH SCHOOL

What is an expression for 43 more than t

Answers

Answer 1
Answer: 43 more than t

t + 43
Answer 2
Answer: 43 more than t = Variable + 43 

t+43

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What is 3/4 of 16/21

Answers

(\not3^1)/(\not4^1)*(\not 16^4)/(\not 21^7) =(4)/(7)

42) According to the 2000 Census the population of Canton was 7,720. Holly Spring's population was 3,200. Canton's population increases at a rate of 80 people a year and Holly Spring's population increases by 120 people a year. Which equation may be used to determine the number of years before the populations are equal?

Answers

Let's construct an equation for Canton's population increase as 7220+80n and Holly Spring's population increase with 3200+120n, where n is the number of years. We have to set these equations to each other in order to find when the population of these two places are equal. 3200+120n=7220+80n and n=100.5. After 100 and half years

As viewed from a cliff 340 feet above sea level, a ship is 450 feet from the shore. What is the angle of depression from the cliff to the ship on the water below?

Answers

the angle of depression is equal to angle of elevation at ship
let m be the angle
tan m=340/450=0.76
therefore m=37.073 degrees

Emily and Sara had a total of $80.after Sara spent 1/3 of her money and Emily spent $17,Emily had twice as much money as Sarah.how much money did Emily have then Sara at first?

Answers

x/3-17=80
x/3=97
x=291

291-97=194

194-97=97

Emily had $97 more than Sara.

The John Jay Theater Dept has tickets at $6 for adults, $4 for teachers, and $2 for students. A total of 280 tickets were sold for one showing with a total revenue of $1010. If the number of adult tickets sold was twice the number of teacher tickets, how many of each type of ticket were sold for the showing?

Answers

Answer:

number of adults tickets sold = x = 90

number of teachers tickets = y = 45

number of students tickets = z = 145

Step-by-step explanation:

Cost of tickets

Adults = $6

Teachers = $4

Students = $2

Total tickets sold = 280

Total revenue = $1010

Let

x = number of adults tickets

y = number of teachers tickets

z = number of students tickets

x + y + z = 280

6x + 4y + 2z = 1010

If the number of adult tickets sold was twice the number of teacher tickets

x = 2y

Substitute x=2y into the equations

x + y + z = 280

6x + 4y + 2z = 1010

2y + y + z = 280

6(2y) + 4y + 2z = 1010

3y + z = 280

12y + 4y + 2z = 1010

3y + z = 280 (1)

16y + 2z = 1010 (2)

Multiply (1) by 2

6y + 2z = 560 (3)

16y + 2z = 1010

Subtract (3) from (2)

16y - 6y = 1010 - 560

10y = 450

Divide both sides by 10

y = 450/10

= 45

y = 45

Substitute y=45 into (1)

3y + z = 280

3(45) + z = 280

135 + z = 280

z = 280 - 135

= 145

z = 145

Substitute the values of y and z into

x + y + z = 280

x + 45 + 145 = 280

x + 190 = 280

x = 280 - 190

= 90

x = 90

Therefore,

number of adults tickets sold = x = 90

number of teachers tickets = y = 45

number of students tickets = z = 145

Differentiate using first principle to show that:

d/dx √tanx = sec^2 x/2√tanx

Answers

Step-by-step explanation:

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