MATHEMATICS HIGH SCHOOL

(3x+1)(2x-5)=39
i need help

Answers

Answer 1
Answer: (3x+1)(2x-5)=39 \n6x^2-15x+2x-5=39 \n6x^2-13x-5=39 \ \ \ \ \ \ \ \ \ \ |-39 \n6x^2-13x-44=0 \n6x^2-24x+11x-44=0 \n6x(x-4)+11(x-4)=0 \n(6x+11)(x-4)=0 \n6x+11=0 \ \lor \ x-4=0 \n6x=-11 \ \lor \ x=4 \nx=-(11)/(6) \ \lor \ x=4 \n\boxed{x=-1 (5)/(6) \hbox{ or } x=4}
Answer 2
Answer:                        (3x + 1)(2x - 5) = 39
              3x(2x - 5) + 1(2x - 5) = 39
3x(2x) + 3x(-5) + 1(2x) + 1(-5) = 39
          6x² + (-15x) + 2x + (-5) = 39
                  6x² - 15x + 2x - 5 = 39
                          6x² - 13x - 5 = 39
                                        - 39 - 39
                        6x² - 13x - 44 = 0
                                            x = -(-13) ± √((-13)² - 4(6)(-44))
                                                                    2(6)
                                            x = 13 ± √(169 + 1056)
                                                               12
                                            x = 13 ± √(1225)
                                                        12
                                            x = 13 ± 35
                                                      12
                                            x = 13 + 35    ∨    x = 13 - 35
                                                      12                         12
                                            x = 48        ∨        x = -22
                                                  12                         12
                                            x = 4         ∨         x = -1⁵/₆
The solution set us equal to {4, -1⁵/₆}.

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If you give me 70 coins I will have three times as much money as you, but if I give you 70 coins, then you will have five times as much as me. How many coins do we each have?​

Answers

Answer:

  • I have 110 coins, you have 130 coins

Step-by-step explanation:

I have x coins and you have y coins.

According to question we set the following equations.

If you give me 70 coins I will have three times as much money as you:

  • x + 70 = 3(y - 70) ⇒ x + 70 = 3y - 210  ⇒ x = 3y - 280

If I give you 70 coins, then you will have five times as much as me:

  • y + 70 = 5(x - 70) ⇒ y + 70 = 5x - 350 ⇒ y = 5x - 420

Solve by substitution:

  • y = 5(3y - 280) - 420
  • y = 15y - 1400 - 420
  • 15y - y = 1820
  • 14y = 1820
  • y = 1820/14
  • y = 130

Find the value of x:

  • x = 3*130 - 280
  • x = 390 - 280
  • x = 110

A number greater than 18.55 and less than 18.6

Answers

A number greater than 18.55 and less than 18.6 is 18.56. Other answers include: 18.57, 18.58, and 18.59.
A number greater than 18.55 and less than 18.6 could be 18.57

Alex received two job offers. He is not sure whether he should take a job at the movie theater that's close to his house and pays $8.50 per hour, or if he should take the job at a grocery store that pays $9.00 per hour, but is a thirty-minute drive away. Use the PACED decision process to decide what Alex should do. Show each step.

Answers

PACED decision making model
P - identify the problem
A - identify the alternatives
C - determine criteria
E - evaluate alternatives
D - make a decision

Problem: What job to take?
Alternatives:
1st job: movie theater ; 8.50/hr ; near his house or walking distance
2nd job: grocery store ; 9.00/hr ; 30 minutes travel
Criteria:
travel time and travel cost
Evaluate:
1st job: walking distance, no traffic worries nor fuel expenses
2nd job: 30 minutes travel time, consider traffic, fuel expenses
Decision:
It is more practical to accept the job in the movie house. Even though it is only 8.50 per hour, travel expenses is 0 and there is no difficulty in going to work.

Answer:

Movie Theater

Step-by-step explanation:

P - identify the problem

A - identify the alternatives

C - determine criteria

E - evaluate alternatives

D - make a decision

1st job; $8.50 an hour

2nd job; $9 an hour

1st job; walking distance, no fuel or car expenses

2nd job; 30 minutes away, need to pay for a bus or gas for a car

I say he should get the job at the movie theater, its closer so he doesnt need to spend money on gas or for a way to get to the other job. It's only $.50 more for the other job but he would cost more for a way to get there.

How do I factor out a constant before factoring out a quadratic? 
Factor completely: 3w^2-3w-90

Answers

3w^2-3w-90 =0 \ \ \:3 \n \nw^2- w-30 =0 \n \na=1 , \ b= -1 , c= -30 \n \n\Delta =b^2-4ac = (-1)^2 -4\cdot1\cdot (-30) =1+120=121 \n \nw_(1)=(-b-√(\Delta) )/(2a)=(1-√(121))/(2 )=( 1-11)/(2)=(-10)/(2)=-5

w_(2)=(-b+√(\Delta) )/(2a)=(1+√(121))/(2 )=( 1+11)/(2)=(12)/(2)=6 \n \n Answer:\n \n w^2- w-30 =(x+5)(x-6)
 

Type the correct answer in each box. If necessary, round your answers to the nearest hundredth. The vertices of ∆ABC are A(2, 8), B(16, 2), and C(6, 2). The perimeter of ∆ABC is (blank) units, and its area is (blank) square units.

Answers

Answer:

The perimeter of ∆ABC is 32.44 units, and its area is 30 square units....

Step-by-step explanation:

The perimeter is the sum of three distances.

To find the distances  BC, CD, DB use the distance formula:

D=√(y2-y1)^2+(x2-x1)^2

We have given A(2, 8), B(16, 2), and C(6, 2).

AB= √(16-2)^2+(2-8)^2

AB= √(14)^2+(-6)^2

AB=√196+36

AB=√232 = 15.23

BC=√(6-16)^2+(2-2)^2

BC=√(-10)^2+0

BC=√100 = 10

CA = √(2-6)^2+(8-2)^2

CA=√(-4)^2+(6)^2

CA=√16+36

CA=√52 = 7.21

Perimeter = AB+BC+CA

Perimeter = 15.23+10+7.21

Perimeter = 32.44 units

For the area BC is the parallel to x-axis

area = (1/2)base * height

=(1/2)10*(ya-yb)

=(1/2)10*(8-2)

=(1/2)10*6

=30 unit²

The perimeter of ∆ABC is 32.44 units, and its area is 30 square units....

Answer:

perimeter of ∆ABC is 32.44 units, and its area is 30 square units

Step-by-step explanation:

plato

In a class, 22 students have been on a plane, 28 on a train, 23 on a boat, 15 on a plane and train, 20 on a train and boat, 14 on a plane and boat, 12 on all three, and 1 on none of them. How many students are in the class?

Answers

Answer:

37 students are in the class

Step-by-step explanation:

There are 8 regions which the most inclusive clue is the inner one with 12.

  • "14 on a plane and boat" so we fill the intersection with plane and boat with 14-12=2
  • "20 on train an boat" 20-12=8 in the intersection
  • "15 on plane and train" = 15-12 = 3

now we look at this:

  • "22 students have been on a plane" 22 - (2+12+3) = 5 on the plane
  • "28 on a train" 28 - (12+8+3) = 5 on the train
  • "23 on a boat" 23-(12+8+2) = 1 on the boat

Just add up all the 8 numbers in the regions:

12+2+8+3+5+5+1+1=37
Best Answer:  Q#1! 
In a class, 22 students have been on a plane, 28 on a train, 23 on a boat, 15 on a plane and train, 20 on a train and boat, 14 on a plane and boat, and 12 on all three, and 1 on none of them. How many students are in the class? 

(1, 5, 3, 12, 2, 5, 8, 1) = 37 

Q#3! 
In a class of 32 students, 17 are wearing jeans, 8 are wearing T-shirts, and 7 are wearing both. How many students are wearing jeans and something other than a T-shirt? 
17 - 7 = 10
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