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Keith_Richards [23]

3 years ago

14

A motor scooter travels 14 mi in the same that a bicycle covers 5 mi. If the rate of the scooter is 4mph more than twice the rat

e of the bicycle, find both rates

1 answer:

nignag [31]3 years ago

8 0

We observe that 14 is 4 more than twice 5.

The scooter's rate is 14 mph.
The bicycle's rate is 5 mph.
_____
time = distance/rate
14/(2b +4) = 5/b . . . . . . let b represent the bicycle's speed in mi/h
14b = 10b +20 . . . . . . . .cross multiply
4b = 20 . . . . . . . . . . . . . subtract 10b
b = 5 . . . . . . . . . . . . . . . divide by 4. Same answer as above.

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is it possible to draw a 2cm, 3cm and a 4cm triangle

3 0

3 years ago

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Help help help please thanks

-Dominant- [34]

Answer:

1/15 gal / mile if your numbers are correct

Step-by-step explanation:

1/5 / 15/4 = 1/5 * 4 / 15 = 4/60 = 1/15

7 0

2 years ago

write the correct Equation and Solve. Use x for the variable. The difference of four times a number and seven is thirteen

Verizon [17]

Answer:

Step-by-step explanation:

Let the number be x

4times a number =4x

The difference of four times a number and seven : 4x - 7

4x - 7 = 13

4x = 13 + 7

4x = 20

x = 20/4

x = 5

7 0

3 years ago

Factor completely.<br> 16n^6+40n^3+25

Andru [333]

Answer:Step 1 :

Equation at the end of step 1 :

((16 • (n6)) + (23•5n3)) + 25

Step 2 :

Equation at the end of step 2 :

(24n6 + (23•5n3)) + 25

Step 3 :

Trying to factor by splitting the middle term

3.1 Factoring 16n6+40n3+25

The first term is, 16n6 its coefficient is 16 .

The middle term is, +40n3 its coefficient is 40 .

The last term, "the constant", is +25

Step-1 : Multiply the coefficient of the first term by the constant 16 • 25 = 400

Step-2 : Find two factors of 400 whose sum equals the coefficient of the middle term, which is 40 .

-400 + -1 = -401

-200 + -2 = -202

-100 + -4 = -104

-80 + -5 = -85

-50 + -8 = -58

-40 + -10 = -50

-25 + -16 = -41

-20 + -20 = -40

-16 + -25 = -41

-10 + -40 = -50

-8 + -50 = -58

-5 + -80 = -85

-4 + -100 = -104

-2 + -200 = -202

-1 + -400 = -401

1 + 400 = 401

2 + 200 = 202

4 + 100 = 104

5 + 80 = 85

8 + 50 = 58

10 + 40 = 50

16 + 25 = 41

20 + 20 = 40 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 20 and 20

16n6 + 20n3 + 20n3 + 25

Step-4 : Add up the first 2 terms, pulling out like factors :

4n3 • (4n3+5)

Add up the last 2 terms, pulling out common factors :

5 • (4n3+5)

Step-5 : Add up the four terms of step 4 :

(4n3+5) • (4n3+5)

Which is the desired factorization

Trying to factor as a Sum of Cubes :

3.2 Factoring: 4n3+5

Theory : A sum of two perfect cubes, a3 + b3 can be factored into :

(a+b) • (a2-ab+b2)

Proof : (a+b) • (a2-ab+b2) =

a3-a2b+ab2+ba2-b2a+b3 =

a3+(a2b-ba2)+(ab2-b2a)+b3=

a3+0+0+b3=

a3+b3

Check : 4 is not a cube !!

Step-by-step explanation: I believe that is the answer because i got it right.

6 0

3 years ago

Read 2 more answers

1. What is the value of the y variable in the solution to the following system of equations?

ollegr [7]

Part 1)

we have

$3x-6y=3$ ------> equation A

$7x-5y=-11$ ------> equation B

Multiply by $-7$ the equation A

$-7(3x-6y)=-7*3$

$-21x+42y=-21$ ------> equation C

Multiply by $3$ the equation B

$3*(7x-5y)=-11*3$

$21x-15y=-33$ -------> equation D

Adds equation C and equation D

$-21x+42y=-21 \\21x-15y=-33\\---------- \\ 42y-15y=-21-33\\27y=-54 \\ y=-2$

therefore

<u>the answer Part 1) is the option A </u>

$y=-2$

Part 2)

we have

$3x+y=6$

$y=-3x+6$ ------> equation A

$6x+2y=8$

Simplify Divide by $2$ both sides

$3x+y=4$

$y=-3x+4$ ------> equation B

the lines A and B are parallel lines, because the slope m is equal

so

The system has no solution

therefore

<u>the answer Part 2) is the option D</u>

There is no x value as there is no solution to the system.

Part 3)

we have

$4x+2y=6$ ------> equation A

$x-y=3$

$y=x-3$ ------> equation B

substitute equation B in equation A

$4x+2[x-3]=6$

$6x-6=6$

$6x=12$

$x=2$

therefore

<u>the answer part 3) is the option D</u>

$x=2$

Part 4)

Let

x---------> The number of one-step equations

y---------> The number of two-step equations

we know that

$x+y=1,120$

$x=1,120-y$ -------> equation A

$3x-2y=1,300$ ------> equation B

substitute equation A in equation B

$3[1,120-y]-2y=1,300$

$3,360-5y=1,300$

$5y=3,360-1,300$

$5y=2,060$

$y=412$

therefore

<u>the answer part 4) is the option D</u>

$y=412$

8 0

3 years ago

Read 2 more answers