Four more than a number is half the number

Determine if the following lines are parallel (never intersect), perpendicular (intersect at a 90 degree angle), intersecting (i

mihalych1998 [28]

Answer:

These lines are perpendicular.

Step-by-step explanation:

Put both equations in the slope intercept form of a line.

y = -6x - 8 This is already in the slope intercept form for a line

-x + 6y = 12 Add x to both sides of the equation

6y = x + 12 Divide through the whole equation by 6

y = 1/6x +2

Now we compare the two slopes of -6 and 1/6. They are negative reciprocals of each other. That means that the line are perpendicular.

7 0

1 year ago

A car is traveling 150 feet per second. Convert this to miles per hour.

Nana76 [90]

There are 3600 seconds in 1 hour.

Multiply feet per second by 3600 to get feet in 1 hour:

150 x 3600 = 540,000 feet in 1 hour.

1 mile = 5280 feet.

Divide feet per hour by 5280 to get miles per hour:

540,000 / 5280 = 102.27 miles per hour.

7 0

2 years ago

a line passes through the point (2,-3) and is perpendicular to the line y=-3 find equation for this line

melamori03 [73]

Answer:

x=2

Step-by-step explanation:

y=-3 is a horizontal line so the one that is perpendicular to it is supposed to be vertical

5 0

2 years ago

R/3+2=21 solve for r

olchik [2.2K]

Answer:

r=63

Step-by-step explanation:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

r/3-(21)=0 r

Simplify —

3

r

— - 21 = 0

3 2.1 Subtracting a whole from a fraction

Rewrite the whole as a fraction using 3 as the denominator :

21 21 • 3

21 = —— = ——————

1 3

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

7 0

2 years ago

Marty made a $220 bank deposit using $10 bills and $5 bills. She gave the teller a total of 38 bills, how many $5 bills were in

Luda [366]

ANSWER: 32 five-dollar bills

======

EXPLANATION:

Let x be number of $5 bills

Let y be number of $10 bills

Since we have total of 38 bills, we must have the sum of x and y be 38

x + y = 38 (I)

Since the total amount deposited is $220, we must have the sum of 5x and 10y be 220 (x and y are just the "number of" their respective bills, so we multiply them by their value to get the total value):

5x + 10y = 220 (II)

System of equations:

$\left\{ \begin{aligned} x + y &= 38 && \text{(I)} \\ 5x + 10y &= 220 && \text{(II)} \end{aligned} \right.$

Divide both sides of equation (II) by 5 so our numbers become smaller

$\left\{ \begin{aligned} x + y &= 38 && \text{(I)} \\ x + 2y &= 44 && \text{(II)} \end{aligned} \right.$

Rearrange (I) to solve for y so that we can substitute into (II)

$\begin{aligned} x + y &= 38 && \text{(I)} \\ y &= 38 - x \end{aligned}$

Substituting this into equation (II) for the y:

$\begin{aligned} x + 2y &= 44 && \text{(II)} \\ x + 2(38 - x) &= 44\\ x + 76 - 2x &= 44 \\ -x &= -32 \\ x &= 32 \end{aligned}$

We have 32 five-dollar bills

======

If we want to finish off the question, use y = 38 - x to figure out number of $10 bills

$y = 38 - 32 = 6$

32 five-dollar bills and 6 ten-dollar bills

7 0

2 years ago