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liq [111]
3 years ago
8

Solve for y. 6 x + 2y = z​

Mathematics
2 answers:
timofeeve [1]3 years ago
6 0

Answer:

y = \frac{z}{2} -3x

Step-by-step explanation:

Isolate the variable, y. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

PEMDAS =

Parenthesis

Exponents & roots

Multiplication

Division

Addition

Subtraction

& is the order of operation.

First, subtract 6x from both sides:

6x (-6x)  + 2y = z (-6x)

2y = z - 6x

Next, divide 2 from both sides:

(2y)/2 = (z - 6x)/2

y = (z - 6x)/2

y = (z/2) - 3x

y = \frac{z}{2} -3x  is your answer.

~

vaieri [72.5K]3 years ago
5 0
The answer to this question is 7
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Universal Studios is looking to expand in Ontario. The new theme park will be located equidistant to
sukhopar [10]
<h3>Answer:  (2, 3)</h3>

===============================================

Explanation:

For now, we're only going to consider Newmarket and Markham, which are points N and M respectively.

Let's find the slope of line NM through use of the slope formula.

m = (y2-y1)/(x2-x1)

m = (3-8)/(7-2)

m = -5/5

m = -1

Line NM has a slope of -1. Its perpendicular slope is +1 or just 1.

Rule: If the slopes multiply to -1, then the lines are perpendicular.

Or you can apply the negative reciprocal rule to go from -1 to 1.

We'll keep this perpendicular slope in mind for later.

----------------

Now let's find the midpoint of points N and M.

Add up the x coordinates and divide by 2: (x1+x2)/2 = (2+7)/2 = 4.5

Do the same for the y coordinates:  (y1+y2)/2 = (8+3)/2 = 5.5

The midpoint of N and M is at (4.5, 5.5)

The perpendicular line must go through these two points. I'm going to skip a few steps here, but basically we go from y = mx+b to y = x+1 after plugging in those x,y values and the perpendicular m we found earlier.

--------------------

In short, the perpendicular bisector for line segment NM is the equation y = x+1.

If you follow the same steps as the previous two sections, but you apply them for points M and V instead, then you should find that the perpendicular bisector is y = -3x+9. I'm skipping steps here as well.

----------------------

At this point, we have the system of equations

\begin{cases}y = x+1\\y = -3x+9\end{cases}

Let's use substitution to solve for x and y

y = x+1

-3x+9 = x+1

-3x-x = 1-9

-4x = -8

x = -8/(-4)

x = 2

y = x+1

y = 2+1

y = 3

So together, x = 2 and y = 3 pair up to get the ordered pair solution (x,y) = (2,3)

This is the location where the theme park should be placed. Let's say that C = (2,3). I'm using C for center.

You can use the distance formula to confirm that segments CN, CM and CV are all the same length, which would verify that point C is equidistant from all the other points. Furthermore, it means that points N, M and V are all on the same circle centered at C.

I know it says not to use a graph, but it still helps to see what's going on. Also, it's a handy way to confirm the answer. I used GeoGebra to make the graph. See the diagram below.

Side note: you only need 2 perpendicular bisectors to find point C. You could use three, but that's overkill since they all intersect at the same location.

7 0
2 years ago
Point A is at (3, 2.5) and point B is at (3, 1.4) on a coordinate grid. The distance between the two points is ____. Input numbe
Brums [2.3K]
The Answer Is , 2.5-1.4 = 1.1
7 0
3 years ago
Read 2 more answers
Select the fraction that is NOT in lowest terms . which of these fractions is not in lowest term?
Kisachek [45]

Answer:

14/21

Step-by-step explanation:

14/21 is divisible by 7, and can reduce to 2/3

6 0
2 years ago
What is the quotient? Negative StartFraction 3 over 8 EndFraction divided by negative one-fourth
anyanavicka [17]

Answer:

\dfrac{3}{2}

Step-by-step explanation:

We are given 2 fractions.

1st fraction is Negative StartFraction 3 over 8

i.e.

-\dfrac{3}{8}

2nd fraction is negative one-fourth

i.e.

-\dfrac{1}{4}

We have to find the quotient when 1st fraction is divided by 2nd fraction.

<u>Definition</u> of quotient is given as:

Quotient is the result obtained when one number is divided by other number.

-\dfrac{3}{8} \div -\dfrac{1}{4} \text{ is to be calculated.}

\div is converted to \times and the 2nd fraction is reversed i.e.

if the fraction is \frac{p}{q} it becomes \frac{q}{p} and the sign \div is changed to \times.

Solving above:

-\dfrac{3}{8} \times -\dfrac{4}{1}\\ \text {Multiplication/Division of 2 negative number gives a positive number}\\\Rightarrow \dfrac{3}{2}

So, the quotient is \frac{3}{2}.

6 0
3 years ago
The length of a rectangle is 6 units and its width is 4 units. What is the approximate length of the diagonal of the rectangle?
ss7ja [257]
The correct answer is:  [D]:  " 7.2 units" .
_______________________________________________________
Explanation:
________________________________________________________
Use the Pythagorean theorem:

a² + b² = c² ;

in which:  "6 units" and "4 units" equal the lengths of the right angle (formed by the rectangle);  and "c" is the length of the diagonal of the rectangle, or the "hypotenuse", of the right triangle formed by the rectangle;  We wish to solve for "c" ;
_______________________________________________

6² + 4² = c² ;  Solve for "c" ;

↔ c² = 6² + 4² ; 

         = (6*6) + (4*4) ;
 
         = 36 + 16 ;

        =  52 ;

    c² = 52 ;

Take the "positive square root" of each side of the equation; to isolate "c" on one side of the equation; and to solve for "c" ; 

  √(c²)  =  √52 ; 

    c = √52 ;  

At this point, we know the 7² = 49 ;  8² = 64 ;  so, the answer is somewhere between "7" and "8" ; yet closer to "7" ;  so among the answer choices given; 

The correct answer is:  [D]:  " 7.2 units" .
_________________________________________
However, let use a calculator:

c = √52 = 7.2111025509279786 ; which rounds to "7.2" ;
   which corresponds to:  
___________________________________________
Answer choice:  [C]:  " 7.2 units" .
___________________________________________
5 0
3 years ago
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