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IrinaK [193]
3 years ago
12

Consider the system of equations

Mathematics
1 answer:
lyudmila [28]3 years ago
4 0
4)
I:3x+4y=67
II:5x-y=35

to eliminate y when they are added one of the equations must contain -ay and the other +ay (with a being some number)
in this case we have in I already a positive term and in II a negative, but they have different numbers
by using multiplication (property of equations) we can multiply II by 4 so the negative and positive parts match

II*4: 20x-4y=140

when I and 4*II get added this results in
3x+20x+4y-4y=67+140
23x=207

5)
in this case I and II were added which can be seen in the left side of the equation((3x+4y)+(5x-y)=8x+3y), so to get the right side we have to also add the right sides 67+35=102

so the full equation would be:
8x+3y=102
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What is the equation of a line parallel to y=1/2×+6 that passes through (-4,1)
IgorC [24]

keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above

y = \stackrel{\stackrel{m}{\downarrow }}{\cfrac{1}{2}}x+6\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}

so we're really looking for the equation of a line whose slope is 1/2 and passes through (-4 , 1)

(\stackrel{x_1}{-4}~,~\stackrel{y_1}{1})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{1}{2} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{1}=\stackrel{m}{ \cfrac{1}{2}}(x-\stackrel{x_1}{(-4)}) \\\\\\ y-1=\cfrac{1}{2}(x+4)\implies y-1=\cfrac{1}{2}x+2\implies y=\cfrac{1}{2}x+3

5 0
1 year ago
What is this problem -12=4(x-7)-8x
Fofino [41]

-12=4(x-7)-8x

One solution was found :

                  x = -4

Rearrange:

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


                    -12-(4*(x-7)-8*x)=0


Step by step solution :

Step  1  :

Equation at the end of step  1  :

 -12 -  (4 • (x - 7) -  8x)  = 0

Step  2  :

Step  3  :

Pulling out like terms :

3.1     Pull out like factors :


  4x + 16  =   4 • (x + 4)


Equation at the end of step  3  :

 4 • (x + 4)  = 0

Step  4  :

Equations which are never true :

4.1      Solve :    4   =  0

Hope this helps you, Have a nice day.

4 0
3 years ago
What polynomial has a graph that passes through the given points?
Evgen [1.6K]
The answer is <span>B. y = x^3 + 4x^2 + 2x - 2 

A line that passes through all given point is the correct choice. Now, substitute x and y in all of the choices:

</span>B. y = x³ + 4x²<span> + 2x - 2 
Point 1: </span><span>(-2, 2) 
x = -2
y = 2
____
2 = (-2)</span>³ + 4 *(-2)² + 2 * (-2) - 2
2 = -8 + 4 * 4 + (-4) - 2
2 = -8 + 16 - 4 - 2
2 = 2
_____

Point 2: (-1, -1) 
x = -1
y = -1
____
-1 = (-1)³ + 4 *(-1)² + 2 * (-1) - 2
-1 = -1 + 4 * 1 + (-2) - 2
-1 = -1 + 4 - 2 - 2 
-1 = -1
____

Point 3: (1, 5) 
x = 1
y = 5
____
5 = (1)³ + 4 *(1)² + 2 * 1 - 2
5 = 1 + 4 * 1 + 2 - 2
5 = 1 + 4 + 2 - 2
5 = 5
____

Point 4: (3, 67) 
x = 3
y = 67
____
67 = (3)³ + 4 *(3)² + 2 * (3) - 2
67 = 27 + 4 * 9 + 6 - 2
67 = 27 + 36 + 6 - 2
67 = 67

So, line B passes through all choices.
3 0
2 years ago
Answer this please I’ll give brainalist + points, please help!
ArbitrLikvidat [17]

Answer:

The answer is C because the largest mode is the longest set with the biggest numbers

Step-by-step explanation:

4 0
2 years ago
32 is 40% of what number? please show working.
blagie [28]
32 40%
80 100


to find the answer, you do 32 times 100, the. divide that by 40 which equals 80
6 0
2 years ago
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