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Svetach [21]
3 years ago
13

Which expression is equivalent to 2(a+3) when a equals 32(3)5(3)2(3)+32(3)+6​

Mathematics
2 answers:
sammy [17]3 years ago
8 0
2(3+3) or 2(3)+6, so the answer is the third option. It’s just using the distributive property.
alukav5142 [94]3 years ago
5 0

Answer:

2(3)+6

Step-by-step explanation:

a = 3

substitute a with 3

2(a+3)

= 2(3+3)

= 2(6)

= 12 ✅

i) 2(3) = 6 ❌

ii) 5(3) = 15 ❌

iii) 2(3)+3 = 6+3 = 9❌

iv) 2(3)+6 = 6+6 = 12 ✅

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A line is perpendicular to x + 3y - 4 = 0 and has the same y-intercept as 2x + 5y - 20 = 0. Find the equation for the line.​
yawa3891 [41]
<h3>Answer:  -3x+y-4 = 0   (standard form)</h3>

This is equivalent to y = 3x+4 (slope intercept form)

By "standard form", I mean the form Ax+By+C = 0.

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

Explanation:

Let's solve the first equation for y

x+3y-4 = 0

x+3y = 4

3y = 4-x

3y = -x+4

y = (-x+4)/3

y = (-x/3) + (4/3)

y = (-1/3)x + (4/3)

The equation is now in y = mx+b form, aka slope intercept form, with m = -1/3 as the slope and b = 4/3 as the y intercept. We'll focus on the slope.

Apply the negative reciprocal to this so that we go from -1/3 to +3/1 or simply 3. Flip the fraction and the sign. Note how -1/3 and 3 multiply to -1. Perpendicular slopes always multiply to -1, assuming neither line is vertical.

So this mystery perpendicular line we're after has a slope of 3.

It has the same y intercept as 2x+5y-20 = 0. Plug in x = 0 and solve for to determine the y intercept.

2x+5y-20 = 0

2(0)+5y-20 = 0

5y-20 = 0

5y = 20

y = 50/5

y = 4

The y intercept of 2x+5y-20 = 0 is y = 4, so it's also the y intercept of our final answer. Let b = 4.

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

We found that:

  • m = 3 is the slope of the perpendicular line
  • b = 4 is the y intercept of the perpendicular line

So we know that,

y = mx+b

y = 3x+4

is the slope intercept form of the answer. Since your teacher gave you the equations in standard form (one version of it anyway), let's convert y = 3x+4 to that form as well

y = 3x+4

y-3x = 4

-3x+y = 4 .... one way to express standard form

-3x+y-4 = 0 .... another standard form

Some math textbooks use Ax+By = C as standard form, while others use Ax+By+C = 0. Unfortunately, it's a bit confusing because the same phrasing is used.

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