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lianna [129]
2 years ago
9

Use substitution to solve the following system of equations. Show all of your work. Write the solution as an ordered pair.

Mathematics
1 answer:
trapecia [35]2 years ago
3 0

Answer:

\left \{ {{x=2} \atop {y=2}} \right.

Step-by-step explanation:

Substitute the second equation into the first one:

4x+(2x-2)=10\\6x-2=10\\6x=12\\x=2

Substitute x=2 into the second equation:

y=2\times 2-2\\y=4-2\\y=2

\therefore \left \{ {{x=2} \atop {y=2}} \right.

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The perimeter of this triangle is 25 units. An angle bisector divides one side of the triangle into lengths of 2 and 3. Find the
grin007 [14]

Answer:

   8 and 12

Step-by-step explanation:

Sides on one side of the angle bisector are proportional to those on the other side. In the attached figure, that means

  AC/AB = CD/BD = 2/3

The perimeter is the sum of the side lengths, so is ...

  25 = AB + BC + AC

  25 = AB + 5 + (2/3)AB . . . . . . substituting AC = 2/3·AB. BC = 2+3 = 5.

  20 = 5/3·AB

  12 = AB

  AC = 2/3·12 = 8

_____

<em>Alternate solution</em>

The sum of ratio units is 2+3 = 5, so each one must stand for 25/5 = 5 units of length.

That is, the total of lengths on one side of the angle bisector (AC+CD) is 2·5 = 10 units, and the total of lengths on the other side (AB+BD) is 3·5 = 15 units. Since 2 of the 10 units are in the segment being divided (CD), the other 8 must be in that side of the triangle (AC).

Likewise, 3 of the 15 units are in the segment being divided (BD), so the other 12 units are in that side of the triangle (AB).

The remaining sides of the triangle are AB=12 and AC=8.

7 0
3 years ago
In this diagram which equation could you prove to be true in order to conclude that the lines are parallel
KiRa [710]
I would say that the correct answer is D. because y is always the numerator while x is the denominator for the equation y2 - y1/x2 - x1 which means if there is two y's or two x's on the same line you subtract the second one from the first one. If there is only one y and/or x and the other is 0 on the same line, it stays at y or x without subtracting y2 - y1 or x2 - x1. 

Since b is on the y coordinate and -a is on the x coordinate, you would make it b/a while -a is gonna be a positive since the lines are going up and to the right. Now, since c is the y coordinate and d is the x coordinate, make C the numerator and d the denominator since y is always the numerator and x is the denominator for these parallel line figures on the graph and the equation will be equaled to the fraction to the other fraction for parallel lines. 

So, your answer would be D. b/a = c/d 

Hope this helps, and is correct! 

<em>~ ShadowXReaper069</em>
3 0
3 years ago
Read 2 more answers
What postulate or theorem can be used to prove that these two triangles are congruent?
Diano4ka-milaya [45]

Answer:

ASA

Step-by-step explanation:

in the place that I have put some marks on it, they have the same angle; so then they will also have the same third angle; and for the rest you should use ASA.

8 0
2 years ago
What is the slope of the line perpendicular to y=-3x+4?
inessss [21]

The perpendicular line would have a slope of 1/3.

Perpendicular lines have opposite and reciprocal slopes.

To do the opposite, take the original slope (-3) and change the sign (3).

To do the reciprocal, take the slope we changed (3) and flip it as a fraction (1/3).

This gives us a new slope of 1/3.

7 0
3 years ago
Travis just got a new credit card that offers inductors APRof 3.6% for first 3 months and standard APR of 14.4% thereafter. If i
Makovka662 [10]

Answer:

Month 1 : 0.002988

Month 2: 0.00299692814

Month 3: 0.00300588297

Step-by-step explanation:

Since we're only finding the interest for the first three months, it's easy to do it by performing the simple interest formula. But first, we need divide 3 by 12, since we calculate interest using years. 3/12 = 1/4 = 0.25

The standard simple interest calculation is done by multiplying the starting amount, by the interest, by the time, then dividing by 100 to put it into a percentage.

1 month = 1/12 or approximately 0.083 of the year.

Let's say P = 1. For the first month, it will be 1 x 3.6 x 0.083 = 0.2988 / 100

The second month, (1 + 0.002988) * 3.6 * 0.083 = 0.299692814 / 100

The third month, (1.002988 + 0.00299692814) x 3.6 x 0.083 = 0.300588297/100

Given the initial amount be 1, those would be the periodic interest rate during the first three months.

5 0
3 years ago
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