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snow_tiger [21]
3 years ago
12

Can someone help me solve this equation? will give brainliest

Mathematics
1 answer:
valentinak56 [21]3 years ago
5 0

Answer:

a = -10

Step-by-step explanation:

33 - 4a = 73

To get <em>a</em> by itself, you must move 33 to the other side. To this, you must subtract it from both sides, canceling it out on the left side.

You will be left with: -4a = 73-33

Subtract 73 and 33, which will get you 40.

Now the equation is -4a = 40

To get <em>a </em>by itself, divide -4 into both sides. Doing this will isolate <em>a</em>.

The equation you will have after that is a = 40/-4.

Divide 40 by -4, which will get you -10.

Therefore, a = -10.

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When two lines intersect, the angles across from the intersection (the "X") are congruent (equal), and referred to as "vertical angles."
So by the rule of vertical angles are congruent, we can set them equal:
{x}^{2}  - 6x = 1\div2 \: x + 42 \\  {x}^{2}  - 6x - 1 \div 2 \: x = 42 \\  {x}^{2}  - 6.5x = 42
{x}^{2}  - 6.5x - 42 = 0 \\ multiply \: both\: sides \: by \: 2 \: to \: get \\ rid \: of \: the \: decimal \\ 2({x}^{2}  - 6.5x - 42) = 2(0)
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to factor we need the factors of 84:
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Now set each factor = 0
1) 2x - 21 = 0 and 2) x + 4 = 0
1) 2x - 21 = 0, 2x = 21, x = 21/2 = 10.5
2) x + 4 = 0, x = -4

Now we plug in each answer to check:
1) x = 10.5
{x}^{2}  - 6x =  {(10.5)}^{2}  - 6(10.5) \\  = 110.25 - 63 = 47.25
1/2x + 42 = 1/2(10.5) + 42 = 5.25 + 42 = 47.25
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BAM SO IT LOOKS LIKE THAT'S IT!!
But let's check 2) first:
2) x = -4
{( - 4)}^{2}  - 6( - 4) = 16 + 24 = 40
1/2x + 42 = 1/2(-4) + 42 = -2 + 42 = 40
40 = 40, so both work!!
But it asks for m<1, and <1 is supplementary because it lies on same line, meaning the sum of both = 189
Therefore m<1 = 180 - 47.25 = 132.75°
OR m<1 = 180 - 40 = 140°


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