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AveGali [126]
3 years ago
10

Solve this equation for x. Round your answer to the nearest hundredth. 0.77 = log x​

Mathematics
1 answer:
Alekssandra [29.7K]3 years ago
8 0

Answer:

x ≈ 5.89

General Formulas and Concepts:

<u>Pre-Algebra</u>

  • Equality Properties

<u>Algebra II</u>

  • Exponential to Logarithmic:                                                                             \displaystyle b^m=x \rightarrow log_bx=m

Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify</em>

0.77 = log(x)

<u>Step 2: Solve for </u><em><u>x</u></em>

  1. [Equality Property] Raise both sides to the 10th power:                                \displaysytle 10^{0.77} = 10^{logx}
  2. Simplify:                                                                                                             \displaysytle x = 10^{0.77}
  3. Evaluate:                                                                                                           \displaysytle x = 5.88844
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Three vertices of parallelogram ABCD are A(2,-6),B(-1,2),C(5,3).find the coordinates of vertex D
salantis [7]

Check the first picture below.


for a parallelogram, it has to have two pairs of parallel sides, so BC || AD and AB || CD.

if two lines are parallel, they have the same slope, namely the <u>same rise and run</u>.

notice, the line BC has a run of 6 and a rise of 1, <u>arrows in red</u>, therefore, AD must also have a run of 6 and a rise of 1, so if we move from A 6 units over and 1 up, we'd end up at point D.


now, for part atop

Check the 2nd picture, in a parallelogram, opposite sides are parallel and opposite angles are equal, so if WLP is 144°, then PNW is also 144°.

in a parallelogram, diagonals bisect each other, so each cut the other in halves, so if PM is 9 then MW is also 9 and thus PW is just 9+9=18.


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\bf 8x+13=11x-23\implies 8x+36=11x\implies 36=3x \\\\\\ \cfrac{36}{3}=x\implies \boxed{12=x} \\\\[-0.35em] ~\dotfill\\\\ 2y+12=4y-4\implies 2y+16=4y\implies 16=2y \\\\\\ \cfrac{16}{2}=y\implies \boxed{8=y}


so then TQ ==> 2(8) + 12 ==> 16 + 12 ==> 28.

∡Q ==> 8(12) + 13 ==> 96 + 13 ==> 109°.

and since in a parallelogram, adjacent interior angles add up to 180°, then ∡Q + ∡T = 180°.

∡T ==> 180 - 109 ==> 71°.

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