firstly let's convert the mixed fraction to improper fraction, then hmmm let's see we have two denominators, 5 and 3, and their LCD will simply be 15, so we'll multiply both sides by that LCD to do away with the denominators, let's proceed,
![\bf \stackrel{mixed}{2\frac{1}{3}}\implies \cfrac{2\cdot 3+1}{3}\implies \stackrel{improper}{\cfrac{7}{3}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{z}{5}-4=\cfrac{7}{3}\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{15}}{15\left( \cfrac{z}{5}-4 \right)=15\left( \cfrac{7}{3} \right)}\implies 3z-60=35 \\\\\\ 3z=95\implies z=\cfrac{95}{3}\implies z = 31\frac{2}{3}](https://tex.z-dn.net/?f=%5Cbf%20%5Cstackrel%7Bmixed%7D%7B2%5Cfrac%7B1%7D%7B3%7D%7D%5Cimplies%20%5Ccfrac%7B2%5Ccdot%203%2B1%7D%7B3%7D%5Cimplies%20%5Cstackrel%7Bimproper%7D%7B%5Ccfrac%7B7%7D%7B3%7D%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%5Ccfrac%7Bz%7D%7B5%7D-4%3D%5Ccfrac%7B7%7D%7B3%7D%5Cimplies%20%5Cstackrel%7B%5Ctextit%7Bmultiplying%20both%20sides%20by%20%7D%5Cstackrel%7BLCD%7D%7B15%7D%7D%7B15%5Cleft%28%20%5Ccfrac%7Bz%7D%7B5%7D-4%20%5Cright%29%3D15%5Cleft%28%20%5Ccfrac%7B7%7D%7B3%7D%20%5Cright%29%7D%5Cimplies%203z-60%3D35%20%5C%5C%5C%5C%5C%5C%203z%3D95%5Cimplies%20z%3D%5Ccfrac%7B95%7D%7B3%7D%5Cimplies%20z%20%3D%2031%5Cfrac%7B2%7D%7B3%7D)
Step-by-step explanation:
Let us consider the task to find the angle between vectors ES and EJ (the first letters are taken to name the vectors).
\overrightarrow{ES} = (4;4) - (4; -3) = \overrightarrow{(0; 7)}
ES
=(4;4)−(4;−3)=
(0;7)
\overrightarrow{EJ} = (-5; -4) - (4; -3) = \overrightarrow{(-9; -1)}
EJ
=(−5;−4)−(4;−3)=
(−9;−1)
cos \alpha=\frac{\overrightarrow{ES}*\overrightarrow{EJ}}{|\overrightarrow{EJ}|*|\overrightarrow{ES}|}cosα=
∣
EJ
∣∗∣
ES
∣
ES
∗
EJ
cos(a) = (0*(-9)+7*(-1)) / (7*9.055) = -0.11043;
a = 96,34°
Solution: 96 degrees.
We can identify that the missing reason in the proof is: Definition of Congruent angles.
<h3>How to give proof of a congruent triangle?</h3>
We know that an angle measure of 90° of ∠ABC in the triangle means that it is a right angle triangle.
We also see that ∠ADB is also a right angle and is equal to 90°.
Now, since they have exactly the same measure, these angles are congruent. Then we can say that the angles are congruent and as such:
∠ABC ≅ ∠ABD
Thus, we can identify that the missing reason is: Definition of Congruent angles.
Read more about Triangle proof at; brainly.com/question/1248322
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Given:
Jake bought 3 drawing pens for $8.07.
Each pen costs the same amount.
To find:
How much did he spend for one pen?
Solution:
Let x be the cost of each pen. Then
Cost of three pens = 3x
Jake bought 3 drawing pens for $8.07.

Divide both sides by 3.


Therefore, he spend $2.69 for one pen.
Answer:
Well 14 2/3 is 14.66 so it would be B but yea it would fit.