6(7+5) + 3
Hope this helps :)
To check:
PEMDAS
7+5 is 12
6(12) + 3
72 + 3
75
Part 1:all triangles have a measure of 180 degrees
so, 3(x+2)+35+52=180
add 35 and 52; 3(x+2) +87=180
subtract 87 from both sides; 3(x+2)= 93
divide both sides by 3; x+2=31
subtract both sides by 2; x=29
Part 2: since 3(x+2) =93, angle C is 93 degrees
Allow ABC to be an
equilateral triangle so AB = AC = BC. Let X be the midpoint of BC, AX is the
median of BC, and BX = CX. Look at triangles BAX and CAX. Obviously, AX = AX since
AB = AC and BX = CX, subsequently by SSS Congruence Test, we have that
triangles BAX and CAX are congruent. Therefore, corresponding angles are
congruent so <ABX = <ACX. Because <ABX and <ABC are the same angle,
they are obviously congruent, and then <ABX = <ABC. Likewise, <ACX and
<ACB are the same angles so <ACX = <ACB. Then, <ABC = <ACB. Please
note that <ABC = <B and <ACB = <C. Therefore, <B = <C. <span>
<span>At present, disregard AX and let Y be the midpoint of AC.
Then BY is the median of AC. Then AY = CY. Evidently, BY = BY. Because AB = BC, we see that triangles ABY
and CBY are congruent by SSS. Then corresponding sames are congruent so <BAY
= <BCY. Since <BAY and <BAC are the same angles then <BAY =
<BAC. Similarly, <BCY = <BCA since they are the same angles. Then
<BAC = <BCA. Note that <BAC = <A and <BCA = <C. Therefore,
<A = <C. </span>
<span>Thus, <A = <C = <B. So all the angles are congruent.</span></span>
<h2>Answer :</h2>
Katherine's marks = 84,92,84,75,70
Total marks = 84+92+84+75+70 = 405
No. of observations = 5
Mean = Total sum of observations/No. of observations
Mean = 405/5=81
Expected mean = 84
Let expected total marks be = n
84=n/5
84×5=n
<h3>n=420</h3>