Answer:
9108
Step-by-step explanation:
23^3+(-12)^3+(-11)^3 remove parentheses
= 23^3-12^3-11^3 group difference of two cubes
= (23-12)(23^2+23*12+12^2) + 11^3 factor difference of two cubes
= 11 (23^2+23*12+12^2-11^2) factor ou 11
= 11(23(23+12) + (12+11)(12-11)) apply difference of two squares
= 11 (23*35+23*1) factor out 23
= 11(23*(35+1)) simplify
= 11*23*36 convert 11*23 into difference of 2 squares
= (17^2-6^2)*6^2 expand parentheses
= 102^2-36^2 evaluate squares
= 10404 - 1296 subtraction
= 9108
(no calculator required)
Answer:
b
Step-by-step explanation:
Answer:
<h3>
m∠UVT = 97°</h3>
Step-by-step explanation:
Given m∠WVU = 169°, m∠WVT = (2x + 20)° and m∠UVT = (3x + 19)°, according to the diagram shown, it is seen that;
m∠WVU = m∠WVT +m∠UVT
Substitute the given parameters into the function as shown;
(2x + 20)°+(3x + 19)° = 169
collect like terms
2x+3x+20+19 = 169
5x+39 = 169
5x = 169-39
5x = 130
x = 130/5
x = 26°
Since m∠UVT = 3x+19, substitute x = 26 into the function
m∠UVT = 3(26)+ 19
m∠UVT = 78+19
m∠UVT = 97°
Option(4) is the answer because
In triangle ABC and triangle EDC
Angle ABC=angle CDE=70
And,
Angle BCA= angle DCE. ( vertically opposite angles)
=> triangle ABC is similar to triangle EDC. ( A.A congruence rule)
=> angle A= angle E. (Corresponding parts of similar triangles) or (CPST)
Hope this helps ..!!!
7. 60
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