Answer:
True
Step-by-step explanation:
Answer:
71.6 degrees
Step-by-step explanation:
Given the vectors
u= <8,4> v = <9.-9> (5 points)
u*v = (8, 4)*(9, -9)
u*v = 8(9)+(4)(-9)
u*v = 72 - 36
u*v = 36
|u| = √8²+4²
|u| = √64+16
|u| = √80
|v| = √9²+9²
|v| = √81+81
|v| = √162
Using the formula
u*v = ||u||v| cos theta
36 = √80(√162)cos theta
36 = √12960 cos theta
cos theta = 36/√12960
cos theta = 36/113.8
cos theta = 0.3162
theta = arccos(0.3162)
theta = 71.56 degrees
Hence the angle between the given vectors to the nearest tenth of a
degree is 71.6 degrees
Answer:
a
Step-by-step explanation:
Using Pythagoras' identity on the right triangle
let x be the other leg to be found, then
155² = 124² + x²
24025 = 15376 + x² ( subtract 15376 from both sides )
8649 = x² ( take the square root of both sides )
= x
Hence x = 93 cm ← length of other leg → a
Answer:
7. ∠CBD = 100°
8. ∠CBD = ∠BCE = 100°; ∠CED = ∠BDE = 80°
Step-by-step explanation:
7. We presume the angles at A are congruent, so that each is 180°/9 = 20°.
Then the congruent base angles of isosceles triangle ABC will be ...
∠B = ∠C = (180° -20°)/2 = 80°
The angle of interest, ∠CBD is the supplement of ∠ABC, so is ...
∠CBD = 180° -80°
∠CBD = 100°
__
8. In the isosceles trapezoid, base angles are congruent, and angles on the same end are supplementary:
∠CBD = ∠BCE = 100°
∠CED = ∠BDE = 80°
Answer:
Step-by-step explanation:
Slope of a line passing through two points
and
is given by the formula,
Slope = 
Slope of the line PQ passing through the two points P(-8, 2) and Q(4, 2) will be,
Slope '
' =
= 0
Therefore, slope of the line PQ parallel to the x-axis = 0
Slope of the line MN passing through the points M(8, 6) and N(8, -8) is,
Slope '
' =
= ∞
Therefore, slope of the line MN parallel to y-axis is undefined.
Since, angle between the x-axis and y-axis is 90°,angle at the intersection point between the lines parallel to x and y axis will be 90°.
These lines are perpendicular to each other.