Ans57 , 58 , 59
Step-by-step explanation:
The volume of a triangular prism is V = 1/2 x a x c x h where a is height of the triangle, c is the base of the triangle and h is the height of the prism.
120 = 1/2 x a x c x h; we write a from the previous equation in terms of c and h thus,
a = 240 / ( c x h)
If the dimensions where halved then a = a/2 ; c = c/2 ; h=h/2
We use the volume formula again and substitute the given values to find the new volume,
V = 1/2 x a/2 x c/2 x h/2
Substitute the previously determined a term,
V = 1/2 x (240/2ch) x c/2 x h/2
We cancel and evaluate the constants therefore the new volume is,
V= 15 cm^3
Applying the angle of intersecting chords theorem, the value of z is: D. 100.
<h3>What is the Angle of Intersecting Chords Theorem?</h3>
According to the angle of intersecting chords theorem, in a circle like the one shown in the image above, where two chords intersect to form vertical angles, the theorem states that the angle formed equals half of the sum of the measures of the arcs intercepted by the angles.
Applying the angle of intersecting chords theorem, let's find x first:
73 = 1/2(96 + x)
Multiply both sides by 2
2 × (73) = 1/2(96 + x) × 2
146 = 96 + x
Subtract both sides by 96
146 - 96 = 96 + x - 96
50 = x
x = 50°
Therefore:
x + z + 96 + 114 = 360° [full circle measure]
Plug in the value of x
50 + z + 96 + 114 = 360
z + 260 = 360
Subtract both sides by 260
z + 260 - 260 = 360 - 260
z = 100°
The answer is: D. 100°.
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Answer:
6 and 1/3
Step-by-step explanation:
the only thing gets reduced is the fraction part and 5 and 15 have common numbers in 5 5 goes into 5 one time and 5 goes into 15 3 times. so it's 6 1/3
