Mathematics Questions & Answers - Free Online Practice

1,571.

find the length XZ in the triangle

\(\sqrt{7m}\)

\(\sqrt{6m}\)

\(\sqrt{5m}\)

\(\sqrt{3m}\)

View answer & explanation

Correct answer is A

xz² = xy² + yx² - 2(xy) (yz) cos 120^o

= 2² + 1² - 2(2) (1) cos 120²

= 4 + 1 - 4x - cos 60 = 5 - 4x - \(\frac{1}{2}\)

5 + 2 = 7

xz = \(\sqrt{7}\)m

1,572.

Find the value of L in the frustum

5cm

6cm

7cm

8cm

View answer & explanation

Correct answer is A

No explanation has been provided for this answer.

1,573.

In the figure, TZ is tangent to the circle QPZ. Find x if TZ = 6 units and PQ = 9 units

View answer & explanation

Correct answer is A

In \(\bigtriangleup\)WOP, b² = r² - (4.50²...........(i)

In \(\bigtriangleup\)WOT, b\(\bigtriangleup\) + (4.5 + x)² = a²...........(ii)

In \(\bigtriangleup\)ZOT, a² = 6² + r² ..........(iii)

subst. equation (iii) and (i) in eqn (ii)

r² - (4.5)² + (4.5 + x)² = 36 = 20.25

= (4.5 + x)² = \(\sqrt{56.25}\) = (4.5 + x)

= 56.25

= 4.5 + x = 7.5

x = 3.0m

1,574.

In the figure, PQRS is a circle with ST||RQ. Find the value of x if PT = pS

70^o

55^o

40^o

35^o

View answer & explanation

Correct answer is B

< PST = < RQT = x(corresponding angle)

< PST = < PTS = < PTS x (PS = PT0

< SRQ = < SPT = 180^o (sum of < on straight line)

< SPT = 180^o - 110^o = 70^o

in < SPT, < PST = PTS = < PSt = 180^o

2x + 70 = 180^o

2x = 180^o - 70^o = 110^o

x = \(\frac{110^o}{2}\) = 55^o

1,575.

In the diagram, EFGH is a cyclic quadrilateral in which EH || FG, EG, and FH are chords. If < FHG = 42º and < EFH = 34º, calculate < HEG.

34^o

42^o

52^o

76^o

View answer & explanation

Correct answer is C

< EFH = < EGH = 34º (angles n the same segment)

< GHF = < GEF = 42º(angles in the same segment)

< FOG = 42 + 34 = 76º (exterior angle)

< FOG = < EOH = 76º (vertically opposite angle)

< EDO = 90º, < DOE = \(\frac{76}{2}\) = 38º

< HEG = 90º - 38º = 52º