24x^2 +25x - 47 53
----------------------- = -8x -3 - ---------------
ax-2 ax-2
add 53/ax-2 to each side
24x^2 +25x - 47+53
----------------------- = -8x -3
ax-2
24x^2 +25x +6
----------------------- = -8x -3
ax-2
multiply each side by ax-2
24x^2 +25x +6 = (ax-2) (-8x-3)
multiply out the right hand side
24x^2 +25x +6 = -8ax^2 +16x-3ax +6
24 = -8a 25 = 16 -3a
a = -3 9 = -3a
a = -3
Choice B
32+48 = 80
Four equivalent expressions are:
40+40 = 80
20+60 = 80
10+70 = 80
30+50 = 80
(5) Angle ADC is the sum of angles ADB and BDC.
(6) Yes, because lines AG and EC form two pairs of vertical angles, including ADC and EDG, as well as ADE and CDG.
(7) Angle HJK is clearly a right angle, and a right angle has measure 90°.
Answer:
750 grams of 60% alloy
Step-by-step explanation:
Define x = amount of 60% alloy and y = amount of 20% alloy
Equating the amounts of gold:
0.6x+0.2y = 1000(0.5)
Since there must be 1000 grams total:
x+y = 1000
Writing the 2 resulting equations together:
0.6x + 0.2y = 500
x + y = 1000
Multiply the first equation by 5:
3x + y = 2500
x + y = 1000
Subtracting the 2nd equation from the 1st:
2x = 1500
x = 750
Answer: 750 grams of 60% alloy
Answer:
(3) 49
Step-by-step explanation:
The circle diagram is attached below. angle mVS = 146°
and angle mST = 64°.
mWT = 360 -64 - 146 = 150 (angle at a point)
∠ VWS = 73° = mVS / 2
MVW = 180 - 146 = 34 (angle in a straight line)
MVW = 180 -73 - 34 = 73° (angle in a triangle)
∠TMR = 180 - 64 = 116° (angle on a straight line)
∠VMT = 116 + 34 = 150°
∠ MVT = ∠ MTV (base angles of an isosceles triangle)
150 +2∠ mTV = 180
∠ MTV = 15°
∠RVW = 73 - 15 = 58°
∠RVW + ∠ VWS + ∠VRW = 180
∠VRW = 180 - 58 - 73 = 49
