Julian fully simplifies this polynomial and then writes it in standard form. 4x2y2 – 2y4 – 8xy3 + 9x3y + 6y4 – 2xy3 – 3x4 + x2y2
2 answers:
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Question:
In triangle FGH, FG = 12.3 cm, GH = 10.6 cm, m angle G=80 degrees, and m angle H=55 degrees. If triangle ABC GHF, which statement is true?
(A) AB = 12.3 cm
(B) AB = 10.6 cm
(C) m∠C = 55°
(D) m∠C = 80°
Answer:
Option B:
AB = 10.6 cm
Solution:
The image of the triangle is attached below.
In ΔFGH,
FG = 12.3 cm, GH = 10.6 cm, m∠G = 80° and m∠H = 55°
Option A: AB = 12.3 cm
Given ΔGHF ΔABC.
Corresponding parts of congruence triangles are congruent.
GH = AB = 10.6 cm
So, option A is not true.
Option B: AB = 10.6 cm
Already proved in option A that AB = 10.6 cm
So, option B is true.
Option C: m∠C = 55°
ΔGHF ΔABC
Corresponding parts of congruence triangles are congruent.
m∠G = m∠A = 80°
m∠H = m∠B = 55°
Sum of the angles of a triangle = 180°
⇒ m∠A + m∠B + m∠C = 180°
⇒ 80° + 55° + m∠C = 180°
⇒ m∠C = 180° – 80° – 55°
⇒ m∠C = 45°
So, option C is not true.
Option D: m∠C = 80°
Already proved in option C that m∠C = 45°.
So, option D is not true.
Hence option B is the true statement that AB = 10.6 cm.
Answer:
The correct option is 4) 0.72.
Step-by-step explanation:
Consider the provided information.
Let us consider that there are 100 members.
(Note: you can take any number the answer will remain the same.)
90% of its members drank protein shakes and of the members who drank protein shakes.
90% of 100 is 90.
Thus, 90 members drank protein shake.
Of the members who drank protein shakes, 30% took weight-loss medication.
30% of 90 is 27.
That means 27 out of 90 took weight loss medication.
Out of 100 members 90 drank protein shakes that means 10 members does not take protein shakes.
Only 10% of members who did not drink protein shakes took weight-loss medication.
10% of 10 is 1, that means 1 member out of 10 took weight loss medication.
Thus the required table is:
Medication Not Medication Total
Drank shakes 27 63 90
Doesn't Drank shakes 1 9 10
Total 28 72 100
Now we need to find the probability that a gym member does not take weight-loss medication.
72 out of 100 members does not take weight-loss medication.
Therefore, the required probability is:
Hence, the correct option is 4) 0.72.