Answer:
(x - 3) • (x^2 - 4x - 7)
Step-by-step explanation:
Step 1 :
Trying to factor by splitting the middle term
1.1 Factoring x2-4x-7
The first term is, x2 its coefficient is 1 .
The middle term is, -4x its coefficient is -4 .
The last term, "the constant", is -7
Step-1 : Multiply the coefficient of the first term by the constant 1 • -7 = -7
Step-2 : Find two factors of -7 whose sum equals the coefficient of the middle term, which is -4 .
-7 + 1 = -6
-1 + 7 = 6
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
Final result :
(x - 3) • (x2 - 4x - 7)
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Part A: The answer is PR = 15.23 by Pythagorean Theorem.
The pythagorean theorem is a^2 + b^2 = c^2.
Plug in 14 for a and 6 for b to find c.
Part B: The answer is QR = 7.75.
Using the same theorem, plug 16 in for c, 14 in for a, and then you can find b.
X = 11
angle LKM = angle KLM = angle LMK because it is an equilateral triangle
180/3 = 60
60=3x-27
60-27=3x
33=3x
x=11
1/4x+7=12
Subtract 7 from both sides
1/4x=5
Divide by 1/4 or multiply by the reciprocal
X=5*4
x=20
We have to calculate the height of a cylinder : h2 = ( 45 - 2 · 15 )/ 2 = 15 / 2 = 7.5 mm
Volume of the bottom of the hourglass:V = 1/3 r² π h1 + r² π h2 = = 1/3 · 6² · 3.14 · 15 + 6² · 3.14 · 7.5 = = 1/3 · 36 · 3.14 · 15 + 36 · 3.14 · 7.5 = = 565.2 + 847.8 = 1,413 mm³The rate is 10 π mm³/ sec = 31.4 mm³/secTime = 1,413 : 31.4 = 45 sec.Answer: It will take 45 seconds.
