2. (01.07 MC)
1 answer:
Part A: subtract 6 from both sides
Divide by -3 on both sides
X=-3
Part B: add like terms (-2K-3k)
Add 12 to both sides
Add 5k to both sides
Divide by 5 on both sides
K=3
Part C: distribute 6 into the parentheses
Add like terms together (36-5)
Subtract 1 from both sides
Subtract 36v from both sides
Divide by -30 on both sides
-1=v
Divide by -3 on both sides
X=-3
Part B: add like terms (-2K-3k)
Add 12 to both sides
Add 5k to both sides
Divide by 5 on both sides
K=3
Part C: distribute 6 into the parentheses
Add like terms together (36-5)
Subtract 1 from both sides
Subtract 36v from both sides
Divide by -30 on both sides
-1=v
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Answer:
Volume of round cake pan = volume of cylinder
Volume of a cylinder = (where r is the radius and h is the height)
Radius = diameter ⇒
⇒ volume of round cake pan =
= 76.97 in³ (nearest hundredth)
Volume of rectangular cake pan = volume of rectangular prism
volume of rectangular prism = (where w is the width, l is the length and h is the height)
⇒ volume of rectangular cake pan = 6 x 9 x 2 = 108 in³
As 108 > 76.97, the rectangular cake pan has a larger volume
Answer:
1) Real and same.
2) Real and distinct
3) Real and distinct
4) Real and distinct
5) Real and distinct
6) Real and distinct
7) Real and distinct
8) Real and distinct
Step-by-step explanation:
If a quadratic equation is in the form of ax² + bx + c = 0, then Discriminant of the equation D = b² - 4ac, which governs the nature of roots the equation has.
If D > 0, then there will be two different real roots.
If D = 0, then two same and real roots.
If D < 0, then two distinct but imaginary roots.
Now, 1) x² + 6x + 9 = 0 has D = 6² - 4 × 9 × 1 = 0. So, there will be two same and real roots.
2) 5x² - x = 4x² + 2
⇒ x² - x - 2 = 0
It has D = (-1)² - 4 × 1 × (-2) = 9. Therefore, the roots will be two distinct and real.
3)
⇒ 5 = x² - 4x
⇒ x² - 4x - 5 = 0.
So, D = (-4)² - 4 × (1) × (- 5) = 36. So, the equation has two real and distinct rools.
4) x(x - 5) = 4(5 - x)
⇒ x² - x - 20 = 0
Hence, D = (-1)² - 4 × 1 × (-20) = 81
So, the roots will be real and distinct.
5) x² + 7x + 1 = 0 has D = 7² - 4 × 1 × 1 = 45
So, the roots will be real and distinct.
6) 2x² + 9x + 3 = 0, has D = 9² - 4 × 2 × 3 = 57.
Hence, the roots will be real and distinct.
7) 5x² - 6 = 13x
⇒ 5x² - 13x - 6 = 0
So, D = (-13)² - 4 × 5 × (-6) = 289
So, the roots will be real and distinct.
8) x² - x = 3(x + 7)
⇒ x² - 4x - 21 = 0
It has D = (-4)² - 4 × 1 × (-21) = 100
So, the roots will be real and distinct. (Answer)