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IceJOKER [234]
3 years ago
10

The function h(x) is quadratic and h(3) = h(–10) = 0. Which could represent h(x)?

Mathematics
2 answers:
MrMuchimi3 years ago
7 0
It would be the last one, h(x) = 2x2 + 14x - 60. If you plug in either 3 or -10 for the x value, the answer comes out to 0. 
liraira [26]3 years ago
5 0

Answer:

Option D.

Step-by-step explanation:

We can solve this question by finding the values of h(3) and h(-10) from each option given.

Option A.

h(x) = x² - 13x - 30

h(3) = 3² - (13×3) - 30

      = 9 - 39 - 30

      = -60

h(-10) = (-10)² - 13(-10) - 30

         = 100 + 130 - 30

         = 200

Therefore, h(3) ≠ h(-10)

Option B.

h(x) = x² - 7x - 30

h(3) = 3² - 7×3 - 30

      = 9 - 21 - 30

      = -42

h(-10) = (-10)² - 7(-10) - 30

         = 100 + 70 - 30

         = 140

h(3) ≠ h(-10)

Option C.

h(x) = 2x² + 26x - 60

h(3) = 2(3)² + 26×3 - 60

      = 18 + 78 - 60

      = 36

h(-10) = 2(-10)² + 26(-10) - 60

         = 200 - 260 - 60

         = -120

h(3) ≠ h(-10)

Option D.

h(x) = 2x² + 14x - 60

h(3) = 2(3)² + 14(3) - 60

      = 18 + 42 - 60

      = 0

h(-10) = 2(-10)² + 14(-10) - 60

         = 200 - 140 - 60

         = 0

h(3) = h(-10) = 0

Therefore, option D is the answer.

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Answer:

(a) x=\dfrac{\pi}{8},\dfrac{3\pi}{8},\dfrac{9\pi}{8},\dfrac{11\pi}{8}

(b) x=\dfrac{3\pi}{2},\dfrac{\pi}{6},\dfrac{5\pi}{6}

Step-by-step explanation:

It is given that 0\leq x\leq 2\pi.

(a)

\sqrt{2}\sin 2x=1

\sin 2x=\dfrac{1}{\sqrt{2}}

\sin 2x=\dfrac{\pi}{4}

2x=\dfrac{\pi}{4},\dfrac{3\pi}{4},\dfrac{9\pi}{4},\dfrac{11\pi}{4}     [\because \sin x=\sin y\Rightarrow x=n\pi+(-1)^ny]

x=\dfrac{\pi}{8},\dfrac{3\pi}{8},\dfrac{9\pi}{8},\dfrac{11\pi}{8}

(b)

\csc^2 x-\csc x-2=0

\csc^2 x-2\csc x+\csc x-2=0

\csc x(\csc x-2)+1(\csc x-2)=0

(\csc x+1)(\csc x-2)=0

\csc x=-1\text{ or }\csc x=2

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Therefore, x=\dfrac{3\pi}{2},\dfrac{\pi}{6},\dfrac{5\pi}{6}.

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Two balls are drawn in turn without replacement from a box containing three green and two white balls.Find the probability of dr
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A. 2/5

B.2/5

C. 3/5

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Megan took out a student loan for $9,075 if she paid $4.537.50 in simple interest over 10 years what percent was her interest ra
madam [21]

Answer:

5%

Step-by-step explanation:

Solving our equation

r = 4537.5 / ( 9075 × 10 ) = 0.05

r = 0.05

converting r decimal to a percentage

R = 0.05 * 100 = 5%/year

The interest rate required to

accumulate simple interest of $ 4,537.50

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