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maksim [4K]
2 years ago
14

the graph of y = x2 11x 24 is equivalent to the graph of which equation? a.y = (x 8)(x 3) b.y = (x 4)(x 6) c.y = (x 9)(x 2) d.y

= (x 7)(x 4)
Mathematics
2 answers:
Goshia [24]2 years ago
7 0
Y = x^2 + 11x + 24 = (x + 8)(x + 3)
Mademuasel [1]2 years ago
3 0

Answer:

Option a is correct.

Step-by-step explanation:

We have been given the expression:

y=x^2+11x+24

We will factorize the given quadratic equation:

x^2+8x+3x+24

\Rightarrow x(x+8)+3(x+8)

\Rightarrow (x+8)(x+3)

Hence, the given equation is equivalent to (x+8)(x+3)

Hence, the graph will be equivalent to y=(x+8)(x+3)

Therefore, option a is correct.

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(a) Use the Quotient Rule to differentiate the function f(x)=tan(x)-1/sec(x). f'(x)=
yKpoI14uk [10]

Answer:

(a) sin(x) + cos(x)

(b) sin(x) + cos(x)

(c) Both answers are equivalent

Step-by-step explanation:

(a) The given function is:

f(x) = \frac{tan(x)-1}{sec(x)}

According to the quotient rule:

f(x) = \frac{g(x)}{h(x)}\\f'(x)= \frac{g'(x)h(x)-g(x)h'(x)}{h(x)^2}

Applying the quotient rule:

f(x) = \frac{tan(x)-1}{sec(x)}\\f'(x)=\frac{sec^2(x)*sec(x)-(tan(x)-1)*sec(x)tan(x)}{sec(x)^2}\\f'(x)=\frac{sec^3(x)-sec(x)tan^2(x)+sec(x)tan(x)}{sec(x)^2}\\f'(x)=sec(x)+\frac{tan(x)-tan^2(x)}{sec(x)}\\ \frac{tan(x)}{sec(x)}=sin(x) \\f'(x)=sec(x)+sin(x)-sin(x)tan(x)\\

This can be simplified to:

f'(x)=sec(x)+sin(x)-sin(x)tan(x)\\f'(x) = \frac{1}{cos(x)}+sin(x)-\frac{sin^2(x)}{cos(x)}\\f'(x)=\frac{1+sin(x)cos(x)-sin^2(x)}{cos(x)}\\f'(x)=\frac{sin^2(x)+cos^2(x)+sin(x)cos(x)-sin^2(x)}{cos(x)}\\f'(x)=\frac{cos^2(x)+sin(x)cos(x)}{cos(x)}\\ f'(x)=sin(x) +cos(x)

(b) Simplifying in terms of sin(x) and cos(x):

f(x) = \frac{tan(x)-1}{sec(x)}\\f(x)=\frac{\frac{sin(x)}{cos(x)}-1 }{\frac{1}{cos(x)} } \\f(x)=sin(x)-cos(x)\\f'(x) = cos(x)+sin(x)

(c) As proven above, both answers are equivalent.

4 0
3 years ago
419% of what number is 33.52
Inessa [10]
419% of 33.52=140.4488
6 0
3 years ago
Welp okie please help
Nataly [62]

Answer:

8:15

Step-by-step explanation:


4 0
2 years ago
Read 2 more answers
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Alex_Xolod [135]

Answer: 200

Step-by-step explanation: 36 by 100 and then divide the total by 18 as follows: (36 x 100) / 18 For 200

8 0
2 years ago
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Can someone help ASAP?<br>​
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Answer

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Step-by-step explanation:

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