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Tema [17]
3 years ago
6

Please help with this

Mathematics
2 answers:
zzz [600]3 years ago
7 0

Answer:

x² + 12x + 35

Step-by-step explanation:

The area of the blue section is x * x = x².

Pink: x * 7 = 7x

Green: x * 5 = 5x

Orange: 7 * 5 = 35

When we add these up we get x² + 12x + 35. Hope this helps!

likoan [24]3 years ago
5 0

Answer: x2 + 12x + 35

Step-by-step explanation:

Area of a rectangle = l x w

A = (x + 7) (x + 5)

= x2 + 5x + 7x + 35

= x2 + 12x + 35

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To solve this equation, let's factor the left side.

Although you can factor it in different ways, I will show you a trick.

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Now, multiply the 3 by the constant to get 15.

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Now factor to get (x - 5)(x - 3).

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<span>Let's analyze Hannah's work, step-by-step, to see if she made any mistakes. 

</span>In Step 1, Hannah wrote \dfrac{d}{dx} (-3+8x) <span> as the sum of two separate derivatives </span>\dfrac{d}{dx}(-3)+ \dfrac{d}{dx} (8x) <span>using the </span><span>sum rule.
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This step is perfectly fine. 

In Step 2, \dfrac{d}{dx}(8x) was kept as it is, and \dfrac{d}{dx}(-3) was rewritten as 0 using the constant rule.Indeed, according to the constant rule, the derivative of a constant number is equal to zero.

This step is perfectly fine. 

In Step 3, \dfrac{d}{dx} (8x)  was rewritten as \dfrac{d}{dx}(8) \dfrac{d}{dx}(x) supposedly using the constant multiple rule.

The problem is that according to the constant multiple rule, \dfrac{d}{dx}(8x)&#10; should be rewritten as 8 \dfrac{d}{dx}(x) and not as \dfrac{d}{dx}(8)\dfrac{d}{dx}(x).  

<span>Therefore, Hannah made a mistake in this step.</span>
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