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Anit [1.1K]
3 years ago
9

Dylan has a square piece of metal that measures 10 inches on each side. He cuts the metal along the diagonal, forming two right

triangles. What is the length of the hypotenuse of each right triangle to the nearest tenth of an inch?
Mathematics
1 answer:
alexandr402 [8]3 years ago
3 0
Use Pythagoras theorem,
c² =a² +b² 
x² =10² +10<span>² 
</span>x<span>² =100+100
</span>x<span>² =200
</span>x=14.14
x=14.1

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Which table describes the behavior of the graph of f(x) = 2x3 – 26x – 24?
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Answer:

For x∈ {-∞,-3} y<0, below x-axis

x∈ {-3,-1} y>0, above x-axis

x∈ {-1,4} y<0, below x-axis

x∈ {4,∞} y>0, above x-axis

Step-by-step explanation:

f(x)=2x^{3}-26x-24

2x^{3}-26x-24=0

2x^{3}-26x-24=0\\2x^{3}-2x-24x-24=0\\2x(x^{2} -1)-24(x+1)=0\\2x(x+1)(x-1)-24(x+1)=0\\(x+1)(2x^{2} -2x-24)=0\\=> x+1=0 => x_{1}=-1\\

=> 2x^{2} -2x-24=0\\=>2(x^{2} -x-12)=0\\=> x^{2} -x-12=0\\=> x^{2} -4x+3x-12=0\\=> x(x-4)+3(x-4)=0\\=> (x-4)(x+3)=0\\

=> x-4=0\\=> x_{2}=4\\=> x+3=0\\=>x_{3}=-3\\

For x∈ {-∞,-3} y<0, below x-axis

x∈ {-3,-1} y>0, above x-axis

x∈ {-1,4} y<0, below x-axis

x∈ {4,∞} y>0, above x-axis



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