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Strike441 [17]
3 years ago
9

Two lines, C and D, are represented by the following equations: Line C: y = x + 5 Line D: y = −2x − 1 Which of the following opt

ions shows the solution to the system of equations and explains why? (4 points) Group of answer choices (−2, 3), because one of the lines passes through this point (−2, 3), because the point does not lie on any axis (−2, 3), because both lines pass through this point (−2, 3), because the point lies between the two axes
Mathematics
1 answer:
klio [65]3 years ago
5 0

Answer:

(−2, 3), because both lines pass through this point

Step-by-step explanation:

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Factor the following binomial using the difference of squares?<br> (49x^2 – 9)
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I think the answer is (7x-3)(7x+3)
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3 years ago
You are creating an open top box with a piece of cardboard that is 16 x 30“. What size of square should be cut out of each corne
Arada [10]

Answer:

\frac{10}{3} \ inches of square should be cut out of each corner to create a box with the largest volume.

Step-by-step explanation:

Given: Dimension of cardboard= 16 x 30“.

As per the dimension given, we know Lenght is 30 inches and width is 16 inches. Also the cardboard has 4 corners which should be cut out.

Lets assume the cut out size of each corner be "x".

∴ Size of cardboard after 4 corner will be cut out is:

Length (l)= 30-2x

Width (w)= 16-2x

Height (h)= x

Now, finding the volume of box after 4 corner been cut out.

Formula; Volume (v)= l\times w\times h

Volume(v)= (30-2x)\times (16-2x)\times x

Using distributive property of multiplication

⇒ Volume(v)= 4x^{3} -92x^{2} +480x

Next using differentiative method to find box largest volume, we will have \frac{dv}{dx}= 0

\frac{d (4x^{3} -92x^{2} +480x)}{dx} = \frac{dv}{dx}

Differentiating the value

⇒\frac{dv}{dx} = 12x^{2} -184x+480

taking out 12 as common in the equation and subtituting the value.

⇒ 0= 12(x^{2} -\frac{46x}{3} +40)

solving quadratic equation inside the parenthesis.

⇒12(x^{2} -12x-\frac{10x}{x} +40)=0

Dividing 12 on both side

⇒[x(x-12)-\frac{10}{3} (x-12)]= 0

We can again take common as (x-12).

⇒ x(x-12)[x-\frac{10}{3} ]=0

∴(x-\frac{10}{3} ) (x-12)= 0

We have two value for x, which is 12 and \frac{10}{3}

12 is invalid as, w= (16-2x)= 16-2\times 12

∴ 24 inches can not be cut out of 16 inches width.

Hence, the cut out size from cardboard is \frac{10}{3}\ inches

Now, subtituting the value of x to find volume of the box.

Volume(v)= (30-2x)\times (16-2x)\times x

⇒ Volume(v)= (30-2\times \frac{10}{3} )\times (16-2\times \frac{10}{3})\times \frac{10}{3}

⇒ Volume(v)= (30-\frac{20}{3} ) (16-\frac{20}{3}) (\frac{10}{3} )

∴  Volume(v)= 725.93 inches³

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3 years ago
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Deffense [45]

Answer:

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Step-by-step explanation:

You have to distribute the -15 into the numbers in the 8m-4.

So, <u>-15 times 8m</u> plus <u>-15 times -4</u>

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What is the diffinition of qutionmbra
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There is no such word as quationbra and I feel like you either spelled it wrong or you got an unreal word.

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Answer:

2100 seconds

Step-by-step explanation:

60x35=2100

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