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3 years ago

The sum of two The perimeter of a rectangle is 30cm. If the length is 3 cm longer than the width, find

Mathematics

1 answer:

Llana [10]3 years ago

4 0

Answer:

Width: 6 cm

Length: 9 cm

Step-by-step explanation:

Width: x

Length: x + 3

2(x)+2(x+3) = 30cm

2x + 2x + 6 = 30

4x = 30-6

x = 24/4

x = 6

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What is the equation of the quadratic graph with a focus of (6, 0) and a directrix of y = −10 ?

Mademuasel [1]

Answer:

$(x-6)^{2}=20(y+5)^{2}$

Step-by-step explanation:

The standard for for the equation of a parabola is $(x-h)^{2}=4p(y-k)$

The focus is given as $(h, k+p)$

The directrix is given by $y=k-p$

Comparing focus given as $(6,0)$ to formula of focus $(h,k+p)$ , we see that $h=6$ and $k+p=0$
Comparing directrix given as $y=-10$ to formula of directrix $y=k-p$ , we can write $k-p=-10$

We can use the two system of equations [ $k+p=0$ and $k-p=-10$ ] to solve for $k$ and $p$ .

Adding the two equations gives us:

$2k=-10\\k=\frac{-10}{2}\\k=-5$

Using this value of $k$ , we can find $p$ by plugging this value in either equation. Let's put it in Equation 1. We have:

$k-p=-10\\-5-p=-10\\-5+10=p\\p=5$

Now, that we know $h=6$ , $k=-5$ , and $p=5$ , we can plug these values in the standard form equation to figure out the parabola's equation. Doing so and rearranging gives us:

$(x-6)^{2}=4(5)(y-(-5))^{2}\\(x-6)^{2}=20(y+5)^{2}\\$

This is the equation of the parabola with focus $(6,0)$ and directrix $y=-10$

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3 years ago

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Dmitry [639]

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8x -5x - 4 ≥ -31

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x ≥ - 9

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Because that drawing represents the number that are less or equel than -9 and the answer is the numbers greater or equal than -9.

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3 years ago

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Answer:

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Step-by-step explanation:

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Now, we calculate the volume of the strawberry section as follows:

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Step-by-step explanation:

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