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3 years ago

Which expressions are factors of the expression -24xyz - 12xy + 20xyz

Mathematics

1 answer:

Alex17521 [72]3 years ago

6 0

Answer:

2xy

Step-by-step explanation:

A factor is a number of term you can factor out of each part of the expression/ or divide it by.

In -24xyz - 12xy + 20xyz

All three parts have xy, so it is a factor

All three don't have 12xz, because -12xy doesn't have z variable for instance.

All three have 2xy.

All three can't factor out 3y, because you can't divide 20 by 3 nicely.

All three can't factor out 4yz, because middle term -12xy doesn't have z.

All three can't factor out 12, because you can't nicely divide 20/12.

All three can factor out 4, because -24, -12, and 20 are all divisible by 4.

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Graph the image of this quadrilateral after a dilation with a scale factor of 4 centered at the origin

Brut [27]

Answer: The image is attached.

Step-by-step explanation:

A Dilation is defined as a transformation in which the image and the pre-image have the same shape, but their sizes are different.

When the scale factor is greater than 1, the image obtained after the dilation is greater than the pre-image and it is an "Enlargement".

When the scale factor is is between 0 and 1, the image obtained after the dilation is smaller than the pre-image and it is an "Reduction".

In this case we know that the scale factor is:

$scale\ factor=4$

Since:

$4>1$

It is an Enlargement.

You can identify that the vertices of the pre-image shown in the figure, are:

$(-2,1)\\\\(-1,2)\\\\(0,0)\\\\(-1,-2)$

So you need to multiply the coordinates of those vertices by 4 in order to get the coordinates of the image;

$((-2)(4),1(4))=(-8,4)\\\\((-1)(4),(2)(4))=(-4,8)\\\\((0)(4),(0)(4)=(0,0)\\\\((-1)(4),(-2)(4))=(-4,-8)$

Now you can draw it (The image is attached).

8 0

3 years ago

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goblinko [34]

Answer:

20.04 units

Step-by-step explanation:

The diagram shows right triangle ABC. Use the definition of the cosine:

$\cos \angle C=\dfrac{\text{Adjacent leg}}{\text{Hypotenuse}}\\ \\\cos \angle C=\dfrac{BC}{AC}\\ \\\cos 51^{\circ}=\dfrac{BC}{27}\\ \\BC=27\cdot \cos 51^{\circ}\\ \\BC\approx 20.04\ units$

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4 years ago

PLEASE HELP. WORTH 50 PINTS IF CORRECT. A gate casts a shadow that is 5 feet long. A nearby cactus is 9 feet tall and casts a sh

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Answer:

The height of the cactus is three times the height of the gate

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Please help with this I am completely stuck on it

vaieri [72.5K]

Answer:

$f(x)=\sqrt[3]{x-4} , g(x)=6x^{2}\textrm{ or }f(x)=\sqrt[3]{x},g(x)=6x^{2} -4$

Step-by-step explanation:

Given:

The function, $H(x)=\sqrt[3]{6x^{2}-4}$

Solution 1:

Let $f(x)=\sqrt[3]{x}$

If $f(g(x))=H(x)=\sqrt[3]{6x^{2}-4}$ , then,

$\sqrt[3]{g(x)} =\sqrt[3]{6x^{2}-4}\\g(x)=6x^{2}-4$

Solution 2:

Let $f(x)=\sqrt[3]{x-4}$ . Then,

$f(g(x))=H(x)=\sqrt[3]{6x^{2}-4}\\\sqrt[3]{g(x)-4}=\sqrt[3]{6x^{2}-4} \\g(x)-4=6x^{2}-4\\g(x)=6x^{2}$

Similarly, there can be many solutions.

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Step-by-step explanation:

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