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mestny [16]
3 years ago
13

What is the reflection of point P(-1, 6) across the line y = x?

Mathematics
1 answer:
gladu [14]3 years ago
3 0
If you are reflecting across the line y = x, then the x value becomes the y-vale and the y-value becomes the x-value.  So the answer would be  (6, -1)  (Just trade places with x and y.)
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The length of a rectangle is 2 ft longer than its width.
tino4ka555 [31]

Hi! I'm happy to help!

To solve this, we first need to look at the perimeter equation:

P=2L+2W

We don't know our length, so we can represent it with x. Since our width is 2 feet shorter than x, we can represent it with x-2. Now, we plug these values into our equation:

56=2x+(2(x-2))

Let's simplify what the width is by multiplying:

56=2x+2x-4

Now, let's combine our 2xs

56=4x-4

Now, we just need to solve for x in order to find our length and width.

First, we need to isolate x on one side of the equation. We can do this by adding 4 to both sides:

56=4x-4

+4      +4

60=4x

Now, all we have to do is divide both sides by 4 and x will be fully isolated:

60=4x

÷4  ÷4

15=x

Now that we know x, let's plug this into our previous equations:

L=x=15

<u>L=15</u>

W=x-2=15-2=13

<u>W=13</u>

To verify our answers, we can plug this into our perimeter equation:

56=2(15)+2(13)

56=30+36

56=56

After double checking our answers, we know that our length is 15 and our width is 13.

I hope this was helpful, keep learning! :D

5 0
3 years ago
Which rock is mainly made up of quartz, feldspar, mica, and usually hornblende?
vazorg [7]

Answer:

What Minerals Form Rocks?

The list of minerals that commonly form rocks is short. With a little practice you will recognize most of them when you see them. Descriptions of some of the minerals, as they look in rocks, follow: Quartz: Quartz is the last mineral to crystallize, so in igneous rocks it never has any definite shape. In rocks, it does not show flat faces. It is usually gray in igneous rocks; gray, white, yellow, or red in sedimentary rocks; and gray or white in metamorphic rocks. It has a glassy, or sometimes waxy, look to it.

Potassic Feldspars*: (microcline, orthoclase) Potassic feldspars are pink or tan, sometimes white. They show flat, shiny faces in igneous rocks. The crystal grains are usually blocky and nearly rectangular. They look like good china.

Plagioclase Feldspars*: (albite, labradorite) Look like the potassic feldspars, except they are white to dark gray, sometimes black. They may show flashes of blue or green.

Micas*: (muscovite, biotite, phlogopite) Micas have very thin layers that peel off (or cleave) very easily. In rocks they are usually flakes or layers of flakes. Muscovite is silvery to brown; biotite is black; phlogopite is a reddish brown. Phlogopite may be found in marble.

Chlorite*: Like mica, but the flakes are usually not as thin and do not peel apart as easily. The color is medium to dark green, sometimes almost black but with a greenish tint.

Hornblende: Hornblende is dark green to black. It shows nearly flat, shiny faces in almost rectangular or long thin needle like crystals in rock. Hornblende is usually found in dark colored metamorphic rocks; sometimes in igneous rocks.

Actinolite and Tremolite: Actinolite and tremolite are usually in long thin blades or needle like crystals. Actinolite is dark green; tremolite is white to gray. The crystals may be parallel to each other, or spread from a point. Actinolite is usually found in schists or gneisses. Tremolite may be found in marble.

Olivine*: Olivine in rocks is an olive green to greenish yellow. In rocks it is in rounded grains. If there is much of it, it is almost sugary. It is found mostly in dark colored igneous rocks.

Calcite and Dolomite: The color is usually white, but can be other colors when impure. Crystal grains show flat shiny faces, often shaped like parallelograms. Calcite and dolomite are both soft. They are easily scratched with a steel point. Powdered calcite will fizz in white vinegar; dolomite will not. The minerals are found in limestone or dolostone ( the rock is dolostone, the mineral is dolomite) and marble.

4 0
3 years ago
Can someone solve the system of equations?
kogti [31]
Y=x^2-5

y=2x-5
y+5=2x
x=(y+5)/2

y=((y+5)/2)^2-5
y=(y^2+10y+25)/4-5
4y=y^2+10y+25-20
0=y^2+6y+5
0=(y+5)(y+1)
y= -5 or -1

y=2x-5   (y= -5 doesn't work for this one so use -1)
-1=2x-5
2x=4
x=2

Using these answers, you can choose answer D with reasonable certainty.
5 0
3 years ago
A 24-foot ladder rests against a house near a second story window 20 feet from the ground. Assume that the ladder and the house
Sauron [17]
The ladder, leaning against the building, forms a right triangle with height "a" being the distance from the ground to the window, and hypotenuse "c" being the length of the ladder.

Because it's a right triangle, we can use trigonometric ratios to find the angles we're missing.

For part A), to solve for the angle between the base of the ladder and the ground, you'll want to use sine, because we know the lengths of the opposite side and the hypotenuse.

Sin(x) = a/c , solve for angle x in degrees or radians.

For part B), finding the angle between the top of the ladder and the building, remember that the sum of the angles in a triangle is 180 degrees, or pi radians, depending on which unit your teacher prefers.

Assuming degrees, we can say that angle y = 180-90-x. You are simply subtracting the two known angles to find the third.

For part C) use the Pythagorean theorem. You're looking for the length of the base, "b". Recall:

a^2 + b^2 = c^2

Plug in the known values, and solve for b.
7 0
3 years ago
#6 please ASAP. Thanks
Kobotan [32]
16 x8 will be the new lenth!
4 0
3 years ago
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