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IRINA_888 [86]
2 years ago
15

When graphing a system of equations with infinitely many solutions, the slopes of the two lines will be ________.

Mathematics
1 answer:
g100num [7]2 years ago
6 0
The slope of both lines will be the exact same.

hope this helps :)
You might be interested in
A television screen's width is 1.778 times its height. If its
Nana76 [90]

Answer:

Let a, b, and c be the height, width, and the diagonal of the screen respectively

Since they form a triangle and the angle between a and b is 90 degrees, according to the Pythagorean Theorem a^2 + b^2 = c^2

Let's assume that the aspect ratio is 16:9. Therefore b/a = 16/9

Now we have a system of two equations with two unknowns. We need to express everything in terms of a single unknown, so let's express a in terms of b.

Since, b/a = 16/9, by cross multiplying 16a = 9b. Therefore a=9b/16.

Now we can subsitute 9b/16 for a in the first equation

a^2+b^2=c^2 becomes (9b/16)^2 + b^2 = c^2

Squaring the nominator and the denominator of the fraction yields

81b^2/256 + b^2 = c^2

To perform the addition, we need to express b^2 as a fraction with denominator 256 which is 256b^2/256, Now we have

81b^2/256 + 256b^2/256 = c^2

Adding fractions with the same denominators is now easy and produces

337b^2/256 = c^2

Cross multiply to get

337b^2 = 256c^2

Divide both sides by 337 to get b^2

b^2=256c^2/337

Take the square root of both sides to get b

b = sqrt(256c^2/337)

Lots of complicated Pythagorean responses. This is much simpler to answer with Trigonometry.

TLDR; just multiply the diagonal by the following two coefficients, and add the bezel width, to get the width and height:

w = diag x 0.872 + 2 x bw

h = diag x 0.49 + 2 x bw

(Where diag is the diagonal size of the screen and bw is the bezel width)

Thats all you need to know to do this.

Now here’s the Teig behind it:

First, calculate the angle of the diagonal relative to the base, using tangent, which yields ::

a = tan(9/16)

This will give you an angle of 0.512 radians (or roughly 30 degrees).

Next, calculate the ratio of the height relative to the hypotenuse (the diagonal length) using arc-sine, which yields the relative proportion of opposite length over the hypotenuse for a given angle:

h = asin(0.512)

The result will be roughly h = 0.49, or 49% of the diagonal.

Finally, get the ratio of eidth to hypotenuse using arc-cosine:

w = acos(0.512)

The result is roughly w = 0.872, or 87.2% of the diagonal.

that’s all the math! Enjoy!

6 0
3 years ago
Mary is booking a 3-night stay at a hotel. The rate is $69 per room plus tax. If
Verdich [7]
It’s D 69x3= 207

6% of 207 = 12.42
2% of 207 = 4.14
1% of 207 = 2.07
12.42 + 4.14 + 2.07 = 18.63
207+18.63 = 225.63
8 0
2 years ago
NEED HELP ASAP FOR HOMEWORK!! IF RIGHT WILL MARK BRAINLIEST!!!​
alexdok [17]

Answer:

It's the 3rd one using the formula a^{-m} = \frac{1}{a^{m} }

Once you follow that step you need to multiply the exponent of 3 and 6 with the exponent outside the parenthesis..... which is why it's the 3rd one.

4 0
3 years ago
Read 2 more answers
Please help me with this
enyata [817]

Answer:

6

Step-by-step explanation:

6 0
3 years ago
2. Alicia is writing the program for a video game. For one part of the game she uses the rule (x,y) ->(x-3,y+4) to move point
Taya2010 [7]

Given rule (x,y) ->(x-3,y+4) to move points on the screen.

a) We are given first input (-6,0).

(-6,0) represents x=-6 and y=0.

Plugging values of x and y in given rule (x,y) ->(x-3,y+4), we get

(-6,0) --> (-6-3, 0+4). It would give us (-9,4)

So, first output is (-9,4).

b) We are given second input (3,-4).

(-6,0) represents x=3 and y=-4.

Plugging values of x and y in given rule (x,y) ->(x-3,y+4), we get

(-6,0) --> (3-3, -4+4). It would give us (0,0).

So, second output is (0,0).



7 0
3 years ago
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