50+t=(3/2)<br> 50=(3/2)t-t<br> 50=(1/2)t <br> 100 =t <br> Where the hell does 1/2 come from

Which inequality is the solution to 20 + 2 < x/3 - 8?

pychu [463]

Answer:

x > 90, C

Step-by-step explanation:

20 + 2 < x / 3 - 8

x / 3 - 8 > 22

x / 3 > 30

x > 90

4 0

2 years ago

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A metronome is a device that ticks at adjustable intervals to help keep time when playing music. The metronome on Ryan’s piano h

SpyIntel [72]

Answer:

c is the right answer

Step-by-step explanation:

6 0

3 years ago

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PLEASE HELP which is a solution to the equation 6 x + y=4

VladimirAG [237]

Its D. x = 2, y = -8
6*2 + (-8) = 12 - 8 = 4

5 0

2 years ago

PLEASE HELP!!! ASAP!! thank you <33 10 points ;)

ahrayia [7]

Answer:

first find the area of the triangle

1/2 base x height

(1/2) 6 x 4 = (1/2) (24) = 12

area of rectangle

base x height

4 x 6 = 24

add them together

24 + 12 = 36

B) 36 inches

hope this helps :)

Step-by-step explanation:

7 0

3 years ago

For integers a, b, and c, consider the linear Diophantine equation ax C by D c: Suppose integers x0 and y0 satisfy the equation;

Dmitrij [34]

Answer:

a.

$x = x_1+r(\frac{b}{gcd(a, b)} )\\y=y_1-r(\frac{a}{gcd(a, b)} )$

b. x = -8 and y = 4

Step-by-step explanation:

This question is incomplete. I will type the complete question below before giving my solution.

For integers a, b, c, consider the linear Diophantine equation

$ax+by=c$

Suppose integers x0 and yo satisfy the equation; that is,

$ax_0+by_0 = c$

what other values

$x = x_0+h$ and $y=y_0+k$

also satisfy ax + by = c? Formulate a conjecture that answers this question.

Devise some numerical examples to ground your exploration. For example, 6(-3) + 15*2 = 12.

Can you find other integers x and y such that 6x + 15y = 12?

How many other pairs of integers x and y can you find ?

Can you find infinitely many other solutions?

From the Extended Euclidean Algorithm, given any integers a and b, integers s and t can be found such that

$as+bt=gcd(a,b)$

the numbers s and t are not unique, but you only need one pair. Once s and t are found, since we are assuming that gcd(a,b) divides c, there exists an integer k such that gcd(a,b)k = c.

Multiplying as + bt = gcd(a,b) through by k you get

$a(sk) + b(tk) = gcd(a,b)k = c$

So this gives one solution, with x = sk and y = tk.

Now assuming that ax1 + by1 = c is a solution, and ax + by = c is some other solution. Taking the difference between the two, we get

$a(x_1-x) + b(y_1-y)=0$

Therefore,

$a(x_1-x) = b(y-y_1)$

This means that a divides b(y−y1), and therefore a/gcd(a,b) divides y−y1. Hence,

$y = y_1+r(\frac{a}{gcd(a, b)})$ for some integer r. Substituting into the equation

$a(x_1-x)=rb(\frac{a}{gcd(a, b)} )\\gcd(a, b)*a(x_1-x)=rba$

or

$x = x_1-r(\frac{b}{gcd(a, b)} )$

Thus if ax1 + by1 = c is any solution, then all solutions are of the form

$x = x_1+r(\frac{b}{gcd(a, b)} )\\y=y_1-r(\frac{a}{gcd(a, b)} )$

In order to find all integer solutions to 6x + 15y = 12

we first use the Euclidean algorithm to find gcd(15,6); the parenthetical equation is how we will use this equality after we complete the computation.

$15 = 6*2+3\\6=3*2+0$