Greatest to least of 2/3, 0.67,5/9,0.58,7/12

How many intersections are there of the graphs of the equations below? One-halfx + 5y = 6 3x + 30y = 36 none one two infinitely

Sergeu [11.5K]

Answer:

infinitely many

Step-by-step explanation:

You have the system

(1/2)x + 5y = 6

3x + 30y = 36

Multiplying the first equation by 6 results in 3x + 30y = 36, which is exactly the same as the second equation. The two graphs coincide, and so there are infinitely many solutions to this system

4 0

2 years ago

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For a polygon to be convex means that all of its interior angles are less than 180 degrees. Prove that for all integers n ≥ 3, t

Alexeev081 [22]

Answer: check explanation

Step-by-step explanation:

Let K(n) be the sum of the interior angles in any n-sided convex polygon which is exactly 180(n −2)

degrees.

CASE: n = 3. A 3-sided polygon is a triangle, whose interior angles were shown always to sum to be 180 degree

INDUCTION HYPOTHESIS: Suppose that K(b) holds for some b ≥ 3. Which means that the interior angles in any b-sided convex

polygon is exactly 180(n −2) degrees.

INDUCTION STEP: We need to show that K(n is greater than or equals to 3) . That is, the interior angles of any b+1-sided convex polygon

is exactly 180(b−2) = 180(b −1) degrees,

Let X be any (b+1)-vertex convex polygon, say with successive vertices x1, x2,..., xb+

Now Y is also a convex polygon , so by the induction hypothesis K(b), the sum of the interior

angles of Y is 180(k −2).

Now let T be the triangle with vertices xk , xb+1, x1. The sum of the interior angles in X is the sum of those

in Y plus the sum of those in T .

So the sum of the interior angles in X is

180(b −2)+180 = 180((b +1)−2) = 180(b −1).

Since X was arbitrary, we conclude that the sum of the interior angles of any (b +1)-sided convex polygon

is 180((b−2)+1) = 180(b−1). That is, P(b +1) holds.

And which means that n is greater or equals to 3

8 0

2 years ago

234,143 rounded to the nearest hundred

larisa86 [58]

Answer:

234,100

anything that is below 50 will go down.

Step-by-step explanation:

4 0

1 year ago

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CD is a perpendicular bisector of . Which of the following could be the slopes of the two lines if plotted on a coordinate grid?

NISA [10]

Step-by-step explanation:

A is the correct answer of this question

8 0

2 years ago

If cos(t) = 2/7 and t is in the 4th quadrant, find sin(t).

Yuliya22 [10]

We can use the Pythagorean Trigonometric Identity which says:
$sin^2(t)+cos^2(t)=1$

Since we need to find sin(t), we have to solve for it:
$sin(t)= \sqrt{1-cos^2(t)}$

Let's plug in the given cos(t) value:
$sin(t) = \sqrt{1-cos^2( \frac{2}{7})}$

And solve sin(t):
$sin(t) = \sqrt{1- \frac{4}{49} } = \frac{x}{y} \sqrt{ \frac{49}{49}- \frac{4}{49} }$

Simplify further:
$sin(t) = \sqrt{ \frac{45}{49} } = \frac{ \sqrt{45} }{7} = \frac{ \sqrt{9*5} }{7}$

And it all simplifies down to:
$sin(t) = \frac{3 \sqrt{5} }{7}$

Since it's in the 4th quadrant, the sin(t) value is going to be negative. So, your final answer is:
$sin(t) = - \frac{ 3\sqrt{5} }{7}$

Hope this helps!

7 0

2 years ago