So for this it's asking to multiply 10,000 glass beads by the length of 0.4 cm.
So to make it easier let's just make it a fraction.
This will make it 4/10 (because 0.4 is just 4 tenths of a whole number)
So now we can upscale the sizes to the proper ratio. This ratio being the thousands.
4000/10000
Meaning the answer is 4000cm in length.
If the equation of the circle is x^2+ y^2 = 41, we must first understand the parts of the equation.
A general circle's equation is (x-h)^2+(y-k)^2= r^2
(h.k) is the radius of the circle
r is the radius of the circle
Another useful fact to know is that tangent lines touch the circle at one point (4,5)
Since in our original equation there are no h or k values, we can assume that the center of the circle is (0,0).
The formula for slope is <u>Y1-Y2</u>
X1-X2
We can break this down with our two points (center and tangent)
(0,0) and (-4,-5)
(X1,Y1) and (X2,Y2)
therefore, we will put the equation as such
<u>0-(-5)= 5</u> = <em> </em><u><em>5</em></u>
0-(-4)= 4 <em> 4</em>
<em>this is our slope from the center to the point of tangency.</em>
We know that tangent lines are perpendicular to the radius, which we've already found the slope of. Perpendicular lines are opposite reciprocals of the line they are perpendicular to.
Therefore, we take our slope from center to the tangent, and make it opposite and then take the reciprocal of that slope, which will give us the slope of the tangent line itself. (note: reciprocal means flip the numerator and denominator)
<u>5</u> = <u>-5</u> = <u>-4</u><u>
</u>4 4 5
Now, we have a point on the line, and the line's slope. We can use slope-intercept equation to find the equation of the line.
Slope-int y=mx+b
(x,y) is a point,
m is the slope
b is the y intercept ( the point where x=0, or where its on the y axis)
now we plug things in
(-4,-5) is our point,
<u>-4</u> is our slope
5
-5=<u>-4</u>(-4)+b After we plug things in, solve for b
5
-5= 3.2+b
-1.8= b or b= <u />1 <u>4</u>
5
Now we just need to rewrite our equation with all our components.
(-4.-5) = point
<u>-4</u> = slope<u>
</u>5
1 <u>4</u> = y-intercept<u>
</u> 5
<em>y=</em><u><em>-4</em></u><em> x+ 1 </em><u><em>4</em></u><em> This is the equation of the tangent line</em><u>
</u><em> 5 5</em>
Hope that helped
Answer:
Equations with one solution: 
Equations with no solution:
Equations with infinite many solutions: 
Step-by-step explanation:
We will solve each equation to see if it has one solution, no solution or infinite many solutions.
An equation where the value of variable can be found has one solution.
An equation with no solution has both sides different.
An equation with infinite solution will have both sides equal after solution(number)
So,
<u>Equation 1:</u>
5(x-2) = 5x-7
As both sides are not equal, equation has no solution.
<u>Equation 2:</u>
As both sides are equal the equation has infinite many solutions.
<u>Equation 3:</u>
As x=3, the equation has only one solution.
<u>Equation 4:</u>
The equation has no solution.
Hence,
Equations with one solution:
Equations with no solution:
Equations with infinite many solutions:
Answer:
Joan drive with a speed of 55 miles per hour.
Step-by-step explanation:
Given:- Travelling time (t) = 4 hours.
Travelled distance (d) = 480 miles.
Speed of Justin is 10 miles per hour faster than Joan.
To find:- Speed of Joan = ?
Solution:-
Let speed of Joan be x,
therefore speed of Justin = x+10 ---------------(from given)
Now, Total speed of Joan and Justin = x+x+10
Total speed of Joan and Justin = 2x+10 ------------(1)
Now formula for speed is,
Speed = 
-------------(from 1 and given)
as x is the speed of Joan,
Therefore Joan drive with a speed of 55 miles per hour.
