Answer:45=3x3x5
Step-by-step explanation:
prime factorization of 45
45 ➗ 3=15
15 ➗ 3=5
5 ➗ 5=1
45=3x3x5
Equation of circle is (x - a)^2 + (y - b)^2 = r^2; where (a, b) is the center and r is the radius.
r^2 = (2 - 3)^2 + (-1 - 4)^2 = (-1)^2 + (-5)^2 = 1 + 25 = 26
Equation is (x - 2)^2 + (y + 1)^2 = 26
Answer:
2/14, 4/28, 5/35, 7/70 or just 2/14
Step-by-step explanation:
Multiply both the numerator and denominator of 1/7 by 2, to get 2/14, or 2:14
And multiply the numerator and denominator of 1/7 by 3, to get 3/21, or 3:21. So 2:14 and 3:21 are two ratios that are equal to 1:7.
Answer:
A noun is most commonly taught a person, place, or thing and sometimes idea. In this sentence, it would be Magazine, Americans, and carbohydrates. And if smith is also part of the sentence, he is a person, so its also a noun. :) Happy learning friend
Here i how I would do it:<span>f(x)=−<span>x2</span>+8x+15</span>
set f(x) = 0 to find the points at which the graph crosses the x-axis. So<span>−<span>x2</span>+8x+15=0</span>
multiply through by -1<span><span>x2</span>−8x−15=0</span>
<span>(x−4<span>)2</span>−31=0</span>
<span>x=4±<span>31<span>−−</span>√</span></span>
So these are the points at which the graph crosses the x-axis. To find the point where it crosses the y-axis, set x=0 in your original equation to get 15. Now because of the negative on the x^2, your graph will be an upside down parabola, going through<span>(0,15),(4−<span>31<span>−−</span>√</span>,0)and(4+<span>31<span>−−</span>√</span>,0)</span>
To find the coordinates of the maximum (it is maximum) of the graph, you take a look at the completed square method above. Since we multiplied through by -1, we need to multiply through by it again to get:<span>f(x)=31−(x−4<span>)2</span></span><span>
Now this is maximal when x=4, because x=4 causes -(x-4)^2 to vanish. So the coordinates of the maximum are (4,y). To find the y, simply substitute x=4 into the equation f(x) to give y = 31. So it agrees with the mighty Satellite: (4,31) is the vertex.</span>