1. 8c^2-26c+15= (4c-3) (2c-5). Break the expression into groups: =(8c^2-6c)+(-20c+15). Factor out 8c^2-6c: 2c(4c-3). Factor out -5 from -20c+ 15: -5(4c-3). Lastly factor out common term (4c-3) and thats how you'll get your answer (4c-3) (2c-5).
2. common factors for 270 and 360 is 90.To find this write the factors of each and find the largest one.270: 1, 270, 2, 135, 3, 90, 5, 54, 6, 45, 9, 30, 10, 27, 15, 18360: 1, 360, 2, 180, 3, 120, 4, 90, 5, 72, 6, 60, 8, 45, 9, 40, 10, 36, 12, 30, 15, 24, 18, 20
3. The factors for 8 a3b2 and 12 ab4 is 4. because 8: 1, 2, 4, 812: 1, 2, 3, 4, 6, 12.
4. 81a^2+36a+4= (9a+2)^2. Break down the expression into groups: (81a^2+18a)+(18a+4). Factor out 9a from 81a^2 +18a: 9a(9a+2). Factor out 2 from 18a+4: 2(9a+2). so the groups you got are now 9a(9a+2)+2(9a+2). Lastley factor out common term (9a+2) to get (9a+2) (9a+2). Finally you get the answer (9a+2)^2.
5. mn-15+3m-5n= (n+3)(m-5). factor out m from nm+3m: m(n+3). Factor out -5 from -5n-15: -5(n+3). And thats how you get the number (n+3)(m-5)
Hope this helped :) Have a great day
The standard form for the equation of a circle is :
<span><span><span> (x−h)^</span>2</span>+<span><span>(y−k)^</span>2</span>=<span>r2</span></span><span> ----------- EQ(1)
</span><span> where </span><span>handk</span><span> are the </span><span>x and y</span><span> coordinates of the center of the circle and </span>r<span> is the radius.
</span> The center of the circle is the midpoint of the diameter.
So the midpoint of the diameter with endpoints at (−10,1)and(−8,5) is :
((−10+(−8))/2,(1+5)/2)=(−9,3)
So the point (−9,3) is the center of the circle.
Now, use the distance formula to find the radius of the circle:
r^2=(−10−(−9))^2+(1−3)^2=1+4=5
⇒r=√5
Subtituting h=−9, k=3 and r=√5 into EQ(1) gives :
(x+9)^2+(y−3)^2=5
Answer: (9, 10800)
Step-by-step explanation:
We will first let x be the number of years and y be the total cost.
In that case, let's plug in the values for each into the equation <em>y=mx+b, </em>where m is the slope and b is the y-intercept.
The y-intercept will be the <u>value we start with before any years pass</u>, so it will be the <u>installation cost</u>. The slope is <u>how fast the total cost will increase</u>. Since the <u>operation costs</u> have to be added on every year, it will be our slope.
With that in mind, let's create both of our equations:
- y = 900x + 2700 (Oil system)
- y = 200x + 9000 (Solar system)
Since y is solved for in the first equation, we can substitute it into the second equation:

<em>[Subtracting 200x from both sides]</em>
<em />
<em>[Subtracting 2700 from both sides]</em>
<em />
<em>[Dividing both sides by 700]</em>
<em />
We can now substitute 9 for x in any equation and solve for y. Here I substituted it into the first one:

<em>[Multiplying]</em>
<em />
<em>[Adding]</em>
Hence, the solution to this linear system is (9, 10800).
Answer: m∠D = 65°
Step-by-step explanation:
The best solve method for problems like this is say the sum of the angle values equals 360.
2x-15+2x-15+x+x = 360
Then from here you just simplify.
4x+2x-30 = 360
6x = 390
x = 65
So the measure of Angle D equals 65 degrees.
Answer:
100+100+100+100+100+10+10+10+10 = 540
100 = 10+10+10+10+10+10+10+10+10+10
400 + 100 + 10 + 10 + 10 _ 10
Step-by-step explanation: