(x^2+4)^2 + 32 = 12x^2 + 48 .... a = x^2 + 4
<span>(x^2 + 4)^2 + 32 = 12(x^2 + 4) </span>
<span>a^2 + 32 = 12a </span>
<span>a^2 - 12a + 32 = 0 </span>
<span>(a - 8)(a - 4) = 0 </span>
<span>a = 8 and a = 4 </span>
<span>for a = 8 ... 8 = x^2 + 4 ... x^2 = 4 ... x = +/- 2 </span>
<span>for a = 4 ... 4 = x^2 + 4 ... x^2 = 0 ... x = 0 </span>
<span>x = -2, 0, +2 so your answer is going to be e
</span>
Answer:
1)Area; A = ¼πr²
Perimeter; P = πr/2 + 2r
2)A = 19.63 cm²
P = 17.85 cm
3) r = 8.885 cm
4) r = 14 cm
Step-by-step explanation:
This is a quadrant of a circle. Thus;
Area of a circle is πr². A quadrant is a quarter of a circle. Thus;
Formula for Quadrant Area is; A = ¼πr²
A) Perimeter of a circle is 2πr. Thus, perimeter of a quadrant is a quarter of the full circle perimeter.
Formula for the quadrant perimeter in the image given is;
P = 2πr/4 + 2r
P = πr/2 + 2r
B) When r is 5 cm;
A = ¼π(5)²
A = 19.63 cm²
P = π(5)/2 + 2(5)
P = 17.85 cm
C) when A is 100cm²:
¼πr² = 100
r² = 100 × 4/π
r² = 78.9358
r = √78.9358
r = 8.885 cm
D) when P = 50 cm.
50 = πr/2 + 2r
50 = (½π + 2)r
r = 50/(½π + 2)
r = 14 cm
Answer
Positive 8 is the missing value
Step-by-step explanation:
-11 + 8 = -3
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).
