Answer:
When we have a quadratic equation:
a*x^2 + b*x + c = 0
There is something called the determinant, and this is:
D = b^2 - 4*a*c
If D < 0, then the we will have complex solutions.
In our case, we have
5*x^2 - 10*x + c = 0
Then the determinant is:
D = (-10)^2 - 4*5*c = 100 - 4*5*c
And we want this to be smaller than zero, then let's find the value of c such that the determinant is exactly zero:
D = 0 = 100 - 4*5*c
4*5*c = 100
20*c = 100
c = 100/20 = 5
As c is multiplicating the negative term in the equation, if c increases, then we will have that D < 0.
This means that c must be larger than 5 if we want to have complex solutions,
c > 5.
I can not represent this in your number line, but this would be represented with a white dot in the five, that extends infinitely to the right, something like the image below:
Answer:
Graph A.
Step-by-step explanation:
When x is equal to 0, why has to be equal to 2. The slope also has to be 3. To find this out, we do y2-y1/x2-x1. For A, the slope is -7--4/-3--2. This is equal to -3/-1. This is equal to 3. Because y=2 when x=0. option A is correct. For option D, when x=0, y=32. Therefore, this option is not correct. For option B, when x=0, y=2 so this could be correct. Plug it into y2-y1/x2-x1. This is equal to -1-0/-1-2. This is equal to -1/-3. 1/3 is not equal 3 so this option is not correct either. When x=0, y=32 for option C. Therefore, this option is not correct. Therefore, the answer is option A.
If this helps please mark as brainliest
Answer:
It is either A or B but I think it is B
Step-by-step explanation:
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Answer:
972 x^16 y^24
Step-by-step explanation:
Simplify the following:
(-2 x^3 y^7)^2 (3 x^2 y^2)^5
Multiply each exponent in -2 x^3 y^7 by 2:
(-2)^2 x^(2×3) y^(2×7) (3 x^2 y^2)^5
2×7 = 14:
(-2)^2 x^(2×3) y^14 (3 x^2 y^2)^5
2×3 = 6:
(-2)^2 x^6 y^14 (3 x^2 y^2)^5
(-2)^2 = 4:
4 x^6 y^14 (3 x^2 y^2)^5
Multiply each exponent in 3 x^2 y^2 by 5:
4 x^6 y^14×3^5 x^(5×2) y^(5×2)
5×2 = 10:
4×3^5 x^6 y^14 x^(5×2) y^10
5×2 = 10:
4×3^5 x^6 y^14 x^10 y^10
3^5 = 3×3^4 = 3 (3^2)^2:
4×3 (3^2)^2 x^6 y^14 x^10 y^10
3^2 = 9:
4×3×9^2 x^6 y^14 x^10 y^10
9^2 = 81:
4×3×81 x^6 y^14 x^10 y^10
3×81 = 243:
4×243 x^6 y^14 x^10 y^10
4 x^6 y^14×243 x^10 y^10 = 4 x^(6 + 10) y^(14 + 10)×243:
4×243 x^(6 + 10) y^(14 + 10)
14 + 10 = 24:
4×243 x^(6 + 10) y^24
6 + 10 = 16:
4×243 x^16 y^24
4×243 = 972:
Answer: 972 x^16 y^24
