Answer:
all real numbers except ±5.
Step-by-step explanation:
Each function (f(x), g(x)) has a domain that is all real numbers. Their quotient (f(x)/g(x)) must exclude values that make g(x) = 0. The quotient is undefined when the denominator is zero. Those excluded values are x = ±5.
The domain of (f/g)(x) is all real numbers except ±5.
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Of course you recognize x^2 -25 = 0 has solutions x = ±√25 = ±5. You can get there two ways:
- add 25 and take the square root: x^2=25; x=±√25.
- factor the difference of squares and set the factors to zero: (x-5)(x+5)=0 has solutions x-5=0 and x+5=0, that is, x = ±5.
Y= 13 over 10x + 2 is the answer. The most important thing to remember when finding the slope of the line is RISE over RUN. When you rise, you go up or down. When you run, you go right or left. Think of RISE over RUN as a fraction.
You find two points on the line and you count up/down a certain amount of spaces, and right/left a certain amount of spaces to go from one point to the other point.
In this equation, we could use the point on the y-axis and the last point we see on the graph located at (10,15). You count up/down vertically first until you reach the horizontal line that the point is on. Then, you count the amount of spaces horizontally it takes you to reach the point. In this problem, you move up 13 spaces, and move to the right 10 spaces. This as a fraction will be 13 over 10, because we rose 13 spaces and we ran 10 spaces to get to our second point. The y-intercept will be the only number that is on the y-axis, which is 2.
Answer:
x = 1
Step-by-step explanation:
Remember that the axis of symmetry is exactly halfway between the x-intercepts. Find the average of -3 and 5 to obtain this x-value: It is:
-3 + 5
x - intercept = ------------ = x = 1
2
Answer:
Step-by-step explanation:
1. area of square=10²=100 cm²
area of circle=πr²=π×2.5²=6.25π cm²
reqd. area=100-6.25π ≈80.375 cm²
2.
area of circle=π×2.5²=6.25π≈6.25×3.14≈19.625 cm²
area of rectangle=4×3=12 cm²
reqd. area=19.625-12≈7.625 cm²
3.
area of two circles=2×π×3²=18π≈18×3.14≈56.52 cm²
area of square=12²=144 cm²
reqd. area=144-56.52≈87.48 cm²
4.
area of smaller circle=π×4²=16π cm²
area of bigger circle=π×8²=64π cm²
area of two circles=16π+64π=80π cm²
diameter of bigger circle=4+4+8+8=24 cm
diameter of biggest circle=π×12²=144π
area of shaded region=144π-80π=64π≈200.96 cm²
