17 answers
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5x-3y=-6
find the x-intercept and y-intercept
Bot GPT 3.5
answered
To find the x-intercept, set y=0 in the equation and solve for x:
5x - 3(0) = -6
5x = -6
x = -6/5
Therefore, the x-intercept is (-6/5, 0).
To find the y-intercept, set x=0 in the equation and solve for y:
5(0) - 3y = -6
-3y = -6
y = -6/-3
y = 2
Therefore, the y-intercept is (0, 2).
anonymous
answered
4x-4y=0
find the x and y intercepts
Bot GPT 3.5
answered
To find the x-intercept, set y=0 in the equation and solve for x:
4x - 4(0) = 0
4x = 0
x = 0
Therefore, the x-intercept is (0, 0).
To find the y-intercept, set x=0 in the equation and solve for y:
4(0) - 4y = 0
-4y = 0
y = 0
Therefore, the y-intercept is (0, 0).
anonymous
answered
find the slope of the line that passes through the points (2,-6) and (4,-12)
Bot GPT 3.5
answered
To find the slope of a line passing through two points, we use the formula:
Slope = (y2 - y1) / (x2 - x1)
Let's substitute the given values into the formula:
(x1, y1) = (2, -6)
(x2, y2) = (4, -12)
Slope = (-12 - (-6)) / (4 - 2)
Slope = (-12 + 6) / (4 - 2)
Slope = -6 / 2
Simplifying the fraction, we get:
Slope = -3
Therefore, the slope of the line passing through the points (2,-6) and (4,-12) is -3.
anonymous
answered
find slope of the line that passes through the points
(2,-1) and (-9,3)
Bot GPT 3.5
answered
To find the slope of a line passing through two points, we use the formula:
Slope = (y2 - y1) / (x2 - x1)
Let's substitute the given values into the formula:
(x1, y1) = (2, -1)
(x2, y2) = (-9, 3)
Slope = (3 - (-1)) / (-9 - 2)
Slope = (3 + 1) / (-9 - 2)
Slope = 4 / (-11)
Therefore, the slope of the line passing through the points (2, -1) and (-9, 3) is -4/11.
anonymous
answered
find the slope of a line passing through the points
(6,5) and (6,8)
(3,10) and (-7,10)
Bot GPT 3.5
answered
To find the slope of a line passing through two points (x1, y1) and (x2, y2), we use the formula:
Slope = (y2 - y1) / (x2 - x1)
For the first set of points (6, 5) and (6, 8):
Slope = (8 - 5) / (6 - 6)
Slope = 3 / 0
Since the denominator is 0, the slope is undefined.
For the second set of points (3, 10) and (-7, 10):
Slope = (10 - 10) / (-7 - 3)
Slope = 0 / -10
Slope = 0
Therefore, the slope of the line passing through the points
(6, 5) and (6, 8) is undefined, and the slope of the line passing through the points (3, 10) and (-7, 10) is 0.
anonymous
answered
(a8)(a2)(a4)
Bot GPT 3.5
answered
To find the product of these three terms, you can combine the exponents:
(a^8) * (a^2) * (a^4) = a^(8+2+4) = a^14
Therefore, the product is a^14.
anonymous
answered
product rule to simplify, write result using exponents
(a8) * (a2) * (a4)
Bot GPT 3.5
answered
To simplify the expression using the product rule and write the result using exponents, we can add the exponents of the same base, which in this case is 'a'.
(a^8) * (a^2) * (a^4) = a^(8 + 2 + 4) = a^14
Therefore, the simplified expression is a^14.
anonymous
answered
simplify expression, write the result using positive exponents only
(-3)^-4
Bot GPT 3.5
answered
To simplify the expression and write the result using positive exponents only, we can use the rule that states when a negative exponent is raised to, it becomes the reciprocal of the positive exponent.
(-3)^-4 = 1 / (-3)^4
Now, we can evaluate (-3)^4:
(-3)^4 = (-3) * (-3) * (-3) * (-3) = 81
Therefore, the simplified expression is 1 / 81.
anonymous
answered
simplify expression, write the result using positive exponents only
(-3)-4
Bot GPT 3.5
answered
To simplify (-3)^-4 and write the result using positive exponents only, we can use the rule that states when a negative exponent is applied to a number, it becomes the reciprocal of that number raised to the positive exponent.
(-3)^-4 = 1 / (-3)^4
Now, we can evaluate (-3)^4:
(-3)^4 = (-3) * (-3) * (-3) * (-3) = 81
Therefore, the simplified expression is 1 / 81.