Multiply both sides by 5 to go from this
x/5 >= -2
to this
x >= -10
The notation ">=" without quotes means "greater than or equal to"
To graph this, plot -10 on the number line as a closed circle. Shade to the right of this closed circle. The shaded region represents all the solutions to the original inequality.
Final Answer: Choice D
Answer:
a reflection over the y-axis, then a dilation by a scale factor of 1.5
Step-by-step explanation:
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Answer:
Step-by-step explanation:
Give the equation 5x² + 27x = 14 − 13x, we are to write the steps needed to solve for x using the completing the square method.
Step 1: Rewrite the equation in a quadratic form by first adding 13x to both sides of the equation.
5x² + 27x +13x= 14 − 13x+13x
5x² + 40x = 14
Step 2: factor out the common constant in the left hand side of the equation.
5(x²+8x) = 14
Step3: The next step to take is to divide through by the the value of 5 to have;
5(x²+8x)/5 = 14/5
x²+8x = 14/5
Step 4: complete the square of the equation at the left hand side by adding the square of half of the coefficient of x to both sides i.e {1/2(8)}² which is 4²
x²+8x +4² = 14/5+4²
x²+8x +16 = 14/5+16
(x+4)² = 94/5
Step 5: Taking the square root of both sides
√(x+4)² = ±√94/5
x+4 = ±√94/5
Step 6: subtract 4 from both sides
x+4-4 = ±√94/5 - 4
x = ±√94/5 - 4
Hence the solution to the equation using completing the square method is x = -4±√94/5
