Ten points to the correct answer

Mathematics

2 answers:

ale4655 [162]2 years ago

8 0

This should be the correct answer.

Rama09 [41]2 years ago

4 0

The blue line has a slope of 1 and a y-intercept at 0. In slope intercept form, this equation is y = x. The line is solid and not dashed. This means the inequality could include numbers ON the line itself. The shading is on the left side of the line so it's a greater than equation.

The blue inequality is y ≥ x.

The red line has a slope of 0 and a y-intercept at 6. Slope-intercept form: y = 6 The line is solid and not dashed meaning numbers on the line are again included. The shading is below the horizontal line created so it is a less than inequality.

The red inequality is y ≤ 6

Your system of linear inequalities would be:

y ≥ x

y ≤ 6

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Rzqust [24]

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2 years ago

Determine the domain of the function f(x)=1/3x^2+10x+8

cricket20 [7]

The function is
f(x) = (1/3)x² + 10x + 8

Write the function in standard form for a parabola.
f(x) = (1/3)[x² + 30x] + 8
= (1/3)[ (x+15)²- 225] + 8
= (1/3)(x+15)² -75 + 8
f(x) = (1/3)(x+15)² - 67

This is a parabola with vertex at (-15, -67).
The axis of symmetry is x = -15
The curve opens upward because the coefficient of x² is positive.
As x -> - ∞, f -> +∞.
As x -> +∞, f -> +∞
The domain is all real values of x (see the graph below).

Answer: The domain is (-∞, ∞)