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Nataliya [291]
3 years ago
13

For f(x) = 3x^2 + 2x - 1, identify the rule for g(x) = f(x + 1) - 6 and it's graph.

Mathematics
1 answer:
PilotLPTM [1.2K]3 years ago
4 0

2x2 + x −#6 _____________

x2 − 1

∙ x

__

2 + 2x + 1

x 2 − 4

Rewrite as multiplication.

(2x − 3)(x + 2) __

(x + 1)(x − 1) ∙ (x + 1)(x + 1) __ (x + 2)(x − 2) Factor the numerator and denominator.

(2x − 3)(x + 2)(x + 1)(x + 1) ___ (x + 1)(x − 1)(x + 2)(x − 2) Multiply numerators and denominators.

(2x − 3)(x + 2)(x + 1)(x + 1) ___ (x + 1)(x − 1)(x + 2)(x − 2) Cancel common factors to simplify.

(2x − 3)(x + 1) __ (x − 1)(x − 2)

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Which of the following is an equation of the line that passes through the point (−2, 3) and is perpendicular to the graph of the
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The equation of the line is y=-\frac{1}{3}+\frac{7}{3}

Explanation:

The given equation is y=3 x-2

<u>Slope:</u>

Since, the equation of the line is perpendicular to the equation y=3 x-2, then, the slope is given by

m=-\frac{1}{3}

Hence, the slope is m=-\frac{1}{3}

<u>Equation of the line:</u>

The equation of the line can be determined using the formula,

y-y_1=m(x-x_1)

Substituting the point (-2,3) and the slope m=-\frac{1}{3}, in the above formula, we get,

y-3=-\frac{1}{3}(x+2)

Simplifying, we get,

y-3=-\frac{1}{3}x-\frac{2}{3}

     y=-\frac{1}{3}x-\frac{2}{3}+3

     y=-\frac{1}{3}+\frac{7}{3}

Therefore, the equation of the line is y=-\frac{1}{3}+\frac{7}{3}

8 0
3 years ago
Complete the following sentence. The coefficient of determination between the dependent variable, TEST SCORE, and the independen
amm1812

Answer: a. variation in the variable, HOURS SPENT STUDYING explains 43% of the variation in the variable. TEST SCORE

Step-by-step explanation:

The coefficient of determination is denoted by R square is the proportion of the variance in the dependent variable that is predictable from the independent variable.

Given:  dependent variable = TEST SCORE

independent variable = HOURS SPENT STUDYING

coefficient of determination = 0.43

That means variation in the variable, HOURS SPENT STUDYING explains 43% of the variation in the variable. TEST SCORE.

Hence, the correct option is a.

8 0
3 years ago
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