help please ! brainliest to first correct answer
What is the solution for x2 –18x < –77?

x < –11 or x > 7
x < –7 or x > 11
–11 < x < 7
7 < x < 11
Question 2(Multiple Choice Worth 2 points)
(07.01 LC)

A two-variable inequality is shown in the graph.

upward opening parabola which is dashed with vertex at 1 comma 2, travels through points negative 1 comma 6 and 3 comma 6, with shading inside the curve

Which point is not included in the solution set for the inequality?

(–1, 3)
(0, 4)
(1, 5)
(2, 4)
Question 3(Multiple Choice Worth 2 points)
(07.01 MC)

Which graph represents the solution of y ≤ x2 + 2?

upward opening parabola formed with a dashed curve, vertex at 0 comma 2, and shading inside parabola
upward opening parabola formed with a dashed curve, vertex at 0 comma 2, and shading outside parabola
upward opening parabola formed with a solid curve, vertex at 0 comma 2, and shading inside parabola
upward opening parabola formed with a solid curve, vertex at 0 comma 2, and shading outside parabola
Question 4(Multiple Choice Worth 2 points)
(07.01 MC)

What is the range of the function f(x) = |x| + 5?

R: {f(x) ∈ ℝ | f(x) < 5}
R: {f(x) ∈ ℝ | f(x) ≥ 5}
R: {f(x) ∈ ℝ | f(x) > 5}
R: {f(x) ∈ ℝ | f(x) ≤ 5}
Question 5(Multiple Choice Worth 2 points)
(07.01 MC)

What is the solution to the inequality |2x + 3| < 7?

4 < x < 10
–5 < x < 2
x < 4 or x > 10
x < –5 or x > 2

Question

gisselleromerolifesu gisselleromerolifesu

25-04-2022
Mathematics

contestada

help please ! brainliest to first correct answer
What is the solution for x2 –18x < –77?

x < –11 or x > 7
x < –7 or x > 11
–11 < x < 7
7 < x < 11
Question 2(Multiple Choice Worth 2 points)
(07.01 LC)

A two-variable inequality is shown in the graph.

upward opening parabola which is dashed with vertex at 1 comma 2, travels through points negative 1 comma 6 and 3 comma 6, with shading inside the curve

Which point is not included in the solution set for the inequality?

(–1, 3)
(0, 4)
(1, 5)
(2, 4)
Question 3(Multiple Choice Worth 2 points)
(07.01 MC)

Which graph represents the solution of y ≤ x2 + 2?

upward opening parabola formed with a dashed curve, vertex at 0 comma 2, and shading inside parabola
upward opening parabola formed with a dashed curve, vertex at 0 comma 2, and shading outside parabola
upward opening parabola formed with a solid curve, vertex at 0 comma 2, and shading inside parabola
upward opening parabola formed with a solid curve, vertex at 0 comma 2, and shading outside parabola
Question 4(Multiple Choice Worth 2 points)
(07.01 MC)

What is the range of the function f(x) = |x| + 5?

R: {f(x) ∈ ℝ | f(x) < 5}
R: {f(x) ∈ ℝ | f(x) ≥ 5}
R: {f(x) ∈ ℝ | f(x) > 5}
R: {f(x) ∈ ℝ | f(x) ≤ 5}
Question 5(Multiple Choice Worth 2 points)
(07.01 MC)

What is the solution to the inequality |2x + 3| < 7?

4 < x < 10
–5 < x < 2
x < 4 or x > 10
x < –5 or x > 2

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MrRoyal MrRoyal · Answer 1 · 2022-05-05T18:47:20+02:00

The questions are illustrations of inequalities

The solution to the inequality is 7 < x < 11
The range of the function is (c) R: {f(x) ∈ ℝ | f(x) > 5}
The solution to the inequality is x < –5 or x > 2

The solution to the inequality

The inequality is given as:

x² - 18x < -77

Add 77 to both sides

x² - 18x + 77 < 0

Expand the inequality

x² - 7x - 11x + 77 < 0

Factorize the inequality

x(x - 7) - 11(x - 7) < 0

Factor out x - 7

(x- 7)(x - 11) < 0

Solve for x

x < 7 or x < 11

This means that the solution to the inequality is 7 < x < 11

The graph that represents the solution

The inequality expression is given as:

y ≤ x² + 2

See attachment for the graph of the inequality

The range of the function

The function is given as:

f(x) = |x| + 5

The smallest value of |x| is 0.

So, we have:

f(x) > 0 + 5

Evaluate

f(x) > 5

Hence, the range of the function is (c) R: {f(x) ∈ ℝ | f(x) > 5}

The solution to the inequality

The inequality expression is given as:

|2x + 3| < 7

Remove the absolute expression

2x + 3 < 7 or 2x + 3 < -7

Subtract 3 from both sides

2x < 4 or 2x < -10

Divide both sides by 2

x < 2 or x < -5

Hence, the solution to the inequality is x < –5 or x > 2