Mathematics, 24.02.2020 06:44 liltay12386

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Which system of inequalities does the graph represent? Which test point satisfies both of the inequalities in that system?

The graph represents the system of inequalities 1. 4x - y is less than or equal to 4 and 2x - 2y is less than or equal to 3, 2. 4x - y is greater than or equal to 4 and 2x - 2y is less than or equal to 3, 3. 4x - y is less than or equal to 4 and 2x - 2y is greater than or equal to 3, 4. 4x - y is greater than or equal to 4 and 2x - 2y is greater than or equal to 3.

The test point satisfies both of the inequalities in the system represented by the graph.

Select the correct answer from each drop-down menu. Which system of inequalities does the graph repr

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Answer from: rachel2005smith

The graph represents the system of inequalities "4 x - y is less than or equal to 4 and 2 x - 2 y is less than or equal to 3" ⇒ 1.

Step-by-step explanation:

To find the answer let us find the equation of each line

Blue line:

∵ The line passes through points (1 , 0) and (0 , -4)

- Find the slope of the line

∵ m = Δy/Δx

∴ $m=\frac{0--4}{1-0}=\frac{4}{1}$

∴ m = 4

- The form of the equation is y = m x + b, where b is the

y-intercept (value y at x = 0)

∵ y = -4 at x = 0

∴ b = -4

- Write the equation of the line

∴ y = 4 x - 4

∴ The equation of the blue line is y = 4 x - 4

- The shading is above the line and the line is solid, that means

y is greater than or equal 4 x - 4

∴ The inequality of the blue line is y ≥ 4 x - 4

Red line:

∵ The line passes through points (1.5 , 0) and (0 , -1.5)

- Find the slope of the line

∴ $m=\frac{0--1.5}{1.5-0}=\frac{1.5}{1.5}$

∴ m = 1

∵ y = -1.5 at x = 0

∴ b = -1.5

- Write the equation of the line

∴ y = x - 1.5

- Multiply the both sides by 2

∴ The equation of the red line is 2 y = 2 x - 3

- The shading is above the line and the line is solid, that means

y is greater than or equal 2 x - 3

∴ The inequality of the red line is 2 y ≥ 2 x - 3

Let us find which answer is the same with this system of inequalities

First

∵ 4 x - y ≤ 4

- Add y to both sides

∴ 4 x ≤ 4 + y

- Subtract 4 from both sides

∴ 4 x - 4 ≤ y

- That means 4 x - 4 is less than or equal y that means y

is greater than or equal 4 x - 4

∴ y ≥ 4 x - 4 ⇒ same with first inequality above

∵ 2 x - 2 y ≤ 3

- Add 2 y to both sides

∴ 2 x ≤ 3 + 2 y

- Subtract 3 from both sides

∴ 2 x - 3 ≤ 2 y

- That means 2 x - 3 is less than or equal 2 y that means 2 y

is greater than or equal 2 x - 3

∴ 2 y ≥ 2 x - 3 ⇒ same with second inequality above

The graph represents the system of inequalities "4 x - y is less than or equal to 4 and 2 x - 2 y is less than or equal to 3"

Answer from: Quest

Intersecting secant-tangent theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.so to break it down: 1. pq acts as the tangent and ps as the secant with an intersection at p.sr = 21rp = 3x + 3pq = 4x + 4following to equation: tangent squared = the two segments multiplied by each otherso (4x + 4) ^ 2 = (3x + 3) • (21) simplifies to 16x^2 - 31x - 47 = 0 or (16x - 47)(x + 1) x = -1 or x = 47/162. pq acts as the tangent and ps as the secant with an intersection at p (again! )sr = 16rp = xpq = 15(15) ^ 2 = 16 • x225 = 16xx = 225/163. the interesting chords are proportional to each other so a ratio is possible to set up: ap dp 10 3 + x = = —— = pc pb 8 xcross multiple to get 10x = (3 + x)(8)x = 12

Answer from: Quest

The answer is biodiversity resulting from new ancestors.

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