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alisha [4.7K]
3 years ago
7

Which answer shows y + 2x < 4x-3

Mathematics
2 answers:
vaieri [72.5K]3 years ago
8 0

y + 2x < 4x - 3     <em>subtract 2x from both sides</em>

y < 2x - 3

y = 2x - 3

for x = 0 → y = 2(0) - 3 = 0 - 3 = -3 → (0, -3)

for x = 2 → y = 2(2) - 3 = 4 - 3 = 1 → (2, 1)

dotted line and shading below a line

lina2011 [118]3 years ago
3 0

Answer with explanation:

The given Inequality is

→y + 2 x < 4 x-3

Subtracting -4 x from both sides

→ y + 2 x - 4 x < 4 x-3-4 x

→ y - 2 x < -3

Dividing both sides by, -1

→ 2 x - y > 3  →→[Used the property of inequality, if , -a > -b, then , a < b , by cancelling negative sign from both sides]

Writing in intercept form

\frac{x}{\frac{3}{2}}+\frac{y}{-3}>1

It cuts the X axis at, (\frac{3}{2},0) and y axis at , (0,-3).

Drawing the graph of Inequality

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aliina [53]

Answer:

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Explanation:

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2 years ago
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Point G is the centroid of the right △ABC with m∠C=90° and m∠B=30°. Find AG if CG=4 ft.
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Answer: \text{Length of AG=}\frac{2\sqrt{63}}{3}

Explanation:  

Please follow the diagram in attachment.  

As we know median from vertex C to hypotenuse is CM  

\therefore CM=\frac{1}{2}AB

We are given length of CG=4  

Median divide by centroid 2:1  

CG:GM=2:1  

Where, CG=4

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\therefore CM=\frac{1}{2}AB\Rightarrow AB=12

In \triangle ABC, \angle C=90^0

Using trigonometry ratio identities  

AC=AB\sin 30^0\Rightarrow AC=6 ft

BC=AB\cos 30^0\Rightarrow BC=6\sqrt{3} ft  

CN=\frac{1}{2}BC\Rightarrow CN=3\sqrt{3} ft

In \triangle CAN, \angle C=90^0  

Using pythagoreous theorem  

AN=\sqrt{6^2+(3\sqrt{3})^2\Rightarrow \sqrt{63}

Length of AG=2/3 AN

\text{Length of AG=}\frac{2\sqrt{63}}{3} ft


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