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Zolol [24]
3 years ago
10

Look at the system of equations below.

Mathematics
1 answer:
Paul [167]3 years ago
7 0

Answer:

\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}

x=2,\:y=-1

Step-by-step explanation:

Considering the system of the equation

\begin{bmatrix}y=-2x+3\\ 4x-3y=11\end{bmatrix}

\mathrm{Subsititute\:}y=-2x+3

\begin{bmatrix}4x-3\left(-2x+3\right)=11\end{bmatrix}

\mathrm{Isolate}\:x\:\mathrm{for}\:4x-3\left(-2x+3\right)=11

4x-3\left(-2x+3\right)=11

4x+6x-9=11

10x-9=11

10x-9+9=11+9

10x=20

x=2

\mathrm{For\:}y=-2x+3

\mathrm{Subsititute\:}x=2

y=-2\cdot \:2+3

y=-1

\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}

x=2,\:y=-1

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Which of these four sets of side lengths will form a right triangle? Set 1 4 cm, 5 cm, 6 cm Set 2 8 in., 12 in., 20 in. Set 3 10
Alenkasestr [34]

Answer:  The correct option is (D) SET 4.

Step-by-step explanation:  We are to select the correct set of side lengths that will form a right-angled triangle.

To form a right-angled triangle, we must have the following relation:

<em>Perpendicular² + Base² = Hypotenuse².</em>

<em>Hypotenuse is the length of the largest side; perpendicular and base are the two legs of the triangle.</em>

SET 1 :  14 cm, 5 cm, 6 cm.  

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Therefore,

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So, this set will not form a right-angled triangle.

SET 2 :  8 in., 12 in., 20 in.  

We have

8^2+12^2=64+144=208,\\\\20^2=400.

Therefore,

<em>Perpendicular² + Base² ≠ Hypotenuse².</em>

So, this set will not form a right-angled triangle.

SET 3 :  10 mm, 20 mm, 30 mm.  

We have

10^2+20^2=100+400=500,\\\\30^2=900.

Therefore,

<em>Perpendicular² + Base² ≠ Hypotenuse².</em>

So, this set will not form a right-angled triangle.

SET 4 :  12 ft, 16 ft, 20 ft.  

We have

12^2+16^2=144+256=400,\\\\20^2=400.

Therefore,

<em>Perpendicular² + Base² = Hypotenuse².</em>

So, this set will form a right-angled triangle.

Thus, the SET 4 will form a right-angles triangle.

Option (D) is correct.

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In a group of 25 students, 6 study both Art and Biology. 10 study Biology but not Art. 3 study neither subject. Given that a ran
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Answer:

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Step-by-step explanation:

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6/12 = 1/2  

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