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Katarina [22]
3 years ago
13

Least value of expression x^2+4y^2+3z^2-4x-20y-12z+45 is.?

Mathematics
1 answer:
Korvikt [17]3 years ago
7 0
Hello,

4 is the least value.

Indeed:
x²-4x+4=(x-2)²
4y²-20y+25=(2y-5)²
3(z²-4z+4)=3(z-2)²

x²+4y²+3z²-4x-20y-12z+45= (x-2)²+(2y-5)²+3(z-2)²+45-4-25-12
=(x-2)²+(2y-5)²+3(z-2)²+4

Minimum is 4 when  x=2,y=5/2 and z=2 for square is always positive.

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elixir [45]

Answer:

The equation for the line of reflection will be x = y.

Step-by-step explanation:

On a coordinate plane, triangle Δ ABC has points (6, 3.7), (5.4, 2), (1, 3). Triangle Δ A'B'C' has points (3.7, 6), (2, 5.4), (3, 1).

And we have to find the equation of the line of reflection of the points.

Now, it is clear from the coordinates of vertices of Δ ABC and Δ A'B'C' that after reflection the x and y-values of the respective coordinates interchange and there is no change in signs.

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3 years ago
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Find the values of x, y, and z. The diagram is not to scale.
rosijanka [135]

Answer:

x= 81°, z= 99°, y°=68°

Step-by-step explanation:

considering the part of the triangle where 36° , 63° and x° is located as ΔABC.

to find the measure of x we use angle sum property.

We know that the sum of the angles of a triangle is always 180°. Therefore, if we know the two angles of a triangle, and we need to find its third angle, we use the angle sum property. We add the two known angles and subtract their sum from 180° to get the measure of the third angle.

so,

∠A + ∠B +∠C = 180°

36° + 63° + x° = 180°

99° + x° = 180°

x° = 180 - 99

x° = 81°

When two lines intersect each other at a single point, linear pairs of angles are formed. If the angles so formed are adjacent to each other after the intersection of the two lines, the angles are said to be linear. If two angles form a linear pair, the angles are supplementary, whose measures add up to 180°.

x° + z° = 180°

81° + z = 180°

z= 180 - 81

z= 99°

considering the next part of the triangle where 13° , z° and y° is located as ΔACD

to find the measure of y we use angle sum property.

∠A + ∠C + ∠D = 180°

13° + z° + y° = 180°

13°+99°+y°= 180°

112°+ y° = 180°

y°= 180- 112

y° = 68°

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2 years ago
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Answer:

0.253

Step-by-step explanation:

since it is greater than 0.243

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mihalych1998 [28]

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is it 8 apples to her mother or 10 since I had this exact problem?

Step-by-step explanation:

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Mary Grace has 3 more Jolly Ranchers than Isabella. If Isabella has 10 Jolly Ranchers, how many do they have total?
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Step-by-step explanation:

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Then if you add 13+10=23

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