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4 years ago

6

Find the number that must be added to each expression to form a perfect square trinomial. Then write the trinomial as a binomial

squared.
x^2-24x+____

( )^2

2 answers:

Korvikt [17]4 years ago

8 0

Answer:

-12 is number that is when added to given expression to form perfect square.

Step-by-step explanation:

Given expression is :

x²-24x + _____

We have to make above expression complete square.

We use following formula to complete this question.

a²+2ab+b² = (a+b)²

Comparing given expression to above formula ,we get

a² = x² ⇒ a = x

2ab = -24x

2ab = 2(x)(-12)

hence, the value of b is -12.

Putting the value of b in above formula,we get

(x)²+2(x)(-12)+(-12)² = x²-24x+144

(x-12)² = x²-24x+144

Hence, the trinomial x²-24x+144 is square of binomial (x-12).

uysha [10]4 years ago

6 0

Answer:

Thus, when 144 is added to the given expression $x^2-24x+144$ to form a perfect square trinomial of $(x-12)^2$

Step-by-step explanation:

We are given an expression $x^2-24x+\_\_$

We have find the number such that expression form a perfect square trinomial.

Using identity $(a-b)^2=a^2+b^2-2ab$

Comparing the above identity with the given expression,

We get $a^2=x^2 \rightarrow a=x$ and $-2ab=-24x$

$-2ab=-24x \Rightarrow ab=12x$

Thus, b = 12

and $b^{2}=144$

Thus, when 144 is added to the given expression $x^2-24x+144$ to form a perfect square trinomial of $(x-12)^2$

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1 year ago

PLEASE HELP ASAP!!!!! Leo drew a line that is perpendicular to the line shown on the grid and passes through point (F, G). Which

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Step-by-step explanation:

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4 years ago

A right rectangular prism has length 3 and one third yd, width 2 and one third yd, and height 1 and one third yd. You use cube

Levart [38]

Answer:

Volume of the rectangular prism = 280 cubes

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Step-by-step explanation:

length 3 and one third yd = 3 + (1/3) yd = (10/3) yd

width 2 and one third yd = 2 + (1/3) yd = (7/3) yd

height 1 and one third yd = 1 + (1/3) yd = (4/3) yd

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Or

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5 0

3 years ago

Where does the helix r(t) = cos(πt), sin(πt), t intersect the paraboloid z = x2 + y2? (x, y, z) = What is the angle of intersect

Colt1911 [192]

Answer:

Intersection at (-1, 0, 1).

Angle 0.6 radians

Step-by-step explanation:

The helix r(t) = (cos(πt), sin(πt), t) intersects the paraboloid

z = x2 + y2 when the coordinates (x,y,z)=(cos(πt), sin(πt), t) of the helix satisfy the equation of the paraboloid. That is, when

$\bf (cos(\pi t), sin(\pi t), t)$

But

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so, the helix intersects the paraboloid when t=1. This is the point

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The <em>tangent vector</em> to the helix in t=1 is

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r'(t) = (-πsin(πt), πcos(πt), 1), hence

r'(1) = (0, -π, 1)

A normal vector to the tangent plane of the surface

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$\bf (\frac{\partial f}{\partial x}(-1,0),\frac{\partial f}{\partial y}(-1,0),-1)$

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$\bf f(x,y)=x^2+y^2$

since

$\bf \frac{\partial f}{\partial x}=2x,\;\frac{\partial f}{\partial y}=2y$

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(-2,0,-1)

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$\bf (0,-\pi,1)-((0,-\pi,1)\bullet(-2,0,-1))(-2,0,1)=(0,-\pi,1)-(-2,0,1)=(2,-\pi,0)$

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where

$\bf \theta$ = angle between the tangent vector and its projection onto the tangent plane. So

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and

$\bf \theta=arccos(0.8038)=0.6371\;radians$

7 0

3 years ago