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4 years ago

Use the distributive property to simplify the expression. [a-4{2a-3(a-2)}]

Mathematics

2 answers:

bekas [8.4K]4 years ago

4 0

A-8a+12-3a+6
The answer is 11a+18

UkoKoshka [18]4 years ago

3 0

For this expression your answer should be 2a +10.

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Y = −5x + 3 slope = −5 −3 5

Aleks04 [339]

First ypu solve the yintercept amd then the x intercept

8 0

4 years ago

Six more than a number cubed.

weeeeeb [17]

n^3 + 6

I'll make n stand for the number

Six more means adding extra 6 onto our number cubed.

So, n x n x n = n^3

(n^3 means n cubed)

Thus, answer is n^3 + 6

Hope this helps!

5 0

2 years ago

Help with 2 questions please.

Y_Kistochka [10]

The first one is C or -6,4

7 0

3 years ago

Read 2 more answers

Consider the paraboloid z=x2+y2. The plane 8x−5y+z−2=0 cuts the paraboloid, its intersection being a curve. Find "the natural" p

Jet001 [13]

Answer:

The parametrization of the curve on the surface is

$c(t) = [x(t) , y(t), z(t)] \equiv [\frac{\sqrt{97} }{2} cost - 4 , \frac{\sqrt{97} }{2} sint + \frac{5}{2} , 5\frac{\sqrt{97} }{2} sint -8 \frac{\sqrt{97} }{2} cost +\frac{93}{2} ]$

Where

$x = \frac{\sqrt{97} }{2} cost - 4$

$y = \frac{\sqrt{97} }{2} sint + \frac{5}{2}$

$z = 5\frac{\sqrt{97} }{2} sint -8 \frac{\sqrt{97} }{2} cost +\frac{93}{2}$

Step-by-step explanation:

From the question we are told that

The equation for the paraboloid is $z = x^2 + y^2$

The equation of the plane is $8x - 5y + z -2 = 0$

Form the equation of the plane we have that

$z = 5y -8x +2$

$x^2 + y^2 = 5y -8x +2$

=> $x^2 + 8x + y^2 -5y = 2$

Using completing the square method to evaluate the quadratic equation we have

$(x + 4)^2 + (y - \frac{5}{2} )^2 = 2 +(\frac{5}{2} )^2 + 4^2$

$(x + 4)^2 + (y - \frac{5}{2} )^2 = \frac{97}{4}$

$(x + 4)^2 + (y - \frac{5}{2} )^2 = ( \frac{\sqrt{97} }{2} )^2$

representing the above equation in parametric form

$(x + 4) = \frac{\sqrt{97} }{2} cost$ , $(y -\frac{5}{2} ) = \frac{\sqrt{97} }{2} sin t$

$x = \frac{\sqrt{97} }{2} cost - 4$

$y = \frac{\sqrt{97} }{2} sint + \frac{5}{2}$

So from $z = 5y -8x +2$

$z = 5[\frac{\sqrt{97} }{2} sint + \frac{5}{2}] -8[ \frac{\sqrt{97} }{2} cost - 4] +2$

$z = 5\frac{\sqrt{97} }{2} sint + \frac{25}{2} -8 \frac{\sqrt{97} }{2} cost + 32 +2$

$z = 5\frac{\sqrt{97} }{2} sint -8 \frac{\sqrt{97} }{2} cost +\frac{93}{2}$

Generally the parametrization of the curve on the surface is mathematically represented as

$c(t) = [x(t) , y(t), z(t)] \equiv [\frac{\sqrt{97} }{2} cost - 4 , \frac{\sqrt{97} }{2} sint + \frac{5}{2} , 5\frac{\sqrt{97} }{2} sint -8 \frac{\sqrt{97} }{2} cost +\frac{93}{2} ]$

3 0

4 years ago

20 points please help! 7(14-x)=3x+18

Illusion [34]

98-7x=3x+18. -7x-3x=-98+18. -10x=-70. X=7.

6 0

4 years ago