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3 years ago

11

Can anyone simplify this equation? 8^2+9(12÷3×2)- 7

1 answer:

Vinvika [58]3 years ago

6 0

Answer:129

Step-by-step explanation:

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What 34 divided by 20196

Komok [63]

Answer:

0.00168350168

4 0

3 years ago

Find three positive numbers whose sum is 140 and whose product is a maximum. (Enter your answers as a comma-separated list.)

Paladinen [302]

Answer:

$\frac{140}{3}, \frac{140}{3}, \frac{140}{3}$

Step-by-step explanation:

Let the numbers be $x, y\ and\ z.$

Such that:

$x + y + z = 140$

Make z the subject

$z = 140 -x - y$

For their product to be maximum, we have:

$f(x,y,z) = xyz$

Substitute $z = 140 -x - y$ in $f(x,y,z) = xyz$

$f(x,y) = xy(140 - x - y)$

Open bracket

$f(x,y) = 140xy - x^2y - xy^2$

Differentiate w.r.t x and y

$f_x=140y - 2xy - y^2$

$f_y=140x - x^2 - 2xy$

Since the products are maximum, then $f_x = f_y = 0$

For $f_x=140y - 2xy - y^2$

$140y - 2xy - y^2 = 0$

Factorize:

$y(140 - 2x - y) = 0$

Split

$y = 0\ or\ 140 - 2x - y = 0$

Make y the subject

$y = 0\ or\ y = 140 - 2x$

For $f_y=140x - x^2 - 2xy$

$140x - x^2 - 2xy = 0$

---------------------------------------------------

Substitute y = 0

$140x - x^2 -2x*0 = 0$

$140x - x^2 = 0$

Factorize

$x(140 - x)= 0$

$x = 0\ or\ 140-x = 0$

$x = 0\ or\ x = 140$

---------------------------------------------------

Substitute $y = 140 - 2x$

$140x - x^2 - 2xy = 0$

$140x - x^2 - 2x(140 - 2x) = 0$

$140x - x^2 - 280x + 4x^2 = 0$

Re-arrange

$4x^2 -x^2 +140x - 280x = 0$

$3x^2 -140x = 0$

Factor x out

$x(3x - 140) = 0$

Divide through by x

$3x - 140 = 0$

$3x = 140$

$x = \frac{140}{3}$

Recall that: $y = 140 - 2x$

$y = 140 - 2 * \frac{140}{3}$

$y = 140 - \frac{280}{3}$

Take LCM

$y = \frac{140*3-280}{3}$

$y = \frac{140}{3}$

Recall that:

$z = 140 -x - y$

$z = 140 - \frac{140}{3} - \frac{140}{3}$

Take LCM

$z = \frac{3 * 140- 140 - 140}{3}$

$z = \frac{140}{3}$

Hence, the numbers are:

$\frac{140}{3}, \frac{140}{3}, \frac{140}{3}$

8 0

3 years ago

If x-3 is a factor of x3+4x2+kx-30.Find the value of k.

Bogdan [553]

Answer:

k=-11

Step-by-step explanation:

$x^{3}+4x^{2}+kx-30$

if $x-3$ is a factor,

$(3)^{3}+4(3)^{2}+k(3)-30=0\\27+4*9+3k-30=0\\27+36+3k-30=0\\33+3k=0\\3k=-33\\k=-11$

3 0

3 years ago

Simplify (n+3)(n-9)

Katarina [22]

From multiplying the binomial expression

(n+3)(n-9)

It would be n^2 - 9n + 3n - 27 or simplified

n^2 -6n - 27.

6 0

4 years ago

Suppose the path of a baseball follows the path graphed by the quadratic function ƒ(d) = –0.6d2 + 5.4d + 0.8 where d is the hori

Vinil7 [7]

Answer:

Domain is all real numbers

Range is

$y\le 12.95$

Step-by-step explanation:

The given function is

$f(d)=-0.6d^2+5.4d+0.8$

This is a maximum quadratic function therefore the domain is all real numbers.

Let us complete the square to find the vertex.

$f(d)=-0.6(d^2-9d)+0.8$

$f(d)=-0.6(d^2+9d)+-0.6(\frac{9}{2})^2- -0.6(\frac{9}{2})^2+ 0.8$

$f(d)=-0.6(d-\frac{9}{2})^2+\frac{243}{20}+ 0.8$

$f(d)=-0.6(d-\frac{9}{2})^2+\frac{259}{20}$

Therefore the range is

$y\le \frac{259}{20}$

$y\le 12.95$

See graph

5 0

3 years ago

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