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3 years ago

11

Ramp 10 feet high and 32 long

2 answers:

madam [21]3 years ago

8 0

A. IMA = 32/10 = 3.2

harkovskaia [24]3 years ago

8 0

we would solve this by using the equation: LMA=L/H

now, we have to plug in the numbers LMA= 32/10

LMA= 3.2

so, the answer is 3.2

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Which of the following is the correct factorization of the trinomial below? -7x^2-5x+18

ryzh [129]

Answer: C. (-7x+9)(x-2)

Step-by-step explanation:

1. Factor out the negative sign.

−(7x^2+5x−18)

2. Split the second term in 7x2+5x−18 into two terms.

−(7x^2+14x−9x−18)

3, Factor out common terms in the first two terms, then in the last two terms.

−(7x(x+2)−9(x+2))

4. Factor out the common term x+2x+2x+2.

−(x+2)(7x−9) or (-7x+9)(x-2)

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2 years ago

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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:

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

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2 years ago

What are the opposites of 5, −2.6, 2.25, and 7 1 4 ? Enter the answers in respective order, each separated by comma.

arsen [322]

-5, 2.6, -2.25,and -714

7 0

2 years ago

Plz help me with these I wanna be done with my homework lol

yaroslaw [1]

3. $69.60
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3 years ago

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Help plz! Which equation is shown in the graph above?

harina [27]

Answer:

The answer is C

Step-by-step explanation:

If you count the rise over un to calculate your slope, which in this case it is drop 2 and to the right 3, that gives you the slope of -2/3

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3 years ago

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