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xenn [34]
3 years ago
10

(x + 2)(x + 3)(x + 4) can be written in the form x + ax² + bx + c

Mathematics
1 answer:
ELEN [110]3 years ago
5 0

Answer:

a=9, b=26, c=24

Step-by-step explanation:

Let's expand the expression bit by bit.

(x+2)(x+3)=(x)(x)+(x)(3)+(2)(x)+(2)(3)=x^2+5x+6 by FOIL.

We have that (x^2+5x+6)(x+4)=x(x^2+5x+6)+4(x^2+5x+6)=x^3+5x^2+6x+4x^2+20x+24=x^3+9x^2+26x+24.

So, the answer is \boxed{a=9, b=26, c=24}

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y² = x² - z²

Step-by-step explanation:

x² - y² = z²

Transpose y the other side

x² - z² = y²

or

y² = x² - z²

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A car travelled at a<br> constant speedof 40m/s<br> for 4.5 s. Calculate the<br> distance covered
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A waitress sold 11 ribeye steak dinners and 12 grilled salmon​ dinners, totaling ​$560.63 on a particular day. Another day she s
Eduardwww [97]

The cost of each ribeye steak dinner is $ 29 and cost of each grilled salmon dinner is $ 20

<em><u>Solution:</u></em>

Let "a" be the cost of each ribeye steak dinners

Let "b" be the cost of each grilled salmon dinners

<em><u>A waitress sold 11 ribeye steak dinners and 12 grilled salmon​ dinners, totaling ​$560.63 on a particular day</u></em>

Thus we frame a equation as:

11 x cost of each ribeye steak dinners + 12 x cost of each grilled salmon dinners = 560.63

11 \times a + 12 \times b = 560.63

11a + 12b = 560.63 -------- eqn 1

<em><u>Another day she sold 16 ribeye steak dinners and 6 grilled salmon​ dinners, totaling ​$584.46</u></em>

Thus we frame a equation as:

16 x cost of each ribeye steak dinners + 6 x cost of each grilled salmon dinners = 584.46

16 \times a + 6 \times b = 584.46

16a + 6b = 584.46 ------------ eqn 2

<em><u>Let us solve eqn 1 and eqn 2</u></em>

<em><u>Multiply eqn 2 by 2</u></em>

32a + 12b = 1168.92 ------- eqn 3

<em><u>Subtract eqn 1 from eqn 3</u></em>

32a + 12b = 1168.92

11a + 12b = 560.63

( - ) ----------------

21a = 1168.92 - 560.63

21a = 608.29

Divide both sides by 21

a = 28.96 \approx 29

<em><u>Substitute a = 29 in eqn 1</u></em>

11(29) + 12b = 560.63

319 + 12b = 560.63

12b = 560.63 - 319

12b = 214.63

Divide both sides by 12

b = 20.13 \approx 20

Thus cost of each ribeye steak dinner is $ 29 and cost of each grilled salmon dinner is $ 20

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3 years ago
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