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kirza4 [7]
3 years ago
11

Explain the steps necessary for solving the following equation. x^2-8x-20=0

Mathematics
2 answers:
kirza4 [7]3 years ago
8 0
First factor the equation
(x-10)(x+2) = 0
Then solve for (x-10) and (x+2)
x=10
x=-2
hodyreva [135]3 years ago
3 0
 (warning: this is quite long :P)
the steps are:

Looking at the expression x² +8x-20,we can see that the first coefficient is 1, the second coefficient is 8 and the last term is -20.
Now multiply the first coefficient (1) by the last term (-20) to get  (1)·(-20)=-20.
Now the question is: what two whole numbers multiply to -20 (the previous product).
factors of -20:
1,2,4,5,10,20
-1, -2, -4, -5, -10, -20
note: list the negative of each factor. This will allow us to find all possible combinations.
These factors pair up to multiply to -20.
1*(-20) = -20
2*(-10) = -20
4*(-5) = -20
(-1)*(20*) = -20
(-2)*(10* = -20
(-4)*(5) = -20
now let's add up each pair of factors to see if one pair adds to the middle coefficient:

first number        second number      sum

     1                           -20              1+(-20)=-19
   2                            -10              2+(-10)=-9
   4                            -5                4+(-5)= -1
 -1                            20                -1 +20= 19
 -2                              10              -2+10=8
  -4                            5                  -4+5=1

From the table above, we can see that the two numbers -2 and 10 multipy to -20 and add up to 8.
Now replace the middle term 8x with -2x+10x. Remember, -2 and 10 add up to 8. so this shows us that -2x+10x=8x.

x²+-2x+10x -20 Replace the second term 8x with -2x +10x.
(x²-2x)+(10x-20) Group the terms into two pairs.
x(x-2x)+(10x-20) Factor out the GCF x from the first group.

x(x-2)+10·(x-2) Factor out 10 from the second group. The goal of this step is to make the terms in the second parenthesis equal to the terms in the first parenthesis.

(x+10)·(x-2) Combine like terms. Or factor out thge common term x-2.
-----
ANSWER:

So, x² + 8·x -20 factors to (x+20)·(x-2.
In other words, x² + 8·x-20=(x+10)·(x-2)

THIS IS HARD TO UNDERSTAND, BUT HOPE THIS HELPED YOU! AND HOPE YOU GET IT TOO!!!
:D

Hope it helps :)


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RUDIKE [14]

Answer:

15.

\left\{\begin{array}{l}x+y=50\\0.2x+0.1y=6\end{array}\right.

16. 10 ml of 20% saline and 40 ml of 10% saline

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A chemist takes x ml of 20% saline and y ml of 10% saline. In total, he takes

x + y ml that is 50 ml, so

x + y = 50.

There are  0.2x ml of salt in x ml of 20% saline and 0.1y ml of salt in 10% saline. There are 0.12\cdot 50=6 ml of salt in 50 ml of 12% saline. Thus,

0.2x+0.1y=6

15. We get the system of two equations:

\left\{\begin{array}{l}x+y=50\\0.2x+0.1y=6\end{array}\right.

16. Solve this system. From the first equation:

x=50-y

Substitute it into the second equation:

0.2(50-y)+0.1y=6\\ \\10-0.2y+0.1y=6\\ \\-0.1y=6-10\\ \\-0.1y=-4\\ \\y=40\\ \\x=50-y=50-40=10

7 0
2 years ago
Karen bought a handbag for $55. Agnes spent 1.5 times as much on hers. How much did Agnes spend?
Rus_ich [418]
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elixir [45]

Answer:

D. 314 yds

Step-by-step explanation:

Given:

Diameter = 100 yds

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Circumference of circle = πd

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Circumference = π × 100

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2 years ago
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natulia [17]

Answer:

diagonal = = 12.8 inches (to the nearest tenth of an inch)

Step-by-step explanation:

As shown in the diagram attached to this solution:

Let the Length of the rectangular board = a

Let the width = b

Let the diagonal = d

where:

a = 10 inches

b = 8 inches

d = ?

Triangle ABC in the diagram is a right-angled triangle, therefore, applying Pythagoras theorem:

(hypotenuse)² = (Adjacent)² + (Opposite)²

d² = 10² + 8²

d² = 100 + 64

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∴ d = √(164)

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