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IceJOKER [234]
3 years ago
10

In parallelogram ABCD, LA = 120°. What is AD? O80° O 120° O60°

Mathematics
1 answer:
erastovalidia [21]3 years ago
3 0
Angle D is 60° because it is a supplementary angle, meaning 180 (straight line) - 120 (angle A) = 60°
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Quadratic form of f(x)=(x+7)^2
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Step-by-step explanation:

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(x + 7)(x + 7) = x^2 + 7x + 7x + 49 = x^2 + 14x + 49

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Y * x = 20<br><br> y + x = 9 <br><br> what numbers are y and x equal to?
Ksivusya [100]

y = 9 - x
Substitute into
y \times x = 20 \\ (9 - x) \times x = 20 \\  { - x}^{2}  + 9x = 20 \\  {x}^{2}  - 9x  + 20 = 0 \\ (x - 5)(x -4) = 0 \\  x = 5 \: or \: x = 4
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Hope this helps. - M
4 0
3 years ago
❊ Simplify :
DiKsa [7]

Answer:

See Below.

Step-by-step explanation:

Problem 1)

We want to simplify:

\displaystyle \frac{a+2}{a^2+a-2}+\frac{3}{a^2-1}

First, let's factor the denominators of each term. For the second term, we can use the difference of two squares. Hence:

\displaystyle =\frac{a+2}{(a+2)(a-1)}+\frac{3}{(a+1)(a-1)}

Now, create a common denominator. To do this, we can multiply the first term by (<em>a</em> + 1) and the second term by (<em>a</em> + 2). Hence:

\displaystyle =\frac{(a+2)(a+1)}{(a+2)(a-1)(a+1)}+\frac{3(a+2)}{(a+2)(a-1)(a+1)}

Add the fractions:

\displaystyle =\frac{(a+2)(a+1)+3(a+2)}{(a+2)(a-1)(a+1)}

Factor:

\displaystyle =\frac{(a+2)((a+1)+3)}{(a+2)(a-1)(a+1)}

Simplify:

\displaystyle =\frac{a+4}{(a-1)(a+1)}

We can expand. Therefore:

\displaystyle =\frac{a+4}{a^2-1}

Problem 2)

We want to simplify:

\displaystyle \frac{1}{(a-b)(b-c)}+\frac{1}{(c-b)(a-c)}

Again, let's create a common denominator. First, let's factor out a negative from the second term:

\displaystyle \begin{aligned} \displaystyle &= \frac{1}{(a-b)(b-c)}+\frac{1}{(-(b-c))(a-c)}\\\\&=\displaystyle \frac{1}{(a-b)(b-c)}-\frac{1}{(b-c)(a-c)}\\\end{aligned}

Now to create a common denominator, we can multiply the first term by (<em>a</em> - <em>c</em>) and the second term by (<em>a</em> - <em>b</em>). Hence:

\displaystyle =\frac{(a-c)}{(a-b)(b-c)(a-c)}-\frac{(a-b)}{(a-b)(b-c)(a-c)}

Subtract the fractions:

\displaystyle =\frac{(a-c)-(a-b)}{(a-b)(b-c)(a-c)}

Distribute and simplify:

\displaystyle =\frac{a-c-a+b}{(a-b)(b-c)(a-c)}=\frac{b-c}{(a-b)(b-c)(a-c)}

Cancel. Hence:

\displaystyle =\frac{1}{(a-b)(a-c)}

4 0
3 years ago
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