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1 answer:
Answer:
The area of the rhombus is 24 units²
Step-by-step explanation:
The area of a rhombus is half the product of the diagonals.
We can easily calculate the length of the diagonals because they are vertical and horizontal line segments.
We use the absolute value approach.
The length of diagonal BD is |7--5|=|7+5|=|12|=12
The length of diagonal AC=|0--4|=|4|=4
Therefore the area of the rhombus is
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Answer:
2) x³ (x² + 1) (x + 1)
3) (x - 6) (x + 6)
6) (x + 3) (x - 4)
8) (5x + 3) (x - 2)
Step-by-step explanation:
I'm providing the solutions for numbers 2, 3, 6, and 8, in order to give you the opportunity to apply and practice the techniques demonstrated here for numbers 9 and 10.
<h3>2) x⁶ + x⁵ + x⁴ + x³ = 0 </h3>
Factor out the highest possible common term, applying the product rule of exponents,
x³ (x³ + x² + x¹ + 1) = 0
Next, apply the special factoring technique into the exponential expressions inside the parenthesis), the factor by grouping:
The factors for the given polynomial are: x³ (x² + 1) (x + 1)
<h3> 3) x² - 36 = 0 </h3>
Use the <u>difference of two squares factoring</u>, where it states: u² - v² = (u - v) (u + v)
Since 36 is a perfect square of 6², then we can establish the following factors using the difference of squares:
Factors: (x - 6) (x + 6).
<h3>6) x² - x - 12 = 0 </h3>
For this quadratic trinomial, find factors that will produce a product of <em>a</em> × <em>c</em> (1 × -12) and sum of b (-1):
The possible factors of -12 that also results to a sum of -1 are:
3 × -4 = -1
Hence, the possible factors of x² - x - 12 = 0 could be (x + 3) (x - 4). Verify whether this is correct by performing the FOIL method:
(x + 3) (x - 4) = x² - 4x + 3x - 12 = x² - x - 12
Therefore, the factors of x² - x - 12 = 0 are: (x + 3) (x - 4).
<h3>8) 5x² - 7x - 6 = 0 </h3>
where a = 5, b = -7, and c = -6
Given this quadratic trinomial, we can use the factoring by grouping, where it states: find the values of u and v such that the product of uv is the same as the product of <em>ac</em>: u × v = a × c, and that the sum of (<em>u</em> + <em>v </em>) is the same as <em>b</em>.
In other words, we must find the factors of u × v that have a product of a × c and a sum of b:
<em>u × v </em>= <em>a × c</em> = 5 × (-6) = -30
u + v = b = -7
The possible factors of -30 are:
-3 × 10 = -30
3 × -10 = -30
Out of these factors, the factors 3 × -10 = -30 will have the same sum as the value of b = -7:
3 + (-10) = -7
Hence, u = 3, v = -10.
Now, we can group the trinomial as follows:
(<em>ax</em>² + <em>ux </em>) + (<em>vx </em>+ <em>c </em>)
(5x² + 3x) + (-10x - 6)
For the last step, factor out the common terms from both groups:
(5x² + 3x) + (-10x - 6)
x (5x + 3) - 2(5x + 3)
Combine common terms together: (5x + 3) and (x - 2)
Therefore, the factors of the given quadratic trinomial are: (5x + 3) (x - 2).
14.08 is correct option
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