4x² - 16 is the algebraic expression that must be added to get the result as 9x²- 2x - 5.
<u>Step-by-step explanation:</u>
The question is asked for the algebraic expression must be added to the sum of 3x²+4x+8 and 2x2−6x+3 to give 9x²- 2x - 5 as the result.
Therefore,
The first step is to find of sum of 3x²+4x+8 and 2x²-6x+3.
To find the sum :
3x²+4x+8
<u>2x²-6x+3 </u>
<u>5x²-2x+11</u>
The sum is 5x²-2x+11.
Now, the second step is to subtract 5x²-2x+11 from the result 9x²- 2x - 5.
9x²- 2x - 5
- <u>(5x²-2x+11)</u>
<u> 4x² -16 </u>
Thus, 4x²-16 is the algebraic expression that must be added with 5x²-2x+11 to get a result of 9x²- 2x - 5.
The trial and error method is used to find an initial factor:
If we let f(x) = x³ - x² - 24x - 36 and all we have to do is sub' in values of x until
f(x) = 0, we can use this to find an initial factor by the factor theorem:
f(1) = (1)³ - (1)² - 24(1) - 36 = -60
f(2) = (2)³ - (2)² - 24(2) - 36 = -80
f(5) = (5)³ - (5)² - 24(5) - 36 = -56
*** f(6) = (6)³ - (6)² - 24(6) - 36 = 0 ***
f(6) = 0 so (x - 6) is a factor of f(x).
This means that: f(x) = x³ - x² - 24x - 36 = (x - 6)(ax² + bx + c).
To find a,b and c, use long division (or inspection) to divide x³ - x² - 24x - 36 by x - 6.
The other 2 factors of f(x) can then be found by factorizing the
ax² + bx + c quadratic the way you would with any other quadratic (i.e. by quadratic formula, CTS or inspection).
<h3><u>The length is equal to 13.</u></h3><h3><u>The width is equal to 8.</u></h3>
l = 2w - 3
2l + 2w = 42
Because we have a value for l, we can plug it into the second equation to solve for w.
2(2w - 3) + 2w = 42
Distributive property.
4w - 6 + 2w = 42
Combine like terms.
6w - 6 = 42
Add 6 to both sides.
6w = 48
Divide both sides by 6.
w = 8
Now that we have a value for w, we can solve for the exact value of l.
l = 2(8) - 3
l = 16 - 3
l = 13
The probability that pitcher will throw no more than 16 strikes is 0.1938.
Answer:
140 cm²
Step-by-step explanation:
The height of the parallelogram is 10cm . And its base is 14cm .We know that the area of parallelogram is product of base and height .
⇒ Area = base × Height
⇒ Area = 14cm × 10cm
⇒ Area = 140 cm² .
<h3>
<u>Hence </u><u>the</u><u> </u><u>area </u><u>of</u><u> the</u><u> </u><u>parall</u><u>elogram</u><u> is</u><u> </u><u>1</u><u>4</u><u>0</u><u> </u><u>cm²</u><u> </u><u>.</u></h3>
