The simplification of the polynomial expression will give 3x² - 20x + 8.
<h3>How to illustrate the polynomial?</h3>
The polynomial expression is given as:
(5x² + 13x4) (17x² + 7x - 19) + (5x-7)(3x + 1)
= 5x² + 13x - 4 - 17x² - 7x + 19 + 15x² + 5x - 21x - 7
Then collect like terms
= 5x² + 15x² - 17x² + (13x - 7x + 5x - 21x) - 4 - 7 + 19
= 3x² - 20x + 8.
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We are given a volume of 160 fluid ounces of chemical which is added to a container that holds 120,000 gallons of water. Assuming that the chemical has the same density as water, we just need to convert 120,000 gallons to ounces.
A conversion factor is taken from literature, 1 gallon is equivalent to 128 fluid ounces. So 160 fluid ounces is only 1.25 gallons, thus occupying minimal space in the container. The employee could add more of the chemical in the container. He can actually add 15360000 fluid ounces in total.
Answer: option 3 is the correct answer
Step-by-step explanation:
Let us look at the various trigonometric ratios
Sin Ф = opposite side/ hypotenuse
Cos Ф = adjacent side / hypotenuse
Tan Ф = opposite side / adjacent side
Therefore, tan Ф = sin Ф / cos Ф
This means that if cos Ф=-8/17 and sin Ф is negative, then the hypotenuse is negative
To determine the adjacent side, we will apply Pythagoras theorem
Hypotenuse ^2 = opposite ^2 + adjacent ^2
-17^2 = 8^2 + adjacent^2
adjacent^2 = 289 - 64 = 225
adjacent = √225 = 15
tan Ф = 8/15
since triangles are similar
4/x = 7x/7
=》 4/x = x
=》x^2 = 4
=》 x = 2
for right triangles a^2 = b^2+c^2
DF^2 = 7^2+2^2 = 53
=》 DF = 7.28
perimeter of DEF = 7 +2+7.28 = 16.28
