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Answer:
a) yes; 12/15/17 ~ 20/25/x; SAS
b) x = 28 1/3
Step-by-step explanation:
The left-side segments are in the ratio ...
top : bottom = 12 : 8 = 3 : 2
The right side segments are in the ratio ...
top : bottom = 15 : 10 = 3 : 2
These are the same ratio, and the angle at the peak is the same in both triangles, so the triangles are similar by the SAS postulate.
Normally, a similarity statement would identify the triangles by the labels on their vertices. Here, there are no such labels, so we choose to write the statement in terms of the side lengths, shortest to longest:
12/15/17 ~ 20/25/x
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The sides of similar triangles are proportional, so the ratio of longest to shortest sides will be the same in the two triangles. In the smaller triangle, the longest side is 17/12 times the length of the shortest side. The value of x will be 17/12 times the length of the shortest side in the larger triangle:
x = 17/12 · 20 = 340/12
x = 28 1/3
The gradient of the tangent to the curve y = 5x³ + 3x² - x + 4 is 15x²+6x-1.
<h3>What is the gradient?</h3>
A differential operator is used for a function having a vector value in three dimensions to produce a vector whose three components are the partial derivatives of the function with respect to its three variables.
The given equation for the curve is;
y = 5x³ + 3x² - x + 4
The gradient of the tangent to the curve is;
Hence,the gradient of the tangent to the curve y = 5x³ + 3x² - x + 4 is 15x²+6x-1.
To learn more about the gradient refer to;
brainly.com/question/13020257
#SPJ1
4.5 cubic feet is the answer
