<h3>Answer: Choice B) 8.57</h3>
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Explanation:
The triangles are similar through the AA (angle angle) similarity rule. Note how the angle markers correspond and match up. Example: angle C and angle F both have triple angle markers to indicate these angles are congruent.
The corresponding sides pair up to form equal fractions. AB and DE form AB/DE which is equal to AC/DF, as these two sides correspond as well.
Therefore: AB/DE = AC/DF
Let's plug in the given values and isolate x
AB/DE = AC/DF
11/7 = (15+x)/15 ...... substitution
11*15 = 7*(15+x) ....... cross multiply
11*15 = 7*15+7*x ...... distribute
165 = 105+7x
165-105 = 105+7x-105 ..... subtract 105 from both sides
60 = 7x
7x = 60
7x/7 = 60/7 ............ divide both sides by 7
x = 8.57142857142858
x = 8.57 ..... rounding to the nearest hundredth
Answer:
15x^2 - 12x^3
Step-by-step explanation:
A rectangular block has 3 parts that play into its volume. length, width and height. The question gives us length and width in the form of x and 3x, so height is what's missing.
It gives us a bit more information saying the sum of its edges is 20. We also have to ask how many lengths, widths and heights are there. That may be a bit hard to understand, but is you are looking at a block I could ask how many edges are vertical, just going up and down. These would be the heights. There are 4 total, and this goes the same for length and width, so 4*length + 4*width and 4*height = 20.
Taking that and plugging in x for length and 3x for width (or you could do it the other way around, it doesn't matter, you get:
4*x + 4*3x + 4*height = 20
4x + 12x + 4h = 20
16x + 4h = 20
4h = 20 - 16x
h = 5 - 4x
Now we have h in terms of x, which lets us easily find the volume just knowing x. To find the volume of a rectangular block you just multiply the length, width and height.
x*3x*(5-4x)
3x^2(5-4x)
15x^2 - 12x^3
Question doesn't give a specific value for x at all so you should be done there. Any number you plug in for x should get you the right answer
Lets represent the side of the square as s , since we know the area is 36. write s
the square root of 36 is 6. So, we know the side is 6. The formula for perimeter is P= s+s+s+s , but since it is a square and all the sides are equal, for a perimeter of a square you can do p= 4s , now substitute 6 for s to get 4(6)=24 so the perimeter of a square would be 24 inches
Answer: Question 1 :B,D.
Question 2:option B,
Question 3:Degree=5.
Question 4:option D.
Question 5: option c.
Step-by-step explanation:
1) A polynomial can not have any exponent as a variable or a fraction.
Options B and D are polynomials.
2) The polynomial is having 3 terms and is of degree 3.so it is a cubic trinomial Option B.
3) Degree is the highest power of the variables in the terms .The term 
has the power=3+2=5
So degree =5.
4)
Option D
5)
Simplifying like terms,
=
Option c.
Answer:
5.6 thousand
Step-by-step explanation:
To find the mean absolute deviation (MAD), first find the mean (or average).
μ = (41 + 38 + 36 + 57 + 43) / 5
μ = 43
Next, subtract the mean from each value and take the absolute value.
|41 − 43| = 2
|38 − 43| = 5
|36 − 43| = 7
|57 − 43| = 14
|43 − 43| = 0
Sum the results and divide by the number of animals.
MAD = (2 + 5 + 7 + 14 + 0) / 5
MAD = 5.6
