Answer:
Option 1,
The triangle MNP is similar to the triangle with side lengths 35 cm, 41 cm, 43 cm
Step-by-step explanation:
Given triangle MNP has side lengths 3.5 cm, 4.1 cm, and 4.3 cm. we have to find the similarity triangle sides from the given option.
As we know, the two triangles are similar if the measures of the corresponding sides of two triangles are proportional.
For the first option: 35 cm, 41 cm, 43 cm
which shows that the sides are proportional.
we have to choose only one option ∴ we needn't have to check the others
Hence, the triangle MNP is similar to the triangle with side lengths 35 cm, 41 cm, 43 cm
Answer: The required derivative is 
Step-by-step explanation:
Since we have given that
![y=\ln[x(2x+3)^2]](https://tex.z-dn.net/?f=y%3D%5Cln%5Bx%282x%2B3%29%5E2%5D)
Differentiating log function w.r.t. x, we get that
![\dfrac{dy}{dx}=\dfrac{1}{[x(2x+3)^2]}\times [x'(2x+3)^2+(2x+3)^2'x]\\\\\dfrac{dy}{dx}=\dfrac{1}{[x(2x+3)^2]}\times [(2x+3)^2+2x(2x+3)]\\\\\dfrac{dy}{dx}=\dfrac{4x^2+9+12x+4x^2+6x}{x(2x+3)^2}\\\\\dfrac{dy}{dx}=\dfrac{8x^2+18x+9}{x(2x+3)^2}](https://tex.z-dn.net/?f=%5Cdfrac%7Bdy%7D%7Bdx%7D%3D%5Cdfrac%7B1%7D%7B%5Bx%282x%2B3%29%5E2%5D%7D%5Ctimes%20%5Bx%27%282x%2B3%29%5E2%2B%282x%2B3%29%5E2%27x%5D%5C%5C%5C%5C%5Cdfrac%7Bdy%7D%7Bdx%7D%3D%5Cdfrac%7B1%7D%7B%5Bx%282x%2B3%29%5E2%5D%7D%5Ctimes%20%5B%282x%2B3%29%5E2%2B2x%282x%2B3%29%5D%5C%5C%5C%5C%5Cdfrac%7Bdy%7D%7Bdx%7D%3D%5Cdfrac%7B4x%5E2%2B9%2B12x%2B4x%5E2%2B6x%7D%7Bx%282x%2B3%29%5E2%7D%5C%5C%5C%5C%5Cdfrac%7Bdy%7D%7Bdx%7D%3D%5Cdfrac%7B8x%5E2%2B18x%2B9%7D%7Bx%282x%2B3%29%5E2%7D)
Hence, the required derivative is
Hey there! :)
Since 2 4/5 is greater than 1/4, the answer is negative.
You can just subtract 2 4/5 and 1/4 and add the (-) sign
2 4/5 - 1/4
Change the fractions so they can have a common denominator: 20
2 4/5 = 2 16/20
1/4 = 5/20
2 16/20 - 5/20 = 2 11/20
Add the (-) sign → -2 11/20
Answer ⇒ -2 11/20
:)
Answer:
C. P- value < 0.04 0.05
Step-by-step explanation:
hello,
we were given the sample size, n = 200
also the probability that the psychic correctly identifies the symbol on the 200 card is
using the large sample Z- statistic, we have
= 
= 1.7678
thus the P - value for the hypothesis test is P(Z > 1.7678) = 0.039.
from the above, we conclude that the P- value < 0.04, 0.05
Problem 1
The two angles 6x and 30 are vertical angles, so they are congruent or the same in measure.
6x = 30
x = 30/6
x = 5 is the answer
====================================================
Problem 2
The two angles form a straight angle which is 180 degrees. We consider them a linear pair (since they are adjacent and supplementary).
So,
5x+(3x+12) = 180
8x+12 = 180
8x = 180-12
8x = 168
x = 168/8
x = 21 is the answer
