Answer:
A
Step-by-step explanation:
∆ABC is similar to ∆DEF if and only if the ratio of their corresponding side lengths are the same.
Let's find out:
DE/AB = 10/5 = 2
EF/BC = 8/4 = 2
FD/CA = 12/6 = 2
The ratio of their corresponding side lengths are equal, therefore, ∆ABC is similar to ∆DEF based on the SSS Similarity Theorem.
Answer:
1. The two triangles are ASA congruent
2. The two triangles are SAS congruent
Answer:
tan(2u)=[4sqrt(21)]/[17]
Step-by-step explanation:
Let u=arcsin(0.4)
tan(2u)=sin(2u)/cos(2u)
tan(2u)=[2sin(u)cos(u)]/[cos^2(u)-sin^2(u)]
If u=arcsin(0.4), then sin(u)=0.4
By the Pythagorean Identity, cos^2(u)+sin^2(u)=1, we have cos^2(u)=1-sin^2(u)=1-(0.4)^2=1-0.16=0.84.
This also implies cos(u)=sqrt(0.84) since cosine is positive.
Plug in values:
tan(2u)=[2(0.4)(sqrt(0.84)]/[0.84-0.16]
tan(2u)=[2(0.4)(sqrt(0.84)]/[0.68]
tan(2u)=[(0.4)(sqrt(0.84)]/[0.34]
tan(2u)=[(40)(sqrt(0.84)]/[34]
tan(2u)=[(20)(sqrt(0.84)]/[17]
Note:
0.84=0.04(21)
So the principal square root of 0.04 is 0.2
Sqrt(0.84)=0.2sqrt(21).
tan(2u)=[(20)(0.2)(sqrt(21)]/[17]
tan(2u)=[(20)(2)sqrt(21)]/[170]
tan(2u)=[(2)(2)sqrt(21)]/[17]
tan(2u)=[4sqrt(21)]/[17]
the rock will be at 11 meters from the ground level after 5.92 seconds
Step-by-step explanation:
The motion of the rock is a free-fall motion, since the rock is acted upon the force of gravity only. Therefore, it is a uniformly accelerated motion, so its position at time t is given by the equation:
where
h = 23 m is the initial height
u = 27 m/s is the initial velocity, upward
is the acceleration of gravity, downward
t is the time
We want to find the time t at which the position of the rock is
y = 11 m
Substituting and re-arranging the equation, we find
This is a second-order equation, which has solutions:
So
The first solution is negative so we neglect it: therefore, the rock will be at 11 meters from the ground level after 5.92 seconds.
Learn more about free fall:
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brainly.com/question/11042118
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#LearnwithBrainly
Length of square side= 2 cm
Dilation factor= 7/3
Simplify 7/3= 2.33
Apply the dilation factor:
Length of side= 2.33 x 2 = 4.67 cm
As the length of the side of the square is increased in length, which means the dilated image is larger than the original image.
Answer: Larger than then original.
