According to HL theorem if one leg and hypotenuse of one right triangle are equal to one leg and hypotenuse of other right triangle, then the triangles are congruent.
By using this theorem we can set up the system of equations as follows:
x=y+1 ...(1)
2x+3= 3y + 3 ..(2)
By using equation (1) next step is to plug in y+1 for x in equation (2). So,
2 ( y + 1) + 3 = 3y + 3
2y + 2 + 3 = 3y + 3 By using distribution property.
2y + 5 = 3y + 3
2y + 5 - 5 = 3y + 3 - 5 Subtract 5 from each side.
2y = 3y - 2
2y - 3y = -2 Subtract 3y from each sides.
-y = -2
So, y=2
Next step is to plug in y=2 in equation (1) to get the value of x. Hence,
x= 2+1
=3
So, x=3 and y=2 make these triangles congruent.
So, the correct choice is 3. x = 3, y = 2.
-4=-1b-(1/3)b
-4=-(4/3)b
-4/-(4/3)=b
b=3
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(1/2)3+(5/3)2
3/6+10/6=13/6
-23/3=13/6a
(-23/3)/(13/6)=a
a=-46/13
Using derivatives, it is found that:
i) 
ii) 9 m/s.
iii) 
iv) 6 m/s².
v) 1 second.
<h3>What is the role of derivatives in the relation between acceleration, velocity and position?</h3>
- The velocity is the derivative of the position.
- The acceleration is the derivative of the velocity.
In this problem, the position is:
item i:
Velocity is the <u>derivative of the position</u>, hence:
Item ii:
The speed is of 9 m/s.
Item iii:
Derivative of the velocity, hence:
Item iv:
The acceleration is of 6 m/s².
Item v:
t for which a(t) = 0, hence:
Hence 1 second.
You can learn more about derivatives at brainly.com/question/14800626
Answer:
20.7
Step-by-step explanation:
Answer:
Sum = 15 8/15, Difference = 1 2/15
Step-by-step explanation:
8⅓, 71/5
A. Sum
8⅓ + 7 1/5
Convert to improper fraction
25/3 + 36/5
Find the LCM of 3 and 5. The result is 15. Divide 15 by the denominator of each fraction and multiply the result obtained with the numerator. The result is shown below:
[(25×5) + (36×3)] / 15
[125 + 108] / 15
233 / 15
Convert to mixed fraction
15 8/15
B. Difference
8⅓ – 7 1/5
Convert to improper fraction
25/3 – 36/5
Find the LCM of 3 and 5. The result is 15. Divide 15 by the denominator of each fraction and multiply the result obtained with the numerator. The result is shown below:
[(25×5) – (36×3)] / 15
[125 – 108] / 15
17 / 15
Convert to mixed fraction
1 2/15
SUMMARY:
Sum = 15 8/15, Difference = 1 2/15
