Since we are already given the amount of jumps from the first trial, and how much it should be increased by on each succeeding trial, we can already solve for the amount of jumps from the first through tenth trials. Starting from 5 and adding 3 each time, we get: 5 8 (11) 14 17 20 23 26 29 32, with 11 being the third trial.
Having been provided 2 different sigma notations, which I assume are choices to the question, we can substitute the initial value to see if it does match the result of the 3rd trial which we obtained by manual adding.
Let us try it below:
Sigma notation 1:
10
<span> Σ (2i + 3)
</span>i = 3
@ i = 3
2(3) + 3
12
The first sigma notation does not have the same result, so we move on to the next.
10
<span> Σ (3i + 2)
</span><span>i = 3
</span>
When i = 3; <span>3(3) + 2 = 11. (OK)
</span>
Since the 3rd trial is a match, we test it with the other values for the 4th through 10th trials.
When i = 4; <span>3(4) + 2 = 14. (OK)
</span>When i = 5; <span>3(5) + 2 = 17. (OK)
</span>When i = 6; <span>3(6) + 2 = 20. (OK)
</span>When i = 7; 3(7) + 2 = 23. (OK)
When i = 8; <span>3(8) + 2 = 26. (OK)
</span>When i = 9; <span>3(9) + 2 = 29. (OK)
</span>When i = 10; <span>3(10) + 2 = 32. (OK)
Adding the results from her 3rd through 10th trials: </span><span>11 + 14 + 17 + 20 + 23 + 26 + 29 + 32 = 172.
</span>
Therefore, the total jumps she had made from her third to tenth trips is 172.
The complete factorization of the equation 81x² - 100 is; (9x - 10)(9x + 10)
<h3>How to factorize quadratic equations?</h3>
We are given the quadratic equation;
81x² - 100
Now, according to quadratic identities, we know that;
(a + b) * (a - b) = a² - b²
Now, our equation can also be expressed as;
81x² - 100 = 9²x² - 10²
Thus, applying the quadratic identity gives us;
(9x + 10)(9x - 10)
Read more about factorization of quadratic equations at; brainly.com/question/1214333
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The values are as follows:
z=50
v= 150
x= 100
y=15
w= 50
<h3>What is parallel lines?</h3>
Parallel lines are lines in a plane that are always the same distance apart.
z+130= 180 (Linear pair)
z=50
v+ 30 = 180 (Linear pair)
v= 150
x= 180- 30 - 50 (angle sum property)
x= 100
2y=30 (alternate interior angle)
y=15
w+x+2y=180 (Linear pair)
w+ 100 + 30 = 180
w= 50
Learn more parallel lines here:
brainly.com/question/16701300
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Answer:
The second one. (The triangle is not acute because 2+4>5)
Step-by-step explanation:
If you try to make the triangle, one angle would be obtuse so it's not acute.
Pls give brainly, im trying to get the most possible :>
Answer:
27 kilograms
Step-by-step explanation:
When she was born, she weighed 3 kilograms. If she gained 24 kilograms, then that is the initial value (3) plus the added value (24) and you get her weight, which is 27.
