Summation of 3n + 2 from n = 1 to n = 14 = (3(1) + 2) + (3(2) + 2) + (3(3) + 2) + . . . + (3(14) + 2) = 5 + 8 + 11 + ... + 44 ia an arithmetic progression with first term (a) = 5, common difference (d) = 3 and last term (l) = 44 and n = 14
Sn = n/2(a + l) = 14/2(5 + 44) = 7(49) = 343
Therefore, the required summation is 343.
Answer:
There are 3 adults in the family.
Step-by-step explanation:
The equations 8x + 4y = 32 and 16x + 12y = 72 represent the cost of lunch and dinner for a family in which x is the number of adults and y is the number of children.
We have to find the number of adults or the value of x by solving these equations.
equations are 8x + 4y = 32 -------(1)
16x + 12y = 72 --------(2)
Now we will multiply equation 1 by 3 and subtract it by equation 2.
(16x + 12y) -3(8x + 4y) = 72 - 96
16x + 12y - 24x - 12y = -24
(16x - 24x) + (12y - 12y) = -24
-8x = - 24
8x = 24
x = 3
Therefore, there are 3 adults in the family.
Answer:
The bird has to fly 7.5 m
Step-by-step explanation:
Please see diagram in attached image.
Notice that there is a right angle triangle that defines the situation, and you know two elements of such triangle;
1) one acute angle (
), and
2) the side opposite to that angle.
What you need to find is the side adjacent to the angle, which is what the bird needs to fly horizontally to be above the fish. We named that "x".
The trig function that relates such triangle elements is the tangent:
which rounded to the nearest tenth is: 7.5 m
step-by-step explanation:
every time we see "a number" or "the same number," we can add a variable (we'll use x here). rewriting the problem, we get: 8 less than 2 times x is gr8er than the sum of x and 9.
next, we can work backwards to write an inequality. we know from the word problem above that the number on the left side of the equation is 8 less than 2x, so we can rewrite that part like this: 2x-8.
for the right side of the equation, all we have to do is simplify "the sum of x and 9" to x + 9. so now the inequality should look like this: 2x - 8 > x + 9.
now we'll solve the inequality just like an equation: subtract x from both sides of the inequality, so now we have: x - 8 > 9.
then, we can add 8 to both sides to get the x by itself, and we get the answer: x > 15
hope this helps! <em>:)</em>
The answer should be 10 I think, because if u multiply 250 * 4% u get 10.
Hope I'm right.
