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nata0808 [166]
2 years ago
10

101 101 Suppose that Σ ai = -12 and Σ bi = -19. i=1 i=1 Compute the sum. 101 Σ( – 5ai – 12bi) i=1​

Mathematics
1 answer:
Roman55 [17]2 years ago
7 0

Distribute the summation over the sum.

\displaystyle \sum_{i=1}^{101} (-5a_i - 12b_i) = -5 \sum_{i=1}^{101} a_i - 12 \sum_{i=1}^{101} b_i

Now plug in the known sums and simplify.

\displaystyle \sum_{i=1}^{101} (-5a_i - 12b_i) = -5(-12) - 12(-19) = \boxed{288}

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Starting with 54 and 36, replace the 54 with the greatest common divisor of 54 and 36, obtaining a1, and then replace 36 with th
nalin [4]

Answer:

1 time

Step-by-step explanation:

Given numbers are 54 and 36.

The greatest common divisor of 54 and 36 = 18

So, a_1 = 18.

The least common multiple of 54 and 36 = 108

So, b_1 = 108.

As 54 is replaced by a_1 and 36 is replaced by b_1, so after applying the given procedure, the new number is

(a_1, b_1)=(18, 108)\cdots(i)

Now, apply the same procedure, to get a_2 and b_2.

The greatest common divisor of 18 and 108 = 18

So, a_2 = 18.

The least common multiple of 18 and 108 = 108

So, b_2 = 108.

As a_1 is replaced by a_2 and b_1 is replaced by b_2, so after applying the given procedure, the new number is

(a_2, b_2)=(18, 108) which is the same as in equation (i)

Hence, after applying the procedure 1 time after (a_1, b_1), the obtained number (a_2, b_2) is the same as (a_1,b_1).

6 0
3 years ago
Show a graph Slope function of -1 with a y intercept of 3
castortr0y [4]

Answer:

<h2>In the attachment.</h2>

Step-by-step explanation:

The slope-intercept form of an equation of a line:

y=mx+b

m - slope

b - y-intercept → (0, b)

We have m = -1 and b = 3. Substitute:

y=-1x+b\to y=-x+3

The graph is a straight line. Therefore we need only two points to plotting the graph.

One we have, the y-intercept (0, 3). Calculate other point.

Put any value of x to the equation of a line and calculate the value of y:

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6 0
3 years ago
Please help me with this
masya89 [10]
X= 30

That’s the answer I think
4 0
3 years ago
Plz help I am being timed
CaHeK987 [17]

Answer:

24

Step-by-step explanation:

7 0
3 years ago
I need some help with this
Korvikt [17]


The following can be deduced from the expressions

m ∠ D = 4 × m ∠ A
m ∠ B = 3 × m ∠ A-12

Please note that the sum of angles in a triangle is 180 degress. Therefore,

M∠ A + m ∠ B + m ∠ D = 180equation(3)

Substitute for equation 1 and 2 in equation 3 as shown below

m ∠ A + 3 × m ∠ A - 12^0 + 4 x m ∠ A =180^0
m ∠ A + 3 × m ∠ A + 4 x m ∠ A = 180^0+12^0
8m ∠ A = 192^0
m ∠ A= 192^0/8
m ∠ A=24^0

Substitute for m∠A= 24 in equation 1 and 2 as shown below

m ∠ D = 4 × m ∠ A
m ∠ D = 4 × 24^0
m ∠ D = 96^0
m ∠ B = 3 × mA - 12^0
m ∠ B = 3 × 24^0 - 12
m ∠ B = 72^0 - 12^0

,

∠= °

∠= °

∠= °
5 0
3 years ago
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