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Ksju [112]
3 years ago
11

Find the sum of first 15 terms of an AP whose 4th and 9th t terms are -15 and -30 respectively.

Mathematics
1 answer:
Serga [27]3 years ago
7 0

Answer:

Sum of the first 15 terms = -405

Step-by-step explanation:

a + 3d = -15 (1)

a + 8d = -30 (2)

Where,

a = first term

d = common difference

n = number of terms

Subtract (1) from (1)

8d - 3d = -30 - (-15)

5d = -30 + 15

5d = -15

d = -15/5

= -3

d = -3

Substitute d = -3 into (1)

a + 3d = -15

a + 3(-3) = -15

a - 9 = -15

a = -15 + 9

a = -6

Sum of the first 15 terms

S = n/2[2a + (n − 1) × d]

= 15/2 {2×-6 + (15-1)-3}

= 7.5{-12 + (14)-3}

= 7.5{ -12 - 42}

= 7.5{-54}

= -405

Sum of the first 15 terms = -405

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Two lines intersect to form a linear pair with equal measures. One angle had the measure 2x and the other angle had the measure
rosijanka [135]

Answer:

x = 45, y = 5

Step-by-step explanation:

It is given that two lines form a linear pair with equal measures. Therefore, the angle between the two lines will be 90. Now, according to the question,

2x + 20y - 10 =90

2x+20y = 100

x + 10y = 50

And

2x = 20y-10

x = 10y -5

x - 10 y = -5

Now, adding x + 10y = 50 and x - 10y =-5, the value of x can be found. The required value will be:

x + 10y =50

x - 10y = -5

------------------

x = 45

Therefore, the value of y after substitution of the value of x in one of the equations will be:

90 = 20y - 10

20 y = 100

y = 5

Hence, the required value of x and y are 45 and 5 respectively.

4 0
3 years ago
Two whole numbers have a least common multiple of 30.
Makovka662 [10]
Yes it is 3, and 10 : )
3 0
2 years ago
Which list orders the numbers from least to greatest?
storchak [24]

Answer:

D.

Step-by-step explanation:

5 0
3 years ago
how many legs do 10 people have? if two people dont have legs. one person has 3 legs and one person has one leg. and mary has a
Ganezh [65]
So here is the answer. Normally, 10 people have 20 legs since each person has 2 legs each. But given the scenario that two people don't have legs, this would mean 20 minus 4, is 16 legs. Then one person has 3 legs, 16 plus 3 and it is 19. And then, another person has one leg, 19 plus 1 is 20. Therefore, the total legs would still be 20. Hope this helps. The dog does not count.
5 0
3 years ago
Read 2 more answers
Find the Area of the figure below, composed of a rectangle and a semicircle.
Mamont248 [21]

Answer:

68.1 units²

Step-by-step explanation:

Start by finding the area of the rectangle...

Area=lw\\Area=6*9\\Area=54

Then, find the area of the semicircle...

Radius=\frac{1}{2}*Diameter=\frac{1}{2}*6=3

Area=\frac{1}{2}\pi r^2\\Area=\frac{1}{2}\pi 3^2\\Area=\frac{1}{2}\pi 9\\Area=\frac{9}{2}\ pi\\Area\approx14.1

Now, add the two to get...

54+14.1=68.1

3 0
2 years ago
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