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3 years ago

H e l p p l e a s e ; - ;

Mathematics

1 answer:

irina1246 [14]3 years ago

5 0

Answer:

9/4

Step-by-step explanation:

if you use cross multiplication you can see that it would cross eachother out and becom one plz vote brainliest

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1 , 3 , 6 , 10 , 15

Bas_tet [7]

First difference,

$\Delta_{1} = a_{2} - a_{1} = 3 - 1 = 2 = 1 + 1$

Second difference,

$\Delta_{2} = a_{3} - a_{2} = 6 - 3 = 3 = 2 + 1$

Third difference,

$\Delta_{3} = a_{4} - a_{3} = 10 - 6 = 4 = 3 + 1$

And so on.

Assuming the pattern holds on, we see that

i-th difference,

$\Delta_{i} = a_{i + 1} - a_{i} = i + 1$

$\implies a_{i + 1} = a_{i} + i + 1$

Then, nth term is,

$\implies a_{n} = a_{n - 1} + n$

$= a_{n - 2}+ (n + (n - 1))$

$= a_{n - 3} + (n + (n - 1) +(n - 2))$

$= a_{n - (n - 1)} + \sum \limits^{n - 2}_{k = 0}(n - k)$

$= a_1 + \sum \limits^{n - 2}_{k = 0}n- \sum \limits^{n - 2}_{k = 0}k$

$= a_1 +n(n -2 + 1 )- \frac{1}{2} (n - 2)(n - 1)$

$= a_1 +n(n -1 )- \frac{1}{2} (n - 2)(n - 1)$

$= a_1 +(n -1 )(n- \frac{1}{2} (n - 2))$

$= a_1 + \frac{1}{2} (n -1 )(2n- n + 2)$

$= a_1 + \frac{1}{2} (n -1 )(n + 2)$

$\implies a_{n} = 1 + \frac{1}{2} (n -1 )(n + 2)$

Now, the 21st term in the sequence is,

$\implies a_{21} = 1 + \frac{1}{2} (21 -1 )(21 + 2)$

$= 1 + \frac{1}{2} \times 20 \times 23$

$= 231$

4 0

3 years ago

A major river flowing out of the Himalayas

trapecia [35]

Answer:

The Ganges

Step-by-step explanation:

4 0

2 years ago

Read 2 more answers

WUCLUJ

mash [69]

Answer:

81 degrees

Step-by-step explanation:

A quadrilateral has four interior angles which sum up to 360 degrees.

As we are given that two angles are right angles which means the sum of two angles will be 180 degrees and the third angle is 99 degrees.

As we know that the four angles sum up to 360 degrees.

Let A,B,C and D denote the four angles,

Then

Sum of angles = 360

A+B+C+D=360

90+90+99+D=360

279+D=360

D=360-279

D= 81 degrees

So the fourth angle is 81 degrees ..

7 0

4 years ago

Ari’s chickens eat their pellets at a constant rate throughout each day.

oksano4ka [1.4K]

If we make the days and ounces be in the ordered pair, the points are: (2, 39), (4, 33), (6, 27), and (8, 21). We may use linear regression from the calculator using the equation,
y = Ax + B
where A is the slope. The value of A from the linear regression is equal to -3.

4 0

3 years ago

Write the equation of the function of a parabola with vertex at (–1,–2) and a point (1,–6) that lies on the curve.

Olenka [21]

Answer:

f(x) = -(x + 1)² - 2

Step-by-step explanation:

f(x) = a(x - h)² + k

-6 = a(1 - -1)² + -2

-6 = a(4) -2

-4 = 4a

a = -1

f(x) = -(x + 1)² - 2

4 0

3 years ago