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3 years ago

Identify the 35th term of an arithmetic sequence where a1 = -7 and a18 = 95

1 answer:

3 0

$a_1=-7;\ a_{18}=95\\\\a_{18}-a_1=17d\\\\17d=95-(-7)\\17d=95+7\\17d=102\ \ \ |divide\ both\ sides\ by\ 17\\d=6\\\\a_{35}=a_1+34d\\\\a_{35}=-7+34\cdot6=-7+204=197\\\\Answer:\boxed{a_{35}=197}$

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Find the value of C that completes the square

MatroZZZ [7]

Answer:

Step-by-step explanation:

y^2-22y+c

complete the square ax^2+bx+c is our old formula quadratic equation

we know that to find c we will divide b/2 and square it

22/2=11

c^2=121

we have y^2-22y+121

6 0

3 years ago

Find the value of the variable and BC, if B is between A and C. AB = 5x, BC = 3x-1, AC = 47

schepotkina [342]

Answer:

Step-by-step explanation:

AC = AB + BC

Since we know what each variable equals, we can write out the equation as shown:

47 = 5x + 3x - 1

Combining like terms:

47 = 8x - 1

Add 1 on both sides:

48 = 8x

Divide 8 on both sides:

X = 6

Now that we know what X equals, we can solve BC.

BC = 3(6) - 1

BC = 18 - 1

BC = 17

Therefore BC = 17.

4 0

3 years ago

What is the coefficient of the x^5y^5- term in the biomial expansion of (2x-3y)^10

jasenka [17]

Answer:

The coefficient of $x^{5} \times y^{5} \text { is }=\left(252 \times 2^{5} \times(-3)^{5}\right)=252 \times 32 \times 243=1959552$

Solution:

The given expression is $(2 x-3 y)^{10}$

As per binomial theorem, we know,

$(x+y)^{n}=\sum n C_{k} x^{n-k} y^{k}$

Now here a = 2x, b = (- 3y) and n = 10 and k = 0,1,2,….10

Now $x^{5}\times y^5$ will be the 6 term where k =5

Now, $\mathrm{T}_{6}=10 \mathrm{C}_{5} \times(2 \mathrm{x})^{(10-5)} \times(-3 \mathrm{y})^{5}=10 \mathrm{C}_{5} 2^{5} \times \mathrm{x}^{5} \times(-3)^{5} \times \mathrm{y}^{5}$

So, the coefficient of $x^{5} \times y^{5} \text { is }=10\left(5 \times 2^{5} \times(-3)^{5}\right$ .

$10 \mathrm{C}_{5}=\frac{10 !}{5 ! \times(10-5) !}=\frac{10 !}{5 !+5 !}=\frac{10 \times 9 \times 8 \times 7 \times 6 \times 5 !}{5 ! \times 5 !}=\frac{10 \times 9 \times 8 \times 7 \times 6}{5 \times 4 \times 3 \times 2 \times 1}=\left(\frac{30240}{120}\right)=252$

The coefficient of $x^{5} \times y^{5} \text { is }=\left(252 \times 2^{5} \times(-3)^{5}\right)=252 \times 32 \times 243=1959552$

6 0

4 years ago

a steel ball has a diameter of 1.6 centimeters what is the volume of this steel ball round your anwser to the nearest tenth if n

emmasim [6.3K]

Volume of a sphere is 4/3 x pi x r(cubed)— so based on that I think it’s 2.14 cm cubed

8 0

3 years ago

How to convert a repeating decimal to a fraction when only 1 digit is repeating?

Alecsey [184]

Example 0.777777

x = 0.77
10(x = 0.77) ----(10 because it is repeating by the tenth digit. if repeating by 2 digits like 0.2828, you'll multiply by 100)

10x = 7.77
-(x = 0.77)
9x = 7.00
x = 7/9

5 0

3 years ago