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2 years ago

9

Determine the sum of the first twenty five terms of the sequence whose first five terms are 5,14,23,32 and 41

1 answer:

Alika [10]2 years ago

5 0

Answer:

Step-by-step explanation:

This is an arithmetic sequence. Each term is 9 more than the preceding term.

The 25th term is 5+24*9 = 1085.

Sum of first 25 terms is 25(5+1085)/2 = 13625

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If f(x-3)=x^2-4x+5, what's f(1-x)

olganol [36]

Answer:

$\large\boxed{f(1-x)=x^2-4x+5}$

Step-by-step explanation:

$f(x-3)=x^2-4x+5\\\\f((x-3)+3)\to\text{put x + 3 to the equation of the function:}\\\\f(x-3+3)=(x+3)^2-4(x+3)+5\\\text{use the distributive property and}\ (a+b)^2=a^2+2ab+b^2\\f(x)=x^2+2(x)(3)+3^2+(-4)(x)+(-4)(3)+5\\f(x)=x^2+6x+9-4x-12+5\qquad\text{combine like terms}\\f(x)=x^2+(6x-4x)+(9-12+5)\\f(x)=x^2+2x+2\\\\f(1-x)\to\text{put 1 - x to the equation of the funtion f(x):}\\\\f(1-x)=(1-x)^2+2(1-x)+2\\\text{use the distributive property and}\ (a-b)^2=a^2-2ab+b^2$

$f(1-x)=1^2-2(1)(x)+x^2+(2)(1)+(2)(-x)+2\\f(1-x)=1-2x+x^2+2-2x+2\qquad\text{combine like terms}\\f(1-x)=x^2+(-2x-2x)+(1+2+2)\\f(1-x)=x^2-4x+5$

4 0

3 years ago

1/9 equals what squared?

Alex

Answer:

1/3 I think??????

7 0

2 years ago

A right prism has a base in the shape of an octagon. The side length of the octagon is 4 inches. The length of the apothem is 4.

EleoNora [17]

Answer:

927 cubic inches

Step-by-step explanation:

The area of the octagonal base is ...

A = (1/2)Pa

where P is the perimeter, and 'a' is the apothem. Using the given numbers, the base area is ...

A = (1/2)(8·4)(4.83) = 77.28 . . . square inches

The volume of the prism is given by ...

V = Bh

where B represents the area of the base, and h is the height.

V = (77.28 in^2)(12 in) = 927.36 in^3

The volume of the prism is about 927 cubic inches.

4 0

2 years ago

The circumference of the circle is 9.42 inches, What is the diameter of the circle?

Elena L [17]

EXPLANATION

Since the circumference of the circle is 9.42, we can get the diameter by applying the following relationship:

$Circumference=2\pi r=2\pi\frac{d}{2}=\pi d$

Isolating the diameter:

$Diameter=\frac{Circumference}{\pi}$

Plugging in the numbers:

$Diameter=\frac{9.42}{3.14}=3$

Therefore, the diameter is equal to 3 inches.

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10 months ago

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