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RSB [31]
3 years ago
13

In the function f(x)=5(x^2-4+___)+15, what number belongs in the blank to complete the square?

Mathematics
1 answer:
Maurinko [17]3 years ago
7 0

Answer:

2² = 4

Step-by-step explanation:

\text{Use}\\(a-b)^2=a^2-2ab+b^2\\\\f(x)=5(x^2-4x+\underline{\ \ \ })+15\\\\x^2-4x\\\\x^2-2(x)(2)\\\\x^2-2(x)(2)+2^2=x^2-4x+4\\\\\text{Therefore}\\\\f(x)=5(x^2-4x+4)+15=5(x-2)^2+15

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Determine the number of terms, n, given the geometric series -1 - 2 - 4 - 8 - ... and Sn=−31.
Gemiola [76]

Answer:

5

Step-by-step explanation:

We are given the geometric series:

-1, - 2, - 4, - 8.......

In the geometric series above, the common ratio = second term/first term = -2/-1

= 2

Where common ratio is greater than 1(r >1)

The sum of a geometric progression =

Sn = a(rⁿ -1)/r - 1

In the question we are asked to find the number of term = n

Sn = -31

a = -1

r = 2

Hence,

-31 = -1(2ⁿ - 1)/2 - 1

-31 = -1(2ⁿ - 1)

-31 = -2ⁿ + 1

2ⁿ = 1 + 31

2ⁿ = 32

2ⁿ = 2^5

n = 5

Therefore, the number of terms(n) = 5

3 0
3 years ago
In his science class, Boris conducted an experiment in which he used a glass prism to make a rainbow. He now wants to find the s
Norma-Jean [14]

Answer:

<u>Use the formula for area of the triangle:</u>

  • A = 1/2bh, where b- base, h- height or altitude
<h3>Part A</h3>

<u>The triangle i has:</u>

  • b = 4 cm, h = 1.5 cm

<u>The area is:</u>

  • A = 1/2*4*1.5 = 3 cm²
<h3>Part B</h3>

Triangles have same area as they are congruent.

<u>Total area is:</u>

  • 3*2 = 6 cm²
4 0
3 years ago
Angle C is inscribed in circle O.
tatuchka [14]

Answer:

The radius of circle O is 8.5 Units

Step-by-step explanation:

Solution

The radius of a circle is refereed to as the  half of the diameter.

Now,

On how to figure out the length of AB, we apply the  Pythagorean's equation or formula which is given below

Thus,

a² + b² = c²

(15)² + (8)² = c²

225 + 64 = c²

√289 = √c²

Then

c = 17

What this shows is that  AB is 17 units.

Since we have gotten the diameter, the next step is to divide into half the know the radius value

Therefore,

17 ÷ 2 = 8.5 Units

= 8.5 Units.

6 0
3 years ago
I have no clue what it is
Orlov [11]
13.95+2.25+2.25+2.25+2.75+2.75+2.75= 28.95

6 0
3 years ago
Please help me with #2
e-lub [12.9K]

Answer:

The answer is B, your welcome

7 0
3 years ago
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