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2 years ago

Complete the square x^2+18x+_

Mathematics

2 answers:

fgiga [73]2 years ago

5 0

Answer:

x²+8x+16

Step-by-step explanation:

To complete the square of the incomplete given equation means finding a constant that will complete the equation such that when it is factorised will give a perfect square.

To complete the equation x²+18x, we must find a constant to complete the quadratic equation. To get that constant, we will divide the coefficient of x by 2 and the square the resulting value as shown;

Step 1: First we get the coefficient of x in the equation which is 8.

Step 2: You will divide the coefficient of x by 2 to give;

8/2 = 4

Step 3: The square of the resulting value in the previous step is taken to get the constant needed i.e 4² which is 16

The complete form of the equation is therefore x²+8x+16

Factorizing the resulting equation will give (x+4)² which is a perfect square

kipiarov [429]2 years ago

3 0

Answer:

x^2 + 18x + 81 complete's the square.

Step-by-step explanation:

y = [x^2 + 18x + (18/2)^2 ] - (18/2)^2

y = [x^2 + 18x + 81] - 81

y = (x + 9)^2 - 81 This is just to make the completion of the square accurate.

You can't just add something to an expression. You have to balance it out.

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PLEASE HELP!!!!! 3, 8, 13, 18, 23, ....<br><br> The recursive formula for this sequence is:

rodikova [14]

Answer:

a₈ = 37

Step-by-step explanation:

The given arithmetic sequence is: 3, 8, 13, 18, 23, . . .

The recursive formula for the sequence is: $a_n = a_{n - 1} + 5$

Here, $a_n$ represents the $n^{th}$ of the sequence.

And, $a_{n - 1}$ represents the $(n - 1)^{th}$ of the sequence.

'+5' denotes that '5' is added to the $(n - 1)^{th}$ term to get the $n^{th}$ term. In other words, the difference between two consecutive numbers in the sequence is 5.

Now, we are asked to find a₈ i.e., n =8.

Substituting in the recursive formula we get: a₈ = a₍₈₋ ₁₎ + 5 = a₇ + 5.

So, to determine a₈ we need to know a₇. From the sequence we see that a₅ = 23.

⇒ a₆ = 23 + 5 = 28.

⇒ a₇ = 28 + 5 = 32.

⇒ a₈ = 32 + 5 = 37.

Therefore, the $8^{th}$ term of the sequence is 37.

8 0

2 years ago

A Galapagos cactus finch population increases by half every decade. The number of finches is

Angelina_Jolie [31]

Answer:

The number of fringes at $d=-2$ is given as 20.

Step-by-step explanation:

Question

A Galapagos cactus finch population increases by half every decade. The number of finches is modeled by the expression

where d is the number of decades after the population was measured. Evaluate the expression for d = −2

Given :

The number of finches is modeled by the expression :

⇒ $45\cdot1.5^d$

where $d$ is the number of decades after the population was measured.

To evaluate the expression for d=-2

Solution:

In order to evaluate the given expression to find the number of finches at $d=-2$ , we will plugin $-2$ for $d$ in the expression and simplify it.

Plugging in $d=-2$ in the expression:

⇒ $45\cdot 1.5^{-2}$

Using negative exponent property. [ $a^{-x}=\frac{1}{a^x}$

⇒ $45\cdot \frac{1}{1.5^2}$

⇒ $45\cdot \frac{1}{2.25}$

⇒ $20$ (Answer)

Thus, the number of fringes at $d=-2$ is given as 20.

This means the number of fringes two decades ago was 20.

6 0

3 years ago

Keiko has a total of $ 5200 comma which she has invested in two accounts. The larger account is $ 900 greater than the smaller a

Ilia_Sergeevich [38]

Keiko has a total of $5200

x is the amount of money in larger account

y is the amount of money in smaller account

x - y = $900

and x + y = $5200

<u>This creates two simultaneous equations:</u>

x - y = $900 ... (i)

x + y = $5200 ... (ii)

Adding (i) and (ii) :

2x = $6100 , x = $3050

y = x - $900 = $3050 - $900 = $2150

The amount of money in larger account (x) = $3050

The amount of money in smaller account (y) = $2150

8 0

3 years ago

Can someone help me with this please?

Elena-2011 [213]

29.) This is simply interpreting the linear function.
The function:
96+2.1x
a.) The 96 is what you start with from the beginning. So, we know Rachel weighed 96 ounces when she was born.
b.) Again, interpretation. The 2.1 is the slope, or the change in the line. So we know that Rachel gains 2.1 ounces each day.
30.) For this one, you just have to plug 9 into the equation for x.

6 0

2 years ago

50 POINTS IF YOU ANSWER!

MatroZZZ [7]

Answer:

2 m/s

Step-by-step explanation:

60*5=300

600/300=2

5 0

2 years ago

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