A system of equations is graphed on a coordinate plane.

Which of the following constants can be added to x^2 + 2/3x to form a perfect square trinomial?

Angelina_Jolie [31]

Hello.

A trinomial is a perfect square if the square root of the first term times the square root of the third term times 2 equals the middle term.

$\boxed{\mathsf{x^{2} + \dfrac{2}{3} x}}$

a) Adding 1/9:

$\cdot \: \mathsf{x^{2} + \dfrac{2}{3} x + \dfrac{1}{9}} \\ \\ \\ \mathsf{\sqrt{x^{2}} \times \sqrt{\dfrac{1}{9}} \times 2 =} \\ \\ \\ \mathsf{x \times \dfrac{1}{3} \times 2 =} \\ \\ \\ \mathsf{\dfrac{2}{3} x \rightarrow it \: is \: a \: perfect \: square \: trinomial}$

b) Adding 4/9:

$\cdot \: \mathsf{x^{2} + \dfrac{2}{3} x + \dfrac{4}{9}} \\ \\ \\ \mathsf{\sqrt{x^{2}} \times \sqrt{\dfrac{4}{9}} \times 2 =} \\ \\ \\ \mathsf{x \times \dfrac{2}{3} \times 2 =} \\ \\ \\ \mathsf{\dfrac{4}{3} x \rightarrow it \: is \: not \: a \: perfect \: square \: trinomial}$

c) Adding 4 and 1/9:

$\cdot \: \mathsf{x^{2} + \dfrac{2}{3} x + \dfrac{1}{9} + 4 = x^{2} + \dfrac{2}{3} x + \dfrac{37}{9}} \\ \\ \\ \mathsf{\sqrt{x^{2}} \times \sqrt{\dfrac{37}{9}} \times 2 =} \\ \\ \\ \mathsf{x \times \dfrac{\sqrt{37}}{3} \times 2 =} \\ \\ \\ \mathsf{\dfrac{2\sqrt{37}}{3} x \rightarrow it \: is \: not \: a \: perfect \: square \: trinomial}$

Hope I helped.

3 0

3 years ago

Abby sold half of her comic books and then bought seventeen more. She now has 32. With how many did she begin?

Art [367]

Answer:

15 because 32 - 17 = 15

Step-by-step explanation:

3 0

3 years ago

Bill rented a truck for one day. There was a base fee of $16.99, and there was an additional charge of 92 cents for each mile dr

Lady_Fox [76]

Answer:

He paid $18 of which $15.95 was

the flat fee.

18.00

- 15.95

---------

$2.05 is the amount paid for mileage.

This is 205 cents for mileage

at 71 cents per mile. Divide

205 by 71 to get the miles driven.

205/71 = 2.9 miles.

Step-by-step explanation:

7 0

3 years ago

Please help me at least 5 long sentences. Thank you. <br> Look at the points.

ivanzaharov [21]

Answer:

this doent make sence

Step-by-step explanation:

8 0

3 years ago

you are rolling a 10-sided die with sides numbered 1-10. you keep rolling the die until you roll a prime number and then stop. l

evablogger [386]

The formula for E(x) would be SUM[ X(n)P(n)] from n = 1 to n = infinity until we get the prime number

In the given problem, a 10-sided die with 1-10 numbers is rolled until we get a prime number

Prime numbers between 1-10 = 2,3,5,7 (4 prime numbers)

Non - prime numbers = 1,4,6,8,9,10( 6 non-prime number)

Let X be the number of times the die is rolled

The probability of getting a prime =

$P(Prime) = \frac{4}{10}$

Now, the value of

E(X)=∑x.P(x) [ x-> {1, infinity}]

= P(1)X(1) +P(2)X(2)+P(3)X(3)+P(4)X(4)........+ P(n)X(n)

= 1. $\frac{4}{10}$ + 2. $\frac{6}{10}$ . $\frac{4}{10}$ + 3. $\frac{6}{10}$ . $\frac{6}{10}$ $\frac{4}{10}$ + 4. $\frac{6}{10}$ . $\frac{6}{10}$ . $\frac{6}{10}$ . $\frac{4}{10}$ .......

Hence, this is the value of E(x)

To learn more about Prime number, here

brainly.com/question/9315685

#SPJ4

4 0

2 years ago