All categories

3 years ago

What number must you add to complete the square? x^2+6x=19

2 answers:

7 0

Well, the idea being, how do we turn x²+6x=19 with a perfect square trinomial

well, recall, the middle term of a perfect square trinomial is just 2 * guy on the left * guy on the right

so... with that in mind, let's nevermind the 19, and take close peek at the 6x, let's do some grouping

( x² + 6x + ? ) = 19

well, 6x is really 2 * 3 * x
since the middle term is just 2 * guy on one side * guy on the other

we can tell one guy is x², already there, but the other will then be 3²

now, let's go to our Mr very good friend Mr Zero, 0, and add that 3², however, if we add whatever, we must also subtract whatever, we're only borrowing from zero

( x² + 6x + 3² ) - 3² = 19

( x + 3) ² - 9 = 19

( x + 3 )² = 28

so, the number we needed was just 3² or 9, courtesy of zero and our fellow the middle term

lorasvet [3.4K]3 years ago

6 0

The number 100 is added to complete the square

You might be interested in

If you reflect any shape across the x-axis and then rotate it 90° clockwise about the origin, do you get the same result as if y

Setler79 [48]

Answer:

Yes, reflecting a shape across the x-axis and then rotating it 90° clockwise about the origin gives the same results as reflecting it across the y-axis followed by rotating it 90° counterclockwise about the origin. This means these two sequences of transformations are equivalent.

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

How do I solve System of Equation 8th grade?

Ivanshal [37]

Hey there,

You could solve it in one of three ways: graphing, substitution method, and elimination method.

3 0

3 years ago

Three siblings date Kate and Sarah spent 100 hours helping Habitat for Humanity build new housing .Sarah worked 15 hours more th

Inessa [10]

The starting equation is
100=S+D+K
S is for Sarah, D is for Dave, and K is for Kate

This is what we know:
S=15+D
and
K=D-5
Now that we know how to find the values of everything, we must plug it in.

100=(15+D)+D+(D-5)
Combine like terms.
100=10+3D
Subtract 10 to isolate variable.
90=3D
Divide by 3 to isolate variable.
30=D
Plug in number to find the answers.

Answer:
Sarah worked for 45 hours
Dave worked for 30 hours
Kate worked for 25 hours

3 0

3 years ago

Read 2 more answers

Consider the situations in the table below ^^^

netineya [11]

Answer:

ACBD

Step-by-step explanation:

Increases, gains, earnings, upward motion are all represented by positive numbers. Decreases, losses, spending, downward motion are all represented by negative numbers. Here are the sums:

A: -33.57 +14.98 = -18.59

B: 7 2/5 -3/5 = 7 +(2/5 -3/5) = 7 -1/5 = 6 4/5

C: 3 1/6 +2 1/2 = (3+2) +(1/6 +3/6) = 5 4/6 = 5 2/3

D: 23.66 -15.84 = 7.82

Least to greatest, their order is ...

A (-18.59), C (5 2/3), B (6 4/5), D (7.82)

4 0

4 years ago

The given matrix is the augmented matrix for a linear system. Use technology to perform the row operations needed to transform t

shtirl [24]

Answer:

$x_{1} = \frac{176}{127} + \frac{71}{127}x_{4}\\\\ x_{2} = \frac{284}{127} + \frac{131}{254}x_{4}\\\\x_{3} = \frac{845}{127} + \frac{663}{254}x_{4}\\$

Step-by-step explanation:

As the given Augmented matrix is

$\left[\begin{array}{ccccc}9&-2&0&-4&:8\\0&7&-1&-1&:9\\8&12&-6&5&:-2\end{array}\right]$

Step 1 :

$r_{1}$ ↔ $r_{1} - r_{2}$

$\left[\begin{array}{ccccc}1&-14&6&-9&:10\\0&7&-1&-1&:9\\8&12&-6&5&:-2\end{array}\right]$

Step 2 :

$r_{3}$ ↔ $r_{3} - 8r_{1}$

$\left[\begin{array}{ccccc}1&-14&6&-9&:10\\0&7&-1&-1&:9\\0&124&-54&77&:-82\end{array}\right]$

Step 3 :

$r_{2}$ ↔ $\frac{r_{2}}{7}$

$\left[\begin{array}{ccccc}1&-14&6&-9&:10\\0&1&-\frac{1}{7} &-\frac{1}{7} &:\frac{9}{7} \\0&124&-54&77&:-82\end{array}\right]$

Step 4 :

$r_{1}$ ↔ $r_{1} + 14r_{2}$ , $r_{3}$ ↔ $r_{3} - 124r_{2}$

$\left[\begin{array}{ccccc}1&0&4&-11&:-8\\0&1&-\frac{1}{7} &-\frac{1}{7} &:\frac{9}{7} \\0&0&- \frac{254}{7} &\frac{663}{7} &:-\frac{1690}{7} \end{array}\right]$

Step 5 :

$r_{3}$ ↔ $\frac{r_{3}. 7}{254}$

$\left[\begin{array}{ccccc}1&0&4&-11&:-8\\0&1&-\frac{1}{7} &-\frac{1}{7} &:\frac{9}{7} \\0&0&1&-\frac{663}{254} &:-\frac{1690}{254} \end{array}\right]$

Step 6 :

$r_{1}$ ↔ $r_{1} - 4r_{3}$ , $r_{2}$ ↔ $r_{2} + \frac{1}{7} r_{3}$

$\left[\begin{array}{ccccc}1&0&0&-\frac{71}{127} &:\frac{176}{127} \\0&1&0&-\frac{131}{254} &:\frac{284}{127} \\0&0&1&-\frac{663}{254} &:\frac{845}{127} \end{array}\right]$

∴ we get

$x_{1} = \frac{176}{127} + \frac{71}{127}x_{4}\\\\ x_{2} = \frac{284}{127} + \frac{131}{254}x_{4}\\\\x_{3} = \frac{845}{127} + \frac{663}{254}x_{4}\\$

6 0

3 years ago