Slove system of equation.

2x - 6y = 8
-3x + 9y = 12

Answer:

  -1 ±4i

Step-by-step explanation:

The quadratic can be written in vertex form as ...

  x² +2x +17 = 0

  (x² +2x +1) +16 = 0 . . . . . . . . identify the part that can be a perfect square

  (x +1)² = -16 . . . . . . . . . . . . subtract 16

  x +1 = ±√(-16) = ±4i . . . . take the square root

  x = -1 ±4i . . . . . . . . . . . subtract 1

The roots of the equation are x = -1-4i and x = -1+4i.

_____

Additional comment

It can be worthwhile to remember the form of a perfect square trinomial:

  (x +a)² = x² +2ax +a²

If you know the coefficient of x, you can use half of it as the constant in each binomial factor.

In the above, we had 2a=2, so a=1 and a²=1. The constant 17 then is resolved into two parts: one part (1) is used to "complete the square" and the other part (16) is the y-coordinate of the vertex. It is used to find the "radical" portion of the roots.

The roots of the equation  [tex]x^2 + 2x + 17 = 0[/tex] are [tex]x = -1 +4i[/tex] and [tex]x = -1 - 4i[/tex].

To find the roots of the equation [tex]x^2 + 2x + 17 = 0[/tex] in simplest a + bi form, we can use the quadratic formula.

The quadratic formula states that for an equation in the form[tex]ax^2 + bx + c = 0[/tex], the roots can be found using the formula:

[tex]x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]

We have a = 1, b = 2, and c = 17.

Substituting these values into the quadratic formula, we get:

[tex]x = \frac{-2 \pm \sqrt{4 - 68}}{2}[/tex]

[tex]x = \frac{-2 \pm \sqrt{-64}}{2}[/tex]

[tex]x = \frac{-2 \pm \sqrt{64i^2}}{2}[/tex]

[tex]x = \frac{-2 \pm 8i}{2}[/tex]

[tex]x = -1 \pm 4i[/tex]

So, [tex]x = -1 +4i[/tex] and [tex]x=-1-4i[/tex] are roots.

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Answer:

C. y= 3(x + 2)^2 + 2

Step-by-step explanation:

A. Rewrite in vertex form and use this form to find the vertex  

( h , k ) . ( 2 , − 2 )

B. Rewrite in vertex form and use this form to find the vertex  

( h , k ) . ( − 2 , 2 )

C. Rewrite in vertex form and use this form to find the vertex  

( h , k ) . ( − 2 , 2 )

D. Rewrite in vertex form and use this form to find the vertex  

( h , k ) . ( 2 , 2 )

Answer:

1 is true

2 is true

3 is true

4 is false

5 is true

6 is true

Step-by-step explanation:

Given:

System as per question:

Or

Step-by-step explanation:

Let the number of apples be a and lemons be l . Then ,

=> a + l = 17

Also ,

=> 35a + 15l = $ 3.95

The time taken by auntie Annie to rake is 25 minutes.

A statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions is called inequality.

Let the time taken by auntie Anne to rake be ab minutes.

Now, according to the given question.

Auntie Anne situation is represented by an inequality

10 < ab <40

Since, it is given that sum of the digits of time taken by Anne to rake is 7.

⇒ a + b = 7

Also, ab is a multiple of 5.

Now,

When, a = 4 and b = 3 (or vice-versa)

4 + 3 = 7 but 43 is not a multiple of five.

When, a = 6 and b = 1 ( or vice versa)

6 + 1 = 7, but 61 is not a multiple of five.

When, a = 2 and b = 5 (or vice versa)

2 + 5 = 7 and 25 is multiple of 5.But 52 is not a multiple of 5.

Also, 25 is less than 40 and greater than 10.

Therefore, the time taken by auntie Annie to rake is 25 minutes.

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[tex] = \: \: \: c = 0 \\ \\ hope \: it \: \: helps \\ \\ see \: \: the \: \: attachement[/tex]

Answer:

A 20

Step-by-step explanation:

If you subtract 89.99 -68.25 you will equal 20

Answer:

y=-x-4

Step-by-step explanation:

[tex]4(x + \frac{8}{x}) - (x + \frac{8}{x}) = 3(x + \frac{8}{x}) = 3x + \frac{24}{x}[/tex]

ok done. Thank to me :>

Answer:

-8<x<2

Step-by-step explanation:

divide everything by 3 to get -6<x+2<4. next subtract 2 from everything to get -8<x<2

Answer:  the range of 12 * 2 + 6 + 6 is 36

Step-by-step explanation:

Answer:  23 + (-27) + 16 + 32 is not correct

Step-by-step explanation:

23 + (-27) + 16 + 32 is not correct

23 + (-27) + 16 + 32   The +16 should be -16

5 in the morning unfortunately cuz I have massive insomnia

Answer:

dose meen nambars

Step-by-step explanation:

dont ansor kweschins nambars kweschins

Answer:

463,488,000,000

Step-by-step explanation:

8.8% = .088

426,000,000,000 * .088 = 37,488,000,000

426,000,000,000 + 37,488,000,000 = 463,488,000,000

Using the concept of variation, there is an inverse relationship between the number of attendees and the contribution made by each attendee.

Since the amount of chocolate decreases as the number of attendees increase;

We use inverse variation to model the scenario :

Taking any pair of points :

3000 = k/8

k = 3000 × 8

k = 24000

Therefore, the variation statement is "the amount paid per attendee is inversely proportional to the number of people in attendance.

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Answer:

25 pesos 80 pw

pesos I'm not sure

Step-by-step explanation:

25. 80

Answer:

50.7 miles per hour

Step-by-step explanation:

I ve seen this question before

Answer:

The length is 40m

Step-by-step explanation:

Length = x

P = 2x + 2W

118 = 2x + 2(19)

118 = 2x + 38

118 - 38 = 2x

     80   = 2x

     80/2 = x

       40 = x   Length

y = amount of $ paid for the job

y  +  $48 = $200          total job for 3 -hours

 y  ÷   3                       amount paid per hour                    

Answer:

I'm sure it's 43 rent a bike cause I'm fat

Answer:

0.38

Step-by-step explanation:

First, we convert the fraction to a decimal number by dividing the numerator by the denominator:

3 / 8 = 0.375

There are two parts to the decimal number above:

Integer Part: 0

Fractional Part: 375

Now, we will make the Fractional Part just two digits (nearest hundredth) by using our rounding rules.*

In this case, Rule II applies, so 3/8 (or 0.375) rounded to the nearest hundredth in decimal format is:

0.38

Answer:

.375

Step-by-step explanation:

3/8=.375

Answer:

D.

Step-by-step explanation:

Well, here we look at the frequency to determine probability. As a dice has 3 even and odd numbers, the probability shall be gotten by dividing the total number of frequencies for even numbers (2,4,6) by the total number of trials.

i.e (10+10+9)/50

so the probability is 29/50 or 0.58 or 58%

Since the probability of getting even numbers is 0.58 and since the total probability is always 1, we can clearly see that the probability of one rolling an even number as per the sample is higher than that of rolling an odd number.

Answer:

Here are your 3 answers!  Hope this helps please mark brainliest! Thanks :)

Step-by-step explanation:

11. X=10

12.X=-9

13.X=7

Answer:

The first one x = 10.

The second one x = -9

The third one x = 7

Step-by-step explanation:

Answer:

P and R

Step-by-step explanation:

P and R are similar because R is the same thing as P but 2 times bigger.

The size of the population increases when the growth rate is positive and

decreases for a negative growth rate.

The completed table is presented as follows;

[tex]\begin{array}{|c|c|c|}2003 \ Population (millions)&Projected \ 2029 \ Population \ (millions)&Growth \ rate \ K \\40.5&20.9&-2.255\%\end{array}\right][/tex]

Reasons:

The table is presented as follows;

[tex]\begin{array}{|c|c|c|}2003 \ Population (millions)&Projected \ 2029 \ Population \ (millions)&Growth \ rate \ K \\40.5&20.9&\end{array}\right][/tex]

The population in growth rate is given by the following formula;

P = a·(1 + r)ˣ

Where;

a = The initial population in 2003 = 40.5 million

P = The population in 2029 = 20.9 million

x = The number of years = 2029 - 2003 = 26

Therefore;

20.9 = 40.5 × (1 + r)²⁹

[tex]\left (1 + r\right)^{29} = \dfrac{20.9}{40.5}[/tex]

[tex]r = \left(\dfrac{20.9}{40.5} \right)^{\dfrac{1}{29} } - 1 \approx -0.02255[/tex]

The population growth rate is r ≈ -0.02255 = -2.255 %

The completed table is therefore;

[tex]\begin{array}{|c|c|c|}2003 \ Population (millions)&Projected \ 2029 \ Population \ (millions)&Growth \ rate \ K \\40.5&20.9&-2.255\%\end{array}\right][/tex]

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Answer: 80

Step-by-step explanation:

16, 32, 48, 64, 80

5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 75, 80

Answer:

56 degrees

Step-by-step explanation:

The midsegment is parallel to a side and the other side is a transversal. Using the Corresponding Angles Theorem, you get that m<1=56 degrees

Answer:

0.81

Step-by-step explanation:8x1x1x 1/10 +1x1/100=0.81