The first three terms of an arithmetic sequence are as follows.

52, 44, 36

Find the next two terms of this sequence.

x intercepts are 5 and 7

The third point I used was (6,-2); however, you can use any other point you want as long as it's not one of the x intercepts mentioned.

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Explanation:

The x intercepts are 5 and 7, where the parabola crosses the x axis. Because of these roots, the two factors are x-5 and x-7.

We can think of the root x = 5 turning into x-5 = 0 after subtracting 5 from both sides. The same goes for x = 7 turning into x-7 = 0.

Put together, the two factors lead to (x-5)(x-7) and we get the equation y = (x-5)(x-7). Plugging either x = 5 or x = 7 into this equation produces y = 0.

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Notice that plugging in x = 6 leads to...

y = (x-5)(x-7)

y = (6-5)(6-7)

y = (1)(-1)

y = -1

However, the graph shows that x = 6 should lead to y = -2 instead. To fix this, we can stick a 2 out front like so

y = 2(x-5)(x-7)

y = 2(6-5)(6-7)

y = 2(1)(-1)

y = -2

The error has been fixed. As you can see, we need this third point to help nail down the parabolic equation. You can pick any other x value you want as long as it's not 5 or 7.

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Let's try another x value. Let's say we pick x = 8

y = 2(x-5)(x-7)

y = 2(8-5)(8-7)

y = 2(3)(1)

y = 6

We see that x = 8 leads to y = 6. This matches what the graph shows that (8,6) is a point on the parabola. I'll let you try other x values.

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In short, we used the roots 5 and 7 to generate the partial factorization (x-5)(x-7). Then we used a third point (6,-2) to help determine the coefficient out front which was 2.

So after using that point, we go from y = (x-5)(x-7) to y = 2(x-5)(x-7) which is the final answer. This is considered x-intercept form because we can quickly read off the x intercepts from this equation.

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Step-by-step explanation:

Answer:

x = 3/8

Step-by-step explanation:

[tex]x + \dfrac{1}{4}=\dfrac{5}{8}\\\\\dfrac{4x + 1}{4}=\dfrac{5}{8}[/tex]

Cross multiply,

8*(4x +1) = 5*4

8*4x + 8*1 = 20

32x + 8 = 20

Subtract 8 from both sides

32x = 20 - 8

32x = 12

Divide both side by 32

x = 12/32

x = 3/8

Answer(s):

Exact Form: x + 2 y − 3 z = 15 , 2 x − 2 z = 6 , 3 2 3

Mixed Number Form: x + 2 y − 3 z = 15 , 2 x − 2 z = 6 , 3 2 3

Improper Fraction Form: x + 2 y − 3 z = 15 , 2 x − 2 z = 6 , 11 3

Decimal Form: x + 2 y − 3 z = 15 , 2 x − 2 z = 6 , 3. ¯ 6

Hope this helps, have a nice day/night! :D

First truck = x

Second truck = y

x + 35 = y

x = 2/3y

So

2/3y +35=y

1/3y = 35

y = 35*3

y = 105

And ,

x = 2/3y = 70

Answer:  (12xy^2)

Step-by-step explanation:

12x^2y^3

(12xy^2)*(xy)

24xy^2

(12xy^2)*(2)

The greatest common factor of the expressions 12x²y³ and 24xy² will be 12xy².

Simply said, it is the biggest common element. The highest consistent element in the above example is 15, making 15 the greatest common factor amongst 15, 30, and 105. The biggest chunk of the common factors is called the "Greatest Common Factor" (of two or more numbers).

The expressions are given below.

12x²y³ and 24xy²

The factor of the expression 12x²y³ is given as,

12x²y³ = 12 × x × x × y² × y

The factor of the expression 24xy² is given as,

24xy² = 2 × 12 × x × y²

The common factors in both expressions are 12, x, and y². Then the greatest common factor will be given as,

⇒ 12 × x × y²

⇒ 12xy²

The best normal component of the articulations 12x²y³ and 24xy² will be 12xy².

More about the greatest common factor link is given below.

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Answer:

This is a contradiction

Slope is the change in y over the change in x.

Slope = (-1 - -2) / (4 - -5)

Slope = 1/9

Answer: Your x value would be 12 and your y value would be 128

X = 12

Y = 128

Answer:

$15

Step-by-step explanation:

6 divided by 2 is 3

3 multiplied by 5 is 15

Hello, hope you are having a remarkable day. :)

These are the multiples of 5:

5, 10, 15, 20, 25, 30, 35...

These are the factors of 5:

1, 5

As we can see, the number 5 is both a multiple of 5 and a factor of 5.

Hope it helps. Ask me if you have any queries.

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Good luck.

Answer:

56/15

Step-by-step explanation:

All we have to do is 8/3 x 7/5 and 8x7 is 56,5x3 is 15

So the answer is 56/15.

Answer:

56/15

Step-by-step explanation:

Based on the amount of juice needed for 6 guests, the amount of juice Larry will need for 26 guests is A. 196 ounces.

First find out the amount of juice a single guest will need:

= Quantity of juice / Number of guests

= 45 / 6

= 7.5 ounces

If a guest needs 7.5 ounces, 26 guests would need:

= 25 x 7.5

= 195 ounces

In conclusion, 196 ounces of juice is needed.

Find out more at https://brainly.com/question/1201888.

Answer:

Step-by-step explanation:

Answer:

Pattern B

A quadratic relationship is characterized by constant second differences.

Pattern A

Sequence: 0, 2, 4, 6

First Differences: 2, 2, 2 . . . . constant indicates a 1st-degree (linear, arithmetic) sequence

__________________________________________________________

Pattern B

Sequence: 1, 2, 5, 10

First Differences: 1, 3, 5

Second Differences: 2, 2 . . . . constant indicates a 2nd-degree (quadratic) sequence

__________________________________________________________

Pattern C

Sequence: 1, 3, 9, 27

First Differences: 2, 6, 18

Second Differences: 4, 12 . . . . each set of differences has a common ratio, indicating an exponential (geometric) sequence

__________________________________________________________

Pattern B shows a geometric relationship between step number and dot count.

Refer to the attachment

Soo :

2a + 3b = 325

2a + 7b = 505 -

-4b = -180

4b = 180

b = 45

[tex] \: [/tex]

2a + 3b = 325

2a + 3(45) = 325

2a + 135 = 325

2a = 325 - 135

2a = 190

a = 95

Answer:

[tex]x=-1.52,2.19[/tex]

Step-by-step explanation:

Hi there!

[tex]3x^2 - 2x - 10 = 0[/tex]

Use the quadratic formula:

[tex]x=\displaystyle\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex] in the form [tex]ax^2+bx+c=0[/tex]

Plug in the a, b and c values

[tex]x=\displaystyle\frac{-(-2)\pm\sqrt{(-2)^2-4(3)(-10)} }{2(3)}\\\\x=\displaystyle\frac{2\pm\sqrt{4+120} }{6}\\\\x=\displaystyle\frac{2\pm\sqrt{124} }{6}\\\\x=\displaystyle\frac{2\pm2\sqrt{31} }{6}\\\\x=\displaystyle\frac{1\pm\sqrt{31} }{3}\\\\x=-1.52,2.19[/tex]

I hope this helps!

Answer:

6869

Step-by-step explanation:

Answer:

Step-by-step explanation:

3x+2y=12   x= −2/ 3 y+4

3x-y=3    x= 1 /3 y+1

i hope this helps in anyway :/

The solution of the system of linear equations 3x + 2y = 12 and 3x − y = 3 is (x = 2, y = 3)

If it is written in the form of ax + by + c = 0, where a, b & c are real numbers and the coefficients of x and y, i.e a and b respectively, are not equal to zero.

Given that the system of linear equations;

3x + 2y = 12 and 3x − y = 3 is

Solving the equations by elimination, we get

x = 2 and y = 3

Hence, The solution of the system of linear equations 3x + 2y = 12 and 3x − y = 3 is (x = 2, y = 3)

For more reference on Linear Equation, click;

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Answer:

-1.2y + -4.2y = -3.78

Answer:  14.5185185185

11 1/3 + 10 5/9 - 7 10/27 = 392/27 = 14 14/27 ≅ 14.5185185

Answer:

x = 33°

Step-by-step explanation:

x = angle

a complement of an angle =(90-x)

x = (90-x) - 24

x = 90 - x - 24

x = 66 -x

2x = 66

x = 33

Answer:

22

Step-by-step explanation:

Answer:

I can't interpret the data the way it is presented.  Are there two columns?  I'll assume "-x2" is really "-x^2."

I've attached a plot of the function.  Check to see which of your points fall on the line.

Step-by-step explanation:

y = -x^2 + 5

Answer:

a

Step-by-step explanation:

Answer:

200points

[tex]x6)266(6( \times [/tex]

hatodf jahahshshshshfidba

Sorry, couldn't help in Q. 10

The question seems undefined or I haven't seen this question before.

Answer:

9/11

Step-by-step explanation: