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3 years ago

Fill in the missing numbers to complete the pattern 615,605,595

Mathematics

1 answer:

Sophie [7]3 years ago

7 0

We are given pattern 615,605,595.

Let us check differences of second term - first term and

Third term - second term

Second term - first term = 605 - 615 = -10.

Third term - second term = 595 - 605 = -10.

So, each time 10 is being subtracted from previous term.

So, the sequnace would be

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49x^2=-21x-2 quadratic functions

lara [203]

Answer: 49x^2=-21x-2 quadratic functions -1/7and -2/7

Step-by-step explanation:

Quadratic function:

In elementary algebra, the quadratic formula is a formula that provides the solution to a quadratic equation. There are other ways of solving a quadratic equation instead of using the quadratic formula, such as factoring, completing the square, graphing and others.

Move terms to the left side

49 $x^{2}$ =-21x-2

49 $x^{2}$ -(-21x-2) =0

Distribute

49 $x^{2}$ -(-21x-2) =0

49 $x^{2}$ +21x+2=0

Use the quadratic formula

x=(-b±√ $b^{2}$ -4ac ) / 2a

Once in standard form, identify a, b, and c from the original equation and plug them into the quadratic formula.

49 $x^{2}$ +21x+2=0

let, a=49

b=21

c=2

Replace with values in this equation

X=(-b±√ $b^{2}$ -4ac ) / 2a

Simplify

Evaluate the exponent

Multiply the numbers

Subtract the numbers

Evaluate the square root

Multiply the numbers

x=(-21±7) /98

Separate the equations

To solve for the unknown variable, separate into two equations: one with a plus and the other with a minus.Separate

x=(-21+7) /98

x=(-21-7) /98

Solve

Rearrange and isolate the variable to find each solution

x=-1/7

x=-2/7

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3 0

2 years ago

URGENT please find the mean and standard deviation too (number 6)

adell [148]

Answer:To calculate the standard deviation of those numbers:

1.Work out the Mean (the simple average of the numbers)

2.Then for each number: subtract the Mean and square the result.

3.Then work out the mean of those squared differences.

4.Take the square root of that and we are done!

Step-by-step explanation:

5 0

3 years ago

3x^2+20x+12 pls show work ;-;

RoseWind [281]

Answer:

$3 {x}^{2} + 20x + 12 \\ 3 {x}^{2} + 18x + 2x + 12 \\ 3x(x + 6) + 2(x + 6) \\( 3x + 2)(x + 6)$

5 0

2 years ago

Find the rate of change for the interval [5,15]

Aleks04 [339]

Left side goes up 5 right side goes up 7

The rate of change between 5,15 is 10

3 0

3 years ago

4TH TIME ASKING THIS!!! Please help me! Someone pleaseeee. I need the correct answers. I don’t want to fail

Alexeev081 [22]

Answer:

The functions are inverses; f(g(x)) = x ⇒ answer D

$h^{-1}(x)=\sqrt{\frac{x+1}{3}}$ ⇒ answer D

Step-by-step explanation:

* Lets explain how to find the inverse of a function

- Let f(x) = y

- Exchange x and y

- Solve to find the new y

- The new y = $f^{-1}(x)$

* Lets use these steps to solve the problems

∵ $f(x)=\sqrt{x-3}$

∵ f(x) = y

∴ $y=\sqrt{x-3}$

- Exchange x and y

∴ $x=\sqrt{y-3}$

- Square the two sides

∴ x² = y - 3

- Add 3 to both sides

∴ x² + 3 = y

- Change y by $f^{-1}(x)$

∴ $f^{-1}(x)=x^{2}+3$

∵ g(x) = x² + 3

∴ $f^{-1}(x)=g(x)$

∴ The functions are inverses to each other

* Now lets find f(g(x))

- To find f(g(x)) substitute x in f(x) by g(x)

∵ $f(x)=\sqrt{x-3}$

∵ g(x) = x² + 3

∴ $f(g(x))=\sqrt{(x^{2}+3)-3}=\sqrt{x^{2}+3-3}=\sqrt{x^{2}}=x$

∴ f(g(x)) = x

∴ The functions are inverses; f(g(x)) = x

* Lets find the inverse of h(x)

∵ h(x) = 3x² - 1 where x ≥ 0

- Let h(x) = y

∴ y = 3x² - 1

- Exchange x and y

∴ x = 3y² - 1

- Add 1 to both sides

∴ x + 1 = 3y²

- Divide both sides by 3

∴ $\frac{x + 1}{3}=y^{2}$

- Take √ for both sides

∴ ± $\sqrt{\frac{x+1}{3}}=y$

∵ x ≥ 0

∴ We will chose the positive value of the square root

∴ $\sqrt{\frac{x+1}{3}}=y$

- replace y by $h^{-1}(x)$

∴ $h^{-1}(x)=\sqrt{\frac{x+1}{3}}$

4 0

3 years ago