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4 years ago

Which ordered pair is a solution to the system of linear equations Y= -7x+2 and y=9x-1

1 answer:

3 0

$\left\{\begin{array}{ccc}y=-7x+2\\y=9x-1\end{array}\right\Rightarrow 9x-1=-7x+2\\\\9x-1=-7x+2\ \ \ |+1\\9x=-7x+3\ \ \ |+7x\\16x=3\ \ \ \ |:16\\x=\dfrac{3}{16}\\\\\text{substitute the value of x to the second equation}\\\\y=9\cdot\dfrac{3}{16}-1\\\\y=\dfrac{27}{16}-\dfrac{16}{16}\\\\y=\dfrac{11}{16}\\\\\text{The solution is}\ \left(\dfrac{3}{16};\ \dfrac{11}{16}\right)$

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The percentage increase is 13.11%.

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4 years ago

There is a theory that children wearing superhero costumes are more likely to harm themselves because of the unrealistic impress

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Answer:

$Mean = 47$

$n = 6$

$s= 16.56$

$\sqrt n = 2.45$

$SEM = 11.55$

Step-by-step explanation:

Given: The above data

Solving (a): Mean of each group

Mean is calculated as:

$Mean = \frac{\sum x}{N}$

$Mean = \frac{55 + 31 + 58 + 20 + 47 + 37+68 + 32 + 85 + 69 +58 + 52+26 + 47 + 30 +35 + 53 + 43}{18}$

$Mean = \frac{846}{18}$

$Mean = 47$

Solving (b): The sample size of each group

This is the number of rows in each group.

Hence:

$n = 6$

Solving (c): Standard deviation (s)

This is calculated as:

$s = \sqrt{\frac{\sum (x - \bar x)^2}{N}}$

So, we have:

$s= \sqrt{\frac{(55 - 47)^2 + (31 - 47)^2 +......... + (43 - 47)^2}{18}}$

$s= \sqrt{\frac{4936}{18}}$

$s= \sqrt{274.22}$

$s= 16.56$

Solving (d): Square root of n

$\sqrt n = \sqrt 6$

$\sqrt n = 2.45$

Solving (e): SEM

This is calculated as:

$SEM = \frac{s}{\sqrt N}$

$SEM = \frac{47}{\sqrt{16.56}}$

$SEM = \frac{47}{4.07}$

$SEM = 11.55$

5 0

3 years ago

If AB=BC,AB=4=4x-2,andBC=3x+3,fine the length of AB

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Answer:

Step-by-step explanation:

First, I'm assuming AB=4=4x-2 was a typo and it's supposed to be AB = 4x - 2

AB=BC

AB = 4x - 2 BC = 3x + 3

4x - 2 = 3x + 3

Solve for x Add 2 to each side

4x - 2 = 3x + 3

4x - 2 + 2 = 3x + 3 + 2

4x = 3x + 5 Subtract 3x from each side.

4x - 3x = 3x- 3x + 5

4x - 3x = 5

x = 5

Now plug back in to the original equations

AB = 4x - 2 BC = 3x + 3

AB = 4 (5) - 2 BC = 3(5) + 3

AB = 20 - 2 BC = 15 + 3

AB = 18 BC = 18

So AB is 18

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4 years ago

Bob bought 5 packs of toilet paper for $42.50. Which equation can be used to determine the price, p, in dollars, of 1 pack of to

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Answer:

42.50/5 = p is the equation; $8.50 per pack

Step-by-step explanation:

DIVIDE 42.50 between the 5 packs of toilet paper.

THIS GETS YOU $8.50 per pack.

THE EQUATION used was 42.50/5 = p.

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3 years ago

How do you do two step equations???

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It takes two steps to solve an equation or inequality that has more than one operation: Simplify using the inverse of addition or subtraction. Simplify further by using the inverse of multiplication or division. When solving an equation in general, we always keep in mind the notion that whatever we do to one side of the equation should also be done to the other side to ensure that the equation remains balanced.We know that we have completely solved a two-step equation if the variable, usually represented by a letter in an alphabet, is isolated on one side of the equation (either left or right) and the number is located on the opposite side. I hope this helps! :D

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3 years ago