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2 years ago

What is the value of x? Enter your answer in the box.

Mathematics

1 answer:

Law Incorporation [45]2 years ago

7 0

Answer:

x=25

Step-by-step explanation:

3x-5=2x+20=4x-30

3(25)-5 = 2(25) + 20 = 4(25) - 30

75-5 = 50 + 20 = 100 - 30

70=70=70

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Factor this polynomial completely.

azamat

Answer:

(x-4) (x-4)

Step-by-step explanation:

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x^2 -8x = 16

(x-4) (x-4) = x^2 -4x -4x +16 = x^2 -8x +16

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2 years ago

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Consider the equation: 3 4 x − 12 = 12 Which statement could be a translation of the given equation? A number minus 12 is three-

musickatia [10]

Answer:

<h3>The translation statement for the given equation $\frac{3}{4}x-12=12$ is " Three-fourths of a number minus twelve is the same as twelve. "</h3>

Step-by-step explanation:

Given equation is $\frac{3}{4}x-12=12$

<h3>To find the statement which could be a translation of the given equation :</h3>

$\frac{3}{4}x-12=12$
The above equation can be written as
Three-fourths of a number x minus twelve is equal to twelve.

<h3>Therefore the translation statement for the given equation $\frac{3}{4}x-12=12$ is " Three-fourths of a number minus twelve is the same as twelve. "</h3>

The option is <u> " Three-fourths of a number minus twelve is the same as twelve. "</u> correct

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3 years ago

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√(5-2x) - √(2-x) = 1

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Square both sides. (5-2x) - (2-x) = 1^2. 5 - 2x - 2 + x = 1. Simplify to get 3 - x = 1. X=2

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The least-squares regression model y =−3.4+5.2x and correlation coefficient r=−0.66 were calculated for a set of bivariate data

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Answer:

$r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}$

For this case the value of r = -0.66

Now we can calculate the determination coeffcient:

$r^2 = (-0.66)^2 = 0.4356$

And then we can conclude that 43.56% of the variation in y can be explained by the explanatory variable

And then 100-43.56 = 56.44 % of the variation in y that cannot be explained by the explanatory variable

Step-by-step explanation:

For this case we need to calculate the slope with the following formula:

$m=\frac{S_{xy}}{S_{xx}}$

Where:

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}$

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}$

$\bar x= \frac{\sum x_i}{n}$

$\bar y= \frac{\sum y_i}{n}$

And we can find the intercept using this:

$b=\bar y -m \bar x$

And the model obtained for this case is:

$y = -3.4 +5.2 x$

The correlation coefficient is a "statistical measure that calculates the strength of the relationship between the relative movements of two variables". It's denoted by r and its always between -1 and 1.

And in order to calculate the correlation coefficient we can use this formula:

$r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}$

For this case the value of r = -0.66

Now we can calculate the determination coeffcient:

$r^2 = (-0.66)^2 = 0.4356$

And then we can conclude that 43.56% of the variation in y can be explained by the explanatory variable

And then 100-43.56 = 56.44 % of the variation in y that cannot be explained by the explanatory variable

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2 years ago