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3 years ago

Find the slope of the line that passes through (18, 86) and (-6, 70).

Mathematics

1 answer:

Tamiku [17]3 years ago

4 0

Slope: (y2-y1)/(x2-x1)
(70-86)/(-6-18) = -16/-24 = 2/3
The slope is 2/3

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Use the given data to find the best predicted value of the response variable. Ten pairs of data yield requals0.003 and the regre

Arada [10]

Answer:

$\hat y=3(2) +2=8$

Step-by-step explanation:

Data given

r=0.003 represent the correlation coefficient

$bar y =5$ represent the sample mean for the y observations

Solution to the problem

We assume that they use least squares in order to find the best regression model. The slope is given by the following formula:

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

Where:

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

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

And the slope on this case is:

$m=3$

Nowe we can find the means for x and y like this:

$\bar x= \frac{\sum x_i}{n}=5$

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

And we can find the intercept using this:

$b=\bar y -m \bar x=5-(3*\bar x)=2$

So the line would be given by:

$\hat y=3x +2$

And the best predicted value for x=2 would be:

$\hat y=3(2) +2=8$

3 0

3 years ago

Does (2, -1) make this a true statement? Why or why not? 3x + 2y = 4

kvv77 [185]

Answer: Yes

Step-by-step explanation:

So a coordinate pair is always set up (x,y) so you plug the x term in the coordinate pair into the x in the equation and the y term in for the y. 3×2 + 2×-1. Multiply them together and you end up with 4.

3 0

3 years ago

Use implicit differentiation to find an equation of the tangent line to the curve at the given point. 7x2 + xy + 7y2 = 15, (1, 1

riadik2000 [5.3K]

Assume $y=y(x)$ .

$7x^2+xy+7y^2=15$
$\dfrac{\mathrm d}{\mathrm dx}[7x^2+xy+7y^2]=\dfrac{\mathrm d}{\mathrm dx}[15]$
$14x+y+x\dfrac{\mathrm dy}{\mathrm dx}+14y\dfrac{\mathrm dy}{\mathrm dx}=0$
$\dfrac{\mathrm dy}{\mathrm dx}(x+14y)=-(14x+y)$
$\dfrac{\mathrm dy}{\mathrm dx}=-\dfrac{14x+y}{x+14y}$

The slope of the tangent line to the curve at $(a,b)$ is then $-\dfrac{14a+b}{a+14b}$ , so the tangent to $(1,1)$ has slope

$\dfrac{\mathrm dy}{\mathrm dx}\bigg|_{x=1,y=1}=-\dfrac{15}{15}=-1$

The point-slope form of the tangent line is then

$y-1=-(x-1)\iff y=-x+2$

7 0

3 years ago

5.7kg in grams convert

dimaraw [331]

Answer:

5700 grams

Step-by-step explanation:

1 kg = 1000 grams

5.7 kg = 5.7 × 1000

=> 5700 grams

hope it helps!

5 0

3 years ago

One number is 10 more than twice another. Their sum is 1 . Find the numbers.

DochEvi [55]

Answer:

One number is 10 more than twice another.Their sum is 1.The numbers are -3 and 4

Solution:

Given that one number is 10 more than twice the other.

Let us consider the two numbers as “x” and “y”

First number = x

Second number = y

From question, consider “y” is 10 more than twice the “x”. This can be represented

y = 10 + 2x – eqn 1

given that the sum of numbers is 1. Hence we get

x + y =1

substituting the value of “y” we get

x + 10 +2x = 1

3x +10 = 1

3x = -9

x = -3

substitute x = -3 in eqn 1 to get the value of “y”

y = 10 +2(-3)

y=10 – 6 = 4

hence the two numbers are -3 and 4

6 0

3 years ago