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Sergio [31]
3 years ago
8

Solve x^2-8x-9=0 algebrically

Mathematics
1 answer:
SVETLANKA909090 [29]3 years ago
7 0

Answer:

X = 9, -1

Step-by-step explanation:

1, Factor it

(x-9) (x+1) = 0

2. Both of a factor will = 0

x-9 = 0

x+1=0

3. Solve

x=9

x=1

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Five observations taken for two variables follow.
I am Lyosha [343]

Answer:

a) Figure attached

b) If we see the scatter plot we can conclude that the possible relation between x and y is linear and with a positive correlation since when the values of x increases the values for y increases as well.

c) Cov (X,Y) = \frac{\sum_{i=1}^n (x_i -\bar X)(y_i -\bar Y)}{n-1}

We can find the numerator like this:

\sum_{i=1}^5 (6-16)(6-10)+(11-16)(9-10)+(15-16)(6-10)+(21-16)(17-10)+(27-16)(12-10)=106

And then:

Cov(X,Y) = \frac{106}{5-1}=26.5

d) r=\frac{5(906)-(80)(50)}{\sqrt{[5(1552) -(80)^2][5(586) -(50)^2]}}=0.693  

Step-by-step explanation:

Part a

For this part we use excel in order to create the scatterplot and we got the result on the figure attached.

Part b

If we see the scatter plot we can conclude that the possible relation between x and y is linear and with a positive correlation since when the values of x increases the values for y increases as well.

Part c

The sample covariance is defined as:

Cov (X,Y) = \frac{\sum_{i=1}^n (x_i -\bar X)(y_i -\bar Y)}{n-1}

We can find the numerator like this:

\sum_{i=1}^5 (6-16)(6-10)+(11-16)(9-10)+(15-16)(6-10)+(21-16)(17-10)+(27-16)(12-10)=106

And then:

Cov(X,Y) = \frac{106}{5-1}=26.5

Part d

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 our case we have this:

n=5 \sum x = 80, \sum y = 50, \sum xy = 906, \sum x^2 =1552, \sum y^2 =586  

r=\frac{5(906)-(80)(50)}{\sqrt{[5(1552) -(80)^2][5(586) -(50)^2]}}=0.693  

So then the correlation coefficient would be r =0.693

3 0
3 years ago
Marco needs to buy some cat food. At the nearest​ store, 5 bags of cat food cost ​$18.75. How much would Marco spend on 3 bags o
Ira Lisetskai [31]

Answer:

$11.25

Step-by-step explanation:

5 bags = $18.75

To find the amount for three bags, we need to find the price for <em>each </em>bag.

Divide 18.75 by 5.

18.75/5 = 3.75

So each bag is 3.75, and since we need to know the price for 3 bags, we need to multiply 3.75 by 3, which is 11.25.

7 0
3 years ago
Consider h(x)=x^2+8+15. identify its vertex and y-intercept.
OleMash [197]

Answer:

Vertex: (-4, -1)

Y-intercept: (0, 15)

Step-by-step explanation:

Given the quaratic function, h(x) = x² + 8x + 15:

In order to determine the vertex of the given function, we can use the formula, [x = \frac{-b}{2a}, h(\frac{-b}{2a})].

<h3>Use the equation:  [x = \frac{-b}{2a}, h(\frac{-b}{2a})]</h3>

In the quadratic function, h(x) = x² + 8x + 15, where:

a = 1, b = 8, and c = 15:

Substitute the given values for <em>a</em> and <em>b</em> into the equation to solve for the x-coordinate of the vertex.

x = \frac{-b}{2a}

x = \frac{-8}{2(1)}

x = -4

Subsitute the value of the x-coordinate into the given function to solve for the <u>y-coordinate of the vertex</u>:

h(x) = x² + 8x + 15

h(-4) = (-4)² + 8(-4) + 15

h(-4) = 16 - 32 + 15

h(-4) = -1

Therefore, the vertex of the given function is (-4, -1).

<h3>Solve for the Y-intercept:</h3>

The <u>y-intercept</u> is the point on the graph where it crosse the y-axis. In order to find the y-intercept of the function, set x = 0, and solve for the y-intercept:

h(x) = x² + 8x + 15

h(0) = (0)² + 8(0) + 15

h(0) = 0 + 0 + 15

h(0) = 15

Therefore, the y-intercept of the quadratic function is (0, 15).

5 0
2 years ago
The sum of the reciprocal of a number and 5/6 is 13/12. Find the number.
ddd [48]

\frac1x+\frac56=\frac{13}{12}\ \ \ \ |\cdot12\\ 12\cdot\frac1x+12\cdot\frac56=12\cdot\frac{13}{12}\\ \frac{12}x+\frac{60}6=13\\ \frac{12}x+10=13\ \to \ \frac{12}x=3\ \to \ \boxed{x=4}

4 0
3 years ago
Read 2 more answers
When the sum of twice a number and 4 is tripled the result is 72?
mafiozo [28]
The unknown value can be called x.
3(2x +4) = 72
6x +12 = 72
72 - 12 = 6x
6x = 60
x = 6x / 6 
x = 10

Hope This Helps You!
<span>Good Luck Studying :)</span>
7 0
3 years ago
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