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3 years ago

18x^2+69x+60 Factor the expression

1 answer:

6 0

3(3x+4)(2x+5)

Because you factor out the 3 and then factor 6x^2+23x+20
That becomes (6x^2+8x)+(15x+20)
Factor out a two from the left and five from the right.
That makes 2x(3x+4) + 5(3x+4)
That becomes (3x+4)(2x+5)
Then put the three back in front.

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This set of ordered pairs shows a relationship between x and y. {(0, -2), (3, 7), (6, 16), (6, 15), (8, 21), (10, 28), (11,31)}

Hunter-Best [27]

Answer:

The closest to the output when the input is approximately 12

Step-by-step explanation:

The given (x, y) coordinates are;

The line of best fit is

x, 0, 3, 6, 6, 8, 10, 11

y, -2, 7, 16, 15, 21, 28, 31

The line of best fit can be obtained from the scatter plot of the given data from where a linear pattern is apparent

A linear line of best fit is a trend line that gives an overall cumulative minimum distance of all the points from the line

The method for constructing a line of best fit includes;

1) The least Squares Method

2) The method of linear regression

3) Construction of line of best fit

a) The area method

b) The dividing method

The least squares equation is given as follows;

$\hat y$ = a + b·x

$b = \dfrac{\Sigma (x_i - \overline x) \cdot (y_i - \overline y)}{\Sigma (x_i - \overline x)^2 }$

From MS Excel, we have;

${\Sigma (x_i - \overline x) \cdot (y_i - \overline y)}{ }$ = 266.8571

${\Sigma (x_i - \overline x)^2 }$ = 89.42857

∴ b = 266.8571/89.42857 ≈ 2.984

$a =\overline y- b \cdot \overline x$

From MS Excel, with the given data, we get;

$\overline y$ = 16.57143

$\overline x$ = 6.285714

Therefore;

a = 16.57143 - 2.984 × 6.285714 = -2.185

Therefore, we get the following regression equation;

$\hat y$ = -2.185 + 2.9·x

Where;

x = The input

$\hat y$ = The output

Therefore, when x = 5, we get;

$\hat y$ = -2.185 + 2.9 × 5 = 12.315

Therefore, the closest to the output when the input is 5, y ≈ 12

8 0

3 years ago

Write an equation for an ellipse centered at the origin, which has foci at (\pm\sqrt{8},0)(± 8 ,0)(, plus minus, square root o

Alchen [17]

Answer:

The equation of ellipse centered at the origin

$\frac{x^2}{18} +\frac{y^2}{10} =1$

Step-by-step explanation:

given the foci of ellipse (±√8,0) and c0-vertices are (0,±√10)

The foci are (-C,0) and (C ,0)

Given data (±√8,0)

the focus has x-coordinates so the focus is lie on x- axis.

The major axis also lie on x-axis

The minor axis lies on y-axis so c0-vertices are (0,±√10)

given focus C = ae = √8

Given co-vertices ( minor axis) (0,±b) = (0,±√10)

b= √10

The relation between the focus and semi major axes and semi minor axes are $c^2=a^2-b^2$

$a^{2} = c^{2} +b^{2}$

$a^{2} = (\sqrt{8} )^{2} +(\sqrt{10} )^{2}$

$a^{2} =18$

$a=\sqrt{18}$

The equation of ellipse formula

$\frac{x^2}{a^2} +\frac{y^2}{b^2} =1$

we know that $a=\sqrt{18} and b=\sqrt{10}$

Final answer:-

The equation of ellipse centered at the origin

$\frac{x^2}{18} +\frac{y^2}{10} =1$

8 0

3 years ago

Read 2 more answers

What is the slope of the line that passes through the points (5,8) and (11,5)? Write your answer in simplest form.

Anna007 [38]

Answer:

-1/2.

Step-by-step explanation:

slope of a line is (y2-y1)/(x2-x1). Plug in points (5-8)/(11-5). That gives -3/6. Reduce the fraction by 2, so -1/2 is the answer.

7 0

3 years ago

What is 256-126 using counting on strategies?

Oxana [17]

256
-126
130

3 strategies

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3 years ago

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A town plans to make a triangular park. The triangle has a base of 120 feet and a height of 115 feet. What will the area of the

emmasim [6.3K]

6,900 ft squared. The equation to find the area of a triangle is " a=1/2b×h"
a= area b=base and h=height

7 0

4 years ago

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