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4 years ago

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Mathematics

1 answer:

MrRissso [65]4 years ago

7 0

Answer:

1. $\dfrac{4}{3}$

2. $y=6x-11$

3. $4$

Step-by-step explanation:

The equation of the line that passes trough the points A(14,-1) and B(2,1) is

$\dfrac{x-14}{2-14}=\dfrac{y-(-1)}{1-(-1)},\\ \\\dfrac{x-14}{-12}=\dfrac{y+1}{2},\\ \\y+1=-\dfrac{1}{6}(x-14),\\ \\y=-\dfrac{1}{6}x+\dfrac{7}{3}-1,\\ \\y=-\dfrac{1}{6}x+\dfrac{4}{3}.$

The y-intercept of this line is

$y=-\dfrac{1}{6}\cdot 0+\dfrac{4}{3}=\dfrac{4}{3}.$

Line BC is perpendicular to line AB, then its slope is $6.$ Line BC passes through the point B, so

$y-1=6(x-2),\\ \\y-1=6x-12,\\ \\y=6x-11.$

If the y-coordinate of point C is 13, then x-coordinate is

$13=6x-11,\\ \\6x=13+11,\\ \\6x=24,\\ \\x=4.$

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Determine if the sequence below is arithmetic or geometric and determine the common difference / ratio in simplest form. 125, 25

Igoryamba

Answer:

Given sequence is an arithmetic sequence.

Step-by-step explanation:

Given sequence is:

125, 25, 5, .. ..

Here

$a_1 = 125\\a_2 = 25\\a_3 = 5$

A sequence is geometric sequence when the common ratio of consecutive terms is same. It is denoted by r.

A sequence is an arithmetic sequence when the common difference of consecutive terms is same. It is denoted by d.

Finding the common ratio

$r = \frac{a_2}{a_1} = \frac{125}{25} = 5\\r = \frac{a_3}{a_2} = \frac{25}{5} = 5$

As we can see that the common ratio is same, the given sequence is a geometric sequence.

5 0

3 years ago

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Solve for x. Solve for x solve for x solve for x

SIZIF [17.4K]

Answer:

x=29

Does the answer help you?

8 0

3 years ago

Which graph represents the solution to this inequality? -1/4(12x+8)<2x+11

bekas [8.4K]

Answer:

Step-by-step explanation:

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3 years ago

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Evaluate the determinate for the following matrix. see photo

kobusy [5.1K]

Answer:

A. 10

Step-by-step explanation:

$3 \{0( - 3) - 4( - 2) \} \\ - 3 \{ - 2( - 3) - ( - 2)( - 2)\} \\ + 1\{ - 2 \times 4 - ( - 2) \times 0\} \\ = 3 \{ 0 + 8\} - 3 \{ 6 - 4\} + 1 \{ - 8 - 0 \} \\ = 3 \times 8 - 3 \times 2 + 1( - 8) \\ = 24 - 6 - 8 \\ = 10$

7 0

3 years ago

The number of horses occupying stalls at the county fairgrounds can be modeled by the following function, where x represents the

Elenna [48]

Answer:
_______________________________________________________
The rewritten equation is:

" - 3x² + 30 + 225 = 0 " ;

which is ultimately simplified to:

" x² − 10 − 75 = 0 " .
___________________________________________________
The number of days is: "15 days" .
___________________________________________________

Explanation:
______________________________________________
Given:

h(x) = - 3x² + 30 + 225 ;

Rewrite as: " - 3x² + 30 + 225 = 0 " ;
__________________________________________________________
Multiply EACH SIDE of the equation by "-1" ; to get rid of the "-3" ;

-1 * {- 3x² + 30 + 225 = 0} ;

to get: " 3x² − 30 − 225 = 0" ;

Divide EACH SIDE of the equation by "3" ; to simplify; since:

"3", "30", and "225" are divisible by "3" ;

{3x² − 30 − 225} / 3 = 0 / 3 ;

to get:
______________________________________
" x² − 10 − 75 = 0 " ;

______________________________________
Let us factor:

-15 + 5 = -10 ;

-15 * 5 = -75 ;
_______________________________________
Rewrite as:

(x − 15) (x + 5) = 0 ;

x = 15; and x = -5 ;
_______________________________________
The number of days cannot be "negative value"; so we stick with:

"x = 15 days"
___________________________________________________
Answer: The rewritten equation is:

" - 3x² + 30 + 225 = 0 " ;

which is ultimately simplified to:

" x² − 10 − 75 = 0 " .
___________________________________________________
The number of days is: "15 days" .
___________________________________________________

6 0

4 years ago