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goldfiish [28.3K]
3 years ago
10

What is the equation of the line with m=6 that goes through the point (1,4)

Mathematics
1 answer:
Valentin [98]3 years ago
5 0
Remember the point slope formula... which is ----->  y - y1 = m(x - x1)

Now substitute the values we have into m, x1, and y1...

y - 4 = 6(x - 1)
y = 6x - 6 + 4
<u>y = 6x -2</u>  -----> there is your answer!

I hope this helps you! :D
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Rationalise the denominator of: (√3 + √2)/(√3-√2) = ?<br>​
krok68 [10]

Step-by-step explanation:

<h3><u>Given</u><u>:</u><u>-</u></h3>

(√3+√2)/(√3-√2)

<h3><u>To </u><u>find</u><u>:</u><u>-</u></h3>

<u>Rationalised</u><u> form</u><u> </u><u>=</u><u> </u><u>?</u>

<h3><u>Solution</u><u>:</u><u>-</u></h3>

We have,

(√3+√2)/(√3-√2)

The denominator = √3-√2

The Rationalising factor of √3-√2 is √3+√2

On Rationalising the denominator then

=>[(√3+√2)/(√3-√2)]×[(√3+√2)/(√3+√2)]

=>[(√3+√2)(√3+√2)]×[(√3-√2)(√3+√2)]

=>(√3+√2)²/[(√3-√2)(√3+√2)]

=> (√3+√2)²/[(√3)²-(√2)²]

Since (a+b)(a-b) = a²-b²

Where , a = √3 and b = √2

=> (√3+√2)²/(3-2)

=> (√3-√2)²/1

=> (√3+√2)²

=> (√3)²+2(√3)(√2)+(√2)²

Since , (a+b)² = a²+2ab+b²

Where , a = √3 and b = √2

=> 3+2√6+2

=> 5+2√6

<h3><u>Answer:-</u></h3>

The rationalised form of (√3+√2)/(√3-√2) is 3+2√6+2.

<h3><u>Used formulae:-</u></h3>

→ (a+b)² = a²+2ab+b²

→ (a-b)² = a²-2ab+b²

→ (a+b)(a-b) = a²-b²

→ The Rationalising factor of √a-√b is √a+√b

8 0
2 years ago
Find the 9th term of the geometric sequence 5, -25, 125
UkoKoshka [18]

Answer:

The previous number keeps getting multiplied by - 5

Step-by-step explanation:

5 × -5 = -25

-25 × -5 = 125

125× -5 = -625

-625 × -5 = 3,125

3125 × -5 = -15,625

-15,625 × -5 = 78,125

78,125 × -5 = -390, 625

-390,625 × -5 = 1,953,125

1,953,125 × -5 = 9,765,625

:)

7 0
3 years ago
Operación 1: (6+(4*12)/12-2)+5​
Julli [10]

Answer:

<h2>13</h2>

Step-by-step explanation:

6+ (4)(12) /12 −2+5

=6+ 48 /12 −2+5

=6+4−2+5

=10−2+5

=8+5

=13

6 0
2 years ago
If f(x) = 2x^3 - 14x^2 + 38x -26 and x-1 is a factor of f(x) find all of the zeros of f(x) algebraically.
Anestetic [448]

Answer:

Step-by-step explanation:

First confirm that x = 1 is one of the zeros.

f(1) = 2(1)^3 - 14(1)^2 + 38(1) - 26

f(1) = 2 - 14 + 38 - 26

f(1) = -12 + 38 = + 26

f(1) = 26 - 26

f(1) = 0

=========================

next perform a long division

x -1  || 2x^3 - 14x^2 + 38x - 26 || 2x^2 - 12x + 26

          2x^3 - 2x^2

          ===========

                    -12x^2 + 28x

                     -12x^2 +12x

                     ==========

                                  26x -26

                                  26x - 26

                                 ========

                                      0

Now you can factor 2x^2 - 12x + 26

                                 2(x^2 - 6x + 13)

The discriminate of the quadratic is negative. (36 - 4*1*13) = - 16

So you are going to get a complex result.

x = -(-6) +/- sqrt(-16)

     =============

                 2

x  = 3 +/- 2i

f(x) = 2*(x - 1)*(x - 3 + 2i)*(x - 3 - 2i)

The zeros are

1

3 +/- 2i

8 0
3 years ago
Write the ratio in fractional notation in lowest terms. 28 inches to 42 inches
ivolga24 [154]

28 to 42 means 28/42

We now reduce 28/42 to lowest terms.

28 ÷ 7 = 4

42 ÷ 7 = 6

We now have 4/6.

We now reduce 4/6.

4 ÷ 2 = 2

6 ÷ 2 = 3

Final answer: 2/3

7 0
3 years ago
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