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steposvetlana [31]
2 years ago
8

A line passes through the points (1, –6) and (4, 3).

Mathematics
1 answer:
Marina CMI [18]2 years ago
6 0

Answer:

y = 3x - 9

Step-by-step explanation:

We first need to find the slope (m)

m = \frac{y_2-y_1}{x_2-x_1} = \frac{3 - (-6)}{4-1} = \frac{9}{3} = 3

y = mx + b

y = 3x + b

(4, 3)

y = 3x + b

3 = 3(4) + b

3 = 12 + b

-12  -12

-9 = b

(1, –6)

y = 3x + b

-6 = 3(1) + b

-6 = 3 + b

-3   -3

-9 = b

y = 3x - 9

To check:  (1, –6)

y = 3x - 9

-6 = 3(1) - 9

-6 = 3 - 9

-6 = -6

Hope this helps!

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Prime numbers are numbers that only have a factor of one and its self.
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3 years ago
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A tangent line and its normal line have a point of tangency to the function f(x) at (x,y). If the slop of the normal line is m=(
alekssr [168]

Answer:

\displaystyle \\\left(\frac{49}{900},\frac{3761}{900}\right) or approximately (0.544, 4.179)

Step-by-step explanation:

A function and its tangent lines intersect when their slopes are the same. Find the x-coordinate when the slope of f(x) is equal to 8/7 by taking the derivative of f(x):

\displaystyle\\f(x)=\sqrt{x}-x+4\\f'(x)=\frac{1}{2}\cdot\frac{1}{\sqrt{x}}-1=\frac{1}{2\sqrt{x}}-1

Set f'(x) equal to 8/7 and solve for x:

\displaystyle \\\frac{1}{2\sqrt{x}}-1=\frac{8}{7},\\x=\frac{49}{900}

Therefore, f(x) will intersect at a point of tangency with a line of slope 8/7 at x=49/900. Plug in x=49/900 into f(x) to get the y-coordinate:

\displaystyle\\y=\sqrt{x}-x+4 \vert_{x=49/900}=\frac{3761}{900}

⇒Answer: (49/900, 3761/900) or approximately (0.544, 4.179)

5 0
2 years ago
Help!!!
nordsb [41]

Answer:

1 1/5 per person.

Step-by-step explanation:

You have to evenly divide the 6 funnel cakes among 5 people, so the equation you have to use is division.

  5/6

= 1 1/5

6 0
2 years ago
Can someone help me with this math homework please!
mamaluj [8]

Answer:

The rock hits the ground between <u>2</u> seconds and <u>2.5</u> seconds after it is dropped

Step-by-step explanation:

The given table is presented as follows;

\begin{array}{ccl}t&h(t)&Description\\0&20&Initial \ height\\0.5&18.8&Rock \ in \ downward \ motion\\1&15.1&\\1.5&9&\\2&0.4&The \ height \ just \ before \ the \ rock \ hits \ the \ ground \\2.5&-10.6&The \ calculated \ height \ after\ the \ rock \ hits \ the \ ground \\3&-24.1&Calculated \ height \ after\ the \ rock \ hits \ the \ ground\end{array}

Therefore, the rock hits the ground between t = 2 seconds and t = 2.5 seconds after it is dropped.

4 0
3 years ago
Find the value of x in the triangle shown below​
CaHeK987 [17]

Answer:

<h2>46.4°</h2>

Step-by-step explanation:

Apply sine formula:

\frac{sin \: a}{a}  =  \frac{sin \: b}{b}  =  \frac{sin \: c}{c}

\frac{sin \: a}{a}  =  \frac{sin \: c}{c}

Plug the values

\frac{sin \: (88)}{6.9}  =  \frac{sin \: x}{5}

Apply cross product property

5 \: sin \: (88) = 6.9 \: (sin \: x)

\frac{5 \: sin \: (88)}{6.9}  = sin \: x

x =  {sin}^{ - 1} ( \frac{5 \: sin \:( 88)}{6.9} )

x = 46.4

Hope this helps .....

Best regards!!!

3 0
3 years ago
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