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Katarina [22]
3 years ago
9

The rate of change in the function y=x+4 is________ the rate of change of the function represented in the table.

Mathematics
2 answers:
Snezhnost [94]3 years ago
4 0
Recall that the slope is the "average rate of change" of any function.

\bf y=\stackrel{slope}{1}x+4\qquad \qquad 
\begin{array}{ccll}
x&y\\
\text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\
0&6\\2&8\\4&10\\6&12
\end{array}
\\\\\\
\textit{let's check what is the slope of the tabled function}\\
\textit{by using two points from it}

\bf \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
%   (a,b)
&({{ 2}}\quad ,&{{ 8}})\quad 
%   (c,d)
&({{ 6}}\quad ,&{{ 12}})
\end{array}
\\\\\\
% slope  = m
slope = {{ m}}= \cfrac{rise}{run} \implies 
\cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{12-8}{6-2}\implies \cfrac{4}{4}\implies 1
Vladimir79 [104]3 years ago
4 0

Answer:

Option C.

Step-by-step explanation:

The slope intercept form of a line is

y=mx+b        .... (1)

The given function is

y=x+4           ..... (2)

On comparing (1) and (2) we get

m=1

Rate of change of first function is 1.

If a line passes through two points (x_1,y_1), and (x_2,y_2), the rate of change of the line is

m=\dfrac{y_2-y_1}{x_2-x_1}

From the given table it is clear that the line passes through two points (0,6) and (2,8). So, the rate of change of second function is

m=\dfrac{8-6}{2-0}

m=\dfrac{2}{2}

m=1

Rate of change of second function is 1.

The rate of change in the function y=x+4 is equal to the rate of change of the function represented in the table.

Therefore, the correct option is C.

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Select the correct answer.
EleoNora [17]

Answer:

Option (B)

Step-by-step explanation:

There are two lines on the graph representing the system of equations.

First line passes through two points (-3, 1) and (-2, 3).

Slope of the line = \frac{y_2-y_1}{x_2-x_1}

                           = \frac{3-1}{-2+3}

                       m = 2

Equation of the line passing through (x', y') and slope = m is,

y - y' = m(x - x')

Equation of the line passing through (-3, 1) and slope = 2 will be,

y - 1 = 2(x + 3)

y = 2x + 7 ----------(1)

Second line passes through (0, 1) and (-1, 4) and y-intercept 'b' of the line is 1.

Let the equation of this line is,

y = mx + b

Slope 'm' = \frac{y_2-y_1}{x_2-x_1}

               = \frac{4-1}{-1-0}

               = -3

Here 'b' = 1

Therefore, equation of the line will be,

y = -3x + 1 ---------(2)

From equation (1) and (2),

2x + 7 = -3x + 1

5x = -6

x = -\frac{6}{5}

x = -1\frac{1}{5}

From equation (1),

y = 2x + 7

y = -\frac{12}{5}+7

  = \frac{-12+35}{5}

  = \frac{23}{5}

  = 4\frac{3}{5}

Therefore, exact solution of the system of equations is (-1\frac{1}{5},4\frac{3}{5}).

Option (B) will be the answer.

5 0
3 years ago
Write the ordered pair that represents MP. Then find the magnitude of MP.
jarptica [38.1K]

Answer:

(23,-4):\sqrt{545} units

Step-by-step explanation:

We are given that M(-19,4)and P(4,0)

We have to find the ordered pair that represents MP and find the magnitude of MP.

MP=P-M

MP=(4,0)-(-19,4)=(4+19,0-4)

MP=(23,-4)

Magnitude of MP=\sqrt{(23)^2+(-4)^2}

Magnitude of MP=\sqrt{529+16}

Magnitude of MP=\sqrt{545} units

Hence, .option c is true.

Answer:c.(23,-4):\sqrt{545} units

5 0
2 years ago
HELP!
Flauer [41]

7/50 = 0.14 therefore In order to write it as a fraction out of 100 you move 2 decimal to the right.

Therefore, the answer for the first box is 14/100

The last box obviously being 0.14

6 0
3 years ago
Read 2 more answers
Gemma's mean speed on her drive home from Chicago is 59mph. If the total trip is 295 miles, how long should she expect the drive
SCORPION-xisa [38]

Answer:

5 hours

Step-by-step explanation:

If shes going 59mph and the total trip is 295mph

then you would divid 295 by 59 and get 5

5 0
2 years ago
Given m||n, find the value of x.<br> +<br> (5x+16)<br> mm<br> (6x-7)
kupik [55]

Based on the definition of congruent angles, the value of x is: 23.

<h3>What are Congruent Angles?</h3>

Congruent angles have the same measure. Examples of angles that are congruent are:

  • Alternate interior angles
  • Alternate exterior angles
  • Corresponding angles

Thus:

(5x + 16) = (6x - 7) -- congruent angles

Combine like terms

5x - 6x = -16 - 7

-x = -23

x = 23

Therefore, based on the definition of congruent angles, the value of x is: 23.

Learn more about congruent angles on:

brainly.com/question/1675117

5 0
2 years ago
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