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Mkey [24]
3 years ago
13

The graph of a linear function passes through the points (2, 4) and (8, 10).

Mathematics
1 answer:
taurus [48]3 years ago
7 0
\bf \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
%   (a,b)
&({{ -2}}\quad ,&{{ 4}})\quad 
%   (c,d)
&({{ 8}}\quad ,&{{ 10}})
\end{array}
\\\\\\
% slope  = m
slope = {{ m}}= \cfrac{rise}{run} \implies 
\cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{10-4}{8-(-2)}\implies \cfrac{10-4}{8+2}\implies \cfrac{6}{10}
\\\\\\
\cfrac{3}{5}

\bf \stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-4=\cfrac{3}{5}[x-(-2)]\implies y-4=\cfrac{3}{5}(x+2)
\\\\\\
y-4=\cfrac{3}{5}x+\cfrac{6}{5}\implies y=\cfrac{3}{5}x+\cfrac{6}{5}+4\implies y=\cfrac{3}{5}x+\cfrac{26}{5}
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3 years ago
22 less than 6 times a number is 92. What is the number?
Romashka [77]

Answer:

n=19

Step-by-step explanation:

6n - 22 = 92

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4 0
3 years ago
An object is launched straight into the air. The projectile motion of the object can be modeled using h(t) = 96t – 16t2, where t
ratelena [41]

Answer with Step-by-step explanation:

We are given that height of projectile after t seconds is given by

h(t)=96t-16t^2

a.h(t)=144 ft

144=96t-16t^2

16t^2-96t+144=0

t^2-6t+9=0

t^2-3t-3t+9=0

t(t-3)-3(t-3)=0

(t-3)(t-3)=0

t-3=0

t=3

After 3 s, the height of the project will be 144 feet in the air.

b.h(t)=0

96t-16t^2=0

16t(6-t)=0

16t=0\implies t=0

6-t=0\implies t=6

At t=0, the initial position of projectile

At t=6 s , the projectile will hit the ground.

6 0
4 years ago
Which rectangle if reflected over the x-axis and then translated 8 units right will result in rectangle E?
Komok [63]

Answer:

Rectangle D is reflected over the x-axis and then translated 8 units right will result in rectangle E

Step-by-step explanation:

The coordinates of rectangle D are:

(-1, 1)

(-1, 4)

(-3, 1) and

(-3, 4)

The rule of reflection across x-axis is given by:

(x, y) \rightarrow (x , -y)

(-1, 1) \rightarrow (-1 , -1)

(-1, 4) \rightarrow (-1 , -4)

(-3, 1) \rightarrow (-3 , -1)

(-3, 4) \rightarrow (-3 , -4)

Next, translate this 8 unit right which is given by:

(x, y) \rightarrow (x+8 , y)

(-1, -1) \rightarrow (-1+8 , -1) =(7, -1)

(-1, -4) \rightarrow (-1+8 , -4) =(7, -4)

(-3, -1) \rightarrow (-3+8 , -1) =(5, -1)

(-3, -4) \rightarrow (-3+8 , -4) =(5, -4)

⇒(7, -1) , (5, -1) , (5, -4) and (7, -4) represents the coordinate of rectangle E.

Therefore, Rectangle D if reflected over the x-axis and then translated 8 units right will result in rectangle E

5 0
3 years ago
Read 2 more answers
3
sergejj [24]

Answer:

The gradient of the graph below is \mathbf{\frac{3}{2} }

Step-by-step explanation:

We need to calculate the gradient of the graph

The gradient of graph is actually slope of the graph.

The slope of graph can be calculated using formula: Slope=\frac{y_2-y_1}{x_2-x_1}

Taking any 2 points on graph i.e

(1,0) and (-1,-3)

We have x_1=1, y_1=0, x_2=-1,y_2=-3

Putting values and finding gradient:

Slope=\frac{y_2-y_1}{x_2-x_1}\\Slope=\frac{-3-0}{-1-1}\\Slope=\frac{-3}{-2}\\Slope=\frac{3}{2}

So, The gradient of the graph below is \mathbf{\frac{3}{2} }

3 0
3 years ago
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