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3 years ago

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

1 answer:

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

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Answer:

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Step-by-step explanation:

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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.

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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

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3 years ago

Read 2 more answers

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 $\mathbf{\frac{3}{2} }$

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3 years ago