Find the value of d so that the line that passes through (a, b) and (c, d) has a slope of 12

Mathematics

1 answer:

fiasKO [112]2 years ago

4 0

Answer:

I'm guessing that in the book or the homework sheet, they gave you

the values of 'a', 'b', and 'c', and you're supposed to find the value of 'd'.

If you have two points on the line, then the slope of the line is

(the change in 'y') divided by (the change in 'x') .

If the two points are (a, b) and (c, d), then the slope of the line is

(d - b) divided by (c - a) ,

and you have to find the value of 'd' that makes that whole expression

equal to 1/2.

(d - b) / (c - a) = 1/2

Multiply each side by (c - a): (d - b) = 1/2(c - a)

Add 'b' to each side: d = 1/2(c - a) + b

If you know the values of 'a', 'b', and 'c', you can find the value of 'd'.

Step-by-step explanation:

You might be interested in

The surface are I cannot find

Ilia_Sergeevich [38]

check the picture below.

so the triangular prism is really just 3 rectangles and 2 right-triangles,

now, we know the base of one of the triangles is 2.6, what's its height?

since it's a right-triangle, we can simply use the pythagorean theorem to get "h".

$\bf \textit{using the pythagorean theorem}
\\\\
c^2=a^2+b^2\implies \sqrt{c^2-a^2}=b
\qquad
\begin{cases}
c=\stackrel{hypotenuse}{5.2}\\
a=\stackrel{adjacent}{2.6}\\
b=\stackrel{opposite}{h}\\
\end{cases}
\\\\\\
\sqrt{5.2^2-2.6^2}=h\implies 4.5\approx h$

so, we can now, simply get the area of both of the triangles and the three rectangles and sum them up, and that's the area of the triangular prism.

$\bf \stackrel{two~triangles}{2\left[ \cfrac{1}{2}(2.6)(4.5) \right]}~~+~~\stackrel{rectangle}{(2.6\cdot 4.3)}~~+~~\stackrel{rectangle}{(4.3\cdot 3.9)}~~+~~\stackrel{rectangle}{(4.3\cdot 5.2)}
\\\\\\
11.7+11.18+22.36\implies \blacktriangleright 45.24 \blacktriangleleft$