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Veseljchak [2.6K]
3 years ago
11

What is the intercept s of 3x+y=6

Mathematics
2 answers:
Ksivusya [100]3 years ago
7 0
To find the x-intercept, substitute in
0
0
for
y
y
and solve for
x
x
.
3
x
+
(
0
)
=
6
3
x
+
(
0
)
=
6
Solve the equation.
Tap for more steps...
x
=
2
x
=
2
To find the y-intercept, substitute in
0
0
for
x
x
and solve for
y
y
.
3
(
0
)
+
y
=
6
3
(
0
)
+
y
=
6
Simplify the left side.
Tap for more steps...
y
=
6
y
=
6
These are the
x
x
and
y
y
intercepts of the equation
3
x
+
y
=
6
3
x
+
y
=
6
.
x-intercept:
(
2
,
0
)
(
2
,
0
)
y-intercept:
(
0
,
6
)
dybincka [34]3 years ago
4 0
2,0,6 are the intercepts
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Please solve the problem ​
jek_recluse [69]

Treat the matrices on the right side of each equation like you would a constant.

Let 2<em>X</em> + <em>Y</em> = <em>A</em> and 3<em>X</em> - 4<em>Y</em> = <em>B</em>.

Then you can eliminate <em>Y</em> by taking the sum

4<em>A</em> + <em>B</em> = 4 (2<em>X</em> + <em>Y</em>) + (3<em>X</em> - 4<em>Y</em>) = 11<em>X</em>

==>   <em>X</em> = (4<em>A</em> + <em>B</em>)/11

Similarly, you can eliminate <em>X</em> by using

-3<em>A</em> + 2<em>B</em> = -3 (2<em>X</em> + <em>Y</em>) + 2 (3<em>X</em> - 4<em>Y</em>) = -11<em>Y</em>

==>   <em>Y</em> = (3<em>A</em> - 2<em>B</em>)/11

It follows that

X=\dfrac4{11}\begin{bmatrix}12&-3\\10&22\end{bmatrix}+\dfrac1{11}\begin{bmatrix}7&-10\\-7&11\end{bmatrix} \\\\ X=\dfrac1{11}\left(4\begin{bmatrix}12&-3\\10&22\end{bmatrix}+\begin{bmatrix}7&-10\\-7&11\end{bmatrix}\right) \\\\ X=\dfrac1{11}\left(\begin{bmatrix}48&-12\\40&88\end{bmatrix}+\begin{bmatrix}7&-10\\-7&11\end{bmatrix}\right) \\\\ X=\dfrac1{11}\begin{bmatrix}55&-22\\33&99\end{bmatrix} \\\\ X=\begin{bmatrix}5&-2\\3&9\end{bmatrix}

Similarly, you would find

Y=\begin{bmatrix}2&1\\4&4\end{bmatrix}

You can solve the second system in the same fashion. You would end up with

P=\begin{bmatrix}2&-3\\0&1\end{bmatrix} \text{ and } Q=\begin{bmatrix}1&2\\3&-1\end{bmatrix}

3 0
3 years ago
How many cubes with edge lengths of 1/4 in. will it take to fill the prism?
Ulleksa [173]

Answer:

1560

Step-by-step explanation:

First (2 1/2)/(1/4) = (5/2)(4) = 20/2 = 10

Next, 3/(1/4) = 3(4) = 12

Lastly, (3 1/4)/(1/4) = (13/4) x 4 = 52/4 = 13

This means we need 10 rows of 12, 13 high. 10(12)(13) = 1560 cubes.

Another way is to multiply 2 1/2 x 3 x 3 1/4 = 5/2 x 3 x 13/4 = 195/8

A 1/4 inch cube is 1/4 x 1/4 x 1/4 for a volume of 1/64

(195/8)/(1/64) = (195/8)(64) = 1560 cubes.

3 0
2 years ago
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