ringearV

2021-08-17

The three straight lines y = x, 7y = 2x, and 4x + y = 60 form a triangle. Find the coordinates of its vertices.

SchulzD

Skilled2021-08-18Added 83 answers

The coordinates of the vertices are the points of intersection of the lines taken two at a time.

Using(1)y=x and (2) 7y=2x, we substitute (1) to (2) and solve for x:

7x=2x

5x=0

x=0

Using(1), we solve for y:

y=0

So, one vertex of the triangle is at (0,0).

Using(1)y=x and (3)4x+y=60, we substitute(1) to (3) and solve for x:

4x+x=60

5x=60

x=12

Using (1), we solve for y:

y=12

So, another vertex of the triangle is at (12,12)

Using (2)7y=2x and (3) 4x+y=60, we first solve for y using (2) to obtain (4):

$y=\frac{2}{7}x$

Substitute (1) and (3) and solve for x:

$4x+\frac{2}{7}x=60$

$\frac{30}{7}x=60$

$x=60\cdot \frac{7}{30}$

x=14

Using(4), we solve for y:

$y=\frac{2}{7}\cdot \left(14\right)$

y=4

So, another vertex of the triangle is at (14,4).

Result: (0,0), (12,12),(14,4)

Using(1)y=x and (2) 7y=2x, we substitute (1) to (2) and solve for x:

7x=2x

5x=0

x=0

Using(1), we solve for y:

y=0

So, one vertex of the triangle is at (0,0).

Using(1)y=x and (3)4x+y=60, we substitute(1) to (3) and solve for x:

4x+x=60

5x=60

x=12

Using (1), we solve for y:

y=12

So, another vertex of the triangle is at (12,12)

Using (2)7y=2x and (3) 4x+y=60, we first solve for y using (2) to obtain (4):

Substitute (1) and (3) and solve for x:

x=14

Using(4), we solve for y:

y=4

So, another vertex of the triangle is at (14,4).

Result: (0,0), (12,12),(14,4)

Describe all solutions of Ax=0 in parametric vector form, where A is row equivalent to the given matrix

$$\left[\begin{array}{cccc}1& 3& 0& -4\\ 2& 6& 0& -8\end{array}\right]$$ Find, correct to the nearest degree, the three angles of the triangle with the given vertices

A(1, 0, -1), B(3, -2, 0), C(1, 3, 3)Whether f is a function from Z to R if

?

a) $f\left(n\right)=\pm n$.

b) $f\left(n\right)=\sqrt{{n}^{2}+1}$.

c) $f\left(n\right)=\frac{1}{{n}^{2}-4}$.How to write the expression ${6}^{\frac{3}{2}}$ in radical form?

How to evaluate $\mathrm{sin}\left(\frac{-5\pi}{4}\right)$?

What is the derivative of ${\mathrm{cot}}^{2}x$ ?

How to verify the identity: $\frac{\mathrm{cos}\left(x\right)-\mathrm{cos}\left(y\right)}{\mathrm{sin}\left(x\right)+\mathrm{sin}\left(y\right)}+\frac{\mathrm{sin}\left(x\right)-\mathrm{sin}\left(y\right)}{\mathrm{cos}\left(x\right)+\mathrm{cos}\left(y\right)}=0$?

Find $\mathrm{tan}\left(22.{5}^{\circ}\right)$ using the half-angle formula.

How to find the exact values of $\mathrm{cos}22.5\xb0$ using the half-angle formula?

How to express the complex number in trigonometric form: 5-5i?

The solution set of $\mathrm{tan}\theta =3\mathrm{cot}\theta $ is

How to find the angle between the vector and $x-$axis?

Find the probability of getting 5 Mondays in the month of february in a leap year.

How to find the inflection points for the given function $f\left(x\right)={x}^{3}-3{x}^{2}+6x$?

How do I find the value of sec(3pi/4)?