$\left\{\begin{array}{ccc}-5x+3y=3\\-4x+y=1&|\text{add 4x to both sides}\end{array}\right\\\\\left\{\begin{array}{ccc}-5x+3y=3\\y=4x+1&(*)\end{array}\right\\\\\text{Substitute }\ (*)\ \text{to the first equation}\\\\-5x+3(4x+1)=3\qquad\text{use distributive property}\\\\-5x+(3)(4x)+(3)(1)=3\\\\-5x+12x+3=3\qquad\text{subtract 3 from both sides}\\\\7x=0\qquad\text{divide both sides by (-5)}\\\\\boxed{x=0}\\\\\text{Substitute the value of x to}\ (*):\\\\y=4(0)+1\\y=0+1\\\boxed{y=1}\\\\Answer:\ x=0\ and\ y=1.$

5 0

2 years ago

Suppose that LMN is isosceles with base LN suppose that M

ira [324]

Given:

In an isosceles triangle LMN, LM=MN.

$m\angle M=(3x+17)^\circ,m\angle L=(2x+36)^\circ$

To find:

The measure of the angles L, M and N.

Solution:

In triangle LMN,

$LM=MN$ (Given)

$m\angle N=m\angle L=(2x+36)^\circ$ (Base angles of an isosceles triangle are equal)

Now,

$m\angle L+m\angle M+m\angle N=180^\circ$

$(2x+36)^\circ+(3x+17)^\circ+(2x+36)^\circ=180^\circ$

$(7x+89)^\circ=180^\circ$

$(7x+89)=180$

On further simplification, we get

$7x=180-89$

$7x=91$

$x=\dfrac{91}{7}$

$x=13$

The value of x is 13. Using this value, we get

$m\angle L=(2(13)+36)^\circ$

$m\angle L=(26+36)^\circ$

$m\angle L=62^\circ$

Similarly,

$m\angle M=(3(13)+17)^\circ$

$m\angle M=(39+17)^\circ$

$m\angle M=56^\circ$

And,

$m\angle N=m\angle L$

$m\angle N=62^\circ$

Therefore, the measure of angles are $m\angle L=62^\circ,m\angle M=56^\circ,m\angle N=62^\circ$ .

5 0

2 years ago

What’s the correct answer for this question?

weqwewe [10]

Answer:

Last answer choice

Step-by-step explanation:

The AAS congruence theorem uses two adjacent angles, followed by a side length on the side (not in between the angles.) Therefore, the first answer is ruled out (because it deals with angles and not sides), and the second answer is ruled out because it involves side lengths between angles. LP=MO may be true, but it does not compare the two triangles that we are interested in. However, the last answer choice is correct, because a midpoint divides a line exactly in half, meaning that both halves are the same length and therefore congruent. Therefore, the last answer choice is correct. Hope this helps!

7 0

2 years ago