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vlabodo [156]
3 years ago
5

If O N = 8 x − 8 , L M = 7 x + 4 , N M = x − 5 , and O L = 3 y − 6 , find the values of x and y for which LMNO must be a paralle

logram. The diagram is not drawn to scale.

Mathematics
1 answer:
posledela3 years ago
7 0

Answer:

x=12\\y=\frac{13}{3}


Step-by-step explanation:

For it to be a parallelogram, opposite sides have to be of same length.

  • OL = NM, and
  • ON = LM

Using the expressions given, we can make 2 equations:

<u>Equation 1:</u>

OL=NM\\3y-6=x-5\\-x+3y=1


<u>Equation 2:</u>

ON=LM\\8x-8=7x+4\\


<em>Solving equation 2, we have x:</em>

8x-8=7x+4\\8x-7x=4+8\\x=12

<em>Plugging this value of x into equation 1, we can solve for y:</em>

-x+3y=1\\-(12)+3y=1\\-12+3y=1\\3y=13\\y=\frac{13}{3}

So,

x=12\\y=\frac{13}{3}



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kirza4 [7]

Answer:

<h2>7.4inches</h2>

Step-by-step explanation:

Check the attachment for the diagram. Sine rule will be used to get the unknown side of the triangle.

According to the rule;

\frac{u}{sinU} =  \frac{v}{sinV} = \frac{w}{sinW}\\\frac{u}{sinU} = \frac{w}{sinW}

Given w = 3 in, ∠W=23° and ∠U=73°, on substituting into the equation above to get u we have;

\frac{u}{sin73^{0} } = \frac{3}{sin23^{0} }\\usin23^{0} = 3sin73^{0}\\u = \frac{3sin73^{0} }{sin23^{0} }\\u = \frac{2.87}{0.39} \\u = 7.358\\u = 7.4in

The length of u is 7.4inches to nearest 10th of an inch

6 0
3 years ago
Find the area of ABC with vertices A(3,-6), B(5,-6), and C(7,–9).
stellarik [79]

Area of a triangle ABC with the given vertices is 3 square units.

Given that, the vertices of a triangle ABC, A(3,-6), B(5,-6), and C(7,–9).

<h3>What is the area of triangle formula in coordinate geometry?</h3>

In Geometry, a triangle is a three-sided polygon that has three edges and three vertices. The area of the triangle is the space covered by the triangle in a two-dimensional plane.

Area of a triangle = \frac{1}{2} ( |x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)|)

Here, (x1, y1) = A(3,-6), (x2, y2) = B(5,-6), and (x3, y3) = C(7,–9)

Now, the area of a triangle = 1/2 (|3(-6+9)+5(-9+6)+7(-6+6)|)

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= 1/2 × 6

= 3 square units

Therefore, area of a triangle ABC with the given vertices is 3 square units.

To learn more about the area of a area of triangle with vertices visit:

brainly.com/question/26633662.

#SPJ1

7 0
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likoan [24]
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Hope this helps!
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Now the expression to determine 23% of 122 is

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7 0
3 years ago
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