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2 years ago

If VX = WZ = 40 cm and m∠ZVX = m∠XWZ = 22°, can ΔVZX and ΔWXZ be proven congruent by SAS? Why or why not?

Mathematics

2 answers:

IgorC [24]2 years ago

7 0

Answer:

I believe the answer is C, No, the sides of the triangles intersect.

Paul [167]2 years ago

4 0

Answer: The ΔVZX and ΔWXZ are not congruent by SAS.

Explanation:

It is given that the VX = WZ = 40 cm and ∠ZVX = ∠XWZ = 22°.

Draw a figure as shown below,

According to the SAS rule of congruence, two triangles are congruent if two sides and their inclined angle is equal.

From the given figure it is easily noticed that in ΔVZX and ΔWXZ,

$VX=WZ=40cm$ (given)

$\angle ZVX=\angle XWZ=22^{\circ}$ (given)

$XZ=XZ$ (common side)

Since we have two sides and one angle is same. but we can not conclude that the ΔVZX and ΔWXZ are congruent by SAS, because the given angle is not the inclined angle of both equal sides.

Therefore, the ΔVZX and ΔWXZ are not congruent by SAS.

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So, the sixth term is C(6,5)(3)(-2x)^5 = 6! / [5! (6-5)! ] * 3 * (-2)^5 x^5 = - 6*3*32 = - 576 x^5.

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The question is incomplete:

The Community Relief Fund receives a large donation of $2800. The foundation agrees to spend the money on $20 school bags, $25 sweaters, $5 books. They want to buy 200 items and send them to schools in earthquake-hit areas. They must order as many books as school bags and sweaters combined. How many of each item should they order?

Answer:

They must order 40 bags, 60 sweaters and 100 books.

Step-by-step explanation:

From the information provided, you can write the following equations:

x+y+z=200 (1)

20x+25y+5z=2800 (2)

z=x+y (3), where:

x=amount of bags

y=amount of sweaters

z=amount of books

Now, you can replace (3) in (1) and (2):

x+y+x+y=200

2x+2y=200 (4)

20x+25y+5(x+y)=2800

20x+25y+5x+5y=2800

25x+30y=2800 (5)

Then, you will have 2 equations:

2x+2y=200 (4)

25x+30y=2800 (5)

You can isolate x in (4):

2x=200-2y

x=100-y (6)

After this, you can replace (6) in (5):

25(100-y)+30y=2800

2500-25y+30y=2800

5y=2800-2500

y=300/5

y=60

Next, you can replace the value of y in (6) to find the value of x:

x=100-60

x=40

Finally, you can replace the value of x and y in (3) to find the value of z:

z=40+60

z=100

According to this, the answer is that they must order 40 bags, 60 sweaters and 100 books.

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