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pshichka [43]
3 years ago
6

Parallelogram ABCD contains two congruent triangles. In two or more complete sentences, use the triangles to prove opposite side

s are congruent in parallelogram ABCD.
Mathematics
1 answer:
Murljashka [212]3 years ago
7 0
Ok so if I am imagining what I think the diagram is correctly, you could say that because they are congruent triangles their sides will be congruent. If their sides are congruent and the lines that you are trying to prove are part of the triangle, they will be congruent due to the CPCTC theorem. The CPCTC theorem just says that if two triangles are congruent, their corresponding parts are congruent.<span />
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TechWiz Electronics makes a profit of $35 for each MP3 player sold and $18 for each DVD player sold. Last week, TechWiz sold a c
Svetllana [295]

Let x be the number of MP3 players TechWiz sold last week.

If TechWiz sold in total 130 MP3 and DVD players, then it sold (130-x) DVD players.

1. TechWiz Electronics makes a profit of $35 for each MP3 player sold, then it makes a profit $35x for x MP3 players sold.

2. TechWiz Electronics makes a profit of  $18 for each DVD player sold , then it makes a profit $18(130-x) for (130-x) DVD players sold.

3. An expression for the combined total profit (in dollars) TechWiz made from MP3 and DVD players last week is

35x+18(130-x).

You can simplify it:

35x+2,340-18x=17x+2,340

Answer: 35x+18(130-x) or 17x+2,340

8 0
3 years ago
In the parabola y = (x + 12 + 2, what is the vertex?
VladimirAG [237]

Answer:

The vertex is the point (-6,-34)

Step-by-step explanation:

we know that

The equation of a vertical parabola into vertex form is equal to

y=a(x-h)^{2}+k

where

(h,k) is the vertex of the parabola

In this problem we have

y=x^{2}+12x+2

Convert in vertex form

Group terms that contain the same variable, and move the constant to the opposite side of the equation

y-2=x^{2}+12x

Complete the square . Remember to balance the equation by adding the same constants to each side.

y-2+36=x^{2}+12x+36

y+34=x^{2}+12x+36

Rewrite as perfect squares

y+34=(x+6)^{2}

y=(x+6)^{2}-34

The vertex is the point (-6,-34)

4 0
3 years ago
The Pythagorean theorem is a² + b² = c². Solve for b. b=±c+a−−−−√ b=±c2−a2−−−−−−√ b=±c2+a2−−−−−−√ b=±c−a−−−−√
uysha [10]

a^{2} +b^{2} =c^{2}

As we have to solve for b, it means we have to isolate b

So first of all subtract a^{2} from both sides

So we get

b^{2} =c^{2} -a^{2}

Now we need b , but its b^2 , so we can take square root on both sides.


taking square roots on both sides

b= +- \sqrt{c^2 -a^2}


Hence option B is correct

4 0
3 years ago
Please answer the question correctly while showing detailed working. ​
kati45 [8]

Step-by-step explanation:

hey buddy it took a long time but it's ready for you

6 0
2 years ago
Factor 9y2 - 12y + 4.<br><br> (3 y - 2)(3 y + 2)<br> (3 y - 4)( y + 1)<br> (3 y - 2) 2
lozanna [386]

Answer:

(y - 2)²

Step-by-step explanation:

9y² - 12y + 4 ← is a perfect square of the form

(ax - b)² = a²x² - 2abx + b²

Compare like terms with 9y² - 12y + 4, thus

a² = 9 ⇒ a = 3

b² = 4 ⇒ b = 2 and

- 2ab = - 2 × 3 × 2 = - 12

Thus

9y² - 12y + 4 = (3y - 2)²

8 0
3 years ago
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