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3 years ago

Brainliest if answered correctly.

Mathematics

1 answer:

allochka39001 [22]3 years ago

6 0

Answer:

a=35°, b=55°, c=110°

Step-by-step explanation:

reason for a and b is that when 2 lines intersect, the opposite angles are equal.

well for c angles on a straight line add upto 180.

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If a + b + c.= 5 and ab + bc +ca = 10 , then prove that a3+ b3+ c3-3abc = -25

Alex Ar [27]

Start with

$(a+b+c)^3=a^3+b^3+c^3+3(a^2b+a^2c+ab^2+ac^2+b^2c+bc^2)+6abc$

Given that $a+b+c=5$ , we know $(a+b+c)^3=125$ .

Also, $ab+bc+ca=10$ , so

$a^2b+a^2c+ab^2+ac^2+b^2c+bc^2=a(ab+ac)+b(ab+bc)+c(ac+bc)$

$=a(10-bc)+b(10-ca)+c(10-ab)$

$=10(a+b+c)-3abc$

$=50-3abc$

So we have

$125=a^3+b^3+c^3+3(50-3abc)+6abc$

$125=a^3+b^3+c^3+150-9abc+6abc$

$\implies -25=a^3+b^3+c^3-3abc$

QED

3 0

3 years ago

Select the polynomial that is a perfect square trinomial. 36x2 − 4x 16 16x2 − 8x 36 25x2 9x 4 4x2 20x 25.

Naya [18.7K]

The polynomial a,b,c,are not perfect square polynomial and the polynomial d is perfect square polynomial.

The given polynomial is

$a) 36x^2-4x+16$

What is the form of perfect square polynomial?

$(ax+b)^2$

we solve this method by using perfect square method

add and subtract 1/9

$36x^2-4x+16+\frac{1}{9}-\frac{1}{9}$

factor 36

$\frac{143}{9}+36(x^2-\frac{x}{9}+\frac{1}{324} )$

Now complete the square

$\frac{143}{9}+36(x^2-\frac{1}{18})^2$

Therefore this is not perfect square trinomial.

Similarly for

$b) 16x^2-8x+36$

Complete square is,

$16(x-\frac{1}{4})^2+35$

This polynomial is also not perfect square trinomial.

$c) 25x^2+9x+4\\$

complete square is,

$25(x+\frac{9}{50})^2+\frac{319}{100}$

This polynomial is not perfect square trinomial.

$d)4x^2+20x+25\\$

complete square is,

$(2x+5)^2$

This polynomial is perfect square trinomial.

Therefore,

The polynomial a,b,c,are not perfect square polynomial and the polynomial d is perfect square polynomial.

To learn more about perfect square trinomial visit:

brainly.com/question/1538726

3 0

2 years ago

Dan received $92 for his birthday. He went to a sporting goods store and bought a few items. He had $17 left over, how much did

Vanyuwa [196]

92-x=17

92-17=x

X= 75

7 0

4 years ago

Read 2 more answers

Use the elimination method to solve the system of equations.

omeli [17]

Answer:

Step-by-step explanation:

6 0

3 years ago

Please help the answer are 12 4 X X+4 -16 16 X+12 X^2

Lorico [155]

Step 1:
x² + 4x = 192

Step 2:
Take x common:
x ( x + 4) = 192

Length is x and width is x+4

Step 3:

x² + 4x - 192 = 0

Step 4:

x² + 16x - 12x - 192 = 0
x(x+16) - 12(x+16) = 0
(x-12)(x+16) = 0

⇒ x=12, x=-16

Because the length can't be -16, the length is 12.

7 0

3 years ago

Read 2 more answers