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3 years ago

Part A: Determine if the expression is one of our special products. If so, identify it by its general form:

Mathematics

1 answer:

Svetradugi [14.3K]3 years ago

8 0

Answer:

Part A: Yes, it is (a - b)².

Part B: a² - 2ab + b² => (x - 6)² = x² - 12x + 36.

Part C: x² - 12x + 36.

Part A: Not a special product.

Part B: Binomial distribution => (x + 8)(x + 1) = x² + 9x + 8.

Part C: x² + 9x + 8.

Part A: Yes, it is (a + b)²

Part B: a² + 2ab + b² => (3x + 2)² = 9x² + 12x + 4.

Part C: 9x² + 12x + 4.

Part A: Yes, it is (a + b)(a - b), a difference of squares.

Part B: a² - b² => 4x² - 49

Part C: 4x² - 49.

Part A: Not a special product.

Part B: Binomial distribution => (x - 5)(2x - 5) = 2x² - 15x + 25.

Part C: 2x² - 15x + 25.

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I DONT KNOW THESE! HELP!

kkurt [141]

Answer:

20. x = 5, y = -2

21. x = 11, y = 12

22. x = 22, y = 11

23. x = 11, y = 10

Step-by-step explanation:

20. Opposite sides in the parallelogram are congruent, so

$2y+18=3x-1\\ \\6x-3=17-5y$

Solve this system of two equations:

$\left\{\begin{array}{l}2y-3x=-19\\ \\6x+5y=20\end{array}\right.$

Multiply the first equation by 2 and add two equations:

$2(2y-3x)+6x+5y=2\cdot (-19)+20\\ \\4y-6x+6x+5y=-38+20\\ \\9y=-18\\ \\y=-2$

Substitute it into the first equation:

$2\cdot (-2)-3x=-19\\ \\-3x=-19+4\\ \\-3x=-15\\ \\x=5$

21. Opposite angles in the parallelogram are congruent, so

$11x+5=10y+6$

Consecutive angles are supplementary, so

$6x-y+11x+5=180^{\circ}$

Solve this system of two equations:

$\left\{\begin{array}{l}11x-10y=1\\ \\17x-y=175\end{array}\right.$

From the second equation

$y=17x-175$

Substitute it into the first equation:

$11x-10(17x-175)=1\\ \\11x-170x+1750=1\\ \\-159x=-1749\\ \\x=11\\ \\y=17\cdot 11-175=187-175=12$

22. Opposite angles in the parallelogram are congruent, so

$2x-5=3y-12$

Consecutive angles are supplementary, so

$2x-5+7y+x=180^{\circ}$

Solve this system of two equations:

$\left\{\begin{array}{l}2x-3y=-7\\ \\3x+7y=185\end{array}\right.$

From the first equation

$x=-3.5+1.5y$

Substitute it into the second equation:

$3(-3.5+1.5y)+7y=185\\ \\-10.5+4.5y+7y=185\\ \\-105+45y+70y=1,850\\ \\115y=1,850+105\\ \\115y=1,955\\ \\y=17\\ \\x=-3.5+1.5\cdot 17=22$

23. Opposite sides in the parallelogram are congruent, so

$2x+9=4y-9\\ \\3x-5=2y+8$

Solve this system of two equations:

$\left\{\begin{array}{l}2x-4y=-18\\ \\3x-2y=13\end{array}\right.$

Multiply the second equation by 2 and subtract it from the first equation:

$2x-4y-2(3x-2y)=-18-2\cdot 13\\ \\2x-4y-6x+4y=-18-26\\ \\-4x=-44\\ \\x=11$

Substitute it into the first equation:

$2\cdot 11-4y=-18\\ \\-4y=-18-22\\ \\-4y=-40\\ \\y=10$

3 0

3 years ago

The figure below shows square ABCD inscribed on square PQRM on a coordinate plane. Which of the following expressions represents

vova2212 [387]

The hypotenuse of the triangle is given by:
$CB ^ 2 = RC ^ 2 + RB ^ 2
$
Substituting values:
$CB ^ 2 = 2 ^ 2 + 4 ^ 2
$
Clearing CB we have:
$CB = \sqrt{ 2 ^ 2 + 4 ^ 2} 

 CB = \sqrt{ 4 + 16} 

 CB = \sqrt{20} 

 CB = \sqrt{4*5} 

 CB = 2\sqrt{5} 



$
Then, the perimeter of the triangle is:
$P = RB + RC + CB
$
Substituting values:
$P = 4 + 2 + 2 \sqrt{5} 

 P = 6 + 2 \sqrt{5}$
Answer:
the perimeter of triangle BRC in units is:
D.6 + 2√5

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2 years ago

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fenix001 [56]

Answer:

Step-by-step explanation:

Because the journey is 120km long, and the mortoristgoes less than 60km per hour. So in 2 hours, the motorist will go less than 120 km. So he needs more than 2 hours to go 120 km

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3 years ago

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Evaluate 8a - 1 + 0.5b when a= 1/4 and b=10.

nikitadnepr [17]

Answer:

Step-by-step explanation:

Substitute 1/4 with 8a. 8/4=2

Next, Substitute 10 for 0.5. 10/2=5

Finally, find the sum

(2-1)+5

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