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3 years ago

identify the similar triangles in the diagram, then sketch them so the corresponding sides and angles have the same orientation.

Mathematics

1 answer:

alexandr1967 [171]3 years ago

6 0

Answer:

Traingle LKJ is similar to triangle LMK is similar to triangle KMJ

Step-by-step explanation:

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Zero to the power of two

Lubov Fominskaja [6]

Answer:

Step-by-step explanation:

because when you square a number, you multiply it by itself. So, you would do 0 x 0 = 0

Hope this helps!

- profparis

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2 years ago

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The ratio of boys to girls in Ms. Ralph's class is 2 to 3. There are 18 girls in the class. What is the total number of students

Mars2501 [29]

Answer:

Step-by-step explanation:

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3 years ago

Write the polynomial as a square of a binomial or as an expression opposite to a square of a binomial:

spayn [35]

Answer:

A) $0.25x^2-0.6xy+0.36y^2=\left(0.5x-0.6y\right)^2$

B) $-a^2+0.6a-0.09=-\left(10a-3\right)^2$

C) $\frac{9a^4}{16}+a^3+\frac{4a^2}{9}=a^2(\left(9a+8\right)^2)$

D) $-16m^2-24mn -9n^2=-\left(4m+3n\right)^2$

Step-by-step explanation:

The square of a binomial is the sum of: the square of the first terms, twice the product of the two terms, and the square of the last term.

$(a+b)^2 = a^2 + 2ab + b^2\\\\(a-b)^2 = a^2 - 2ab + b^2$

To find the square of the binomial of the following polynomials you must:

A) $0.25x^2-0.6xy+0.36y^2$

Apply radical rule: $a=\left(\sqrt{a}\right)^2$

$0.25=\left(\sqrt{0.25}\right)^2\\0.36=\left(\sqrt{0.36}\right)^2$

$\left(\sqrt{0.25}\right)^2x^2-0.6xy+\left(\sqrt{0.36}\right)^2y^2$

Apply exponent rule: $a^mb^m=\left(ab\right)^m$

$\left(\sqrt{0.25}\right)^2x^2=\left(\sqrt{0.25}x\right)^2\\\left(\sqrt{0.36}\right)^2y^2=\left(\sqrt{0.36}y\right)^2$

$\left(\sqrt{0.25}x\right)^2-0.6xy+\left(\sqrt{0.36}y\right)^2$

Rewrite $0.6xy$ as $2\cdot \:0.5x\cdot \:0.6y$

$\left(\sqrt{0.25}x\right)^2-2\cdot \:0.5x\cdot \:0.6y+\left(\sqrt{0.36}y\right)^2$

Apply perfect square formula: $\left(a-b\right)^2=a^2-2ab+b^2$

$a=0.5x,\:b=0.6y$

$\left(\sqrt{0.25}x\right)^2-2\cdot \:0.5x\cdot \:0.6y+\left(\sqrt{0.36}y\right)^2=\left(0.5x-0.6y\right)^2$

B) $-a^2+0.6a-0.09$

Multiply both sides by 100

$-a^2\cdot \:100+0.6a\cdot \:100-0.09\cdot \:100\\-100a^2+60a-9$

Factor out common term -1

$-\left(100a^2-60a+9\right)$

Break the expression into groups and factor out common terms

$-(\left(100a^2-30a\right)+\left(-30a+9\right))\\-(10a\left(10a-3\right)-3\left(10a-3\right))\\-(\left(10a-3\right)\left(10a-3\right))\\-\left(10a-3\right)^2$

C) $\frac{9a^4}{16}+a^3+\frac{4a^2}{9}$

Apply exponent rule: $a^{b+c}=a^ba^c$

$a^3=aa^2\\a^4=a^2a^2$

$\frac{9a^2a^2}{16}+aa^2+\frac{4a^2}{9}$

Factor out common term $a^2$

$a^2\left(\frac{9a^2}{16}+a+\frac{4}{9}\right)$

Factor $\frac{9a^2}{16}+a+\frac{4}{9}\right$

Find the Least Common Multiplier (LCM) of 16, 9 which is 144.

Multiply by LCM

$\frac{9a^2}{16}\cdot \:144+a\cdot \:144+\frac{4}{9}\cdot \:144\\81a^2+144a+64$

$81a^2+144a+64=\left(9a\right)^2+2\cdot \:9a\cdot \:8+8^2$

Apply perfect square formula: $\left(a+b\right)^2=a^2+2ab+b^2$

$a=9a,\:b=8$

$81a^2+144a+64=\left(9a+8\right)^2$

$\frac{9a^4}{16}+a^3+\frac{4a^2}{9}=a^2(\left(9a+8\right)^2)$

D) $-16m^2-24mn -9n^2$

Factor out common term -1

$-\left(16m^2+24mn+9n^2\right)$

Break the expression into groups and factor out common terms

$\left(16m^2+12mn\right)+\left(12mn+9n^2\right)\\4m\left(4m+3n\right)+3n\left(4m+3n\right)\\\left(4m+3n\right)\left(4m+3n\right)\\-\left(4m+3n\right)\left(4m+3n\right)\\-\left(4m+3n\right)^2$

$-16m^2-24mn -9n^2=-\left(4m+3n\right)^2$

3 0

4 years ago

If a and b are two angles in standard position in Quadrant I, find cos(a+b) for the given function values. sin a=3/5and cos b=12

insens350 [35]

You have to find the cos of angle A, so use the Pythagorean equation and trig laws to find the other side of the triangle created by angle A. 3^2 + x^2 = 5^2. x=4. This means cos(A) = 4/5). Make both cos (A) and cos (B) have equal denominators, and add. 148/185 + 60/185 = 208/185. This answer is correct, though it doesn’t appear to be any of the answers you wrote, so either those answers are wrong or you wrote something incorrectly in the problem.

6 0

3 years ago

Read 2 more answers

-3 x -6 = 9

Lynna [10]

You are correct.
Explanation: An even number of negatives always equal a positive and an odd number of negatives always equals a negative.

7 0

3 years ago