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Dvinal [7]
4 years ago
5

Which inequality is graphed on the coordinate plane?

Mathematics
1 answer:
Olegator [25]4 years ago
7 0

Answer:

B

Step-by-step explanation:

The slope is 4/1 which equals 4

the y int is 2

this gives us 4x+2

the line is dotted which mean there is no equal sign with the inequality

The shaded area is above the line, meaning y is greater

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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
What is the length of segment QV
Lyrx [107]

Answer:

44

Step-by-step explanation:

ΔTRS ≅ ΔTRQ

TS = TQ

2x + 8 = 40

x = 16

The same situation

SV = QV

3 * 16 - 4 = 44

8 0
3 years ago
Read 2 more answers
The functions f(x) and g(x) are described below:
sesenic [268]

Suppose that the <u>function</u> f(x) is the <u>parrent</u> function and the<u> graph</u> of the function g(x)=f(x)-a can be obtained from the graph of the parrent function f(x) by <u>shifting down</u> a units.

Rewrite the expression for the function g(x) in the following way:

g(x)=32x-9=32x+8-8-9=32x+8-17=f(x)-17.

This shows that the shift down is made by 17 units.

Answer: 17 units

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3 years ago
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Find the missing ANGLE <br><br> Someone plsss helpppp!!! I’ll give brainliest!!! :(((
Romashka [77]
The answer is triangle sum c is 74
6 0
3 years ago
Determine the nth term of the sequence 2,4,6,8​
Mariana [72]

1. Find the difference ( diff is 2 )

2. Apply the concept diN+0 (more easier use this :) )

* di is difference

* N is nth term

* 0 is first term - difference

3. Find 0

- first term (2) - difference (2) = 0

answer: 2n

8 0
3 years ago
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