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3 years ago

1. WILL GIVE BRAINLIST TO BEST ANSWER

Mathematics

1 answer:

Varvara68 [4.7K]3 years ago

4 0

Answer:

90/100

Step-by-step explanation:

if you look at the graph on the bottom part it tells you the study time if you line it the left side which says the test score. so if they studied for 80 mins they are expected to have the score of between 85 and 90.

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3 years ago

409,821,735,673 value of the digit 4 in this number.

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4 years ago

Read 2 more answers

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

Abby counts 12 large boxes and 18 small boxes of pencils in the supply cabinet. Each large box contains 144 pencils. Each small

Maru [420]

The total number of pencils is 2,160. When estimating to the nearest hundredth one gets 2,200, which is an underestimate.

The advantage of underestimating is that your answer is more accurate than an overestimate.

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4 years ago