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3 years ago

The area of a square can be represented by the trinomial 9x^2 - 54x + 81. Which of the following is the length of one side of th

e square?
*free response question

Mathematics

1 answer:

Mnenie [13.5K]3 years ago

3 0

$Use\ (a-b)^2=a^2-2ab+b^2\\\\9x^2-54x+81=\underbrace{(3x)^2-2(3x)(9)+9^2}_{(*)}=(3x+9)^2\\\\\text{The formula of an area of a square with a side x:}\ A=x^2.\\\\\text{Therefore we have answer:}\ The\ length\ of\ side\ of\ the\ square\ is\ 3x+9.$

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Find the value of Y helpppp

DIA [1.3K]

Answer:

y = 4

Step-by-step explanation:

Both the triangles are congruent by SSS postulate.

Therefore,

$4y + 8 = 24 \\ (corresponding \: sides \: of \: \\ congruent \: \triangle s) \\ 4y = 24 - 8 \\ \\ 4y = 16 \\ \\ y = \frac{16}{4} \\ \\ y = 4$

3 0

3 years ago

Please help its due tomorrow 83% of £408 41% of 53kg 97% of 345m

stepan [7]

Step-by-step explanation:

338.64
21.73
334.65

You can use a calculator. Do 83% * 408, 41% * 53, and

97% * 345.

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3 years ago

Erica earns a salary of Rs 20 000 a week plus 10% commission on all sales.If the total sales for the week amounts for Rs 3500,wh

madam [21]

Answer:

Rs. 20350

Step-by-step explanation:

Total salary for the week

= Rs 20,000 + 10% of Rs 3500

$= 20,000 +\frac{10}{100} \times 3500\\\\= 20000+350\\= Rs\: 20350$

7 0

3 years ago

A machine is designed to fill 16-ounce bottles of shampoo. When the machine is working properly, the amount poured into the bott

Andreyy89

Answer:

(15.8495,16.2505)

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 16.05 ounces

Standard Deviation, σ = 0.2005 ounces

We are given that the distribution of amount poured into the bottles is a bell shaped distribution that is a normal distribution.

Empirical rule:

It states that for a normal distribution, almost all data falls within three standard deviations (denoted by σ) of the mean (denoted by µ).

It shows that 68% falls within the first standard deviation (µ ± σ), 95% within the first two standard deviations (µ ± 2σ), and 99.7% within the first three standard deviations (µ ± 3σ).

Confidence interval:

$\mu \pm 2\frac{\sigma}{\sqrt{n}}$

Putting the values, we get,

$16.05 \pm 2(\frac{0.2005}{\sqrt{4}} ) = 16.05 \pm 0.2005 = (15.8495,16.2505)$

4 0

3 years ago

What are the three angle measures in the triangle shown below

Zanzabum

Answer:

B. 31°, 106°, and 43°.

Step-by-step explanation:

the sum of the measures of the angles in a triangle add up to 180°, so:

3x+1+11x-4+5x-7=180

19x-10=180

19x=190

x=10

now that we know x is equal to 10, we can find the three angle measures:

3x+1 -> 3(10)+1 = 31°

11x-4 -> 11(10)-4 = 110-4 = 106°

5x-7 -> 5(10)-7 = 50-7 = 43°

so, the answer is B.

7 0

3 years ago