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3 years ago

What is the factored form of this expression?

Mathematics

1 answer:

kirill [66]3 years ago

6 0

Answer:

= (3t+2)(3t-2)(3t-4)

Step-by-step explanation:

Given the expression 27t^3 - 36t^2 - 12t + 16

On factoring:

(27t^3 - 36t^2) - (12t + 16)

= 9t²(3t-4)-4(3t-4)

= (9t²-4)(3t-4)

factoring 9t²-4

9t²-4 = (3t)² - 2²

From different of two square, a²-b² = (a+b)(a-b)

Hence (3t)² - 2² = (3t+2)(3t-2)

= (9t²-4)(3t-4)

= (3t+2)(3t-2)(3t-4)

Hence the factored form of the expression is (3t+2)(3t-2)(3t-4)

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If the output number y is -52 (y=5x-2) what is the input number? SHOW WORK

nordsb [41]

Answer:

the input number is -10

Step-by-step explanation:

output is always y

input is always x

so instead of y, put -52

-52=5x-2 add 2 to each side to ger 5x by itself

-50=5x divide both sides by 5 to get x by itself

-10=x

x is the input so the input is -10

8 0

3 years ago

Roland's Boat Tours sells deluxe and economy seats for each tour it conducts. In order to complete a tour, at least 14 economy s

dmitriy555 [2]

At least 14 economy and at least 5 deluxe...total of 45 seats. He makes a bigger profit from selling economy seats....so we need the most economy seats we can get.

45 seats - 5 deluxe = 40 economy

so the most profit would be 40 economy and 5 deluxe
40 economy = (40 x 30) = 1200 profit
5 deluxe = (5 x 25) = 125 profit
for a maximum profit of : $ 1325

5 0

3 years ago

Use the definition of a derivative to find f’(x).

tatyana61 [14]

Answer:

f'(x) = $-\frac{9}{x^2}$

Step-by-step explanation:

i) f(x) = 9 / x

ii) f'(x) = $$\lim_{h\to 0} \frac{f(x+h) - f(x)}{h} $ \hspace{0.2cm}$

$= $\lim_{h\to 0} \frac{\frac{9}{x+h} - \frac{9}{x} }{h} = \hspace{0.1cm} $\lim_{h\to 0} \frac{9x - 9(x+h)}{hx(x+h)} $ \hspace{0.1cm} = \hspace{0.1cm}$\lim_{h\to 0} \frac{-9h}{hx(x+h)} = $\lim_{h\to 0} \frac{-h}{x(x+h)} = \frac{-9}{x^2}$$

7 0

3 years ago

3.57 x 10 <br> write in standard form

Bess [88]

$\huge\text{Hey there!}$

$\textsf{3.57}\times\textsf{10}^\mathsf{3}\\\\\mathsf{10^3}\\\mathsf{\rightarrow 10\times10\times10}\\\mathsf{\rightarrow100\times10}\\\mathsf{\rightarrow 1,000}\\\\\textsf{3.57}\times\textsf{1,000}\\\rightarrow\textsf{3,570}\\\rightarrow\mathsf{3.57\times10^3}\\\\\huge\boxed{Answer: {\frak{3.57\times 10^3}}}\huge\checkmark$

$\huge\text{Good luck on your assignment \& enjoy your day!}$

~ $\frak{Amphitrite1040:)}$

7 0

3 years ago

Please please help. I have a bunch of these and I don’t understand it at all

shtirl [24]

The correct option is: Option (B) $\sum_{i=1}^{7} (5i-2)$

Explanation:

First thing is that the difference between each number in the series with the next number is 5. It means it must be the multiple of 5. There are two options that contain multiples of 5: Option B and Option D. Now in the option D, the upper limit is 6. If we put 6 in the expression: 5(6)-2, the last term would be 28. However in the series given in the question, the last term is 33. Hence 5(7) - 2 = 35 - 2 = 33 which is Option B.

When i=1: 5(1)-2 = 3
When i=2: 5(2)-2 = 8
When i=3: 5(3)-2 = 13
.
.
When i=7: 5(7)-2 = 35-2 = 33
Hence the correct option is (B).

3 0

3 years ago