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2 years ago

Expand and simplfy (x+3)(x-3)(3x+2)

Mathematics

1 answer:

tester [92]2 years ago

4 0

Answer:

${3x}^{3} + {2x}^{2} - 27x - 18$

Step-by-step explanation:

1) Use difference of squares: a² - b² = (a + b) (a - b).

$( {x}^{2} - {3}^{2} )(3x + 2)$

2) Simplify 3² to 9.

$( {x}^{2} - 9)(3x + 2)$

3) Use The FOIL method: (a + b) (c + d) = ac + ad + bc + bd.

${3x}^{3} + {2x}^{2} - 27x - 18$

Therefor, the answer is 3x³ + 2x² + -26x -18.

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The sum of two terms of gp is 6 and that of first four terms is 15/2.Find the sum of first six terms.

Gnoma [55]

Given:

The sum of two terms of GP is 6 and that of first four terms is $\dfrac{15}{2}.$

To find:

The sum of first six terms.

Solution:

We have,

$S_2=6$

$S_4=\dfrac{15}{2}$

Sum of first n terms of a GP is

$S_n=\dfrac{a(1-r^n)}{1-r}$ ...(i)

Putting n=2, we get

$S_2=\dfrac{a(1-r^2)}{1-r}$

$6=\dfrac{a(1-r)(1+r)}{1-r}$

$6=a(1+r)$ ...(ii)

Putting n=4, we get

$S_4=\dfrac{a(1-r^4)}{1-r}$

$\dfrac{15}{2}=\dfrac{a(1-r^2)(1+r^2)}{1-r}$

$\dfrac{15}{2}=\dfrac{a(1+r)(1-r)(1+r^2)}{1-r}$

$\dfrac{15}{2}=6(1+r^2)$ (Using (ii))

Divide both sides by 6.

$\dfrac{15}{12}=(1+r^2)$

$\dfrac{5}{4}-1=r^2$

$\dfrac{5-4}{4}=r^2$

$\dfrac{1}{4}=r^2$

Taking square root on both sides, we get

$\pm \sqrt{\dfrac{1}{4}}=r$

$\pm \dfrac{1}{2}=r$

$\pm 0.5=r$

Case 1: If r is positive, then using (ii) we get

$6=a(1+0.5)$

$6=a(1.5)$

$\dfrac{6}{1.5}=a$

$4=a$

The sum of first 6 terms is

$S_6=\dfrac{4(1-(0.5)^6)}{(1-0.5)}$

$S_6=\dfrac{4(1-0.015625)}{0.5}$

$S_6=8(0.984375)$

$S_6=7.875$

Case 2: If r is negative, then using (ii) we get

$6=a(1-0.5)$

$6=a(0.5)$

$\dfrac{6}{0.5}=a$

$12=a$

The sum of first 6 terms is

$S_6=\dfrac{12(1-(-0.5)^6)}{(1+0.5)}$

$S_6=\dfrac{12(1-0.015625)}{1.5}$

$S_6=8(0.984375)$

$S_6=7.875$

Therefore, the sum of the first six terms is 7.875.

5 0

2 years ago

Answer my math question I asked so many times I lost most of points by

kumpel [21]

Answer:

i think ur in a higher grade then me but im good w/ equations so OoOO0p

Step-by-step explanation:

equation: y = x - 6 + x^2

(6,0) (7,1) (8,4) (9,9)

I figured this out by looking at the point (6,0). To get 0 (y), you have to subtract 6. Knowing this, I subtracted 6 from the rest of the coordinates, leaving me with numbers that are able to be squared to get y. This led me to the equation x - 6 + x^2.

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3 years ago

Help will give max points and branlisest plls HELP ASAP BY 1230pt thanks ;]

Murljashka [212]

Answer:

120cm^3

Step-by-step explanation:

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2 years ago

Read 2 more answers

There are only two orthodontists in a village and both wore braces until last month. Dr. Carter now has straight teeth and a cle

lana66690 [7]

Answer:

Dr Carter

Step-by-step explanation:

I would want to visit Dr. Carter for an orthodontis appointment for multiple reasons. One, he can prove that he doesn’t do his work sloppily as his office is clean, and two, he can prove that his treatments work. since his teeth are now perfectly straight, that shows that his Braces really work, whereas Dr. Shuman’s treatments either don’t work or take a lot longer for results to appear.

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3 years ago

Mr.McNeil bought two magazines for 7.45 and one book for 14.95. If the sales tax is 6% , what is the total cost of Mr.McNeil’s p

blagie [28]

Answer:

total cost = $22.4 + $1.12 = $23.52

Step-by-step explanation:

Mr McNeil bought 2 magazines for $7.45 and 1 book for $14.95 . The sales tax is 6% . The total cost of Mr McNeil can be calculated as follows.

He bought 2 magazines for $7.45 .This means the sum of the prize of the 2 magazine he bought is $7.45 and the prize for the single book he bought is $14.95. The total cost of the items he bought excluding the sales tax is the sum of the whole items he bought.

total cost excluding sales tax = $7.45 + 14.95 = $22.4

The sales tax is 5% which can be calculated as follows

5/100 × 22.4 = 112/100 = $1.12

The total cost of Mr McNeil purchase including his sales tax is

total cost = $22.4 + $1.12 = $23.52

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3 years ago