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wolverine [178]
3 years ago
11

...............what is (9x^2-3)^6

Mathematics
1 answer:
Lelu [443]3 years ago
8 0
Step 1. Factor out the common term 3

(3(3 x^{2}-1)^{6}

Step 2. Use <span>Multiplication Distributive Property: </span>(xy)^{a} = x^{a}  y^{a}
<span>
</span>3^{6}(3 x^{2}-1)^{6}
<span>
Step 3. Simplify </span>3^{6} to 729

729(3 x^{2}-1)^{6}

Done!
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How much must be added to each of the three numbers 1, 11, and 23 so that together they form a geometric progression?
Sliva [168]

Answer:

49

Step-by-step explanation:

Let x be unknown number which should be added to numbers 1, 11, 23 to get geometric progression. Then numbers 1 + x, 11 + x, 23 + x are first three terms of geometric progression.

Hence,

b_1=1+x\\ \\b_2=11+x\\ \\b_3=23+x

and

b_2=b_1\cdot q\Rightarrow 11+x=(1+x)q\\ \\b_3=b_2\cdot q\Rightarrow 23+x=(11+x)q

Express q:

q=\dfrac{11+x}{1+x}=\dfrac{23+x}{11+x}

Solve this equation. Cross multiply:

(11+x)^2=(1+x)(23+x)\\ \\121+22x+x^2=23+x+23x+x^2\\ \\121+22x=23+24x\\ \\22x-24x=23-121\\ \\-2x=-98\\ \\2x=98\\ \\x=49

5 0
3 years ago
−8−1+4 ⋅ 2 find the answer to this equation
jeyben [28]

Answer:

-1

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
F(x) = 2(x+3)2 -7<br><br><br> a= <br><br> h=<br><br> k=
vlabodo [156]

Answer:

Step-by-step explanation:

In vertex form, the equation is

y = a(x-h)^2 + k

So just read off the values!

6 0
3 years ago
Is 6,8,9 a pythagorem theorem? pls help me due rn
Naddika [18.5K]

Answer:

No, it isn't.

Step-by-step explanation:

Pythagorean theorem is x^2 + y^2 = z^2.

6^2 + 8^2 = 9^2

36 + 64 = 81

100 = 81

So, it isn't.

4 0
2 years ago
Read 2 more answers
Noah manages a buffet at a local restaurant. He charges $10 for the buffet. On average, 16 customers choose the buffet as their
kicyunya [14]

Answer:

$3 max

Step-by-step explanation:

Charge= b, Customer= c, Revenue= r

r= bc, currently, r= 16*10= $160

We know that: b+1 ⇒ c-2  and the target is r ≥ 130

So, this will all be reflected as:

b=10+x ⇒ c= 16-2x

  • (10+x)(16-2x) ≥ 130
  • 160 -20x +16x - 2x² ≥ 130
  • -2x² - 4x + 30 ≥ 0
  • x² + 2x -15 ≤ 0
  • (x+1)² ≤ 4²
  • x+1 ≤ 4 (negative value not considered)
  • x ≤ 3

As we see the max increase amount is $3, when the revenue will be:

(10+3)*(16-3*2)= 13*10= $130

8 0
3 years ago
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