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Dahasolnce [82]

2 years ago

13

Solve 9x^2 + 12x – 24 = 0 using the quadratic formula.

1 answer:

Nataliya [291]2 years ago

8 0

Quadratic formula = (-b +- sqrt(b^2 - (4ac))) / 2a

$\frac{ -12 + \sqrt{(12)^2 -((4)(9)(-24))}}{2(9)}$

and

$\frac{ -12 - \sqrt{(12)^2 -((4)(9)(-24))}}{2(9)}$

then simplify and solve

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20 points!!! Please Help<br><br> Does the equation x2 - 4x + y2 = -3 intersect the x-axis?

OverLord2011 [107]

Answer:

Yes, twice

Step-by-step explanation:

The equation will intersect the x-axis when y = 0, so we have

x² - 4x = -3 now solve this quadratic for x...

x² - 4x + 3 = 0

factor...

(x - 3)(x - 1) = 0,

so at x = 1 and x = 3, the function crosses the x-axis

See the graph below

6 0

2 years ago

Read 2 more answers

Match each series with the equivalent series written in sigma notation

PIT_PIT [208]

Answer:

$3 + 12 + 48 + 192 + 768 = \sum\limits^4_{n=0} 3 * 4^n$

$4 + 32 + 256 + 2048 + 16384 = \sum\limits^4_{n=0} 4 * 8^n$

$2 + 6 + 18 + 54 + 162 = \sum\limits^4_{n=0} 2* 3^n$

$3 + 15 + 75 + 375 + 1875 = \sum\limits^4_{n=0} 3* 5^n$

Step-by-step explanation:

Given

See attachment for complete question

Required

Match equivalent expressions

Solving (a):

$3 + 12 + 48 + 192 + 768$

The expression can be written as:

$3 \to 3*4^{0$ --- 0

$12 \to 3 * 4^{1$ ---- 1

$48 \to 3 * 4^{2$ --- 2

$192 \to 3 * 4^{3$ ---- 3

$768 \to 3 * 4^{4$ ---- 4

For the nth term, the expression is:

$Term = 3 * 4^{n$ ---- n

So, the summation is:

$3 + 12 + 48 + 192 + 768 = \sum\limits^4_{n=0} 3 * 4^n$

Solving (b):

$4 + 32 + 256 + 2048 + 16384$

The expression can be written as:

$4 \to 4 * 8^0$ --- 0

$32 \to 4 * 8^1$ ---- 1

$256 \to 4 * 8^2$ --- 2

$2048 \to 4 * 8^3$ ---- 3

$16384 \to 4 * 8^4$ ---- 4

For the nth term, the expression is:

$Term \to 4 * 8^n$ ---- n

So, the summation is:

$4 + 32 + 256 + 2048 + 16384 = \sum\limits^4_{n=0} 4 * 8^n$

Solving (c):

$2 + 6 + 18 + 54 + 162$

The expression can be written as:

$2 \to 2 * 3^0$ --- 0

$6 \to 2 * 3^1$ ---- 1

$18 \to 2 * 3^2$ --- 2

$54 \to 2 * 3^3$ ---- 3

$162 \to 2 * 3^4$ ---- 4

For the nth term, the expression is:

$Term \to 2 * 3^n$ ---- n

So, the summation is:

$2 + 6 + 18 + 54 + 162 = \sum\limits^4_{n=0} 2* 3^n$

Solving (d):

$3 + 15 + 75 + 375 + 1875$

The expression can be written as:

$3 \to 3 * 5^0$ --- 0

$15 \to 3 * 5^1$ ---- 1

$75 \to 3 * 5^2$ --- 2

$375 \to 3 * 5^3$ ---- 3

$1875 \to 3 * 5^4$ ---- 4

For the nth term, the expression is:

$Term \to 3 * 5^n$ ---- n

So, the summation is:

$3 + 15 + 75 + 375 + 1875 = \sum\limits^4_{n=0} 3* 5^n$

5 0

2 years ago

Given ƒ(x) = −10x + 45, find x when ƒ(x) = 15.

Temka [501]

Answer:

x = 3

Step-by-step explanation:

Given

f(x) = - 10x + 45 and f(x) = 15, then equating gives

- 10x + 45 = 15 ( subtract 45 from both sides )

- 10x = - 30 ( divide both sides by - 10 )

x = 3

5 0

2 years ago

What is the median of the following string of values?

GaryK [48]

Answer:

the value is 52

Step-by-step explanation:

pls brain list me

5 0

2 years ago

I've tried to get the answer for this 13 times now (not joking), plzzz help: write a formula that represents the number of peopl

gtnhenbr [62]

Answer:

2820 seats
aₙ = 3n + 9

Step-by-step explanation:

<u>This is an AP with:</u>

The first term a₁ = 12
Common difference d = 3
Number of terms n = 40

<u>Number of the seats:</u>

Sₙ = 1/2*n(a₁ + aₙ) = 1/2n(2a₁ + (n - 1)d)
S₄₀ = 1/2*40(12*2 + 39*3) = 2820 seats

<u>Formula of nth term:</u>

aₙ = a₁ + (n - 1)d
aₙ = 12 + (n - 1)*3 = 12 + 3n - 3 = 3n + 9
aₙ = 3n + 9

6 0

2 years ago