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Vesna [10]
2 years ago
8

What are the solutions to 3x^2 = 8x — 6?

Mathematics
1 answer:
Bond [772]2 years ago
5 0

Answer:

First, let's move all terms to one side,

\sf x^2-8x+6=0

When given this form (ax^2+bx+c=0), there will be two solutions at the end.

1) \sf x=\frac{-b+\sqrt{b^2-4ab} }{2b}

2) \sf x=\frac{-b-\sqrt{b^2-4ab} }{2b}

where, a=1, b=-8, c=6

\sf x=\frac{8+\sqrt{(-8)^2-4\times6} }{2} ,\frac{8-\sqrt{(-8)^2-4\times6} }{2}

Simplify,

\sf x=\frac{8+2\sqrt{10} }{2} ,\frac{8-2\sqrt{10} }{2}

Simplify,

\sf x=4+\sqrt{10}, 4-\sqrt{10}

Hope it helps!

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What term is 1/1024 in the geometric sequence,-1,1/4,-1/6..?
Trava [24]

Answer:

\large\boxed{\text{sixth term is equal to}\ \dfrac{1}{1024}}

Step-by-step explanation:

The explicit formula for a geometric sequence:

a_n=a_1r^{n-1}

a_n - n-th term

a_1 - first term

r - common ratio

r=\dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}=...=\dfrac{a_n}{a_{n-1}}

We have

a_1=-1,\ a_2=\dfrac{1}{4},\ a_3=-\dfrac{1}{6},\ ...

The common ratio:

r=\dfrac{\frac{1}{4}}{-1}=-\dfrac{1}{4}\\\\r=\dfrac{-\frac{1}{6}}{\frac{1}{4}}=-\dfrac{1}{6}\cdot\dfrac{4}{1}=-\dfrac{2}{3}\neq-\dfrac{1}{4}

<h2>It's not a geometric sequence.</h2>

If a_3=-\dfrac{1}{16} then the common ratio is r=\dfrac{-\frac{1}{16}}{\frac{1}{4}}=-\dfrac{1}{16}\cdot\dfrac{4}{1}=-\dfrac{1}{4}

Put to the explicit formula:

a_n=-1\left(-\dfrac{1}{4}\right)^{n-1}

Put a_n=\dfrac{1}{1024} and solve for <em>n </em>:

-1\left(-\dfrac{1}{4}\right)^{n-1}=\dfrac{1}{1024}\qquad\text{use}\ a^n:a^m=a^{n-m}\\\\-\left(-\dfrac{1}{4}\right)^n:\left(-\dfrac{1}{4}\right)^1=\dfrac{1}{1024}\\\\-\left(-\dfrac{1}{4}\right)^n\cdot(-4)=\dfrac{1}{1024}\\\\(4)\left(-\dfrac{1}{4}\right)^n=\dfrac{1}{1024}\qquad\text{divide both sides by 4}\ \text{/multiply both sides by}\ \dfrac{1}{4}/\\\\\left(-\dfrac{1}{4}\right)^n=\dfrac{1}{4096}\\\\\dfrac{(-1)^n}{4^n}=\dfrac{1}{4^6}\qquad n\ \text{must be even number. Therefore}\ (-1)^n=1

\dfrac{1}{4^n}=\dfrac{1}{4^6}\iff n=6

5 0
3 years ago
One number is 5 more than the other. Their sum is 33. Find the numbers.
dimaraw [331]

Answer:

19,14

Step-by-step explanation:

x=5+y

x+ y= 33

we will solve using substitution

(5+y) +y= 33

5+y+y=33

5+2y=33

subtract 5 from both sides

2y=28

y=14

We got y now we will find what x is

for this, we will substitute y's value (14) into the first equation

x=5+(14)

x=19

we got x too

3 0
3 years ago
Plz help right now illl give brainlist 5.0 and say thanks
Bess [88]
4+4+1 is the answer
8 0
2 years ago
Read 2 more answers
14 is what percent of 92
Lana71 [14]

Answer:

14 is what percent of 92? = 15.22.

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
Given h(x) = 3x + 4, find h(-1).
larisa86 [58]
Plug in -1 for x
h(-1) = 3(-1) + 4
h(-1) = -3 + 4
Solution: h(-1) = 1
6 0
3 years ago
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