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MaRussiya [10]
3 years ago
5

What is the least five-digit even number with no repeated digits?

Mathematics
1 answer:
artcher [175]3 years ago
6 0
Your answer is 10234
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Solve using the quadratic formula. Show all work. Write each solution in simplest form. No decimals.
r-ruslan [8.4K]

Given:

The given quadratic equation is:

12a^2+9a+7=0

To find:

The solution for the given quadratic equation in simplest form by using the quadratic formula.

Solution:

Consider a quadratic equation is defined as ax^2+bx+c=0, then the quadratic formula is:

x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}

The given quadratic equation is:

12a^2+9a+7=0

We have, a=12,b=9,c=7. Using the quadratic formula, we get

x=\dfrac{-(9)\pm \sqrt{(9)^2-4(12)(7)}}{2(12)}

x=\dfrac{-9\pm \sqrt{81-336}}{24}

x=\dfrac{-9\pm \sqrt{-255}}{24}

x=\dfrac{-9\pm i\sqrt{255}}{24}              [\because \sqrt{-a}=i\sqrt{a}]

The solutions of the given equations are x=\dfrac{-9-i\sqrt{255}}{24} and x=\dfrac{-9+i\sqrt{255}}{24}.

Hence, the correct option is B.

3 0
3 years ago
The function h is defined by h(y)=2 y-7 . what is the value of h(8)
gtnhenbr [62]
I believe the answer is 2
7 0
4 years ago
5x+25=75 pls help appreciated
Dafna11 [192]

Answer:

x=10

Step-by-step explanation:

I guess solve for x

5x=50

x=10

3 0
3 years ago
Read 2 more answers
When constructing an equilateral triangle by hand, which step comes after constructing a circle?
KonstantinChe [14]

Answer:

set compass to the radius of the circle

Step-by-step explanation: when constructing an equilateral triangle by hand . circle constructing by set compass to the radius of the circle and rotate it and come to the initial point

4 0
3 years ago
Read 2 more answers
X ^ (2) y '' - 7xy '+ 16y = 0, y1 = x ^ 4
nignag [31]
Standard reduction of order procedure: suppose there is a second solution of the form y_2(x)=v(x)y_1(x), which has derivatives

y_2=vx^4
{y_2}'=v'x^4+4vx^3
{y_2}''=v''x^4+8v'x^3+12vx^2

Substitute these terms into the ODE:

x^2(v''x^4+8v'x^3+12vx^2)-7x(v'x^4+4vx^3)+16vx^4=0
v''x^6+8v'x^5+12vx^4-7v'x^5-28vx^4+16vx^4=0
v''x^6+v'x^5=0

and replacing v'=w, we have an ODE linear in w:

w'x^6+wx^5=0

Divide both sides by x^5, giving

w'x+w=0

and noting that the left hand side is a derivative of a product, namely

\dfrac{\mathrm d}{\mathrm dx}[wx]=0

we can then integrate both sides to obtain

wx=C_1
w=\dfrac{C_1}x

Solve for v:

v'=\dfrac{C_1}x
v=C_1\ln|x|+C_2

Now

y=C_1x^4\ln|x|+C_2x^4

where the second term is already accounted for by y_1, which means y_2=x^4\ln x, and the above is the general solution for the ODE.
4 0
4 years ago
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