A quadratic equation is shown below: 4x2 − 12x + 9 = 0
Part A: Describe the solution(s) to the equation by just determining the radicand. Show your work. (5 points)
Part B: Solve 9x2 − 30x + 25 = 0 by using an appropriate method. Show the steps of your work, and explain why you chose the method used. (5 points)

Final answer:

To write each number in scientific notation, express it as a product between 1 and 10 and a power of 10. Each adult spent an average of 570.55 hours per day online at home.

Explanation:

To write each number in scientific notation, we need to express it as a product of a number between 1 and 10 and a power of 10.

163 million can be written as 1.63 x 10⁸

93 billion can be written as 9.3 x 10¹⁰

To convert the units to hours per day, we need to divide the total number of hours by the number of adults.

So, each adult spent an average of (93 x 10¹⁰) / (163 x 10⁸) = 570.55 hours per day online at home. Scientific notation simplifies large numbers, facilitating computations and providing a concise representation of quantities in mathematical contexts.

Answer:

24/23

Step-by-step explanation:

- vs - = + after -24,-23 =

Answer = 24, 23

The solution for the system of equation x - y = 4 and x + y = 2 is (3, -1).

An equation is a combination of different variables, in which two mathematical expressions are equal to each other.

The given pair of equations,

x - y = 4       (1)

And x + y = 2         (2)

To find the solution of the equations,

Add both the equations,

x - y + x + y = 4 + 2

2x = 6

x = 3,

Substitute the value of x = 3 in equation (1),

3 - y = 4

y = -1

The values of x and y are 3 and -1 respectively.

Hence, option (A) is correct.

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Answer:

There are [tex]26[/tex] alternative schools in the country

Step-by-step explanation:

Let

x------> the number of charter schools

y----->  the number of alternative schools

we know that

[tex]x=48[/tex]

[tex]x=2y-4[/tex] -----> equation A

substitute the value of x in the equation A and solve for y

[tex]48=2y-4[/tex]

[tex]2y=48+4[/tex]

[tex]2y=52[/tex]

[tex]y=26[/tex]

Answer: 13 units

Step-by-step explanation:

The distance formula to calculate distance between two points (a,b) and (c,d) is given by :-

[tex]d=\sqrt{(d-b)^2+(c-a)^2}[/tex]

Given points : (13, 20) and (18, 8)

Now, the distance between the points (13, 20) and (18, 8)is given by ;-

[tex]d=\sqrt{(8-20)^2+(18-13)^2}\\\\\Rightarrow\ d=\sqrt{(-12)^2+(5)^2}\\\\\Rightarrow\ d=\sqrt{144+25}\\\\\Rightarrow\ d=\sqrt{169}\\\\\Rightarrow\ d=13\text{units}[/tex]

Hence, the distance between the points (13, 20) and (18, 8) is 13 units.

a) radius 6 inches, height 3 inches

b) diameter 6 inches, height 3 inches

c) diameter 4 inches, height 6 inches

d) diameter 6 inches, height 6 inches

Now you can probe those options to see which leads to an approximate volume of 28 cubic inches.

a) radius 6 in, height 3 in

=> V = (1/3)*3.14*(6in)^2 * 3in = 113.04 in^3 => not possible

Answer:

[tex]\frac{60 - 10\sqrt10-6\sqrt3+\sqrt30}{97}[/tex]

Step-by-step explanation:

Hello!

To rationalize the denominator, we have to remove any root operations from the denominator.

We can do that by multiplying the numerator and denominator by the conjugate of the denominator. The conjugate simply means the same terms with different operations.

The answer is [tex]\frac{60 - 10\sqrt10-6\sqrt3+\sqrt30}{97}[/tex].

There are 84 three digit numbers can be made from the digits 1, ..., 9

What is Combination?

A combination is a technique to determines the number of possible arrangements in a collection of items where the order of the selection does not matter.

Given that;

The numbers are,

⇒ 1, 2, ..., 9

Now,

All the three digit numbers can be made from the digits 1, ..., 9 are;

⇒ [tex]^{9} C_{3}[/tex]

⇒ 9! / 3! 6!

⇒ 9 × 8 × 7 / 6

⇒ 84

Thus, There are 84 three digit numbers can be made from the digits

1, ..., 9.

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The measure of XWZ is 285

The arc of a circle is defined as the part or segment of the circumference of a circle.

Given:

<XYZ = 75

As, we know central angle of 360

So, arc(XWZ) + <XYZ = 360

arc (XWZ) = 360 - 75

arc(XWZ) = 285

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Discriminant 0 in quadratic equation means 1 real solution—a repeated root where parabola touches x-axis once.

When the discriminant of a quadratic equation is 0, it means that the quadratic equation has exactly one real solution. This solution is considered a "double root" or "repeated root," meaning that the parabola defined by the quadratic equation touches the x-axis at exactly one point. Mathematically, this occurs when the quadratic equation has two identical roots.

The general form of a quadratic equation is [tex]\(ax^2 + bx + c = 0\)[/tex], and the discriminant, denoted by [tex]\(b^2 - 4ac\),[/tex] helps determine the nature of the roots.

When the discriminant is zero [tex](\(b^2 - 4ac = 0\))[/tex], the quadratic equation has one real root. This happens when the parabola defined by the equation just touches the x-axis at one point. The solution is given by:

[tex]\[x = \frac{{-b \pm \sqrt{b^2 - 4ac}}}{{2a}}\][/tex]

The following conditions are:

D < 0      ; there are two non-real or imaginary roots which are complex conjugates

D = 0      ; there is one real root and one imaginary (non-real)

D > 0      ; there are two real distinct roots

Therefore the answer to this question is:

The solution has one real root and one imaginary root.

The complex solutions to the equation[tex]3x^2+3x+4=0 are x = (-3 + i\sqrt{39})/6 and x = (-3 - i\sqrt{39})/6.[/tex]

To find all complex solutions of the quadratic equation [tex]3x^2+3x+4=0[/tex]e the quadratic formula:

[tex]x = \((-b \pm \sqrt{b^2-4ac})/(2a)\).[/tex]

Here, a = 3, b = 3, and c = 4. Plugging these values into the formula, we get:

[tex]x = \((-3 \pm \sqrt{3^2-4 \cdot 3 \cdot 4})/(2 \cdot 3)\).[/tex]

This simplifies to:

[tex]x = \((-3 \pm \sqrt{-39})/6\).[/tex]

Since the discriminant (under the square root sign) is negative, we know that the solutions will be complex. Using i to represent the square root of -1, we can write the solutions as:

[tex]x = \((-3 \pm i\sqrt{39})/6\).[/tex]

So, the complex solutions are [tex]x = (-3 + i\sqrt{39})/6 and x = (-3 - i\sqrt{39})/6.[/tex]

Answer:

the radius is perpendicular to the chord.

Step-by-step explanation:

The geometry is drawn in the image shown below in which AB is the chorh and O is the centre of the circle. Om is the radius which bisects the chord.(Given) So, AN = NB

From the image, considering ΔAON and ΔBON,

AO = BO (radius of circle)

AN = NB (given)

ON = ON (common)

So,

ΔAON ≅ ΔBON

Hence, ∠ANO = ∠BNO

Also, ∠ANO + ∠BNO = 180° (Linear Pair)

So,

∠ANO = ∠BNO = 90°

Hence, it is perpendicular to the chord.

Answer:

B.

Step-by-step explanation:

The value of x makes the denominator of the function equal zero is 10

An equation is a mathematical expression that contains an equals symbol. Equations often contain algebra.

Given that:

y = [tex]\frac{6}{4x-40}[/tex]

Now the denominator is: 4x - 40

So, 4x =40

      x =40/4

      x =10

So, make the denominator 0, put x= 10.

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