How would I solve this?

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 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:

(B) flip the inequality sign.

Step-by-step explanation:

If we consider an inequality such that [tex]-x\leq7[/tex], then if we multiply the inequality with a negative number such as [tex]-1[/tex], then the inequality becomes [tex]x\geq-7[/tex].

Also, if we divide the above inequality  [tex]-x\leq7[/tex], by a negative number that is  [tex]-1[/tex], then the inequality becomes [tex]x\geq-7[/tex].

Therefore, if we multiply or divide an inequality by a negative number, then it flips the inequality sign.

Hence, option (B) is correct.

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].

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

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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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]

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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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.

The values of x and y after solving both the equations by the elimination method are  -4 and -1. So option A is correct

An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.

For example, 3x+2y=0.

Types of equation

1. Linear Equation

2. Quadratic Equation

3. Cubic Equation

Given that,

Two linear equations

−2x − y = 9

2x − 9y = 1

by using elimination method,

−2x − y = 9

2x − 9y = 1  

0  - 10y  =  10

y  = -1

2x − 9× -1 = 1

2x   = -8

x  = -4

Hence, the values are, -4 and -1

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52% = 0.52

78/0.52 =150

 150 students voted

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:

24/23

Step-by-step explanation:

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

Answer = 24, 23

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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To calculate the number of ways to seat 13 people around a table with 9 actors sitting together, we treat the 9 actors as one unit and then arrange the five units around the table, resulting in (4! * 9!) different possible arrangements.

The question asks us to calculate the number of ways to seat 13 people around a table if 9 actors must sit together. This can be approached as a permutations problem in combinatorics.

Firstly, treat the 9 actors as one unit since they must sit together. With this in mind, we effectively have 5 units to arrange: the group of 9 actors and the remaining 4 individuals. As the seating arrangement is around a circular table, we can fix one person's seat and arrange the remaining units. As a result, there are (5-1)! ways to arrange these units since circular permutations eliminate the concept of a distinct 'starting' point that linear permutations have.

Now we need to consider the arrangements of the 9 actors within their group. Since their relative positions to each other matter, they can be permuted in 9! ways.

Therefore, the total number of seating arrangements would be the product of the two permutations: (5-1)! * 9!.

Calculating this gives us (4!) * 9! = (4*3*2*1) * (9*8*7*6*5*4*3*2*1) different possible arrangements.