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By using the quadratic formula, the roots of the equation are,

⇒ x = 2 ± (√3/2) i

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The quadratic equation is,

⇒ x² - 4x + 13 = 0

Now, By using the quadratic formula, the roots of the equation are,

⇒ x² - 4x + 13 = 0

⇒ x = - (- 4) ± √ (- 4)² - 4×1×13 / 2

⇒ x = 4 ± √16 - 52 / 2

⇒ x = 4 ± √- 36 / 2

⇒ x = 4 ± √6 i / 2

⇒ x = 2 ± (√3/2) i

Thus, We get;

⇒ x = 2 ± (√3/2) i

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Final answer:

The roots of the quadratic equation x² - 4x + 13 = 0 are complex numbers, specifically 2 + 3i and 2 - 3i, obtained through applying the quadratic formula.

Explanation:

To solve the quadratic equation x² – 4x + 13 = 0 using the quadratic formula, we first identify a, b, and c from the equation. Here, a=1, b=-4, and c=13. The quadratic formula is ‘x' equals minus ‘b’, plus-or-minus the square root of ‘b’ squared minus four ‘a’ ‘c', all over two 'a'. Applying these values, we get:

x = – (-4) ± √((-4)² – 4(1)(13)) / (2)(1)

This simplifies to:

x = 4 ± √(16 – 52) / 2

x = 4 ± √(-36) / 2

Since the square root of -36 is 6i (where i is the imaginary unit √(-1)), the solutions are:

x = (4 ± 6i) / 2

x = 2 ± 3i

Therefore, the roots of the equation are 2 + 3i and 2 - 3i, which are complex numbers.

Answer:

3602

Step-by-step explanation:

The population of the town after 15 years will be approximately 3495.

To find the population of the town after 15 years, we need to use the formula for compound interest: A = P(1 + r)^t, where A is the final amount, P is the initial amount, r is the growth rate expressed as a decimal, and t is the number of time periods. In this case, P = 2000, r = 0.04, and t = 15.

Using this formula, we can calculate the population after 15 years:

A = 2000(1 + 0.04)^15

A = 2000(1.04)^15

A ≈ 2000(1.747422)

A ≈ 3494.84

Rounding to the nearest whole number, the population after 15 years will be approximately 3495.

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Answer:

The correct option is D.

Step-by-step explanation:

From the given number line it is clear that A=0, B=2, C=8, D=14, F=20 and G=22.

The length of line segment AC is

[tex]AC=C-A=8-0=8[/tex]

The length of line segment CF is

[tex]CF=F-C=20-8=12[/tex]

The ratio of line segment AC to CF is

[tex]\frac{AC}{CF}=\frac{8}{12}[/tex]

Cancel out the common factors.

[tex]\frac{AC}{CF}=\frac{2}{3}[/tex]

The simplified ratio of [tex]\frac{AC}{CF}[/tex] is 2/3.

Therefore the correct option is D.

The calculated measure of the angle x is 76 degrees

From the question, we have the following parameters that can be used in our computation:

The figure

Also, we have

Angle with a measure of 76 degrees

By the theorem of corresponding angles, we have

x = 76

Hence, the measure of the angle x is 76 degrees

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Answer:

y1= |x-12|

y2= 22

Which graph represents the two functions? Graph 3

Step-by-step explanation:

Answer:

60 of the people who ordered the spicy fried chicken sandwich got a chocolate milk.

Step-by-step explanation:

Consider the provided information.

60 people order the grilled chicken sandwich, and 90 people order the spicy fried chicken sandwich.

40 Out of 60 people who order grilled chicken sandwich got a chocolate milk to drink.

Let say x number of people out of 90 got chocolate milk drink.

Now we need to find the people who ordered the spicy fried chicken sandwich got a chocolate milk.

The above information can be written as:

[tex]\frac{40}{60}=\frac{x}{90}[/tex]

[tex]\frac{40}{60}\times 90=x[/tex]

[tex]x=20\times 3[/tex]

[tex]x=60[/tex]

Hence, 60 of the people who ordered the spicy fried chicken sandwich got a chocolate milk.

The number of people who ordered the spicy fried chicken sandwich and got a chocolate milk is calculated as 50.

The number of people who ordered the spicy fried chicken sandwich and got a chocolate milk is to be determined.

Step-by-step explanation:

Answer:

The given expression “ seven more than half of a number” can be written mathematically as [tex]7+\frac{1}{2}N[/tex]

Step-by-step explanation:

Given phrase “ seven more than half of a number”

We have to write the algebraic expression for the given phase.

Algebraic expression is the  way of writing an expression in mathematical form using mathematical operations and variables.

Consider the given phrase “ seven more than half of a number”

Let the number be N,

Then half of number is [tex]\frac{1}{2}N[/tex]

and seven more means seven is added to this, the expresion becomes [tex]7+\frac{1}{2}N[/tex]

Thus, the given expression “ seven more than half of a number” can be written mathematically as [tex]7+\frac{1}{2}N[/tex]

Answer:

She will burn 960 calories if she runs 8 miles

The smallest possible set that contains the given sets as subsets is,

⇒ {jill, john, jack, Susan, sharon}

What is mean by Subsets?

A set 'A' is a subset of another set 'B' , if all the element of the set A are element of set of 'B'.

Given that;

The subsets are;

⇒ {jill, john, jack} , {Susan, sharon}

Now,

Clearly, A subsets of a set is contain all the elements of subsets.

So, We get the set;

Set = {jill, john, jack, Susan, sharon}

Thus, The smallest possible set that contains the given sets as subsets is,

⇒ {jill, john, jack, Susan, sharon}

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Answer:

6 and 11

Step-by-step explanation:

A trapezoid becomes an isosceles trapezoid when its non-parallel sides, or legs, are of equal length. Thus, for a given length x, an isosceles trapezoid requires both legs to be x in length.

A trapezoid is a geometric shape with one pair of parallel sides. A trapezoid becomes an isosceles trapezoid when the non-parallel sides (the legs) are equal in length. If we denote the length of the legs as x, then the trapezoid becomes an isosceles trapezoid when both legs are of equal length, meaning x equals x.

Without additional information such as the lengths of the base and height of the trapezoid or the angles within it, we cannot provide a specific numerical value for x. The key to remember here is that an isosceles trapezoid has equal length legs - so whatever value you have for one leg, the other leg must be the same for it to qualify as an isosceles trapezoid.

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Answer:

11+c=15

Step-by-step explanation:

4 pups have their eyes closed

ITS 10

Then 1.5% thank this

Answer:

The graph shows the given straight line.    

Step-by-step explanation:

We are given an equation:

[tex]y = \displaystyle\frac{1}{3}x + 3[/tex]

The attached image shows the graphical plot for the given equation.

If we compare the given equation to the

[tex]y = mx+c[/tex]

where m is the slope and c is the y-intercept of the straight line.

Comparing, we get:

[tex]m = \displaystyle\frac{1}{3}\\\\c = 3[/tex]

The line will pass by the points (-3, 2), (0, 3), and (3, 4)

Given is an equation y = x/3+3 we need to graph it,

Let's pick a few x-values and determine the y-values that go with them:

Y equals (1/3) when x = -3(-3) + 3 = -1 + 3 = 2

Y = (1/3)(0) + 3 = 0 + 3 = 3 when x = 0.

Y = (1/3)(3) + 3 = 1 + 3 = 4 for x = 3.

The points (-3, 2), (0, 3), and (3, 4) can now be plotted on the coordinate plane.

A straight line running across these locations will form the graph.

The line will have a positive slope because the value of x is positive (1/3).

Given that the y-intercept is 3, the line will cross the y-axis at (0, 3).

The plotted points (-3, 2), (0, 3), and (3, 4) lie on the line, and the line continues indefinitely in both directions.

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