Triangle XYZ is drawn with vertices X(4, −5), Y(6, −1), Z(10, −8). Determine the line of reflection if Y′(−6, −1).

y-axis
x-axis
y = −1
x = 6

Step-by-step explanation:

w = width

2w + 2 =  Length

Area = W x L  = 84 = w (2w+2)

                          84 = 2w^2 + 2w

                            0 = 2w^2 + 2w - 84        Use Quadratic Formula

                                                                 a = 2    b=2    c = -84

to find  

W = 6      then     L =  14 inches

The probability that a randomly selected score will be between 63 and 66 is approximately 0.0718, or 7.18%.

What is mean?

In statistics, the mean is a measure of central tendency, which is a way of describing the typical or central value of a set of data. The mean is also known as the average, and it is calculated by adding up all the values in a set of data and then dividing by the number of values in the set.

To find the probability that a randomly selected score will be between 63 and 66, we need to calculate the z-scores for these values and then find the area under the normal curve between these z-scores.

The z-score for a score of 63 is:

z = (63 - 74.4) / 8.3

z = -1.37

The z-score for a score of 66 is:

z = (66 - 74.4) / 8.3

z = -1.01

We can use a standard normal distribution table or calculator to find the area under the normal curve between these z-scores.

Using a standard normal distribution table, we find that the area to the left of a z-score of -1.01 is 0.1562, and the area to the left of a z-score of -1.37 is 0.0844. To find the area between these z-scores, we subtract the area to the left of -1.37 from the area to the left of -1.01:

P(-1.37 < z < -1.01) = 0.1562 - 0.0844 = 0.0718

So the probability that a randomly selected score will be between 63 and 66 is approximately 0.0718, or 7.18%.

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Answer:

A.  h'(2) = 5

B.  m'(2) = -24

C.  y = 8x - 31

D.  j'(2) = 3/25 = 0.12

Step-by-step explanation:

When differentiating composite functions, use the chain rule.

[tex]\boxed{\begin{minipage}{5.4 cm}\underline{Chain Rule for Differentiation}\\\\$\left[f\left(g(x)\right)\right]'=f'\left(g(x)\right) \cdot g'(x)$\\\end{minipage}}[/tex]

Chain Rule: The derivative of a composite function is the product of the derivative of the outer function evaluated at the inner function and the derivative of the inner function.

Using the chain rule, if h(x) = g(f(x)) then h'(x) = g'(f(x)) ⋅ f'(x).

To find h'(2), substitute x = 2 into the differentiated equation:

[tex]\begin{aligned}h'(x)& = g'(f(x)) \cdot f'(x)\\\\\implies h'(2)& = g'(f(2)) \cdot f'(2)\\& = g'(5) \cdot 1\\& = 5 \cdot 1\\&=5\end{aligned}[/tex]

Therefore, h'(2) = 5.

Using the chain rule, if m(x) = f(x²) then m'(x) = f'(x²) ⋅ 2x.

To find m'(2), substitute x = 2 into the differentiated equation:

[tex]\begin{aligned}m'(x) &= f'(x^2) \cdot 2x\\\\\implies m'(2) &= f'(2^2) \cdot 2(2)\\&=f'(4) \cdot 4\\&=-6 \cdot 4\\&=-24\end{aligned}[/tex]

Therefore, m'(2) = -24.

To find the slope of the tangent line to the graph of k at x = 4, substitute x = 4 into the derivative of k(x).

If k(x) = f(g(x)) then k'(x) = f'(g(x)) ⋅ g'(x).

Therefore, the slope of the tangent line is:

[tex]\begin{aligned}k'(x) &= f'(g(x)) \cdot g'(x)\\\\\implies k'(4) &= f'(g(4)) \cdot g'(4)\\&= f'(5) \cdot 4\\&= 2 \cdot 4\\&= 8\end{aligned}[/tex]

Now calculate k(x) when x = 4:

[tex]\begin{aligned}k(x)&=f(g(x))\\\\\implies k(4) &= f(g(4))\\&=f(5)\\&=1\end{aligned}[/tex]

To write the equation of the tangent line, substitute the found slope m = 8 and point (4, 1) into the point-slope equation:

[tex]\begin{aligned}y-y_1&=m(x-x_1)\\y-1&=8(x-4)\\y-1&=8x-32\\y&=8x-31\end{aligned}[/tex]

Therefore, an equation for the line tangent to the graph of k at x = 4 is:

To find the derivative of j(x) use the quotient rule.

[tex]\textsf{If\;\;$j(x)=\dfrac{g(x)}{f(x)}$\;\;then:}\\\\\\j'(x)=\dfrac{f(x)g'(x)-g(x)f'(x)}{(f(x))^2}[/tex]

To calculate j'(2), substitute x = 2 into the equation:

[tex]\begin{aligned} \implies j'(2)&=\dfrac{f(2)g'(2)-g(2)f'(2)}{(f(2))^2}\\\\&=\dfrac{5 \cdot 1-2 \cdot 1}{(5)^2}\\\\&=\dfrac{5-2}{25}\\\\&=\dfrac{3}{25}\\\\&=0.12\end{aligned}[/tex]

Therefore, j'(2) = 3/25 = 0.12.

Answer:

39.96

Step-by-step explanation:

the shape is a parallelogram ao the formula is base x height

A=10.8 x 3.7

A=39.97

the system of equations is: [tex]300x + 450y = 6000[/tex]

[tex]y = x + 5[/tex]

Let's define the variables:

Let "x" be the number of cans of soup purchased by Samuel.

Let "y" be the number of frozen dinners purchased by Samuel.

According to the given information, each can of soup has 300 mg of sodium and each frozen dinner has 450 mg of sodium. Samuel purchased 5 more frozen dinners than cans of soup, so we can write the following equations:

The total sodium from cans of soup: 300x mg

The total sodium from frozen dinners: 450y mg

The total sodium from both cans of soup and frozen dinners: [tex]6000 mg[/tex]

So the first equation is:

[tex]300x + 450y = 6000[/tex]  (since the total sodium from cans of soup and frozen dinners is 6000 mg)

Since Samuel purchased 5 more frozen dinners than cans of soup, we can write the second equation:

[tex]y = x + 5[/tex] (since y is 5 more than x)

Therefore,  the system of equations is:

[tex]300x + 450y = 6000[/tex]

[tex]y = x + 5[/tex]

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Answer: An even function is a function that satisfies the condition:

f(-x) = f(x)

Let's check which of the given functions satisfies this condition:

f(x) = (x - 1)^2

f(-x) = (-x - 1)^2 = x^2 + 2x + 1

f(x) = (x - 1)^2

The two expressions are not equal, so f(x) is not an even function.

f(x) = 8x

f(-x) = -8x = -f(x)

f(x) = 8x

The two expressions are equal with opposite signs, so f(x) is an odd function.

f(x) = x^2 - x

f(-x) = (-x)^2 - (-x) = x^2 + x

f(x) = x^2 - x

The two expressions are not equal, so f(x) is not an even function.

f(x) = 7

f(-x) = 7 = f(x)

f(x) = 7

The two expressions are equal, so f(x) is an even function.

Therefore, the only even function among the given functions is:

f(x) = 7.

Step-by-step explanation:

Answer:

2004

Step-by-step explanation:

Answer:

32 I hope this helps please make me a brianlist that would help :)

The solution to the inequality is x ≤ 10, which means that each row of seats on the floor must have 10 seats or fewer in order to meet the fire safety regulations.

What is inequality?

In mathematics, the inequality of two lines refers to the relationship between the slopes and y-intercepts of two different lines on a coordinate plane. Specifically, if the slope of one line is greater than the slope of another line, and their y-intercepts are not equal, then the inequality symbol (< or >) can be used to represent their relationship. For example, if line A has a slope of 2 and a y-intercept of -3, and line B has a slope of 1 and a y-intercept of 1, we can write A > B to represent that line A is steeper than line B.

To solve this problem, we need to use the information given to us to set up an inequality that represents the total number of seats in the theater and then use that inequality to determine the maximum number of people that can be in the theater while still meeting the fire safety regulations.

Let's start by calculating the total number of seats in the theater. We know that there are 90 seats in the balcony and 15 rows on the floor. We don't know the exact number of seats in each row, but we do know that each row has the same number of seats, which we will call x. Therefore, the total number of seats in the theater is 90 + (15 × x)

Now we can set up an inequality to represent the maximum number of people that can be in the theater while still meeting the fire safety regulations. We know that this number must be less than or equal to 240. Therefore, our inequality is 90 + (15 × x) ≤ 240

Now we can solve for x by first subtracting 90 from both sides of the inequality,

15 × x ≤ 150

Next, we can divide both sides of the inequality by 15,

x ≤ 10

Therefore, the solution to the inequality is x ≤ 10, which means that each row of seats on the floor must have 10 seats or fewer in order to meet the fire safety regulations.

To check this solution, we can plug x = 10 into our expression for the total number of seats,

Total number of seats = 90 + (15 × 10) = 240

This confirms that the maximum number of people in the theater is 240, which is the limit imposed by the fire safety regulations.

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Answer: The altitude of the triangle is [tex]h = 7 \sqrt{3}.[/tex]

Step-by-step explanation:

Suppose that we separate the equilateral triangle with the altitude of the triangle, as shown in the diagram I attached.

Then the length of the altitude [tex]h[/tex] can be found through the Pythagorean theorem:

[tex]h = \sqrt{14^2-\left( \frac{14}{2} \right)^2} = \sqrt{147} = \boxed{7 \sqrt{3}}.[/tex]

Therefore, the altitude of the equilateral triangle is [tex]h = 7 \sqrt{3}.[/tex]

The equation a² + b² = c² represents the Pythagorean theorem.

This is a theorem that  states that in a right-angled triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b).

The Pythagorean theorem is used to find the length of one of the sides of a right-angled triangle when the lengths of the other two sides are known.

To solve the problem, you need to have at least two side lengths given. Then, you can use the equation to find the length of the third side. For example:

If you know the lengths of sides a and b and need to find the length of the hypotenuse (c):

Plug in the known values for a and b into the equation and solve for c.

Example: If a = 3 and b = 4, then 3² + 4² = c², which gives 9 + 16 = c², so c² = 25, and c = sqrt(25) = 5.

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We find that P(Z > 2.46) is roughly 0.007 using a calculator or a basic normal distribution table. The probability that a bag will contain more than 20% blue jellybeans is therefore approximately 0.007 or 0.7%.

The probability of an event is the ratio of good outcomes to all other potential outcomes. The number of successful outcomes for an experiment with 'n' outcomes can be expressed using the symbol x.

Here in the question,

We can utilise the binomial distribution formula to resolve this issue. In a bag of 200 jelly beans, let X represent the proportion of blue jelly beans. Following that, X exhibits a binomial distribution with parameters of n = 200 and p = 0.15, where p is the likelihood of drawing a blue jellybean.

The formula for determining the likelihood of finding more than 20% blue jellybeans in a bag is:

P (X > 0.2 × 200) = P (X > 40)

Since n is large (200) and p is not too near to 0 or 1, we can utilise the usual approximation to the binomial distribution. We may determine the equivalent mean and standard deviation of the normal distribution by using the mean and variance of the binomial distribution:

μ = np = 200 × 0.15 = 30

σ = √ (np(1-p)) = √ (200 × 0.15 × (1-0.15)) = 4.07

Then, we can standardize the random variable X as:

Z = (X - μ) / σ

So, we have:

P(X > 40) = P((X - μ) / σ > (40 - μ) / σ)

= P(Z > (40 - 30) / 4.07)

= P(Z > 2.46)

We find that P(Z > 2.46) is roughly 0.007 using a calculator or a basic normal distribution table. The likelihood that a bag will contain more than 20% blue jellybeans is therefore approximately 0.007 or 0.7%.

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The percentage of females with brown eyes as follows is 25%.

Percentage is a way of expressing a number as a fraction of 100. It is represented by the symbol "%". The word "percent" means "per hundred".

Let's assume that the total population of Math town is 100 people for the sake of simplicity. Then, we can use the following information to create a table:

Population Males Females

Total         60         40

Brown eyes 18         ?

From the table, we can see that 60% of the population are males, so there are 60 x 0.3 = 18 males with brown eyes.

We also know that the total population with brown eyes is 28%, so there are 100 x 0.28 = 28 people with brown eyes. Therefore, there must be 28 - 18 = 10 females with brown eyes.

Finally, we can calculate the percentage of females with brown eyes as follows:

% of females with brown eyes = (10 / 40) x 100% = 25%

Therefore, the answer is (C) 25%.

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The diameter of the semicircle is with an area of 76.97 square yards is 14 yards.

Semicircle is half that of a circle, hence the area will be half that of a circle. Area of semi circle = 1/2 × πr²

Where r radius and π is constant pi.

Since we are given the area of the semicircle as 76.97 square yards, we can set up the following equation:

76.97 = 1/2 × (πr²)

Multiplying both sides by 2, we get:

153.94 = πr²

Dividing both sides by π, we get:

r² = 49

Taking the square root of both sides, we get:

r = 7

Therefore, the diameter of the semicircle is: d = 2r  = 2(7) = 14 yards

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The skydiver is in the air for 23 seconds.

A diagram or pictorial representation that organises the depiction of facts or values is known as a graph.  

The relationships between two or more items are frequently represented by the points on a graph.

The skydiver is in the air as long as their height is greater than zero. From the graph, we can see that the skydiver reaches a height of zero at t = 23 seconds. Therefore, the skydiver is in the air for:

t = 23 seconds - 0 seconds = 23 seconds

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The answers are: A)H0: μ1 − μ2 = 0; Ha: μ1 − μ2 ≠ 0

(b)  Means: Company A___50.6___ min.; Company B___52.75___ min.

c)The t-value is -0.30107., The p-value is 0 .764815.

A hypothesis is a testable statement about the relationship between two or more variables or a proposed explanation for some observed phenomenon

A)H0: μ1 − μ2 = 0

i.e there is no difference between the means of delayed flight for two different airlines

Ha: μ1 − μ2 ≠ 0

i.e there is a difference between the means of delayed flight for two different airlines

(b)

Company A___50.6___ min.

Company B___52.75___ min.

Mean of Company A = x`1= ∑x/n =34+ 59+ 43+ 30+ 3+ 32+ 42+ 85+ 30+ 48+ 110+ 50+ 10+ 26+ 70+ 52+ 83+ 78+ 27+ 70+ 27+ 90+ 38+ 52+ 76/25

= 1265/25= 50.6

Mean of Company B = x`2= ∑x/n =

=46+ 63+ 43+ 33+ 65+ 104+ 45+ 27+ 39+ 84+ 75+ 44+ 34+ 51+ 63+ 42+ 34+ 34+ 65+ 64/20

= 1055/20= 52.75

Difference Scores Calculations

Company A

Sample size for Company A= n1= 25

Degrees of freedom for company A= df1 = n1 - 1 = 25 - 1 = 24

Mean for Company A= x`1=  50.6

Total Squared Difference (x-x`1) for Company A= SS1: 16938

s21 = SS1/(n1 - 1) = 16938/(25-1) = 705.75

Company B

Sample size for Company B= n1= 20

Degrees of freedom for company B= df2 = n2 - 1 = 20 - 1 = 19

Mean for Company B= x`2=  52.75

Total Squared Difference (x-x`2) for Company B= SS2=7427.75

s22 = SS2/(n2 - 1) = 7427.75/(20-1) = 390.93

T-value Calculation

Pooled Variance= Sp²

Sp² = ((df1/(df1 + df2)) * s21) + ((df2/(df2 + df2)) * s22)

Sp²= ((24/43) * 705.75) + ((19/43) * 390.93) = 566.65

s2x`1 = s2p/n1 = 566.65/25 = 22.67

s2x`2 = s2p/n2 = 566.65/20 = 28.33

t = (x`1 - x`2)/√(s2x`1 + s2x`2) = -2.15/√51 = -0.3

The t-value is -0.30107.

The total degrees of freedom is = n1+n2- 2= 25+20-2=43

The critical region for two tailed test at significance level ∝ =0.05 is

t(0.025) (43) = t > ±2.017

Since the calculated value of t=  -0.30107.  does not fall in the critical region t > ±2.017, null hypothesis is not rejected that is there is no difference between the means of delayed flight for two different airlines.

The p-value is 0 .764815. The result is not significant at p < 0.05.

C) Do not reject H0. There is no statistical evidence that one airline does better than the other in terms of their population mean delay time.

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Answer:

To solve the equation 2x + 6/5 = -1(x - 11), we can use the distributive property of multiplication over addition/subtraction to simplify the right-hand side of the equation:

2x + 6/5 = -x + 11

Next, we can rearrange the terms so that all the x terms are on one side of he equation and all the constant terms are on the other side:

2x + x = 11 - 6/5

Combining like terms and simplifying the right-hand side, we get:

3x = 49/5

Dividing both sides by 3, we get:

x = 49/15

Therefore, the value of x in the equation 2x + 6/5 = -1(x - 11) is 49/15.

Answer:

x < 11    &   x < 12

Step-by-step explanation:

x - 3 < 8 and 6x < 72

x < 11    &   x < 12

Answer:

[tex]81\pi[/tex] [tex]mm^2[/tex]

Step-by-step explanation:

Let's recall the formula for the area of a circle:

[tex]A = \pi r^2[/tex]

We are given the diameter, but the formula uses the radius. Since the radius is equal to one-half of the diameter, we can find the radius by doing this:

[tex]r = \frac{1}{2}d=\\\\r=\frac{1}{2}(18)= \\\\r=9[/tex]

Now that we've found the radius is 9 mm, let's substitute the values into the formula for the area of a circle. We have:

[tex]A = \pi r^2=\\A=\pi (9^2)=\\A=\pi (81)=\\A=81\pi[/tex]

So, we've found that the exact area, in terms of pi, of either face of the coin is [tex]81\pi[/tex] [tex]mm^2[/tex].

To find the area of the coin/a circle use this equation:

(a = area, r = radius, d = diameter)

[tex]\text{a = r}^2[/tex]

So we need to do for the radius.

[tex]\text{r} = \dfrac{\text{d}}{2}[/tex]

[tex]\text{r} = \dfrac{18}{2}[/tex]

[tex]\text{r} = 9[/tex]

Then solve

[tex]\text{a = 9}^2[/tex]

[tex]\boxed{\bold{a = 81}}[/tex]

The value of Cscθ is 1/y.

What is a trigonometric function?

The right-angled triangle's angle and the ratio of its two side lengths are related by the trigonometric functions, which are actual functions. They are extensively employed in all fields of geometry-related study, including geodesy, solid mechanics, celestial mechanics, and many others.

Here, we have

Given: if p(x,y) is the point on the unit circle defined by the real number theta.

We have to find the value of the csc theta.

P(x,y) is the point on the unit circle  (the unit circle has a radius of 1 and center (0,0))

Now in a diagram, we can see that

OA= x

AP= y

radius OP =1

∠POA =θ

Now in ΔAOP

Cscθ = hypotenuse/opposite side

Cscθ = OP/AP

Cscθ = 1/y

Hence, the value of Cscθ is 1/y.

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The amount of taxes owed on a taxable income of $51, 100 is $6,919.00. The correct option is B.

To determine the amount of taxes owed on a taxable income of $51,100, we need to use the federal income tax brackets and rates for the tax year in question.

For the tax year 2021, the federal income tax brackets and rates for single filers are:

10% on taxable income from $0 to $9,950

12% on taxable income from $9,951 to $40,525

22% on taxable income from $40,526 to $86,375

24% on taxable income from $86,376 to $164,925

32% on taxable income from $164,926 to $209,425

35% on taxable income from $209,426 to $523,600

37% on taxable income over $523,600

To calculate the taxes owed on a taxable income of $51,100, we need to determine the amount of income that falls into each tax bracket, and then apply the corresponding tax rate to each portion of income.

Income up to $9,950 is taxed at 10%. This gives us a tax of 0.10 x $9,950 = $995.

Income from $9,951 to $40,525 is taxed at 12%. This gives us a tax of 0.12 x ($40,525 - $9,951) = $3,384.48.

Income from $40,526 to $51,100 is taxed at 22%. This gives us a tax of 0.22 x ($51,100 - $40,526) = $2,312.72.

Adding these three amounts together, we get the total tax owed:

$995 + $3,384.48 + $2,312.72 = $6,692.20

Therefore, the closest answer choice is B) $6,919.00.

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The amount of taxes owned on a taxable income of $51100 is $11242 which is approximately equal to option (c).

An income refers to the money that an individual or organization receives on a regular basis from various sources, such as employment, investments, or business activities. It is typically reported as gross income before taxes and other deductions are taken out.

Tax is a mandatory financial charge imposed by the government on individuals, businesses, and other entities, based on their income or property value. The revenue generated from taxes is used to fund public services and infrastructure.

=$51100* 22/100

=$11242

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The correct option - A) conflict of interest is caused due to ABC Ad Agency has two automotive tire chains as clients.

A conflict of interest arises when a person's personal interests, such as those related to their family, friends, finances, or social standing, potentially impair their judgement, choices, or actions at work. Conflicts of interest are taken seriously enough by government organisations that they are governed.

For the given data- The ABC Ad Agency has two automotive tire chains as clients.

This, could  lead to a(n) conflict of interest.

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Answer: 3:7

Step-by-step explanation: since the simplest form of the fraction 36/84 is 3/7 that means 36:84 in simplest form is 3:7.

Answer:

x = 7

Step-by-step explanation:

8x + 5 + 3x + 8 = 90

11x + 5 + 8 = 90

11x + 13 = 90

11x = 77

x = 7

Let's Check

8(7) + 5 + 3(7) + 8 = 90

56 + 5 + 21 + 8 = 90

61 + 21 + 8 = 90

82 + 8 = 90

90 = 90

So, x = 7 is the correct answer!

Answer:

7

Step-by-step explanation:

First, collect common factors. This means put the x's together and the regular numbers together.

8x+3x=11x

5+8=13

11x+13=90

Subtract 13 from both sides

11x+13=90

    -13  -13

11x=77

Divide 77 by 11

x=7

Hope this helps! :)

The shaded area covers around 0.8664 square feet of space.

The mean and standard deviation of the standard normal distribution are 0 and 1, respectively. The standard deviation shows how much a particular measurement deviates from the mean, and the standard normal distribution is centred at zero.

Using a conventional normal distribution table, we must first determine the areas to the left of z= -1.5 and z=1.5, and then subtract those two areas to determine the area of the shaded zone.

Using a standard normal distribution table, we find that the area to the left of z= -1.5 is 0.0668, and the area to the left of z=1.5 is 0.9332. As a result, the darkened region's area is:

0.9332 - 0.0668 = 0.8664

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We can estimate that there are approximately 134 glass beads in the bin.

What is probability?

Probability is a measure of the likelihood of an event occurring.

To estimate the number of glass beads in the bin, we can use the proportion of glass beads in the handful that Jasper selected.

There are 15 beads in the handful, and 4 of them are glass. So, the proportion of glass beads in the handful is:

4/15 ≈ 0.267

We can assume that the proportion of glass beads in the bin is similar to the proportion in the handful. Therefore, we can estimate the number of glass beads in the bin as

0.267 x 500 ≈ 134

Therefore, we can estimate that there are approximately 134 glass beads in the bin.

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The statistical question that can result in numerical data is "How many hours this week did you spend on homework?"

The statistical question that can result in numerical data is "How many hours this week did you spend on homework?"

This is because the question is asking for a numerical response that can be measured and counted. The other options are not statistical questions that can result in numerical data.

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1. The total amount of your emergency fund will be $11,403.75.

2. $8,552.81 is in the CD, and $2,850.94 is in the regular savings account.

Your FICA deduction is 7.65% of your gross income:

7.65% of $4,520.00 = $345.98

Your federal tax withholding is 11.75% of your gross income:

11.75% of $4,520.00 = $531.40

Your state tax withholding is 8.5% of your gross income:

8.5% of $4,520.00 = $384.40

Your total deductions are:

= $345.98 + $531.40 + $384.40

= $1,261.78

Your monthly income after deductions is:

= $4,520.00 - $1,261.78

= $3,258.22

Your fixed expenses are 30% of your realized income:

= 30% of $3,258.22

= $977.47

Your monthly savings amount is:

= $3,258.22 - $977.47

= $2,280.75

You saved 5 months' worth in an emergency fund, so the total amount in your emergency fund is:

= 5 x $2,280.75

= $11,403.75

Regenerate response

You placed 75% of your emergency fund in a 60-day CD at a 5.25% APR:

= 75% of $11,403.75 = $8,552.81

You placed the remaining 25% of your emergency fund in a regular savings account at a 3.8% APR:

= 25% of $11,403.75

= $2,850.94.

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To solve the equation x^2 + 4x - 11 = 0 by completing the square, we can follow these steps:

Move the constant term to the right side of the equation:

x^2 + 4x = 11

Complete the square by adding the square of half the coefficient of x to both sides of the equation:

x^2 + 4x + (4/2)^2 = 11 + (4/2)^2

Simplifying the left side:

x^2 + 4x + 4 = 11 + 4

Factor the perfect square on the left side of the equation:

(x + 2)^2 = 15

Take the square root of both sides of the equation:

x + 2 = ±√15

Solve for x by subtracting 2 from both sides:

x = -2 ± √15

Therefore, the solutions to the equation x^2 + 4x - 11 = 0 by completing the square are x = -2 + √15 and x = -2 - √15.