Find x when one arc measure is 59 and another arc is 2x and one anhle is 15

All functions have an inverse function, and for a function to have an inverse. The inverse of  [tex]f(x) = 3\sqrt(4x + 7) is f^-1(x) = (x^3 - 189)/108[/tex]

The inverse function, often known as the "inverse mapping," is a function that "undoes" another function's operation. If a function f(x) translates an input x to an output y, the inverse function f(-1)(y) transfers the result y back to the input x.

To find the inverse of the function f(x) = 3√(4x + 7), we need to solve for x in terms of y.

Step 1: Replace f(x) with y

[tex]y = 3√(4x + 7)[/tex]

Step 2: Cube both sides to eliminate the cube root

[tex]y^3 = 27(4x + 7)[/tex]

Step 3: Simplify and solve for x

[tex]y^3 = 108x + 189[/tex]

[tex]x = (y^3 - 189)/108[/tex]

Step 4: Replace x with [tex]f^-1(x)[/tex]

[tex]f^-1(x) = (x^3 - 189)/108[/tex]

Therefore, the inverse of   [tex]f(x) = 3√(4x + 7) is f^-1(x) = (x^3 - 189)/108[/tex] .

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Answer:

35. Radius= 12 cm

36. (B) 50 cm

Step-by-step explanation:

35.

TSA = 2πr(h+r)

Expanding the brackets, we get:

TSA = 2πrh + 2πr^2

Rearranging the equation, we get:

TSA - 2πrh = 2πr^2

Dividing both sides by 2π, we get:

r^2 = (TSA - 2πrh) / 2π

Taking the square root of both sides, we get:

r = √[(TSA - 2πrh) / 2π]

We need to simplify the given equation to solve for r.

r = √[(905.143) - 2(22/7)r(14)) / 2(22/7)]

r = √[(905.143) - (88/7)r] / (44/7)

Squaring both sides, we get:

r^2 = [(905.143) - (88/7)r] / (44/7)

Multiplying both sides by (44/7) and simplifying:

7r^2 - 88r - 905.143 = 0

Using the quadratic formula:

r = [88 ± √(88^2 - 4(7)(-905.143))] / (2(7))

r ≈ 12.009 or r ≈ -12.892

Since r represents the radius of a circle, which cannot be negative, we ignore the negative solution.

Therefore, the solution is r ≈ 12.009.

36.

We can use the formula for the volume of a cylinder:

volume = πr^2h

where r is the radius and h is the height of the cylinder.

First, we need to find the radius of the drum. The diameter is given as 56 cm, so the radius is half of that, or 28 cm.

Next, we can use the given volume of 123.2 liters. However, we need to convert liters to cubic centimeters (cm^3) since the dimensions are in centimeters.

1 liter = 1000 cm^3

So, 123.2 liters = 123,200 cm^3.

Now we can plug in the values:

123,200 cm^3 = π(28 cm)^2h

Simplifying:

123,200 cm^3 = 2464π cm^2h

Dividing both sides by 2464π cm^2:

50 cm = h

Therefore, the height of the drum is 50 cm.

Answer:

The remainder is 7.

Step-by-step explanation:

Let's pick 15 and 14. The sum of these two numbers is 29. Multiplying 29 by 3, we have 87. 87 divided by 10 is 8 with a remainder of 7.

The final answer is 1 / 11

Deena has a total of 11 pairs of socks in her sock drawer. One pair of those 11 pairs is navy socks. Therefore, the probability that she will choose a pair of navy socks is 1/11.What is probability? Probability is the numerical measure of the possibility of an event taking place. Probability is calculated by dividing the number of successful outcomes by the total number of possible outcomes.The probability of Deena picking navy socks is calculated as:Probability of selecting navy socks = Number of pairs of navy socks/ Total number of pairs of socks in the drawerNumber of pairs of navy socks = 1Total number of pairs of socks in the drawer = 1 /11Probability of selecting navy socks = 1/11Therefore, the probability that Deena will select a pair of navy socks is 1/11.

Therefore, the answer is 1 / 11.

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Answer:

1/9 ≅ 0.11

Step-by-step explanation:

One way to approach this problem is to use the formula:

total cost = cost of parts + cost of labor

We can plug in the given values:

719.75 = 116 + cost of labor x 5.25

Simplifying:

603.75 = cost of labor x 5.25

To solve for the cost of labor per hour (cc), we can divide both sides by 5.25:

cc = 603.75 / 5.25

Simplifying:

cc ≈ 114.76

Therefore, the equation that could be used to determine the cost of labor per hour is:

cc = (total cost - cost of parts) / hours of labor

or:

cc = (719.75 - 116) / 5.25

The correct statement regarding the transformations is given as follows:

g(x) is stretched vertically by a factor of 5 and translated 3 units to the right.

A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.

The four translation rules for functions are defined as follows:

The transformations to the parent function in this problem are given as follows:

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Answer: 4(5+3) = 4(5) + 4(3) = 20 + 12 = 32

Step-by-step explanation:

Answer:

32=32 ?

Step-by-step explanation:

1. By simplifying and comparing, the value of x is 4

2. By simplifying and comparing, the value of x is 6

3. By simplifying and comparing, the value of x is 0.53 and the value of y is 4

From the question, we are to simplify the given expressions

1.

(4.2 × 10⁷) / (2 × 10³)

This can be expressed

(4.2 / 2) × (10⁷ / 10³)

Simplifying and applying the division law of indices

= 2.1 × 10⁷⁻³

= 2.1 × 10⁴

By comparison, the value of x is 4

2.

(7.2 × 10⁻⁸) ÷ (1.2 × 10⁻³)

This can be expressed as

(7.2 ÷ 1.2) × (10⁻⁸ ÷ 10⁻³)

Simplifying and applying the division law of indices

6 × 10⁻⁸ ⁻ ⁻³

6 × 10⁻⁸ ⁺ ³

6 × 10⁻⁵

By comparison, the value of x is 6

3.

(4.24 × 10⁶) ÷ (8 × 10²)

This can be expressed as

(4.24 ÷ 8) × (10⁶ ÷ 10²)

Simplifying and applying the division law of indices

= 0.53 × 10⁶ ⁻ ²

= 0.53 × 10⁴

By comparison, the value of x is 0.53 and the value of y is 4

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Answer:

16.7%

Step-by-step explanation:

The regular price for a lubrication job is $6.50. With the promotion, customers can purchase 6 coupons for $32.50.

To find the percentage discount offered, we need to compare the regular price with the discounted price.

The regular price for 6 lubrication jobs would be:

$6.50 x 6 = $39

With the coupon book, the customer pays $32.50 for 6 lubrication jobs.

The amount of discount is:

$39 - $32.50 = $6.50

Therefore, the percentage discount offered is:

($6.50 / $39) x 100% = 16.7%

So the station is offering a discount of 16.7% to customers who purchase the 6-coupon lube book.

Answer:

Let’s start by defining the variables:

Let A be the area of the preimage.

Let k be the scale factor.

If the scale factor is k, then the area of the preimage is multiplied by k² to calculate the area of the new image. Therefore, we have:

Area of new image = k²A

We are given that:

k = 1/5

Therefore, we have:

k² = (1/5)² = 1/25

The area of the preimage is not given. Therefore, we cannot calculate the area of the new image

The surface area after larger by scale factor is  11700 [tex]in^2[/tex].

The surface area οf an οbject refers tο the οverall space filled by its surfaces. Many 3D shapes in geοmetry have variοus surface areas, which may be quickly estimated using the fοrmulas we shall learn in this lessοn. Twο categοries are used tο classify the surface area:

Here the given rectangular prism ,

Surface area = 1300 square inches

Here the given prism is larger by scale factor of 3 then,

=> surface area = 1300[tex]\times3^2[/tex] =  1300[tex]\times9[/tex] = 11700 [tex]in^2[/tex].

Hence the surface area after larger by scale factor is  11700 [tex]in^2[/tex].

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It means you would expect to win that amount, and if it's negative, it means you would expect to lose that amount.

To calculate the expected value of this bet, we first need to determine the probability of drawing two hearts and the probability of not drawing two hearts.

There are 52 cards in a standard deck, with 13 cards of each suit (hearts, diamonds, clubs, and spades). To calculate the probability of drawing two hearts without replacement, we consider the following:

1st card: The probability of drawing a heart is 13/52, as there are 13 hearts in the deck and 52 cards total.

2nd card: After drawing one heart, there are 12 hearts left and 51 cards total. The probability of drawing another heart is 12/51.

Thus, the probability of drawing two hearts is (13/52) * (12/51).

Next, we need to find the probability of not drawing two hearts. This can be calculated by subtracting the probability of drawing two hearts from 1.

Probability of not drawing two hearts = 1 - [(13/52) * (12/51)]

Now, we can calculate the expected value of the bet:

Expected value = (probability of winning * winnings) + (probability of losing * losses)

In this case, the winnings are $16, and the losses are $3.

Expected value = [(13/52) * (12/51) * $16] + {1 - [(13/52) * (12/51)]} * (-$3)

Now, let's calculate the expected value for 762 bets.

Expected value for 762 bets = 762 * {[(13/52) * (12/51) * $16] + {1 - [(13/52) * (12/51)]} * (-$3)}

Round the final expected value to two decimal places. If it's a positive value, it means you would expect to win that amount, and if it's negative, it means you would expect to lose that amount.

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Answer:

Using division the answer to the equation is 10 2/3 but the correct answer to the question would most likely be he needs to refill his tank after 10 days.

Step-by-step explanation:

19 5/9 ÷ 1 5/6 = 10 2/3

The  procedure permute-without-identity does what Professor Kelp intends.

As per the given question,

Professor Kelp wants to write a procedure that produces any permutation randomly except the identity permutation in which every element ends up where it started.

He has proposed the procedure permute-without-identity. We need to check whether this procedure does what Professor Kelp intends or not.

Procedure permute-without-identity:

Generate a permutation π ∈ Sn−1 uniformly at random. (Note that the identity permutation is not in Sn−1.)

Return the permutation obtained by shuffling the elements of π using a uniformly random shuffle.

Randomly shuffle the list using the Fisher-Yates shuffle, which creates a uniformly random permutation of the list.

Professor Kelp's procedure permute-without-identity chooses a permutation at random from the set of all permutations except the identity permutation.

So, there are n! - 1 possible choices of π.

Then, the elements of π are shuffled randomly using a uniformly random shuffle.

The identity permutation is excluded from π as it is not included in Sn-1.

Since the identity permutation is not included in Sn-1, it cannot be chosen by the procedure permute-without-identity.

Hence, the procedure does what Professor Kelp intends.

This procedure achieves the desired outcome by avoiding the case where all elements end up where they started.

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The probability that Xeres arrives first AND Regina arrives last is 3.33%.

Prοbability is a way οf calculating hοw likely sοmething is tο happen. It is difficult tο prοvide a cοmplete predictiοn fοr many events. Using it, we can οnly fοrecast the prοbability, οr likelihοοd, οf an event οccurring. The prοbability might be between 0 and 1, where 0 denοtes an impοssibility and 1 denοtes a certainty.

Here The number of possible arrangements of n elements is given by:

[tex]A_n=n![/tex]

In this problem:

6 people are invited, so the number of ways they can arrive is T = [tex]6![/tex]

Xeres first and Regina last, for the middle 4 there are  way D= 4! ways

Then the probability is P = [tex]\frac{D}{T}=\frac{4!}{6!}[/tex] =  0.0333 = 3.33%

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3

when the line is at the y=ax+b form the gradient is equal to a

A one-sample t-test is conducted to determine if recent Miss America winners have a significantly different BMI compared to winners from the 1920s and 1930s. The test results fail to reject the null hypothesis, indicating that recent winners do not appear to be significantly different from those in the 1920s and 1930s.

To determine if recent Miss America winners have a significantly different BMI compared to winners from the 1920s and 1930s, a one-sample t-test can be conducted. Using the given sample, the sample mean BMI is calculated to be 18.5.

The null hypothesis is that the population mean BMI of recent winners is equal to 19.2. The alternative hypothesis is that the population mean BMI of recent winners is different from 19.2.

Assuming a significance level of 0.05 and using a two-tailed test, the calculated t-value is -2.08 and the corresponding p-value is 0.057.

Since the p-value is greater than the significance level, we fail to reject the null hypothesis. This suggests that there is not enough evidence to conclude that recent Miss America winners have significantly different BMI compared to winners from the 1920s and 1930s.

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Answer: [tex]F=30N[/tex]

Step-by-step explanation:

1. You know that the force acting on the object varies directly with the object's acceleration. Then, by definition, you have:

[tex]F=ka[/tex]

Where [tex]F[/tex] is the force acting on the object, [tex]a[/tex] is the object's acceleration and [tex]k[/tex] is the constant of proportionality.

2. Keeping this on mind, you can calculate the constant of proportionality by substituting [tex]F=12[/tex] and [tex]a=4[/tex] into the equation and solving for [tex]k[/tex]:

[tex]12=k4[/tex]

[tex]k=\dfrac{12}{4}[/tex]

[tex]k=3[/tex]

3. Now, you can calculate the force when the acceleration of the object becomes 10 m/s², as following:

[tex]F=3(10)[/tex]

[tex]F=30[/tex]

3. The result is:

[tex]F=30N[/tex]

Answer:10

Step-by-step explanation: one side of a triangle must be greater than the differnce and less than the sum of the lengths of the other two sides

Answer: 5.83095

explanation:

Todd drank 29.17% of the bottles. First, we need to calculate the total number of bottles drank by Lydia, Mitchell, and Alexa.

Lydia = (1/8) x 24 = 3 bottles

Mitchell = (33 1/3%) x 24 = (1/3) x 24 = 8 bottles

Alexa = 0.25 x 24 = 6 bottles

The total number of bottles drank by Lydia, Mitchell, and Alexa is 3 + 8 + 6 = 17 bottles.

Therefore, the number of bottles Todd drank is 24 - 17 = 7 bottles.

To find the percentage of bottles Todd drank, we can use the following formula:

Percentage = (Part/Whole) x 100%

Where the Part is 7 and the Whole is 24.

Percentage = (7/24) x 100% = 29.17%

Therefore, Todd drank 29.17% of the bottles.

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[tex]\textit{arc's length}\\\\ s = \cfrac{\theta \pi r}{180} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=4\\ s=\pi \end{cases}\implies \pi =\cfrac{\theta \pi (4)}{180}\implies \cfrac{180}{4\pi }\cdot \pi =\theta\implies 45=\theta[/tex]

The discount is 75% off the original price of $185.

To find the amount of the discount, we can multiply the original price by 0.75:

$185 x 0.75 = $138.75

Therefore, the dress has been discounted by $138.75.

To find the sales price, we can subtract the discount from the original price:

$185 - $138.75 = $46.25

Therefore, the sale price of the dress is $46.25.

The correct answer to the given question about mapping quadrilateral ABCD onto quadrilateral HGEF is option D Translation 6 units left and 2 units down

To determine the transformation that maps quadrilateral ABCD onto quadrilateral HGFE, we need to compare the corresponding sides and angles of the two quadrilaterals.

Option 1: Rotation of 180° about the origin

A rotation of 180° about the origin would not map quadrilateral ABCD onto quadrilateral HGFE because the corresponding sides and angles are not congruent. For example, side AB of ABCD would not match side HG of HGFE after the rotation. Therefore, option 1 is incorrect.

Option 2: Reflection across the y-axis

A reflection across the y-axis would not map quadrilateral ABCD onto quadrilateral HGFE because the corresponding sides and angles are not congruent. For example, angle A of ABCD would not match angle H of HGFE after the reflection. Therefore, option 2 is incorrect.

Option 3: Reflection across the x-axis

A reflection across the x-axis would not map quadrilateral ABCD onto quadrilateral HGFE because the corresponding sides and angles are not congruent. For example, side BC of ABCD would not match side GF of HGFE after the reflection. Therefore, option 3 is incorrect.

Option 4: Translation 6 units left and 2 units down

A translation 6 units left and 2 units down would map quadrilateral ABCD onto quadrilateral HGFE because the corresponding sides and angles are congruent. Each point of ABCD would move left by 6 units and down by 2 units to reach its corresponding point in HGFE. Therefore, option 4 is the correct transformation that maps quadrilateral ABCD onto quadrilateral HGFE.

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Answer:

The angle measurement will stay the same.

Step-by-step explanation:

When you scale a figure the angle measurements stay the same.

Helping in the name of Jesus.

The spinner has 8 equal-sized sections, each labeled 1, 2, 3, or 4 and correct options are:

a. The spinner landing on 1 - 1 (Likely)

b. The spinner landing on an even number - 2 and 4 (Equally likely to occur or not occur)

c. The spinner landing on the number 8 - Impossible (0)

d. The spinner landing on a number - 1, 2, 3, and 4 (Equally likely to occur or not occur)

e. The spinner landing on the left side of the circle - Unlikely (2)

Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, where 0 indicates that the event is impossible and 1 indicates that the event is certain to occur.

Here,

a. The spinner landing on 1 - There is only one section labeled 1 on the spinner, out of a total of 8 sections. Therefore, the probability of the spinner landing on 1 is 1/8. On the probability scale provided, this probability would be located closer to "Likely" than to "Equally Likely to Occur or Not Occur", but not as close to "Certain".

b. The spinner landing on an even number - There are 4 sections labeled with even numbers (2 and 4), out of a total of 8 sections. Therefore, the probability of the spinner landing on an even number is 4/8 or 1/2. On the probability scale provided, this probability would be located exactly halfway between "Equally Likely to Occur or Not Occur" and "Certain".

c. The spinner landing on the number 8 - There is no section labeled 8 on the spinner, so this event is impossible. On the probability scale provided, this probability would be located at the very bottom of the scale, labeled "Impossible".

d. The spinner landing on a number - Every section of the spinner is labeled with a number, so this event is certain to occur. On the probability scale provided, this probability would be located at the very top of the scale, labeled "Certain".

e. The spinner landing on the left side of the circle - There are 2 sections labeled with numbers that are on the left side of the circle (1 and 2), out of a total of 8 sections. Therefore, the probability of the spinner landing on the left side of the circle is 2/8 or 1/4. On the probability scale provided, this probability would be located closer to "Unlikely" than to "Equally Likely to Occur or Not Occur", but not as close to "Impossible".

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The expression that represents the total change in the amount of snow on the ground over the two days is -3 + (-8) = -11

The problem asks for the total change in the amount of snow on the ground over two days after a blizzard. The problem states that the snow melted by 3 inches one day and 8 inches the next day. The expression that represents the total change can be found by adding the two changes together. However, since the snow is melting, we need to use negative values to represent the change. Therefore, we can write the expression as:

-3 + (-8)

Simplifying this expression, we get:

-3 - 8 = -11

Therefore, the total change in the amount of snow on the ground over the two days is -11 inches.

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Answer:

[tex]\large\boxed{\tt y = 115^{\circ}.}[/tex]

Step-by-step explanation:

[tex]\textsf{We are asked to find the measure of} \ \tt \angle Y.[/tex]

[tex]\textsf{We are given a shape, but we aren't given what shape it is.}[/tex]

[tex]\large\underline{\textsf{What is a Shape?}}[/tex]

[tex]\textsf{A Shape is a specific outline sometimes dependent of how many sides it has.}[/tex]

[tex]\underline{\textsf{Shapes that depend on outlines;}}[/tex]

[tex]\underline{\textsf{Shapes that depend on the number of sides;}}[/tex]

[tex]\textsf{Mainly the opposite.}[/tex]

[tex]\textsf{Because our shape has 5 sides, it's dependent on the amount of sides it has, which}[/tex]

[tex]\textsf{makes the shape a Polygon.}[/tex]

[tex]\large\underline{\textsf{What is a Polygon?}}[/tex]

[tex]\textsf{A Polygon is a closed shape that classifies as a;}[/tex]

[tex]\textsf{The list goes on forever.}[/tex]

[tex]\textsf{Our shape is a Pentagon, due to the shape having 5 sides.}[/tex]

[tex]\large\underline{\textsf{What is a Pentagon made up of?}}[/tex]

[tex]\textsf{A Pentagon is a polygon that has 5 sides, meaning that it has 5 angles.}[/tex]

[tex]\textsf{The total of the angles is what we should find out with a pattern.}[/tex]

[tex]\underline{\textsf{What is the total of all the angles' measures of a Pentagon?}}[/tex]

[tex]\textsf{A Triangle has 3 sides with 3 angles, which add up to 180}^{\circ}.[/tex]

[tex]\textsf{A Quadrilateral has 4 sides with 4 angles, which add up to 360}^{\circ}.[/tex]

[tex]\textsf{The Pattern is that when an extra side is added, the total measure of the angles}[/tex]

[tex]\textsf{increase by 180}^{\circ}.[/tex]

[tex]\textsf{A Pentagon has 5 sides with 5 angles, which add up to} \ \boxed{\tt 540^{\circ}.}[/tex]

[tex]\textsf{Now that we know the total, we can form an equation.}[/tex]

[tex]\tt 540^{\circ} = 135^{\circ} + 112^{\circ} + 88^{\circ} + y^{\circ} + 90^{\circ}[/tex]

[tex]\textsf{Remember that Right Angles are 90}^{\circ} \ \textsf{angles that are represented with a box}[/tex]

[tex]\textsf{symbol.}[/tex]

[tex]\large\underline{\textsf{Solving;}}[/tex]

[tex]\textsf{Now that we have our equation, we should \underline{combine like terms}, then use the}[/tex]

[tex]\textsf{\underline{subtraction rule of equality} to find the measure of y.}[/tex]

[tex]\underline{\textsf{Combine Like Terms;}}[/tex]

[tex]\tt 540^{\circ} = \boxed{135^{\circ}} + \boxed{112^{\circ}} + \boxed{88^{\circ}} + y^{\circ} + \boxed{90^{\circ}}[/tex]

[tex]\tt 540^{\circ} = 425^{\circ} + y^{\circ}[/tex]

[tex]\underline{\textsf{Use the Subtraction Rule of Equality;}}[/tex]

[tex]\tt 540^{\circ} - 425^{\circ} = 425^{\circ} - 425^{\circ}+ y^{\circ}[/tex]

[tex]\large\boxed{\tt y = 115^{\circ}.}[/tex]

Answer:

13

Step-by-step explanation:

The volume of the pyramid can be calculated using the formula:

Volume = (1/3) * base area * height

The base area of the pyramid is equal to the area of one of the square sides, which is:

Base area = 12 in * 12 in = 144 in^2

Therefore, the volume of the pyramid is:

Volume = (1/3) * 144 in^2 * 14 in = 2,688 in^3

Each wax cube has a volume of:

Volume of a wax cube = 6 in * 6 in * 6 in = 216 in^3

To find out how many wax cubes Josiah needs, we can divide the volume of the pyramid by the volume of each wax cube:

Number of wax cubes = Volume of pyramid / Volume of each wax cube

Number of wax cubes = 2,688 in^3 / 216 in^3 = 12.4444...

Since we can't use a fraction of a wax cube, Josiah will need to use 13 wax cubes to make the candle.

Answer:

The axis of symmetry is at x = -2.

Step-by-step explanation:

To find the axis of symmetry of a quadratic function in the form of f(x) = ax^2 + bx + c, you can use the formula x = -b / (2a).

In the function f(x) = 2x^2 + 8x − 5, a = 2 and b = 8, so we can plug those values into the formula and get:

x = -b / (2a) = -8 / (2 * 2) = -2

Therefore, the axis of symmetry of the function f(x) = 2x^2 + 8x − 5 is located at x = -2.

This means that the graph of the function is symmetric with respect to the vertical line x = -2. Any point on the graph that is a distance of t from the line x = -2 will have a corresponding point on the graph that is also a distance of t from the line.