: A 2,230-foot cable stretches from the starting point of a ski lift to the top of a tower that sits on the highest point of a ski slope. The mountain is 2,150 feet tall, and the starting point of the ski lift is 370 feet from a point directly under the tower. How tall is the tower?

Answer:

3.87 miles

Step-by-step explanation:

The attached figure gives the relative locations of the courthouse, the library and the pool.

The three locations represent a right triangle with the distance between courthouse - pool as the hypotenuse and the distance between courthouse - library as the vertical leg

By the Pythagorean theorem if c is the hypotenuse and a, b the other two legs

[tex]c^2 = a^2 + b^2[/tex]

a = distance between courthouse and library = 7 miles
c = distance between courthouse  and pool = 8 miles
and we have to find b

So plugging in known values
[tex]8^2 = 7^2 + b^2\\\\b^2 = 8^2 - 7^2\\\\b^2 = 64 - 49\\\\b^2 = 15\\\\b= \sqrt{15} = 3.87298 \approx 3.87 \;miles[/tex]

Answer:

Let's denote the measures of the other two angles by 13x and 16x, where x is a constant.

Since the sum of the angles in a triangle is always 180 degrees, we can write an equation:

35 + 13x + 16x = 180

Simplifying this equation, we get:

29x = 145

x = 5

Therefore, the measures of the other two angles are:

13x = 13(5) = 65 degrees

16x = 16(5) = 80 degrees

So, the measures of the other two angles are 65 degrees and 80 degrees.

Step-by-step explanation:

The intermediate step in the form (x+a)²=b as a result of completing the square is: (x + 7)² = -4. We can calculate it in the following manner.

To complete the square for the equation x² + 22x = 8x - 53, we need to move the constant term to the right side and the linear term to the left side, and then add a constant value to both sides so that the left side becomes a perfect square trinomial. The steps are as follows:

x² + 22x = 8x - 53 (original equation)

x² + 14x = -53 (subtract 8x from both sides)

x² + 14x + (14/2)² = -53 + (14/2)² (add (14/2)² to both sides)

x² + 14x + 49 = -53 + 49 (simplify)

(x + 7)² = -4 (factor the left side and simplify the right side)

So the intermediate step in the form (x+a)²=b as a result of completing the square is:

(x + 7)² = -4

Note that this equation has no real solutions, since the square of any real number is always nonnegative, whereas the right side of this equation is negative.

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Option B is the true statement based on the given information by solving the method of average.

In mathematics, the average (also called the arithmetic mean) is a measure of central tendency that represents the sum of a set of numbers divided by the total number of values in the set.

Since both tests had a median score of 78, we know that there were nine scores below 78 and nine scores above 78 on each test.

If the original test had a range of 20, that means the highest score was 20 points above the lowest score. Therefore, the lowest score on the original test was 78 - 10 = 68, and the highest score was 68 + 20 = 88.

If the retest had a range of 2, that means the highest score was only 1 point above the lowest score. Therefore, the lowest score on the retest was 78 - 1 = 77, and the highest score was 77 + 2 = 79.

We don't know the mean score for either test, so we cannot determine if option A is true or false. We also don't know if any student scored exactly 78 on the retest, so we cannot determine if option C is true or false. Finally, we know that the highest score on the retest is 79, so option D is false.

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The equation [tex]24 + n = 39[/tex] may be used to get n, the quantity of scarves Rebecca purchases.

The concept of an equation in algebra is a logical statement that demonstrates the equality of two mathematical equations. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

A formula that describes how contain a copy on either sides of a symbol are connected. It typically has an equal sign and one variable. The variable x is included in the preceding example.

The cost of one scarf is $[tex]5[/tex]

The cost of one purse is $[tex]12[/tex]

Rebecca buys 2 purses, so the cost of the purses is [tex]2*12=24[/tex]

The total cost of the purchase is $[tex]39[/tex]

[tex]Total cost = Cost of scarves + Cost of purses[/tex]

[tex]39 = 5n + 24[/tex]

Now we can solve n,

[tex]39 - 24 = 5n[/tex]

[tex]15 = 5n[/tex]

[tex]n = \frac{15}{5}[/tex]

[tex]n=3[/tex]

Therefore, Rebecca buys [tex]3[/tex] scarves.

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Charlotte, North Carolina had an approximate population of  531,145 in 2000.

To approximate Charlotte's population in 2000, we can use the formula for exponential growth:

P(t) = [tex]P0 \times e^{(rt)[/tex]

where P(t) is the population at time t, P0 is the initial population, r is the annual rate of growth as a decimal, and e is the mathematical constant e (approximately 2.71828).

Let's let t = 13 be the number of years between 2000 and 2013. We know that P(13) = 775,000, and r = 0.032. We can solve for P0 as follows:

775,000 = [tex]P0 \times e^{(0.03213)[/tex]

P0 = [tex]775,000 / e^{(0.03213)[/tex]

Using a calculator, we can approximate P0 as:

P0 ≈ 531,145

Therefore, an approximation of Charlotte's population in 2000 is  531,145.

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Step-by-step explanation:

Volume of a cylinder = πr²h

[tex]\pi = 3.14[/tex]

[tex]r = \frac{d}{2} [/tex]

[tex]d = 14[/tex]

[tex]r = \frac{14}{2} [/tex]

[tex]r = 7[/tex]

[tex] {r}^{2} = 49[/tex]

[tex]h = 12[/tex]

substitute the formular with the values above

[tex]3.14 \times 7 \times7 \times 12 = 1846.32[/tex]

To one decimal place

[tex] = 1846.3[/tex]

[tex]1846.3[/tex]

Therefore , the solution of the given problem of unitary comes out to be the school supply business may distribute 500 chalkboards.

By combining what was learned and implementing this variable technique, which also includes all supplemental information from two people who used a particular tactic, the task can be finished. In other words, if the desired result occurs, either the entity specified in the expression will also be identified, or both crucial procedures will actually skip the colour. A refundable fee of Rupees ($1.01) may be needed for forty pens.

Here,

Assuming each chalkboard costs the company $5 and they can spend up to $2,500 on the chalkboards:

Number of chalkboards Equals Total allowable spending / Chalkboard cost

=> Chalkboard count =  $2,500 / $5

=> 500 chalkboards are present.

Consequently, the school supply business may distribute 500 chalkboards.

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The number of integers between two given integers is 124.

The two given integers are 48 and 172.

We know that, number of integers between two integers = Difference of two integers

Here, number of integers = 172-48

= 124

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The estimated transistors count in a computer in 2023 is given as follows:

1,680,085,700,000

The standard definition of an exponential function is given as follows:

y = a(b)^(x/n).

In which:

The number of transistors doubles every 24 months = 2 years, hence the parameters b and n are given as follows:

b = 2, n = 2.

The amount in the reference year of 2020 was 59,400,000,000, hence the parameter a is given as follows:

a = 59,400,000,000.

Then the function estimating the amount in x years after 2020 is given as follows:

y = 59,400,000,000(2)^(x/2).

The amount in 3 years after 2020 is given as follows:

y(3) = 59,400,000,000(2)^(3/2)

y(3) = 1,680,085,700,000.

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Answer: 412.5 ml

Step-by-step explanation:

500 ( 1 - 25%) ( 1 + 10%)

= 412.5 ml

Answer:

412.5 ml

Step-by-step explanation:

To decrease 500 ml by 25%, you would need to multiply 500 by 0.25 to find the amount of decrease:

Subtract that amount from the original value:

Therefore decreasing 500 ml by 25% would give us 375 ml.

To then increase this value by 10%, you would multiply it by 0.10 to find the amount of increase:

Now, add that amount to the previous value:

Therefore, if you decrease 500 ml by 25% and then increase it by 10%, the final result is 412.5 ml.

It would cost $288.00 to recarpet the shop with carpet that costs $3.00 per square meter.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.com

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

The area of the shop can be found by multiplying its length by its width:

Area = Length x Width

        = 8 meters x 12 meters

        = 96 square meters

To recarpet the entire shop, we need to purchase 96 square meters of carpet.

If the carpet costs = $3.00 per square meter.

The total cost can be found by multiplying the area by the cost per square meter:

Total cost = Area x Cost per square meter

Total cost = 96 square meters x $3.00 per square meter

Total cost = $288.00

Therefore,

It would cost $288.00 to recarpet the shop with carpet that costs $3.00 per square meter.

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The number of hours it will take for them to plant the same number of vegetable rows is equals to one hour. Total twelve rows of vegitables they will each have completed.

We have, Malik and his mom are planting vegetables in their garden.

For Malik : he has finished planting 7 rows of carrots and his planting rate = 5 rows per hour.

For his mom : She has finished 10 rows of tomatoes and continue.

Her planting rate = 2 rows per hour.

Let they finish an equal number of carrot and tomato rows in "x hours". That is we can wright the provide information in equation form : Malik plants 5 rows of vegitable per hour, so he will plant 5x rows in x hours. Similarly, his mother will plant 2x rows of vegitables in x hours. Thus, after x hours, (Malik) 7 + 5x = 10 + 2x (mom)

Simplify the above equation,

=> 5x - 2x = 10 - 7

=> 3x = 3

=> x = 1

So, x = 1 be the hours it will take for them to plant the same number of vegetable rows. Now, total rows they will each have completed = 7 + 5×1 = 12 rows or 10 +2×1

= 12

Thus, total 12 rows they finally completed.

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Answer: The answer is 40

Explanation: The picture

The evaluation of the statements and the values of the side lengths and angles of the quadrilateral are;

A. 1.) [tex]\overline{BD}[/tex] ≅ [tex]\overline{AC}[/tex]; False

2.) [tex]\overline{BO}[/tex] ⊥ [tex]\overline{CO}[/tex]; True

3. ∠BDA ≅ ∠BDC; False

4. ∠BOA ≅ ∠CBD; False

5.) m∠BAD + m∠ADC = 180°; True

6.) [tex]\overline{CO}[/tex] ≅ [tex]\overline{AO}[/tex]; True

7.) ∠BCD = 90°; False

8.) ∠BOA = 90°; True

9.) ∠ABD = 45°; False'

10. [tex]\overline{BC}[/tex] ≅ [tex]\overline{CD}[/tex]; True

B. I. ∠NAL = 124°

∠CNL = 28°

∠CLN = 28°

∠NLA = 28°

II. 5.) ∠1 = 45°

∠2 = 90°

III 7.) [tex]\overline{OP}[/tex] = 7 cm

8.) [tex]\overline{OE}[/tex] = 12 cm

9.) [tex]\overline{EO}[/tex] = 13 cm

10. ∠5 = 60°

A quadrilateral is a four sided polygon.

The evaluation of the quadrilaterals are presented as follows;

1. [tex]\overline{BD}[/tex] ≅ [tex]\overline{AC}[/tex]

[tex]\overline{BD}[/tex] and [tex]\overline{AC}[/tex] are the diagonals of the rhombus, and the properties of a rhombus indicates that the diagonals of a rhombus are not congruent, the statement,  [tex]\overline{BD}[/tex] ≅ [tex]\overline{AC}[/tex] is therefore false

[tex]\overline{BD}[/tex] ≅ [tex]\overline{AC}[/tex]; False

2.  [tex]\overline{BO}[/tex] ⊥ [tex]\overline{CO}[/tex]

[tex]\overline{BO}[/tex] and [tex]\overline{CO}[/tex] are segments on the two diagonals of the rhombus which are perpendicular. The statement, [tex]\overline{BO}[/tex] ⊥ [tex]\overline{CO}[/tex] is therefore; True

3. ∠BDA ≅ ∠BDC

∠ADC = ∠BDA + ∠BDC

The diagonals of a rhombus do not bisect the vertex angles, therefore;

m∠BDA ≠ m∠BDC

∠BDA [tex]\ncong[/tex] ∠BDC

The statement, ∠BDA ≅ ∠BDC, therefore is; False

4.) ∠BOA ≅ ∠CBD

The diagonals of a rhombus are perpendicular, therefore angle ∠BOA = 90°

∠CBD is an interior angle of the rhombus, and ∠CBD = 90° if the rhombus is a square.

The specified rhombus is not shaped like a square. The statement, ∠BOA ≅ ∠CBD, is therefore; False

5.) m∠BAD + m∠ADC = 180°

The angles, ∠BAD and ∠ADC are adjacent interior angles, therefore, according to the properties of a rhombus, m∠BAD + m∠ADC = 180°. The statement is therefore; True

6.) [tex]\overline{CO}[/tex] ≅ [tex]\overline{AO}[/tex]

The segments [tex]\overline{CO}[/tex] and [tex]\overline{AO}[/tex] are formed by the intersection of the diagonal [tex]\overline{BD}[/tex] and [tex]\overline{AC}[/tex] at O. The diagonals of a rhombus bisect each other. The statement, [tex]\overline{CO}[/tex] ≅ [tex]\overline{AO}[/tex] is therefore; True

7.) ∠BCD = 90°

∠BCD = 90° when the rhombus is a square, the statement is therefore False

8.) ∠BOA = 90°

∠BOA is formed by the intersection of the diagonals of a rhombus, which are perpendicular to each other. Therefore, ∠BOA = 90°, the statement is therefore; True

9) ∠ABO = 45°

∠ABO = 45° if the rhombus is a square, the statement is therefore; False or more information required

10) [tex]\overline{BC}[/tex] ≅ [tex]\overline{CD}[/tex]

[tex]\overline{BC}[/tex] and [tex]\overline{CD}[/tex] are side lengths of the rhombus and are therefore, congruent. The statement, [tex]\overline{BC}[/tex] ≅ [tex]\overline{CD}[/tex] is; True

B. I. ∠NAL and ∠CNA are supplementary, therefore;

∠NAL + ∠CNA = 180°

∠NAL= 180° - ∠CNA

∠CNA = 56°

∠NAL= 180° - 56° = 124°

2.) Whereby the diagonal of the rhombus bisects the angle ∠CNA, we get;

∠CNL = ∠ANL = 56°/2 = 28°

3.) ∠CLN = ∠CNL = 28°

4.) ∠NLA = ∠CNL = 28°

II. The properties of a square indicates that we get;

The diagonals of a square bisect the vertex angles, therefore;

∠1 which is the angle formed by the the diagonal [tex]\overline{AT}[/tex] that bisects the angle ∠CAR = 90° is; ∠1 = 90°/2 = 45°

6.) The diagonals of a square are perpendicular, therefore;

∠2 = 90°

III. 7.) The facing sides of a rectangle are congruent, therefore;

[tex]\overline{HE}[/tex] ≅ [tex]\overline{OP}[/tex]

[tex]\overline{OP}[/tex] = [tex]\overline{HE}[/tex] = 7 cm

8.) The diagonals of a square have the same length, therefore;

The length of [tex]\overline{OE}[/tex] = The length of [tex]\overline{HP}[/tex] = 12 cm

9.) Pythagorean Theorem indicates, that we get;

[tex]\overline{EO}[/tex] = √([tex]\overline{OP}[/tex]² + [tex]\overline{EP}[/tex]²)

Therefore;  [tex]\overline{EO}[/tex] = √(5² + 12²) = 13

[tex]\overline{EO}[/tex] = 13 cm

10.) ∠2 and ∠5 are vertical angles, therefore;

∠2 ≅ ∠5

∠5 ≅ ∠2 (Symmetric property)

m∠5 = m∠2 = 60° (Definition of congruency)

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Answer: C

Step-by-step explanation:

For A, look at the slope of the graph: 70/2 = 35

For B, slope calculation: m = y-y / x-x = 315-105 / 9-3 = 35

=> C

If you buy three hamburgers, the cost of each hamburger is $2.50.

One hamburger costs $2.50.

To determine the price of one hamburger, first take the total cost of all three hamburgers, which is $7.50.

Then, divide the total cost of all three hamburgers by the number of hamburgers, which is three.

This yields $2.50, which is the price of one hamburger.

One of the four fundamental arithmetic operations, or how numbers are joined to create new numbers, is division.

The other operations are multiplication, addition, and subtraction.

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The angle that has the sine ratio, 4/5, is: A. Angle P.

Sine Ratio:

The sine ratio is the ratio of the side opposite the hypotenuse of a right triangle to a given reference angle. When the ratio is found using the opposite and the hypotenuse, we call it the sine ratio rather than the tangent ratio.

Example:

Then we say that the sine of 45 degrees is equal to 0.707. In short, we can use the notation sin instead of sine and write sin(45 degrees) = 0.707

In general, the sine of angle A = leg length of opposite angle A / hypocenter

sin(A ) = opposite / hypotenuse

Given:

sine ratio of 4/5, then it means:

Opposite side (side directly opposite to the reference angle) = 4

Hypotenuse (longest side) = 5.

Thus, in the image given, using P as the reference angle, the sine ratio of P is:

QR/PQ

= 16/20 = 4/5

Therefore, the angle with the sine ratio of 4/5 is: A (P)

Complete Question:

Using the side lengths of △PQR and △STU, which angle has a sine ratio of 4/5?

A. P

B. Q

C. T

D. U

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The cot(cos−1(a))= a/√(1-a^2).

Value of cos(sin−1(1)): Let's assume that θ= sin−1(1). It means that sinθ= 1. The value of θ is π/2, therefore we can say that cos(sin−1(1))=cos(π/2)= 0b) Value of tan(cos−1(-23)): Let's suppose that θ= cos−1(-23). It implies that cosθ= -23/25. As we know that tanθ= sinθ/cosθ, Therefore;tan(cos−1(−23))= sin(θ)cos(θ) = -24/25.2. a) Value of sin(cos−1(3/2)): Let's suppose that θ= cos−1(3/2). It implies that cosθ= 3/2. As we know that sin^2θ= 1- cos^2θ, Therefore;sin(cos−1(3/2))= √(1- (3/2)^2)= √(1/4)= 1/2.b) Value of csc(tan−1(-5/1)): Let's assume that θ= tan−1(-5/1). It implies that tanθ= -5/1. As we know that cscθ= 1/sinθ, Therefore;csc(tan−1(−51​))= 1/sin(θ)= 1/√(1+tan^2θ) = 1/√(1+25)= -1/√26.3. a) Value of sin(tan−1(a^2)): Let's suppose that θ= tan−1(a^2). It implies that tanθ= a^2. As we know that sinθ= tanθ/√(1+tan^2θ), Therefore;sin(tan−1(a2​))= (a^2)/√(1+(a^4)).b) Value of cot(cos−1(a)): Let's suppose that θ= cos−1(a). It implies that cosθ= a. As we know that cotθ= cosθ/sinθ, Therefore;cot(cos−1(a))= a/√(1-a^2).

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The value of x:z = 1:4.

To find the ratio of x to z, we need to have a common term between x, y, and z. Since we have y in both ratios, we can use it as the common term.

From the given ratios:

x:y = 3:4

y:z = 1:3

We can see that the y in the first ratio and the y in the second ratio are the same.

To find the ratio of x to z, we can "connect" the two ratios by canceling out the y:

x:y = 3:4

y:z = 1:3

x:y × y:z = 3:4 × 1:3

x:z = 3:12

Simplifying the above ratio by dividing both terms by 3, we get:

x:z = 1:4

we can use the cubic equation formula to solve for t. The answer is t=1988, which means that there were 31.35 thousand European students in 1988.

To solve this problem, we need to find the value of t that corresponds to 31.35 thousand European students. We can use the given equation S=0.05(t3-11t+45t+277) and solve it for t. To do this, we can first subtract 277 from both sides to get S-277=0.05(t3-11t+45t). Then, we can divide both sides by 0.05 to get (S-277)/0.05=t3-11t+45t. Finally, we can use the cubic equation formula to solve for t. The answer is t=1988, which means that there were 31.35 thousand European students in 1988.

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Answer:The answer is 7 pancakes, I think.

Step-by-step explanation:

28:20

?:5

Divide 28 by 20.

You get 1.4 because every person eats 1.4 .

Multiply 1.4 by 5. You give all of the five people 1.4 pancakes each.

The total will be 7 pancakes.

Answer:

percentage = (part/whole) x 100

where the "part" is the number of swimmers who finished in less than 39 minutes, and the "whole" is the total number of swimmers.

So, if 29 out of 50 swimmers finished in less than 39 minutes:

percentage = (29/50) x 100

percentage = 58

Therefore, 58% of swimmers finished the race in less than 39 minutes.

An equivalent fraction to represent 58% is 29/50.

Step-by-step explanation:

On solving the question we have that Therefore, the center of the circle equation is (3/10, -7/10) and the radius is √(1/5).

A math equation is a mechanism for connecting two statements and indicating equivalence with the equals sign (=). To explain the connection between the two sentences put on each side of a letter, a statistical method can be employed. The software and the logo are usually interchangeable. 2x - 4 equals 2, for example. An equation is a logical expression that asserts the equality of some mathematical expressions in algebra. In the equation 3x + 5 = 14, for example, the equal sign separates the numbers 3x + 5 and 14.

The given equation is that of a circle in standard form:

[tex](x - h)^2 + (y - k)^2 = r^2[/tex]

where the center of the circle is (h, k) and the radius is r.

To convert the given equation to this form, we need to complete the square for both x and y terms. Let's start with the x terms:

[tex]5x^2 - 3x = 5(x^2 - (3/5)x)\\5(x^2 - (3/5)x + (3/10)^2 - (3/10)^2)\\5((x - 3/10)^2 - 9/100)\\5y^2 + 7y = 5(y^2 + (7/5)y)\\5(y^2 + (7/5)y + (7/10)^2 - (7/10)^2)\\5((y + 7/10)^2 - 49/100)\\5((x - 3/10)^2 - 9/100 + (y + 7/10)^2 - 49/100) - 1 = 0\\5(x - 3/10)^2 + 5(y + 7/10)^2 = 1\\[/tex]

Therefore, the center of the circle is (3/10, -7/10) and the radius is √(1/5).

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Answer:

22 rows

Step-by-step explanation:

Divide 48 by 2.25 and round up

Therefore, the other two zeros of the function are approximately -1.802 and -0.198.

An equation is a mathematical statement that shows that two expressions are equal. It consists of two sides separated by an equal sign (=). The expressions on both sides of the equation can contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. The goal in solving an equation is to find the value of the variable that makes the equation true. Equations are used extensively in mathematics and science to model real-world phenomena and solve problems.

by the question.

To find the zeros of the function, we need to solve the equation F(x) = 0. Since the given function has one known zero, which is 2 under the root, we can use this to simplify the expression.

Let's start by factoring out (x - 2^(1/2)) from the expression:

[tex]F(x) = (x - 2^(1/2))(6x^2 + 12x + 2^(1/2) - 4\sqrt{2})[/tex]

Now we need to find the zeros of the quadratic factor:

[tex]6x^2 + 12x + 2^(1/2) - 4\sqrt{2} = 0[/tex]

Using the quadratic formula, we get:

[tex]x = [-12±\sqrt((12)^2 - 4(6)(2^(1/2) - 4\sqrt{2}))]/(2(6))[/tex]

Simplifying the expression under the square root gives:

[tex]\sqrt((12)^2 - 4(6)(2^(1/2) - 4\sqrt{2})) = \sqrt(144 - 24\sqrt{2} - 96) = sqrt(48 - 24\sqrt{2})[/tex]

So, the zeros of the function are:

[tex]x = 2^(1/2), (-1 -\sqrt{6 + 3\sqrt{2}})/3, (-1 + \sqrt{6 + 3\sqrt{2}})/3[/tex]

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The required perpendicular segment to DE is EF.

In simple geometry, two geometric objects are perpendicular if the intersection at the place of intersection known as a foot results in right angles. The perpendicular symbol can be used to graphically depict the condition of perpendicularity.

In the given diagram we can see that segment DE and EF.

So, we can say that,

Segment DE is perpendicular to segment EF.

Thus, required perpendicular segment to DE is EF.

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Complete question: