The perimeter of the pentagon below is 64 units. Find the length of side PQ.
Write your answer without variables.

Answer:

Step-by-step explanation:

To find the location of the point that is of the way from A=31 to B=6, we need to find the midpoint of the segment AB.

The formula for finding the midpoint of a segment with endpoints (x₁, y₁) and (x₂, y₂) is:

Midpoint = ((x₁ + x₂) / 2, (y₁ + y₂) / 2)

In this case, we have A = 31 and B = 6, so x₁ = 31 and x₂ = 6. Plugging these values into the formula, we get:

Midpoint = ((31 + 6) / 2, (y₁ + y₂) / 2)

Midpoint = (37/2, (y₁ + y₂) / 2)

We still need to find y₁ and y₂, which are the positions of A and B on the number line. Since the number line is one-dimensional, we can simply use their values:

y₁ = 31

y₂ = 6

Plugging these values into the formula, we get:

Midpoint = (37/2, (31 + 6) / 2)

Midpoint = (37/2, 37/2)

Therefore, the location of the point on the number line that is of the way from A=31 to B=6 is at a distance of 37/2 units from point A and also at a distance of 37/2 units from point B. So, the midpoint of AB is located at the point (37/2, 0).

However, since the question only asks for the location of the point on the number line, we only need to consider the x-coordinate of the midpoint, which is 37/2. This point is on the number line, which means that it is a real number. Therefore, the answer is option (A) 21.

The best definition of phi is:

golden ratio, also known as the golden section, golden mean, or divine proportion, in mathematics, the irrational number (1 + Square root of√5)/2, often denoted by the Greek letter ϕ or, which is approximately equal to 1.618.

Phi = 1/phi Phi = 1 + phi The latter facts together give the definition of the golden ratio: x = 1/x + 1 This equation (equivalent to x^2 - x - 1 = 0) is satisfied by both Phi and -phi, which therefore can be called the _golden ratios_.

Hence, Phi is the value of the golden ratio which is the best definition of phi.

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In this case we have a translation of 8 units to the left and 11 units upwards.

To find the translation, we just need to compare the two known vertices before and after the translation.

If we have a translation of a units in the x-axis and b units in the y-axis, we will get:

T(a, b)L ---> L'

We know that L = (7, -3) and L' = (-1, 8)

Then we can write:

(7 + a, -3 + b) = (-1, 8)

Then we have two equations:

7 + a = -1 ---> a = -1 - 7 = -8

-3 + b = 8 ---> b = 8 + 3 = 11

Then we have a translation of 8 units to the left and 11 units up-.

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Complete question:

"Right triangle LMN has vertices L(7, –3), M(7, –8), and

N(10, –8). The triangle is translated on the coordinate plane so the coordinates of L’ are (–1, 8).

Find the translation done"

"UX = sup X," means that the union of the set X, denoted by UX, is equal to the supremum of X. In other words, if X is a nonempty set of ordinal numbers, then the union of those ordinals, UX, is itself an ordinal number, and it is equal to the supremum of X.

In set theory, the symbol "∪" denotes the union of sets. So, when we say "∪X," it represents the union of all the elements in the set X.

On the other hand, "sup X" stands for the supremum (or least upper bound) of the set X. The supremum of a set is the smallest ordinal number that is greater than or equal to all the elements in the set.

Therefore, when it is stated that "UX = sup X," it means that the union of the set X, denoted by UX, is equal to the supremum of X. In other words, if X is a nonempty set of ordinal numbers, then the union of those ordinals, UX, is itself an ordinal number, and it is equal to the supremum of X.

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When a technician is faced with such issue, the following options can be considered:

Apply pressure to the back of the rivet with a screwdriver or other blunt object. This will help to keep the rivet from spinning and will also help to break the seal between the rivet and the sheet metal.

Use a carbide drill bit. Carbide drill bits are more durable than standard drill bits and are less likely to break when drilling through rivets.

Use a lubricant: Lubricants can help to prevent the drill bit from grabbing the rivet and can also help to cool the drill bit.

Therefore, any of the mentioned options could be taken in such situation .

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1) It's possible that Lia had a mean smirk because she found the situation amusing or thought it was funny to accuse someone.

2) Lia might have accused you based on the assumption that you were laughing

3) Nyla might have looked at you out of curiosity or suspicion, wanting to see your reaction to the accusation.

4) Ms. Nee might have asked you to move in an attempt to diffuse the situation or prevent any further disruptions.

Lia could have been amused by the event or thought it was hilarious to blame someone, hence her cruel smirk. Another possibility is that she made the charge because she was upset with you personally and wanted to humiliate or degrade you.

Lia could have charged you if she thought you were laughing, which she took to be an admission of guilt. Additionally, she might have been looking for someone to point the finger at and chose you as the victim of choice without any solid proof.

Nyla may have glanced your way to see how you would respond to the charge out of curiosity or suspicion. Her lack of laughter could indicate that she wasn't sure about your involvement or that she simply didn't find the situation amusing.

Everyone present may find it distracting and uncomfortable when jokes and accusations are made in the classroom. Ms. Nee might have asked you to relocate in an effort to bring back some sense of calm and concentration in the classroom.

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Answer:

1. True

Explanation:

In geometry, a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions— length, width, and height. 

The equation of a line perpendicular to the x-axis is x = 3

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

The equations

By definition, the equation of a line perpendicular to the x-axis is represented as

x = k

Where

k is a real value

Using the above as a guide, we have the following:

x = 3

Hence, the equation is x = 3

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Answer:

b c and d

Step-by-step explanation:

if not let me know

41.37%

43.15%

75%

The code represented by the word "AFGAN" would be "02034."

To find the code represented by the word "AFGAN," we need to refer to the given code representation of the word "AFGANISTAN," which is "02034560."

From the given code, we can determine that the letters "AFGAN" correspond to the first five digits of the code.

Therefore, the code represented by the word "AFGAN" would be "02034."

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The probability that the sample proportion of households spending more than $125 a week is less than 0.27 is approximately 0.35.

To find the probability that the sample proportion of households spending more than $125 a week is less than 0.27, we can use the sampling distribution of sample proportions and the Central Limit Theorem.

Given:

Population proportion (p) = 0.28

Sample size (n) = 273

First, we need to calculate the standard deviation of the sampling distribution, which is known as the standard error. The formula for the standard error is:

Standard Error = sqrt((p * (1 - p)) / n)

Substituting the given values:

Standard Error = sqrt((0.28 * (1 - 0.28)) / 273)

Standard Error ≈ 0.0258

Next, we can standardize the sample proportion using the formula:

Z = (sample proportion - population proportion) / standard error

Z = (0.27 - 0.28) / 0.0258

Z ≈ -0.3886

Now, we need to find the probability that the sample proportion is less than 0.27. This is equivalent to finding the area under the standard normal distribution curve to the left of Z = -0.3886. We can use a standard normal distribution table or a statistical software to find this probability.

The probability can be rounded to 4 decimal places:

Probability = 0.35 (approximately)

Therefore, the probability that the sample proportion of households spending more than $125 a week is less than 0.27 is approximately 0.35.

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To find the distance above the ground at which the tack is, we need to calculate the vertical displacement of the front wheel when the tack was picked up.

First, let's determine the circumference of the front wheel. The circumference of a circle is given by the formula C = πd, where C is the circumference and d is the diameter. Given that the diameter is 26 inches, we can calculate the circumference:

C = π × 26

C ≈ 81.64 inches

This means that for every complete revolution of the wheel, Devon travels a distance of approximately 81.64 inches.

Next, we need to determine how many complete revolutions the front wheel made as Devon rolled another 100 feet (1200 inches). Since the circumference of the wheel is 81.64 inches, we can divide 1200 inches by 81.64 inches to find the number of revolutions:

1200 / 81.64 ≈ 14.68 revolutions

Now, we know that the tack was picked up after one full revolution. Therefore, out of the 14.68 revolutions, 13 complete revolutions have occurred. The tack is located at the point where the 14th revolution starts.

Since each revolution covers a distance equal to the circumference of the wheel, the vertical displacement of the tack is the height of the wheel, which is the radius of the wheel. The radius is half the diameter, so in this case, it is 26 / 2 = 13 inches.

Therefore, the tack is located 13 inches above the ground.

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Answer:

B. 0

Step-by-step explanation:

The answer would be y=0, and it is not undefined. Undefined lines go up and down.

Answer:

XYZThe name of angle below is XYZ

Answer:

Step-by-step ex-plane

The zeros of a polynomial function can be used to determine how the graph behaves at those points. The multiplicity of a zero also plays an important role in shaping the graph of a polynomial function.

The graph of the seventh degree polynomial function with zeros 1, 2 (multiplicity of 3), 4, and 6 (multiplicity of 2) will cross the x-axis at 1 only. This is because the zero at 1 has a multiplicity of 1.

The graph will only touch (be tangent to) the x-axis at 2. This is because the zero at 2 has a multiplicity of 3.

At the zero of 2, the graph of the function will flatten out against the x-axis.

Therefore, the correct answers are:

- The graph of the function will cross through the x-axis at 1 only.

- The graph will only touch (be tangent to) the x-axis at 2.

- At the zero of 2, the graph of the function will flatten out against the x-axis.

Answer:

9 squares

Step-by-step explanation:

Anne bought a piece of ribbon = 7 over 9 m long = 63 m²

she used = 3 over 18 m = 54 m²

left = 9 m²

maximum number of squares she could form of 1 m = 9

6. Mr. Chao's students measured the length of different markers in inches. The data

collected is below.

Data set: 4, 5.5, 4.25, 5, 6.25, 6, 5.5, 5.25, 6.25, 4, 6.25, 5, 4.75

Answer: The transformed function is y = -0.4√(x - 2).

Step-by-step explanation:

From the given equation, we can identify the following transformations:

Reflected over the x-axis: The negative sign in front of the function (-0.4) indicates a reflection over the x-axis.

Translated 2 units left: The "-2" inside the square root indicates a translation of 2 units to the right.

Compressed by a factor of 0.4: The coefficient "0.4" in front of the square root indicates a vertical compression by a factor of 0.4.

Translated 2 units down: There is no direct indication of a vertical translation in the equation, so this transformation is not applicable.

Therefore, the correct descriptions of the graph of the transformed function compared with the parent function are:

Reflected over the x-axis

Translated 2 units right

Compressed by a factor of 0.4

Answer:

look at attachment

Step-by-step explanation:

The true statements are:

below in bold

Work/explanation:

The statements which apply to the given scenario are the following:

The base is Three-fifths.

The expanded form is three-fifths times three-fifths times three-fifths.

The exponent is 3.

Let's take a closer look at the expression [tex]\sf{\bigg(\dfrac{3}{5}\bigg)^3}[/tex].

What is the base and what is the exponent?

Think of the expression [tex]\sf{x^n}[/tex]. Here, x is the base, and n is the exponent.

Similarly, with our exercise here, 3/5 is the base and 3 is the exponent.

[tex]\rule{350}{4}[/tex]

Now, what is the expanded form of the expression? If we have something cubed, what does it mean?

It means that this something is multiplied by itself 3 times.

So the expanded form is three-fifths times three-fifths times three-fifths.

Finally, when we raise a fraction to a power, we raise both the numerator and the denominator to that power.

The time Jack left Santa Clara is 1 : 55 pm

A word problem in math is a math question written as one sentence or more. These statements are interpreted into mathematical equation or expression.

The time for Jack to walk to lose Altos is 25 min and he uses another 25mins to work to Palo alto.

Therefore, the total time he spent is

25mins + 25 mins = 50 mins

He arrived Palo at 2 :45 pm, therefore the time he left Santa Clare will be ;

2:45 pm = 14 :45

= 14:45 - 50mins

= 13:55

= 1 : 55pm

Therefore he left at 1:55 pm

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Answer:

Step-by-step explanation:

easily find on chrome

Answer:

To find the angles of intersection between the curves f(x) = x^2 and g(x) = |x|, we need to find the points where the two curves intersect.

Substituting g(x) into f(x), we get:

x^2 = |x|

To solve this equation, we need to consider two cases:

Case 1: x ≥ 0

In this case, the equation simplifies to:

x^2 = x

Solving for x, we get:

x(x - 1) = 0

So x = 0 or x = 1.

Case 2: x < 0

In this case, the equation simplifies to:

x^2 = -x

Solving for x, we get:

x(x + 1) = 0

So x = 0 or x = -1.

Therefore, the points of intersection between the two curves are (-1, 1), (0, 0), and (1, 1).

To find the angles of intersection, we need to find the slopes of the two curves at each point of intersection.

At (0, 0), the slopes of both curves are 0.

At (-1, 1) and (1, 1), the slope of f(x) = x^2 is 2x, and the slope of g(x) = |x| changes direction at x = 0, so we need to consider the left and right limits separately:

At x = -1, the slope of g(x) = -1, and at x = 1, the slope of g(x) = 1.

Therefore, the angles of intersection between the two curves are:

- At (0, 0), the two curves are tangent and intersect at a right angle.

- At (-1, 1) and (1, 1), the two curves intersect at acute angles.

Answer:

To solve for C, we would need to know the length of side c. Without that information, we cannot determine the value of angle C.

Step-by-step explanation:

Using this assumption, we can rewrite the equation as:

c² = 16² + 17² - 2(16)(17)·cos(C)

c² = 256 + 289 - 544·cos(C)

c² = 545 - 544·cos(C)

Answer:

C = 83.0°

Step-by-step explanation:

This triangle has three sides, with lengths of 8 units, 16 units, and 17 units. The angle formed between the sides measuring 8 units and 16 units is angle C. Angle C is opposite the side measuring 17 units.

To find the measure of angle C, we can use the Law of Cosines.

[tex]\boxed{\begin{array}{l}\underline{\textsf{Law of Cosines}}\\\\c^2=a^2+b^2-2ab \cos C\\\\\textsf{where $a, b$ and $c$ are the sides,}\\\textsf{and $C$ is the angle opposite side $c$.}\\\end{array}}[/tex]

In this case:

Substitute the values of a, b, and c into the formula, and solve for C:

[tex]\begin{aligned}c^2&=a^2+b^2-2ab\cos C\\\\17^2&=8^2+16^2-2(8)(16)\cos C\\\\289&=64+256-256\cos C\\\\289&=320-256\cos C\\\\289-320&=320-256\cos C-320\\\\-31&=-256\cos C\\\\\dfrac{-31}{-256}&=\dfrac{-256\cos C}{-256}\\\\\dfrac{31}{256}&=\cos C\\\\\cos C&=\dfrac{31}{256}\\\\C&=\cos^{-1}\left(\dfrac{31}{256}\right)\\\\C&=83.04476981...^{\circ}\\\\C&=83.0^{\circ}\; \sf (nearest\;tenth)\end{aligned}[/tex]

Therefore, the measure of angle C, rounded to the nearest tenth, is:

[tex]\Large\boxed{\boxed{C=83.0^{\circ}}}[/tex]

The equation is proved.

G[tex]`tan(x-1)(sin2x-2cos2x)=2(1-2sinxcosx)`[/tex]

We need to prove the given equation. Solution: Using the identity [tex]`sin2x=2sinxcosx` and `cos2x=1-2sin^2x`[/tex]

in the given equation, we get

[tex]`tan(x-1)(sin2x-2cos2x)=2(1-2sinxcosx)`⟹ `tan(x-1)(2sinxcosx-2(1-[/tex]

[tex]2sin^2x))=2(1-2sinxcosx)`⟹ `tan(x-1)(4sin^2x-2)=2-4sinxcosx`⟹ `2sin(x-1)[/tex]

[tex](2sin^2x-1)=2(1-2sinxcosx)`⟹ `2sin(x-1)(2sin^2x-1)=2(1-2sinxcosx)`⟹[/tex]

[tex]`2sinxcos(x-1)(4sin^2x-2)=2(1-2sinxcosx)`⟹ `2sinxcos(x-1)(2sin^2x-1)=1-[/tex]

[tex]sinxcosx`⟹ `2sinxcos(x-1)(2sin^2x-1)=sin^2x+cos^2x-sinxcosx`⟹[/tex]

`[tex]2sinxcos(x-1)(2sin^2x-1)=(sinx-cosx)^2`⟹ `sinxcos(x-1)(2sin^2x-1)=(sinx-cosx)^2/2`[/tex]

For `LHS`, using identity

[tex]`sin(90 - x) = cosx`⟹ `sinxcos(x-1)(2sin^2x-1)=(sinx-sin(91-x))^2/2`⟹[/tex]

[tex]`sinxcos(x-1)(2sin^2x-1)=(-sin(x-1))^2/2`⟹ `sinxcos(x-1)(2sin^2x-1)=sin^2(x-[/tex]

[tex]1)/2`⟹ `sinxcos(x-1)(4sin^2x-2)=sin^2(x-1)`⟹ `sinxcos(x-1)(2sin^2x-1)=1/2`⟹ `1/2=1/2`.[/tex]

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The completed table is as follows:

x | y

8 | 0

9 | 3

36 | 6

8 | 2√2

8 | -2√2

To solve the equation x = y², we can substitute the values of x and find the corresponding values of y in the table.

Let's fill in the missing entries one by one:

For x = 9, we need to find y. Since x = y², we take the square root of both sides to solve for y. So, y = √9 = 3. Therefore, the corresponding value for y is 3.

For x = 36, again, we apply the square root operation to both sides, giving y = √36 = 6. Hence, the corresponding value for y is 6.

For y = 2√2, we need to find x. Squaring both sides of the equation, we have [tex]x = (2\sqrt2)^2 = 4 \times 2 = 8[/tex]. Therefore, the corresponding value for x is 8.

For y = -2√2, we follow the same process as in step 3. Squaring both sides, we get [tex]x = (-2\sqrt2)^2 = 4 \times 2 = 8[/tex]. So, the corresponding value for x is 8.

After filling in the missing entries, the completed table is as follows:

x | y

8 | 0

9 | 3

36 | 6

8 | 2√2

8 | -2√2

Please note that there can be multiple valid solutions for this equation, but this table provides one possible solution.

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Answer:

$828.53

Step-by-step explanation:

The formula is: A = P(1 + r/k)^(kt)

A = 750(1 + 0.02/12)^(12*5)

A = 750(1 + 0.00166667)^60

A = 750(1.00166667)^60

A = 750(1.104713)

A = $828.53 (rounded to the nearest cent)

So, the accumulated amount after 5 years with a 2% interest rate compounded monthly is $828.53.