Which graph represents the function of f(x) =9x²-36/3x +6

Answer:

The length of the short side was 12 and the length of the long side was 32

Step-by-step explanation:

We will say that the length is the shorter side, and be using l as the variable, and that width is the longer side, and be using w as the variable. The first two equations we have are:

w = l + 20

And

2(2l + 3w) = 240

We will start with the second equation, then substitute in the first equation for w. We have:

4l + 6w = 240

Divide both sides by 2:

2l + 3w = 120

Then, we substitute in l + 20 for w, giving us:

2l + 3l + 60 = 120

Subtract 60 from both sides and combine like terms:

5l = 60

l = 12

So, the original length was 12, now substituting this into our first equation gives us:

w = 12 + 20 = 32

So the original width was 32. So, the length of the short side was 12 and the length of the long side was 32.

Hope this helped!

It is not possible to construct a triangle with 6cm, 9cm, and 17cm.

The sides measure 6 cm, 9 cm, and 17 cm in length.

Only when the third side is greater than the sum of any two sides can a triangle be drawn. This the condition.

Let's verify the rule now.

6 + 9 > 17        Not true

6 + 17 > 9        True

9 + 17 > 6        True

As 6 + 9 > 17 does not satisfy the condition.

Hence, it is not possible to construct a triangle having 6cm, 9cm, and 17cm in length.

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Lebron would make 41 foul shots.

The formula used to calculate the number of made foul shots is Number of Made Foul Shots = Foul Shooting Average * Number of Shots Attempted.

Therefore, the number of made foul shots for Lebron is 55% * 75 = 41.25. Since this is a decimal number, we can round it down to 41 made foul shots.

In calculation way, Lebron would make 41 foul shots. This can be calculated by multiplying his foul shooting average 55% with the number of shots attempted, which is 75. 55% can also be written as 0.55, so the equation can be written as 0.55 * 75 = 41.25 which rounds down to 41.

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Receipt of May is 835

Net cash flow of April is 210

Cumulative balance of March is 240

Explanation

Net cash flow = Receipt - Expense

Receipts amount = Expenses+Net cash flow

Cumulative balance amount =Cumulative amount for April-Net cash flow for April

Answer:

200 + 50 + 8 + 0.5 +0.03 = 258.53

The required number of ways are 24 and the situation is permutation.

An arrangement of items in a specific order is referred to as a permutation. Here, the components of sets are arranged in a linear or sequential order. For instance, the set A=1,6 has a permutation of 2, which is 1,6,1.

It depicts a permutation since the order of the people in this situation matters.

According to the number of ways, the first position can be filled by four people, the second by three (because the first position has already been taken by one person), the third by two, and the fourth by one.

This results in 4321 = 4! = 24 ways as the total number of ways.

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Each puppy would weigh approximately 2.13 grams if all the puppies weighed the same amount.

To estimate the weight of each puppy, we need to subtract the weight of the basket from the total weight of the basket and puppies to find the total weight of the puppies.

Total weight of puppies = Total weight of basket and puppies - Weight of basket alone

= 2,977 - 1,077 = 1,900 grams

Then we divide the total weight of the puppies by the number of puppies to find the weight of each puppy:

Weight of each puppy = Total weight of puppies / Number of puppies

= 1,900 / 888

= approximately 2.13 grams

Each puppy would weigh approximately 2.13 grams if all the puppies weighed the same amount.

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The probability of selecting a three-digit number with the property that one digit is equal to the product of the other two is 1/90.

1/90

The probability of selecting a three-digit number with the property that one digit is equal to the product of the other two is 1/90. This is because there are only 9 possible digits (1, 2, 3, 4, 5, 6, 7, 8, 9) to choose from, and each of these digits can be multiplied by itself twice to give 9 possible combinations. Therefore, there are 9 three-digit numbers that satisfy the given condition, and these 9 numbers can be chosen from a total of 900 three-digit numbers (10 x 10 x 10 = 1000, minus the 100 numbers beginning with 0). Thus, the probability of selecting a three-digit number with the property that one digit is equal to the product of the other two is 9/900, which can be simplified to 1/90.

The probability of selecting a three-digit number with the property that one digit is equal to the product of the other two is 1/90.

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The square root of 13 in decimal form is an non-terminating non-recurring decimal

A decimal number that never ends and never repeats itself is known as a non-terminating, non-repeating decimal.

Such decimals are irrational numbers since they cannot be expressed as fractions.

Examples. Pi is a decimal that doesn't end or repeat.

Since the square root of 13 will result to infinite number the number cannot fully reach the required value but an approximate

Because of this the decimal form of he square root of 13 will lack accuracy

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Answer:

no

Step-by-step explanation:

a triangle can never only have acute sides. The other sides will either be: obtuse or a right angle.

By using The Pythagoras theorem, the expression g = f/2 represents the relationship between g and f if j = h and k = m option (A), i.e. g = 1/2  is correct.

Pythagoras theorem:

The Pythagorean Theorem, also known as the Pythagorean Theorem, describes the relationship between the three sides of a right triangle. According to the Pythagorean theorem, the square of the hypotenuse equals the sum of the squares of the other two sides of the triangle. If AB and AC are the sides and BC is the hypotenuse of the triangle then BC2 = AB2 + AC2 .where AB is the base, AC is the height or altitude and BC is the hypotenuse.

The area of ​​the square formed by the longest sides (hypotenuses) of right-angled triangles is equal to the sum of the areas. The number of squares formed by the other two sides of a right triangle. In a right triangle, the formula for the Pythagorean theorem is expressed as:

c² = a² + b²

where

'c' = hypotenuse of a right triangle

'a' and 'b' are the other two legs.

In the question:

It is given that:

If j = h and k = m

From the given question, C is a right-angle triangle as j = h and k = m

From the definition of the Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides

         h² +k²= g²

From the triangle ΔABC

(j + h)² +(m + h)² = f²

⇒ (h + h)² +(k+ k)² = f²

⇒ (2h)² +(2k)²= f²

⇒ 4h²+ 4k² = f²

⇒ 4(h²+k²) = f²

⇒ 4×g² = f²

⇒ (2g)² = f²

⇒ 2g = f

⇒ g = f/2

Thus, the expression g = f/2 represents the relationship between g and f if j = h and k = m option (A) is correct.

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Answer: 3062 pounds

Step-by-step explanation: 10.5x7x10 is 735 and divided by 0.24 is 3062.2 pounds rounded to 3062

Angle C is the biggest.

The longest side in a triangle is opposite the largest angle, and the shortest side is opposite the smallest angle.

Answer: Parallel

Step-by-step explanation:

To solve this question, we need to find the slopes of both lines q and r.

First, let's find the slope of line q.

Δx/Δy=-7/-6 = 7/6

Next, the slope of line r.

Δx/Δy=-7/-6 = 7/6

Both lines have the same slope.

Therefore, they are parallel.

The unknown values are ∠ACE = 64.5°, ∠PRQ = 90°, ∠AOC = 40° and  ∠a = 50° along with question no. 2, ∠B = 105°, all solved using angle sum property.

When three line segments intersect at three different angles, the result is a figure known as an Angle Sum Triangle. Triangles always contain a total of 180 degrees of angles.

Any triangle's angles add up to 180 degrees, according to the Angle Sum Triangle Theorem. By applying fundamental geometry concepts, this theorem can be demonstrated. Obtuse, right, or acute angles can all be found in triangles.

Triangle-related issues can be resolved using the Angle Sum Triangle theorem, a crucial geometry theorem. It can be used to gauge a triangle's angle sizes or to establish whether it is acute, right, or obtuse.

A)

∠ABC =∠BCA

∠BAC + ∠ABC + ∠BCA = 180

55 + 2∠ABC =

2∠ABC = 180 - 55

2∠ABC = 125

∠ABC =∠BCA = 75.5

100 + 2∠ECD =  180

∠ECD = 40

∠ACE = 180 - 75.5+40

∠ACE = 64.5°

B) ∠PRQ = 90°  any triangles one side crosses through centre then the opposite angle is 90°.

C) ∠AOC = 40° when inside a circle, the angle on centre is double the angle touching the circumference

D) ∠a = 360 - 90 + (180-60) + (180-80)

∠a = 50°

2. The value of angle be can be calculated using angle sum property of triangle i.e.

(x+5) + 3x + x = 180

5x + 5 = 180

5x = 175

x = 175/5

x = 35

∠B = 3(35)

∠B = 105°

Thus, the unknown values are ∠ACE = 64.5°, ∠PRQ = 90°, ∠AOC = 40° and  ∠a = 50° along with question no. 2, ∠B = 105°.

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Since J, P, and L are the midpoints of KH, HM, and MK, respectively, the values of x, y, and z are as follows;

x = 4.75.

y = 6.

z = 1.

In Geometry, the centroid theorem states that the centroid of a triangle is located at two-third (2/3) of the distance from the vertex to the midpoint of the (opposite) sides.

Generally speaking, the centroid of a triangle simply refers to the point where the three (3) medians of the triangle meet or intersect. By applying the centroid theorem to triangle KHM (ΔKHM);

Side HQ = 2/3(LH)

y = 2/3(3 + y)

3y = 2(3 + y)

3y = 6 + 2y

y = 6.

Side KQ = 2/3(KP)

7 = 2/3(7 + 2x - 6)

21 = 2(1 + 2x)

10.5 = 1 + 2x

2x = 9.5.

x = 4.75.

Side QM = 2/3(JM)

4 = 2/3(2z + 4)

12 = 2(2z + 4)

6 = 2z + 4

2z = 2.

z = 1.

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The equation of the piecewise function is:

        { 5/3(x),  -4 ≤ x≤ -1

f(x) = { 2,          -1 ≤ x ≤ 3

        {-2,          3 ≤ x ≤4

A piecewise function is a function that is defined by multiple sub-functions, each of which applies to a certain range of the input (or domain) values.

In the graph, we have five points with coordinates (-4, -3), (-1, 2), (3, 2), (3, -2) and (4, -2)

To find the f(x) for (-4, -3) to (-1, 2):

First, find the slope using slope = (y2-y1)/(x2-x1)

Slope = (2-(-3)) / (-1-(-4)) = 5/3

f(x) = 5/3(x)

For  (-1, 2) to (3, 2):

f(x) = 2

For (3, -2) to (4, -2):

f(x) = -2

Therefore, the equation of the piecewise function will be:

         { 5/3(x),  -4 ≤ x ≤ -1

f(x) = { 2,          -1 ≤ x≤ 3

          {-2,         3 ≤ x ≤ 4

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Longitudinal waves are waves where the displacement of the medium is in the same direction as the direction of the travelling wave.

The distance between the centres of two consecutive regions of compression or the rarefaction is defined by wavelength, λ. When the compression and rarefaction regions of two waves coincide with each other, it is known as constructive interference and if the regions of compression and rarefaction do not coincide, it is known as destructive interference.

Compression

In a longitudinal wave, compression is a region in which the particles of the wave are closest to each other.

Rarefaction

Rarefaction in a longitudinal wave takes place when the particles are farthest apart from each other.

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Answer: s=6

Step-by-step explanation: so you have -7=s+(-13)

simplify: -7=s-13

add 13:

Answer: Gill is 16 now

Step-by-step explanation: If the horse was 3 one year ago, and gill is five times as old as it, shed be 15. one year from now, the horse is 5 and Gill is 17, which combined, is 22. If she is 17 in one year, she is 16 now.

Answer:

x = 19

Step-by-step explanation:

5x - 37 = 3x + 1      (move over the 3x by subtracting)

2x - 37 = 1      (move over the 37 by adding)

2x = 38      (divide both sides by 2)

x = 19

x=19

Step-by-step explanation:

(5x-37) = (3x+1)

5x - 3x = 1 + 37

5x - 3x = 38

2x = 38

x = 19

Question 9

[tex]\frac{\sin x}{23}=\frac{\sin 27^{\circ}}{11}\\\\\sin x=\frac{23\sin 27^{\circ}}{11}\\\\x \approx 71.7^{\circ}, 108.3^{\circ}[/tex]

Both of these cases satisfy the angle sum of a triangle.

Question 11

[tex]\frac{\sin x}{27}=\frac{\sin 74^{\circ}}{26}\\\\\sin x=\frac{27 \sin 74^{\circ}}{26}\\\\x \approx 86.6^{\circ}, 93.4^{\circ}[/tex]

Both of these cases satisfy the angle sum of a triangle.

The turning point of the function is x = 1 and it is a local minima.

The curve of a function has peaks and troughs called maxima and minima. A function may have any number of peaks and minima. Calculus allows us to determine any function's maximum and lowest values without ever consulting the function's graph. Maxima will be the curve's highest point within the specified range, while minima will be its lowest.

Extrema is the result of maxima and minima combined. The graph in the graphic below shows several peaks and falls. We obtain the function's maximum and lowest values at x = a and 0 respectively, and at x = b and c respectively. The valleys are the minima and all the peaks are the maximum.

In a function, maxima and minima can be of two different types:

Local Maxima and Minima

Global or Absolute Maxima and Minima

The function is

y = [tex](x-1)^{2}[/tex] for -3 ≤ x ≤ 3

differentiating both side with respect to x we get

[tex]\frac{dy}{dx} = 2(x-1)[/tex]

for maxima and minima [tex]\frac{dy}{dx} = 0[/tex]

or, 2(x-1) = 0

or x = 1

Now, for x > 1 [tex]\frac{dy}{dx} > 0[/tex]

So, the function's turning point is a minima.

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The interquartile range is a useful tool for measuring variability in a set of data because it overcomes the difficulty of the range being influenced too much by extreme values

The interquartile range is a measure of variability that is commonly used in statistics to describe the spread of a set of data. It is particularly useful because it overcomes the difficulty of the range being influenced too much by extreme values.

In mathematical terms, the interquartile range is defined as the difference between the upper quartile (Q3) and the lower quartile (Q1).

The upper quartile represents the 75th percentile of the data and the lower quartile represents the 25th percentile of the data.

This means that 25% of the data falls below the lower quartile and 75% of the data falls above the upper quartile.

The interquartile range provides a better representation of the spread of the data because it eliminates the influence of extreme values.

These values, also known as outliers, can have a significant impact on the range and can make it appear as though the data is more spread out than it actually is.

By using the interquartile range, the outliers are excluded and a more accurate representation of the spread of the data is obtained.

Therefore, option (a) is correct.

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The mean of these scores is 16.

The mean is a measure of central tendency that indicates the average value of a set of data. It is calculated by adding up all of the individual values in a dataset and dividing that sum by the number of values in the dataset. In mathematical terms, the mean is represented by the symbol "µ" (mu) and is calculated as:

µ = (sum of all observations) / (number of observations)

To find the mean of these scores, you would add up all of the individual scores and divide by the total number of scores.

First, we find the total score of the 5 students who scored 10: 5 students * 10 points/student = 50 points

Then, we find the total score of the 10 students who scored 15: 10 students * 15 points/student = 150 points

Then, we find the total score of the 10 students who scored 20: 10 students * 20 points/student = 200 points

Now we add all the total scores of students: 50+150+200 = 400 points

Finally, to find the mean score, we divide the total score by the number of students: 400 points / 25 students = 16 points/student.

Therefore, the mean of these scores is 16.

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There are 6 different ways to set up the tournament.

We can make two pairs of teams (a,b and c,d) and then arrange each pair in two different ways (ab, cd and cd, ab). Thus, there are a total of 6 combinations.

(b) There are 8 different outcomes for this tournament. Each pair of teams (a,b and c,d) can play in either the first or second round, and each team can either win or lose. We can calculate the number of outcomes by multiplying the different combinations of the first round (6) with the number of outcomes in the second round (2x2). Therefore, total number of outcomes = 6x2x2 = 8.

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a) The cost for 96 hotdogs from Value Market = $94.04.

b) The cost for 96 hotdogs from Sammy's Bulk Store = $75.84.

a) The cost for 96 hotdogs from Value Market would be $96 x $0.99/hotdog = $94.04.

b) The cost for 96 hotdogs from Sammy's Bulk Store would be $96 x $0.79/hotdog = $75.84.

For bottled water, Sammy's Bulk Store offers the better buy, with $0.69/bottle, compared to Value Market's $0.99/bottle. The reasoning is that Sammy's Bulk Store has a lower price per bottle of water.

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The three quartiles is the value of Q₂ [Median] is 73 (on the 7th value), The value of Q₁ is 70 (the 3.5th value), The value of Q₃ is 77 (is the 10.5th value). and Interquartile range = Q₃ - Q₁ = 77 - 70 = 7

A quartile is a particular kind of quantile that splits the total number of data points into four roughly equal portions, or quarters. Quartiles are a type of order statistic since they require the data to be arranged from smallest to largest in order to be computed.

The median of the data set is the number in the midpoint between the smallest number (minimum) and the first quartile (Q1).

The median of a data set is known as the second quartile (Q2).

The median value and the highest value (maximum) in the data set are the two values that make up the third quartile (Q3).

To find the quartiles, first, we need to put the data in ascending order.

65,  68,  70,  70,  71,  72,  73,  74,  75,  77,  77,  78,  80

The value of Q₂ [Median] is on the 7th value, which is 73

The value of Q₁, the lower quartile, is the 3.5th value [(3rd value+4th value)/2] , which is 70

The value of Q₃, the upper quartile, is the 10.5th[(10th value+11th value)/2]  value, which is 77

and

Interquartile range = Q₃ - Q₁ = 77 - 70 = 7.

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Answer:

c. 2

Step-by-step explanation:

The valueof v

-9v - 9 = -27

= -9v = -27 + 9

= -9v = -18

= -9v/-9 = -18/-9

v = 2.

Note: negative will cancel negative.