Solve for x

2,4, and 6 i need help with

Answer: 50 Cups

Step-by-step explanation:

16 cups in a gallon. so times that by 2, which equals 32. There are four cups in one quart so times 4 by 4 which is 16 and add to 32. 16 + 32 = 48

Two cups in a pint so add 2 to 48 which is 50

Answer:

You will get 25 cups if you mix 2 gallons, 4 quarts, and 1 pint.

Step-by-step explanation:

To convert between gallons, quarts, and pints, we need to use the following conversions:

1 gallon = 4 quarts

1 quart = 2 pints

Here's the step-by-step process to convert the given volume to cups:

Convert gallons to quarts: 2 gallons * 4 quarts/gallon = 8 quarts

Add the number of quarts from step 1 to the number of quarts given: 8 quarts + 4 quarts = 12 quarts

Convert pints to quarts: 1 pint * 1 quart/2 pints = 0.5 quarts

Add the number of quarts from step 3 to the number of quarts from step 2: 12 quarts + 0.5 quarts = 12.5 quarts

Convert quarts to cups: 12.5 quarts * 2 cups/quart = 25 cups

Therefore, you will get 25 cups if you mix 2 gallons, 4 quarts, and 1 pint.

Answer:

Right, Isosceles

Step-by-step explanation:

The little square in the corner means its right angled, so a right triangle. This also means that it cannot be acute or obtuse.

The two hash marks shows two sides are the same. So it is isosceles. This also means it cannot be scalene or equilateral.

Answer:

50:7

Step-by-step explanation:

You just put ":" in between the numbers requested.

Answer:

D

Step-by-step explanation:

ASA = 2 non included angles + 1 included side

by knowing angle c is congruent to angle z we can prove the triangles are congruent by ASA postulate.

The correct statements would need to be congruent to show that

Δ ABC= ΔXYZ by ASA are,

⇒ ∠ B ≅ ∠ Y

⇒ ∠ C ≅ ∠ Z

An angle is a combination of two rays (half-lines) with a common endpoint. The latter is known as the vertex of the angle and the rays as the sides, sometimes as the legs and sometimes the arms of the angle.

Given that;

AC = XZ

∠ A = ∠ X

Now, To prove the triangles are congruent by ASA , we get;

AC = XZ

∠ A = ∠ X

⇒ ∠ Z = ∠ C

or, ∠ B = ∠ Y

Thus, The correct statements would need to be congruent to show that

Δ ABC= ΔXYZ by ASA are,

⇒ ∠ B ≅ ∠ Y

⇒ ∠ C ≅ ∠ Z

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Answer:yo no se como ablar ingles

Step-by-step explanation: perdoname

The amount of force between two objects 10 mm away from each other is G[tex]m_1m_2[/tex] / 100.

All physical things with mass are drawn to the gravitational force, which can be thought of as an attracting force. It is the known natural force that is by far the weakest.

Given:

Distance = 10 mm

As, the Gravitation force between two objects

F = G[tex]m_1m_2[/tex] / r²

or, F = G[tex]m_1m_2[/tex] / 10²

F = G[tex]m_1m_2[/tex] / 100

Also, the force between two objects decreases as the far they are apart from each other.

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The Question attached is Incomplete/ inappropriate, the Complete Question is

What would be the amount of force between two objects 10 mm away from each other having the [tex]m_1[/tex] and [tex]m_2[/tex]?

a ) Construction of stem and leaf display of the data is:

For n = 129 and with splint unit = 0.1, the stem and splint map of the given data on Shower- inflow rate( L/ min) is as follows

a stem-and-leaf display of the data.

   Stems                                                Leaves

       2                                                       28

       3                                                1344567789

       4                                                 01356889

       5                                          00001114455666789

       6                              0000122223344456667789999

       7                                     00012233455555668

       8                                                02233448

       9                                         012233335666788

      10                                             2344455688

      11                                                2335999

      12                                                     17

      13                                                      9

      14                                                     36

      15                                                  0035

      16                                                  None

      17                                                  None

      18                                                     3

b) From brume and splint map we note that minimal Shower inflow rate is2.2 whereas outside is18.3 L/ mim. farther typical or representative rate is7.0 L/min.

c) The display of data on steam and leaf chart shows that data is positively skewed means concentration of data on left side or lower value side is high as compared to other side.

d) Distribution is not symmetric rather very clear positive skew ness is observed through steam and leaf chart. Even distribution is Unimodal.

e) From steam and leaf chart is indicative to conclude that the highest observation 18.3 is outlier.

A stem and splint plot, also known as a stem and splint illustration, is a way to arrange data so that it's simple to see how constantly colorful feathers of values do. It's a graph that displays ordered numerical data. A stem and a splint are divided into each piece of data.

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Complete question:

The accompanying data set consists of observations on shower-flow rate (L/min) for a sample of n = 129 houses:

4.6 12.1 7.1 7.0 4.0 9.2 6.7 6.9 11.5 5.1

11.2 10.5 14.3 8.0 8.8 6.4 5.1 5.6 9.6 7.5

7.5 6.2 5.8 2.8 3.4 10.4 9.8 6.6 3.7 6.4

8.3 6.5 7.6 9.3 9.2 7.3 5.0 6.3 13.9 6.2

5.4 4.8 7.5 6.0 6.9 10.8 7.5 6.6 5.0 3.3

7.6 3.9 11.9 2.2 15.0 7.2 6.1 15.3 18.3 7.2

5.4 5.5 4.3 9.0 12.7 11.3 7.4 5.0 3.5 8.2

8.4 7.3 10.3 11.9 6.0 5.6 9.5 9.3 10.4 9.7

5.1 6.7 10.2 6.2 8.4 7.0 4.8 5.6 10.5 14.6

10.8 15.5 7.5 6.4 3.4 5.5 6.6 5.9 15.0 9.6

7.8 7.0 6.9 4.1 3.6 11.9 3.7 5.7 6.8 11.3

9.3 9.6 10.4 9.3 6.9 9.8 9.1 10.6 4.5 6.2

8.3 3.1 4.9 5.0 6.0 8.2 6.3 3.8 6.0

(a) Construct a stem-and-leaf display of the data. (Enter numbers from smallest to largest separated by spaces. Enter NONE for stems with no values.)

Stems Leaves

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

(b) What is a typical, or representative, flow rate?

L/min

(c) Does the display appear to be highly concentrated or spread out?

highly concentrated, except for a few values on the positive sidehighly concentrated in the middle highly concentrated, except for a few values on the negative sidespread out

(d) Does the distribution of values appear to be reasonably symmetric? If not, how would you describe the departure from symmetry?

Yes, the distribution appears to be reasonably symmetric.No, the data are skewed to the right, or positively skewed. No, the data are skewed to the left, or negatively skewed.No, the distribution of the values appears to be bimodal.

(e) Would you describe any observation as being far from the rest of the data (an outlier)?

Yes, the value 2.2 appears to be an outlier.Yes, the value 15.5 appears to be an outlier. Yes, the value 18.3 appears to be an outlier.No, none of the observations appear to be an outlier.

B) h = 38p

An equation represents a proportional relationship if the ratio of the dependent variable to the independent variable is constant. In this equation, h is directly proportional to p, meaning that if p increases, h increases, and if p decreases, h decreases. The constant of proportionality is 38.

In other words, the equation h = 38p can be written as h/p = 38, which shows that the ratio of h to p is always equal to 38. This means that the equation represents a proportional relationship.

The other equations listed do not represent a proportional relationship because the ratio of the dependent variable to the independent variable is not constant. For example, in equation A, h is not directly proportional to p because the constant of proportionality changes as p changes. In equation C, h and p are inversely proportional because h decreases as p increases, and h increases as p decrease. And in equation D, the equation is not in the form of a proportion because there is an additional constant term on the right-hand side.

The probability that their average length is less than 10 inches is; 5.71%

The formula for z-score is;

z = (x' - μ)/(σ/√n)

where;

x' is sample mean

μ is population mean

σ is standard deviation

n is sample size

We are given;

x' = 10 inches

μ = 9.7 inches

σ = 1.2 inches

n = 40

Thus;

z = (10 - 9.7)/(1.2/√40)

z = 0.3/0.1897367

z = 1.58

From online p-value from z-score calculator, we have;

P(z < 1.58) = 0.0571 or 5.71%

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The first mistake in Ismail's proof is that (3) cos(90 - Ф) = AC/BC

The complete question is added as an attachment

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

The two column proof

In the two column proof, we have

cos(90 - Ф) = AC/BC

This equation is incorrect because by the definition of cosine, we have

cos(90 - Ф) = AB/BC

i.e. cos(x) = adjacent/hypotenuse

Hence, the mistake in his proof is cos(90 - Ф) = AC/BC

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The US EIA should use a sample size of at least 25 for a margin of error of $0.10, at least 49 for a margin of error of $0.07, and at least 97 for a margin of error of $0.05 to report the average price of a gallon of regular gasoline with 95% confidence.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

We can use the formula for the margin of error for a 95% confidence interval:

margin of error = z× (standard deviation / √n)

where z is the z-score for a 95% confidence interval, which is 1.96.

a. The desired margin of error is $0.10:

0.10 = 1.96(0.25 /√n)

√n = 1.96×0.25 / 0.10

√n= 4.9

n = 4.9^2

n = 24.01

So the appropriate sample size for a margin of error of $0.10 is at least 25.

b. The desired margin of error is $0.07:

0.07 = 1.96 (0.25 / √n)

√n = 1.96 × 0.25 / 0.07

√n= 6.97

n = 6.97²

n = 48.53

So the appropriate sample size for a margin of error of $0.07 is at least 49.

c. The desired margin of error is $0.05:

0.05 = 1.96 (0.25 / √n)

√n= 1.96 × 0.25 / 0.05

√n= 9.8

n = 9.8²

n = 96.04

So the appropriate sample size for a margin of error of $0.05 is at least 97.

Therefore, the US EIA should use a sample size of at least 25 for a margin of error of $0.10, at least 49 for a margin of error of $0.07, and at least 97 for a margin of error of $0.05 to report the average price of a gallon of regular gasoline with 95% confidence.

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Joan completed the race 1.66 standard deviations faster than the typical female of her age group. The standard deviation will be denoted by the symbol “” and the women's average finish time by the symbol “”. Then, Joan's remaining time was plus 1.66.

The proportion of women who finished the race sooner than Joan. In this case, it is possible to apply the normal distribution.

The percentage of values to the left of z = 1.66 can then be calculated or found using a standard normal distribution table. The number of women who finished the race ahead of Joan is represented by the percentage in the table below.

According to a normal distribution table or calculator, there are approximately 0.9525 numbers to the left of the value z = 1.66.

Therefore, This means that out of the 410 female runners in Joan's age group, about 0.9525 × 410 = 391.23 of them beat her. The final count is 391 women, rounded to the next whole number.

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At the school play, 225 adult tickets were sold.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Let, The number of adult tickets sold be 'x',

Therefore, The number of student tickets would be 'x - 68'.

Therefore, The expression can be formed as,

x + (x - 68) = 382.

2x - 68 = 382.

2x = 450.

x = 225.

So, The number of adult tickets sold is 225.

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Answer:

It would be a little over 2 hours or so since 16:41 is just 4:41.

2 hours and 16 minutes

Step-by-step explanation:

You're welcome.

Answer:

The fraction 14/16 is greater than 7/8.

Step-by-step explanation:

Answer:

26 kangaroos on the farm
32 goats on the farm

Step-by-step explanation:

To find the number of goats and kangaroos on the farm, we need to determine the number of legs each animal has. Let's say that there are 'g' goats and 'k' kangaroos.

Since each goat has 4 legs, the total number of legs for all the goats is 4g. Similarly, since each kangaroo has 2 legs, the total number of legs for all the kangaroos is 2k.

Adding these two quantities, we have:

4g + 2k = 180

Since each goat has 1 head, the total number of heads for all the goats is g. Similarly, since each kangaroo has 1 head, the total number of heads for all the kangaroos is k.

Adding these two quantities, we have:

g + k = 58

Now, we have two equations and two unknowns. To solve for 'g' and 'k', we can use substitution or elimination method.

Let's use substitution method:

From the second equation, we can find g:

g = 58 - k

Substituting this in the first equation, we get:

4(58 - k) + 2k = 180

Expanding and solving, we get:

232 - 4k + 2k = 180

232 - 2k = 180

-2k = -52

k = 26

So, there are 26 kangaroos on the farm. To find the number of goats, we can use the first equation:

g = 58 - k = 58 - 26 = 32

Therefore, there are 32 goats on the farm.

The mean of the given data is 1744 days, median of the given data is 1460.5 days, mode of the given data is 1461 days & 4422 days.

To find the mean, median, and mode of the lengths of terms of the US Presidents that preceded Joe Biden:

Mean:

To find the mean, we add up all of the term lengths and divide by the total number of terms:

Mean = (4422 + 2922 + 2865 + 2840 + 2728 + 2041 + 2027 + 1886 + 1654 + 1503 + 1461 + 1460 + 1430 + 1419 + 1262 + 1036 + 969 + 895 + 881 + 492 + 199 + 31) / 44

Mean = 1743.77 days

Median:

To find the median, we need to arrange the term lengths in order from smallest to largest, and then find the middle term. In this case, since we have an even number of terms, we will take the average of the two middle terms:

31 199 492 881 895 969 1036 1262 1419 1430 1460 1461 1503 1654 1886 2027 2041 2728 2840 2865 2922 4422

Median = (1460 + 1461) / 2

Median = 1460.5 days

Mode:

The mode is the most frequently occurring term length. In this case, there are two modes: 1,461 days and 4,422 days.

Since the term length of FDR is much higher than all the other term lengths, it has pulled up the mean to a higher value than the other measures of central tendency. Additionally, the mode being a high value is likely due to the fact that FDR served for more than three terms, which is an outlier in the data set.

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The number of ways for which he can choose 7 lures if more than 5 must be jigs is of:

372 ways.

The number of different combinations of x objects from a set of n elements is obtained with the formula presented as follows, using factorials.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The possible combinations are given as follows:

Hence the number of ways is given as follows:

n = 9!/(6! x 3!) x 4!/(1! x 3!) + 9!/(7! x 2!)

n = 372 ways.

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Answer: D, 3x+12

Step-by-step explanation: Distributing a number means that you have to multiply the number by all of the numbers inside the parentheses. 3*x is 3x, and 3*4 is 12.  3x+12 is 3x+12.

Translation the graph of the function  [tex]y=f(x)[/tex]a units to the right gives you the function [tex]y=f(x-a)[/tex]

If the graph of the function [tex]f(x)=3^{x}[/tex] is translated 6 units to the right, then the function becomes

[tex]g(x)=f(x-6)=3^{x-6}[/tex]

Answer: correct choice is A

The candidates received ;

Person A = 734 votes

Person B = 793 votes

Person C = 798 votes

From the information given, we have that;

Now, substitute the values

Person A + Person B + Person C = 2325

Person B - 59 + Person B + Person + B = 2325

Let Person B = x

x -59 + x + x + 5 = 2325

collect like terms

3x = 2325 +54

Add the like terms

3x = 2379

Make 'x' the subject of formula

x = 2379/3

x = 793 votes

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Therefore, the area of the triangle ABC is approximately 18096.3 square units.

What is the area of the triangle?

To calculate the area of a triangle, use the formula area = 1/2 * base * height.

We can use Heron's formula to find the area of the triangle ABC when the lengths of its three sides are known:

[tex]Area = {\sqrt{(s(s-a)(s-b)(s-c))}[/tex]

where "s" is the semiperimeter of the triangle, which is half the sum of the lengths of its three sides:

s = (a + b + c)/2

In this case, we have:

a = AB = 154

b = BC = 346

c = AC = 349

So the semiperimeter is:

s = (a + b + c)/2 = (154 + 346 + 349)/2 = 424.5

Now we can use Heron's formula to find the area of the triangle

[tex]Area = \sqrt{(s(s-a)(s-b)(s-c))}\\\\Area = \sqrt{(424.5(424.5-154)(424.5-346)(424.5-349))}\\\\Area= 18096.3[/tex]

Therefore, the area of the triangle ABC is approximately 18096.3 square units.

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The solution to the question on the equilibrium of the cheese and bagels have been given below

a) If the equilibrium price of cream cheese and the equilibrium quantity of bagels have both risen, this could be caused by a fall in the price of flour, one of the inputs used to produce bagels.

This decrease in the cost of production would cause the supply of bagels to increase, leading to a rightward shift in the supply curve. At the same time, the demand for bagels would increase as consumers substitute away from other breakfast foods and toward bagels, leading to a rightward shift in the demand curve.

These two shifts would result in a higher equilibrium price for cream cheese, since bagels and cream cheese are complements. The increased demand for bagels would lead to an increase in the demand for cream cheese, causing the demand curve for cream cheese to shift rightward.

The diagram below illustrates this relationship. The initial equilibrium is at point A, with a price of P1 and a quantity of Q1. After the decrease in the price of flour, the supply curve for bagels shifts rightward to S', and the demand curve for bagels shifts rightward to D'. The new equilibrium is at point B, with a higher price of P2 and a higher quantity of Q2. The increase in the demand for bagels leads to an increase in the demand for cream cheese, causing the demand curve for cream cheese to shift rightward to D'''. The new equilibrium for cream cheese is at point C, with a higher price of P3 and a higher quantity of Q3.

b) If the equilibrium price of cream cheese has risen but the equilibrium quantity of bagels has fallen, this could be caused by a rise in the price of milk, one of the inputs used to produce cream cheese.

This increase in the cost of production would cause the supply of cream cheese to decrease, leading to a leftward shift in the supply curve. At the same time, the demand for cream cheese would decrease as consumers substitute away from cream cheese and toward other breakfast foods, leading to a leftward shift in the demand curve.

These two shifts would result in a higher price for cream cheese, but a lower quantity of bagels consumed. The decreased demand for cream cheese would lead to a decrease in the demand for bagels, causing the demand curve for bagels to shift leftward.

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In these triangles, the largest angle and the largest side have been measured. This means that the two smaller sides and the two smaller angles are proportional to each other. This is known as the triangle inequality, which states that the sum of any two sides of a triangle must be greater than the third side. This means that the two smaller angles and the two smaller sides of the triangle must add up to be larger than the largest angle or side.

The Triangle Inequality states that the sum of any two sides of a triangle must be greater than the third side. This means that two other inequalities can be written:

a > |c - b| and b > |c - a|,

where |x| is the absolute value of x. This means that the length of each side must be greater than the difference between the other two sides

The value of f(3) is 2.

Option B is the correct answer.

A function has an input and an output with a relationship between them.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

f(x) = 1/4 x [tex]2^x[/tex]

Substitute x = 3.

f(3) = 1/4 x 2³

f(3) = 1/4 x 8

f(3) = 2

Thus,

The value of f(3) is 2.

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The relation is a function only if for element x in Set X, there is only one element in Set Y so, the choice B shows the relation.

Function is a type of relation, or rule, that maps one input to specific single output.

In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable (the dependent variable) (the dependent variable).

When a relation will be called as a function .

Consider there be a relation R from a set X to a set Y .

Since the relation will be called a function if each element of set X is related to exactly one element in set Y.

which is, an element x in X, there is only one element in Y that x is related to.

Therefore , the correct option is B.

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The dual problem of the primal problem "Maximize Z = 7X1 + 5X2, Subject to X1 + 2X2 ≤ 6, 4X1 + 3X2 ≤ 12, X1, X2 ≥ 0" is:

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Greater than (or greater than or equal to), less than (or less than or equal to), or not equal to signs are used in place of the equal sign.

Minimize Z = 6Y1 + 12Y2

Here

Y1 + 4Y2 ≥ 7

2Y1 + 3Y2 ≥ 5

Y1, Y2 ≥ 0

(b) The dual problem of the primal problem "Maximize Z = 3X1 + 4X2, Subject to 5X1 + 4X2 ≤ 200, 3X1 + 5X2 ≤ 150, 8X1 + 4X2 ≥ 80, X1, X2 ≥ 0" is:

Minimize Z = 200Y1 + 150Y2

Subject to:

4Y1 + 5Y2 ≥ 3

5Y1 + 3Y2 ≥ 4

4Y1 + 8Y2 ≤ -80

Y1, Y2 ≥ 0

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"Your question is incomplete, probably the complete question/missing part is:"

Write the dual of following problems:

(a) Maximize Z = 7X1 + 5X2

Subject to:

X1 + 2X2 ≤ 6

4X1 + 3X2 ≤ 12

X1, X2 ≥ 0

(b) Maximize Z= 3X1 + 4X2

Subject to:

5X1 + 4X2 ≤ 200

3X1 + 5X2 ≤ 150

8X1 + 4X2 ≥ 80

X1, X2 ≥ 0

[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

The identity to be used here is [ (a - b)² = a² - 2ab + b² ]

First, try to get the given expression in form of terms on the RHS of the above identity

[tex]\qquad \sf  \dashrightarrow \: 4y {}^{2} - 6yz + 9 {z}^{2} [/tex]

[tex]\qquad \sf  \dashrightarrow \: (2 {}^{2})( {y}^{2}) - 2(3)(y)(z) + (3 {}^{2} ) {z}^{2} [/tex]

[tex]\qquad \sf  \dashrightarrow \: (2y) {}^{2} - (2y)(3z) + (3z) {}^{2} [/tex]

[ it's in form of a² - ab + b² now, add and deduct ab here ]

[tex]\qquad \sf  \dashrightarrow \: (2y) {}^{2} - (2y)(3z) + (9z) {}^{2} - (2y)(3z) + (2y)(3z)[/tex]

[tex]\qquad \sf  \dashrightarrow \: (2y) {}^{2} - 2(2y)(3z) + (3z) {}^{2} + (2y)(3z)[/tex]

[ Apply the identity ]

[tex]\qquad \sf  \dashrightarrow \: (2y - 3z) {}^{2} + (2y)(3z)[/tex]

[tex]\qquad \sf  \dashrightarrow \: (2y - 3z) {}^{2} + 6yz[/tex]

[ That's probably the answer, it can't be simplified more ]

To factorize the expression [tex]\sf\:4y^2 - 6yz + 9z^2 \\[/tex], we can use the quadratic formula.

We have the quadratic expression [tex]\sf\:ax^2 + bx + c \\[/tex], where $$\sf\:a = 4$$, $$\sf\:b = -6y $$, and $$\sf\:c = 9z^2 $$.

The quadratic formula states that for any quadratic equation of the form [tex]\sf\:ax^2 + bx + c = 0 \\[/tex], the solutions for $$\sf\:x $$ can be found using the formula:

[tex]\sf\:x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \\[/tex]

Applying this formula to our quadratic expression, we get:

[tex]\begin{align}\sf\:x &= \frac{-(-6y) \pm \sqrt{(-6y)^2 - 4(4)(9z^2)}}{2(4)} \\ &= \frac{6y \pm \sqrt{36y^2 - 144z^2}}{8} \\ &= \frac{6y \pm \sqrt{36(y^2 - 4z^2)}}{8} \\ &= \frac{6y \pm 6\sqrt{y^2 - 4z^2}}{8} \\ &= \frac{3}{4}y \pm \frac{3}{4}\sqrt{y^2 - 4z^2}\end{align} \\[/tex]

Thus, the factored form of the expression [tex]\sf\:4y^2 - 6yz + 9z^2 \\[/tex] is [tex]\sf\:(\frac{3}{4}y + \frac{3}{4}\sqrt{y^2 - 4z^2})(\frac{3}{4}y - \frac{3}{4}\sqrt{y^2 - 4z^2}) \\[/tex].

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The estimate of the number 7th grader who play in the school band will be 120.

It is important to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator.

Some of the mathematical operations that are illustrated in this case include addition, subtraction, etc. The estimate of the number 7th grader who play in the school band will be:

= 60 / 200 × 400

= 120

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Answer: [tex]f^{-1} (x) = \sqrt{x} +1[/tex]

Step-by-step explanation:

[tex]y = x^2 - 2x + 1[/tex]

We know straight away the inverse will be a square root function. We also know that this inverse will have a restriction on the domain, (because you can only take the square root of a positive number).

So, to find the inverse, first we'll switch the x and y and solve for y:

[tex]x = y^2 - 2y +1[/tex]

[tex]x = (y-1)^2[/tex], (factor!)

±[tex]\sqrt{x} = y - 1[/tex]

So, the inverse "function" is:

[tex]f^-1(x)[/tex] = ±[tex]\sqrt{x} +1[/tex]

But theres an issue here!

If we tried graphing this, this "function" would not pass the vertical line test, so its not really a function at all!

We need to restrict the domain to only include the values that are above the x axis.

So our final inverse function is:

[tex]f^{-1} (x) = \sqrt{x} +1[/tex]