Solve for the 2 unknown sides and the missing angle

The quotient is 3x + 7, and the remainder is (28x + 9) / (x^2 - 3x).

A division is a process of splitting a specific amount into equal parts.

We have to find 3x³-2x²+7x+9 divided by x²-3x

3x³-2x²+7x+9 is the dividend and x²-3x is the divisor.

The steps to solve this are given below.

Step 1: Take the first digit of the dividend from the left. Check if this digit is greater than or equal to the divisor.

Step 2: Then divide it by the divisor and write the answer on top as the quotient.

Step 3: Subtract the result from the digit and write the difference below.

Step 4: Bring down the next digit of the dividend (if present).

Step 5: Repeat the same process.

Hence, the quotient is 3x + 7, and the remainder is (28x + 9) / (x^2 - 3x).

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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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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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The lowest values of x are;

1. x = 1/2, x = 2/4, x = 3/6

2. x = 14, 15, 16

From the information given, we have that;

10-3x > 8

collect the like terms, we get;

-3x > 8 - 10

subtract the values

-3x > -2

Make 'x' the subject

x > 2/3

5x-27 > 7x

collect the like terms

5x - 7x> 27

subtract the like terms

-2x> 27

Make 'x' the subject

x > -27/2

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The percentage change in the price is 15.78% decrease.

What is the percentage?

A percentage is a figure or ratio that may be stated as a fraction of 100 in mathematics. If we need to compute the percentage of a number, divide it by the entire and multiply by 100. As a result, the percentage denotes a part per hundred. Per 100 is what the term percent signifies. The sign "%" represents it.

Here are some percentage examples:

Now,

Initial price=4.1

Final price=3.5

Change=3.5-4.1= -0.6 , minus means decrease in price

final value + initial value=7.6

then

percentage change by midpoint approach = (final value-initial value) / ((final value + initial value)/2) *100

=0.6/3.8*100

=0.1578*100

=15.78%

hence,

         The percentage change in the price is 15.78% decrease.

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Answer:

x <-1.5

or

x <9.6

Step-by-step explanation:

12x + 7 < - 11

12x < -11 - 7

12x < - 18

12x/12 < -18/12

x = -1.5

OR.

5x - 8 > 40

5x > 40 + 8

5x > 48

5x/5 > 48/5

x > 9.6.

Answer: interest= 670

Step-by-step explanation:

(1+r)^t*principal

Answer:

1 this is the answer because 1 is more than other number

We can see here that simplifying, we have:

a. h²

b. h³

c. 1/(1 + h)

d. 3h

e. 3h/(64 + 4h)

f. h/(4h + 2h²)

Simplification is the process of reducing something to its most basic form or removing any unnecessary complexity.

In mathematics, simplification is often used to make equations or expressions easier to work with, solve, or understand. This can involve combining like terms, cancelling out common factors, or using rules of exponents and logarithms to simplify an expression.

We see here that the below gives us the workings:

a. (5 + h)³ - 125/ h = h³ +  5³ - 125/h = h²

b. [tex]\frac{(3 + h)^{4} - 81 }{h} =\frac{ 3^{4} + h^{4} - 81}{h} = \frac{ h^{4} + 81 - 81}{h} = h^{3}[/tex]

c. (1/1+h) - 1/h = 1/1+h - 1 ÷ h = 1/1+h

d. 3(1 + h)² -3/h = 3h² + 3 - 3/h = 3h²/h = 3h

e. [(3/4+h) - 3/4]/4 = (3/4+h - 3/4) ÷ 4 = 3h/64+4h

f. (-1 + 2 + h) + 1/2 ÷ h = h/4 + 2h × 1/h = h/4h + 2h²

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Step-by-step explanation:

a. £5,37

b.£2,07

c.£15,70

If the numbers of subsets of {1, 2, 3, 4, 5, 6, 7, 8, 9} that are subsets of neither {1, 2, 3, 4, 5} nor {4, 5, 6, 7, 8, 9} is K, then the sum of digits of K is 9

Let the sets be

A =  {1, 2, 3, 4, 5, 6, 7, 8, 9}

B = {1, 2, 3, 4, 5}

C = {4, 5, 6, 7, 8, 9}

Then

B ∩ C = {4, 5}

Subsets of B ∩ C = {4}, {5}, {4,5}, {}

If we exclude the null set then the subsets remaining will be {4}, {5}, {4,5}

No. of elements in A = 9

No. of subsets of A = [tex]2^9[/tex]

No. of elements in B = 5

No. of subsets of B = [tex]2^5[/tex]

No. of elements in C = 6

No. of subsets of C = [tex]2^6[/tex]

If we subtract the no. of subsets of B and C from the no. of subsets of A we get the no. of subsets of A that are not the subsets of B or C

But the null set will be subtracted twice

Also as the subsets of B ∩ C excluding null set will be subtracted twice

Therefore, total number of subsets of A not the subsets of B or C

[tex]k=2^9-2^5-2^6+1\\k=512-32-64-2\\\\k=414[/tex]

The sum of the digits of k=9

The complete question is-

If the numbers of subsets of {1, 2, 3, 4, 5, 6, 7, 8, 9} that are subsets of neither {1, 2, 3, 4, 5} nor {4, 5, 6, 7, 8, 9} is K, then find the sum of digits of K.

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Answer:

Step-by-step explanation:

The sum of the exterior angles of a triangle is equal to 360 degrees, while the sum of the interior angles of a triangle is equal to 180 degrees.

When you combine the sum of the exterior angles and the sum of the interior angles of a triangle, you get:

360 degrees + 180 degrees = 540 degrees

So, the sum of the exterior angles and the sum of the interior angles of a triangle is equal to 540 degrees.

Answer:

16x(1+2x^2)^3

Step-by-step explanation:

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

Use chain rule

4(1+2x^2)^3(4x)

Solving the provided question, we can say that By, Pythagorean theorem PR = √277 and b = 11.31

The Pythagοrean Theorem, sometimes known as the Pythagοrean Theorem, is the basic Euclidean geοmetry relationship between a right triangle's three sides. Accοrding to this rule, the area of a square with the hypotenuse side equals the sum οf the areas of squares with the other twο sides. The Pythagοrean Theorem, often knοwn as the generic algebraic nοtation a² + b² = c², states that the square that crοsses the hypotenuse οf a right triangle οpposite the right angle equals the sum of the squares that span the sides of a right triangle.

By, Pythagοrean theorem

PR² = PQ² + QR²

PR² = 14² + 9²

PR² = 196 + 81

PR = √277

Again by Pythagorean theorem

c² - a² = b²

18² - 14² = b²

b² = 324 - 196

b = √128

b = 11.31

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Types of Goals in line with Anelisa's story:

Goal setting helps individuals focus their efforts, prioritize their time and resources, and measure their progress towards achieving their goals. In the context of career choice, goal setting can help individuals:

Challenges Anelisa experienced:

Anelisa's personal values, such as determination, resilience, and a strong work ethic, likely played a significant role in her success. These values likely gave her the motivation and drive to pursue her goals, despite the challenges she faced. Additionally, her values may have helped her stay focused on her goals, maintain her sense of purpose, and make decisions that aligned with her vision for her life.

Relationships can impact the achievement of goals in both positive and negative ways. On the positive side, supportive relationships can provide individuals with emotional support, encouragement, and practical resources that can help them achieve their goals. On the negative side, relationships can also be a source of conflict and distraction, especially if they are not aligned with the individual's goals or values.

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Answer:

Step-by-step explanation:

lack of financial stability Nd resoouces

Answer:

[tex]10\sqrt{7}+8\sqrt{2}[/tex]

Step-by-step explanation:

Lets simplify.

[tex]3\sqrt{28}+4\sqrt{7} +2\sqrt{32}[/tex]

Rewrite [tex]28[/tex] as [tex]2^2*7[/tex]

[tex]3\sqrt{2^2*7}+4\sqrt{7} +2\sqrt{32}[/tex]

Pull terms out from under the radical.

[tex]3\left(2\sqrt{7} \right)+4\sqrt{7} +2\sqrt{32}[/tex]

[tex]6\sqrt{7} \right)+4\sqrt{7} +2\sqrt{32}[/tex]

Add [tex]6\sqrt{7}[/tex] and [tex]4\sqrt{7}[/tex].

[tex]10\sqrt{7} +2\sqrt{32}[/tex]

Rewrite [tex]32[/tex] as [tex]4^2*2[/tex].

[tex]10\sqrt{7} +2\sqrt{4^2*2}[/tex]

Pull terms out from under the radical.

[tex]10\sqrt{7}+2\left(4\sqrt{2}\right)[/tex]

[tex]10\sqrt{7}+8\sqrt{2}[/tex]

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The mean for this population is 55. The variance and standard deviation for this population are 94.8 and 9.74

The data is given for five families and their children are tested to see how many words they can speak in Swahili.

Toddler     Number of words(X)        X - M         (X - M)²

   A                        47                          - 8                64

   B                        73                           18               324

   C                        56                            1                  1

   D                        46                          -9                 81

   E                        53                          -2                  4

                                                                              424

Mean of the population(M) = (∑X)/n

                                             = (47 + 73 + 56 + 46 + 53)/5

                                             = 275/5 = 55

Variance f population (σ²) = (X - M)²/n = 474/5 = 94.8

Standard deviation of population(σ) = √94.8 = 9.74

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The values that make the inequality true are -5, -2, 0, 2, 2.9, 2.99 and 2.999.

An inequality is a relationship that makes a non-equal comparison between two numbers or other mathematical expressions e.g 2x > 4

Since the inequality is a < 3. Thus, any value that is less than 3 will make the inequality true.

Therefore, the values are -5, -2, 0, 2, 2.9, 2.99 and 2.999.

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From the provided graph, Due to the greater impact of the internet on education and news, PPF on the x-axis (education and news axis) moves more than the shift on the y-axis.

Mathematicians use graphs to lοgically convey facts or values using visual representations or charts. A graph pοint will typically reflect a relationship between two or more things. Nοdes, or vertices, and edges make form a graph, a nοn-linear data structure. Glue together the nodes, often referred tο as vertices. This graph has vertices V=1, 2, 3, 5, and edges E=1, 2, 1, 3, 2, 4, and (2.5), (3.5), (4.5). Statistical charts (bar charts, pie charts, line charts, etc.) graphical representatiοns of expοnential growth. a lοgarithmic graph in the shape of a triangle.

Assume that in the "οld PPF," which existed befοre the internet, equal amounts of news, educatiοn, and other commodities and services are generated.

Due to the greater impact οf the internet on education and news, PPF on the x-axis (education and news axis) moves mοre than the shift on the y-axis.

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9.19% of the total is made up of Green.

The percentage formula is dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

Number of green cars = 120

Number of green planes = 250

Number of green trains = 500

Total = 870

Now,

The total number of all colors of the car, plane, and train.

= 870 + 1250 + 820 + 800 + 990 + 4730

= 9460

Now,

The percentage of green cars, planes, and trains.

= 870/9460 x 100

= 9.19%

Thus,

9.19% of the total is made up of Green.

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Answer:

18x+9

Step-by-step explanation:

Answer: 18x + 9

Step-by-step explanation:

1) Combine like terms 23x -5x to get a new equation of 18x + 9.

The solution of inequalities is (1.714 , 4.857).

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

Given:

y > 4x-2

2y-x ≤ 8

Now, solving the inequalities.

y > 4x-2 is given by purple region and 2y-x ≤ 8 is shown by Grey region.

The two lines of inequalities intersect at (1.714 , 4.857).

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Answer:

...here is the answer...

Answer:

∠ a = 30° , ∠ b = 90°

Step-by-step explanation:

∠ a and 150° are a linear pair and sum to 180° , that is

∠ a + 150° = 180° ( subtract 150° from both sides )

∠ a = 30°

------------------

the sum of the 3 angles in a triangle = 180° , that is

∠ b + ∠ a + 60° = 180°

∠ b + 30° + 60° = 180°

∠ b + 90° = 180° ( subtract 90° from both sides )

∠ b = 90°

Answer:

44 in^2

Step-by-step explanation:

V = L×W×H

Bottom rectangle prism

L= 6 W= 4 H= 1

V = 6×4×1

V=24

Top rectangle prism

L= 2 W= 2 H= 5

V=2×2×5

V= 20

Add both of the rectangle prisms

24+25= 44

Answer:

Step-by-step explanation:

The function f(x) = |x − 1| is a absolute value function that calculates the distance of a number x from the number 1 on the number line. On the number line, numbers to the left of 1 are negative and numbers to the right of 1 are positive.

To find the value of f(x), we first subtract 1 from x to find the distance between x and 1. If the result is positive, then x is to the right of 1 and the absolute value of the result is equal to the distance. If the result is negative, then x is to the left of 1 and the absolute value of the result is equal to the distance.

For example, let's find f(-5):

f(-5) = |-5 - 1| = |-6| = 6

The interpretation of f(-5) is that the number -5 is a distance of 6 units away from the number 1 on the number line.

Now let's find f(3):

f(3) = |3 - 1| = |2| = 2

The interpretation of f(3) is that the number 3 is a distance of 2 units away from the number 1 on the number line.

The domain of the function is all real numbers. The range of the function is all non-negative real numbers.

A. The firm's short-run total cost curve can be calculated as TC = 2K + 4L. The short-run average cost curve function will be SAC = TC/Q, where Q is the output.

B. The firm's short-run marginal cost function is MC = 4/Q. The short-run total cost (STC) at 25 and 200 levels of output will be 800 and 2400 respectively. The short-run average cost (SAC) at 25 and 200 levels of output will be 32 and 12 respectively. The short-run marginal cost (SMC) at 25 and 200 levels of output will be 16 and 8 respectively.

C. The graph of the SAC and SMC curves is shown below.

SAC and SMC Graph

D. The SMC curve intersects the SAC curve at its lowest or minimum point because at this point, the SAC curve is at its most cost-efficient level, meaning that the firm's costs are minimized. This is because at this point, the marginal cost is lower than the average cost, meaning that the firm can produce additional units of output with a decreasing cost.

The transformations taking place in the given function is a horizontal left ward shift of 9 units and 1 unit upward vertical shift.

A Transformation in Math is a process of moving an object (two-dimensional shape) from its original position to a new position.

Given that, a function f(x) undergo some transformations to become f(x+9)-1,

We know that,

Vertical Shifting:

Adding a constant to a function will shift its graph vertically (i.e. y = f (x) + c). Adding a positive constant c will shift the graph upward c units, while adding a negative constant c will shift it downward c units.

Horizontal Shifting:

Horizontal shifts are inside changes that affect the input (x-) axis values and shift the function left or right. Combining the two types of shifts will cause the graph of a function to shift up or down and right or left.

Therefore, there is transformation of a horizontal and vertical shift.

Hence, the transformations taking place in the given function is a horizontal left ward shift of 9 units and 1 unit upward vertical shift.

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Answer:

Below

Step-by-step explanation:

The exterior angles for any polygon  sum to 360 °

so

 6 * n   = 360 °     <=====  where 'n' is the number of sides

 n = 60   sides