Enter the value for x that makes the equation-36-3x - 18 = 7 + 4x -19 true.

The product of the given polynomials is -2x² + 5x - 2.

Given two polynomial functions, f(x) and g(x).

f(x) = 2x - 1 and g(x) = -x + 2

We have to find the product of these polynomials.

Numerically, we can find the area as,

f(x) g(x) = (2x - 1) (-x + 2)

            = -2x² + x + 4x - 2

            = -2x² + 5x - 2

Area model can be done by drawing a rectangle and then marking the length of the rectangle as 2x - 1 and the width of the rectangle as -x + 2.

Area of the rectangle = length × width                                                                                                      

Hence the product of the given polynomials is -2x² + 5x - 2.

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The solution of the system of equations is (0, 3).

The correct option is B.

The elimination method is one of the techniques to solve the system of linear equations.

Given

The system of equations is;

\(\rm 4x+2y=66\\\\x-4y=-12\)

Solving the equation by using the elimination method.

Multiply equation 1 by 4

\(\rm 4x+2y=6\\\\ 16x+8y=24\)

Multiply equation 2 by 2

\(\rm 6x-4y=-12\\\\12x-8y=-24\)

Adding both the equations

\(\rm 16x+8y+12x-8y=24-24\\\\ 28x=0\\\\x=0\)

Substitute the value of x in equation 1

\(\rm 4x+2y=6\\\\4(0)+2y=6\\\\2y=6\\\\y=\dfrac{6}{2}\\\\y=3\)

Hence, The solution is (0, 3).

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To determine the number of gallons of paint needed to cover office 143, we need to know the square footage of the office.

Once we have that information, we can divide the square footage by the coverage rate per gallon to calculate the required amount of paint.

Let's assume the square footage of office 143 is 800 square feet.

Number of gallons needed = Square footage / Coverage rate per gallon

Number of gallons needed = 800 square feet / 50 square feet per gallon

Number of gallons needed = 16 gallons

Therefore, you would need approximately 16 gallons of paint to cover office 143, assuming each gallon covers 50 square feet.

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There are 40 different ways to perform a symphony and then a piano concerto.

To find how many ways are there to play first a symphony and then a piano concerto:

Therefore, 40 ways are there to play first a symphony and then a piano concerto

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Answer:

C: People who came to California looking for gold in 1849.

Step-by-step explanation:

Answer:

People who came to California looking for gold in 1849.

Answer:

X= -22/9 which also equals to -2.4444444 ( repeating )

Step-by-step explanation:Step 1: Simplify both sides of the equation.

45(2x+5)−4=1

(45)(2x)+(45)(5)+−4=1(Distribute)

90x+225+−4=1

(90x)+(225+−4)=1(Combine Like Terms)

90x+221=1

90x+221=1

Step 2: Subtract 221 from both sides.

90x+221−221=1−221

90x=−220

Step 3: Divide both sides by 90.

90x/90

=

−220/90

x= −22/9

Hoped I could help-

Sleepy~

Answer:

-2.44

Step-by-step explanation:

90x+225-4=1

90x+221=1

90x=1-221

90x=-220

x=-220/90

x=-2.44 \(Ans\)

Statisticians calculate the Consumer Price Index (CPI) by combining the 80,000 prices of individual products using a weighted average based on their relative importance or expenditure weights.

The Consumer Price Index is a measure of the average change over time in the prices paid by urban consumers for a basket of goods and services. To calculate the CPI, statisticians collect price data for a representative sample of approximately 80,000 individual products that are commonly purchased by urban consumers. These products cover a wide range of categories, including food, housing, transportation, healthcare, and more.

Each product's price is then multiplied by its respective expenditure weight, which represents the proportion of total consumer spending allocated to that product. These weights are determined through surveys and data analysis to reflect the typical spending patterns of urban consumers. The resulting values are then summed up to obtain a total expenditure amount.

To calculate the CPI, statisticians divide the total expenditure by a base period expenditure and multiply the result by 100. The base period is typically a reference point or benchmark year against which the price changes are measured. This process allows for tracking and comparing price changes in the basket of goods and services over time, providing insight into inflation and changes in the cost of living.

In summary, statisticians calculate the Consumer Price Index by combining the prices of 80,000 individual products using a weighted average based on their expenditure weights, representing the relative importance of each product in urban consumers' spending patterns. This method allows for measuring and monitoring changes in the overall price level and cost of living.

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Answer:

Option D. is correct.

Step-by-step explanation:

Let us assume that x = seven square root three plus two square root nine  

i.e. x = 7√3 + 2√9

⇒ x = 7√3 + 2 × 3 {Since 9 = 3²}

⇒ x = 7√3 + 6

Here, 7√3 is an irrational number and 6 is a rational number.

The answer is seven square root of three plus six is irrational because the sum of a rational number and an irrational number is an irrational number.

Therefore, option D. is correct.

The correct answer is  7√3 + 6 is irrational because the sum of a rational number and an irrational number is an irrational number.

Rational numbers are numbers which can be written in the form of \(\dfrac{a}{b}\) where a and b are integers. Example: 1/2, 3.5 (which is writable as 7/5) etc.

Irrational numbers are those real numbers which are not rational numbers.

Assume that x be the seven square root three plus two square root nine ;

i.e. x = 7√3 + 2√9

Now

⇒ x = 7√3 + 2 × 3 {Since 9 = 3²}

x = 7√3 + 6

Here, we can see that 7√3 is an irrational number and 6 is a rational number.

The correct answer is seven square root of three plus six is irrational because the sum of a rational number and an irrational number is an irrational number.

Therefore, option D is correct.

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To find the equation of a parabola given its focus and directrix, we use the standard form of the equation of a parabola which is:

\(\frac{(y-k)^2}{4a} = x-h\)

Where (h,k) is the vertex of the parabola, and a is the distance between the vertex and the focus (or between the vertex and directrix, they're equal).

Therefore, the answer is option D, (y-3)²-4(x-3).

Using this formula, let's first find the vertex of the parabola. Since the directrix is a horizontal line, the vertex lies halfway between the focus and directrix on the y-axis. Thus, the vertex is at (3,3).

Since the focus is above the vertex, a is positive, and its value is the distance between the vertex and focus:

a = 4 - 3

= 1

Substituting these values into the standard form of the equation of a parabola gives:

\(\frac{(y-3)^2}{4(1)} = x - 3$$\)

\(\frac{(y-3)^2}{4} = x - 3$$\)

Multiplying both sides by 4 gives:

y - 3 = 2(x - 3)

y = 2x - 3

Therefore, the answer is option D, (y-3)²-4(x-3).

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Thee factory is able to provide 94.38 boxes per hour to the warehouse.

Rate = (2000 - 1245) / 8 = 94.38 boxes per hour

Therefore, the factory is able to provide 94.38 boxes per hour to the warehouse.

Boxes added in 40 hours = rate * time = 94.38 * 40 = 3,775.2

Therefore, the inventory at the end of a 40-hour work week would be:

1245 + 3775.2 = 5020.2 boxes

rate = (50000 - 1245) / time

Simplifying this equation, we get:

time = (50000 - 1245) / rate = 511.64 hours (rounded to two decimal places).

Therefore, it will take approximately 511.64 hours to fill the warehouse to its 50,000 box capacity,

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Step-by-step explanation:

From the figure it is clear that:

x+110°=180

x=180-110

x=70

For y:

the left exterior angle of line q is also70.

By the definition of alternate exterior angle:

y=70

Note:if you need to ask any question please let me know.

Answer:

Options (1), (2) and (5) are true.

Step-by-step explanation:

Option (1). m∠1 = (2x + 10)°

lines c and d are the parallel lines and t is a transverse.

Therefore, m∠1 = (2x + 10)° [corresponding angles]

This option is true.

Option (2). m∠3 = 87°

Since ∠3 and angle having measure equal to 87° are the vertical angles therefore, both the angles will be equal in measure.

This option is true.

Option (3). m∠2 = (2x + 10 + 5x - 1)°

m∠2 = (5x - 1)° [Since both the angles are interior alternate angles]

Therefore, this option is not true.  

Option (4). m∠1 + m∠2 = m∠3

(5x - 1) + (2x + 10) + 87 = 180° [Sum of liner angles at a point is 180°]

7x + 96 = 180

7x = 180 - 96

x = \(\frac{84}{7}\)

x = 12

Therefore, m∠1 = (2x + 10) = 34°

                 m∠2 = (5x - 1) = 59°

                 m∠3 = 87°

For the given relation,

m∠1 + m∠2 = m∠3

34 + 59 = 87

93 = 87

Not true.

Therefore, this option is not correct.

Option (5). 87 + 2x + 10 + 5x - 1 = 180°

True.

Since these angles are the linear angles so the sum of all angles = 180°

Therefore, the given option is correct.

Options (1), (2) and (5) are the true.

Answer:

answer 1 2 and 5

Step-by-step explanation:

right on edge

Answer:that would be

7w-3

Step-by-step explanation:

4

cause then 12-6=6

You do parenthesis first and get six, then you subtract

Answer:

B i think

Step-by-step explanation:

Sorry if wrong

Illinois city-to-airport distances can be discovered using a distance spatial join. The utilized unit is while linear measurements utilize meters or feet, angular units for measurement use degrees.

A system called a geographic information system (GIS) is one that collects, organizes, processes, and maps all kinds of data.

Illinois city-to-airport distances can be discovered using a distance spatial join.

Thus, the utilized unit is while linear measurements utilize meters or feet, angular units for measurement use degrees.

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Answer:

A; D

Step-by-step explanation:

The first is mostly because of the slope is larger so i guessed-sorry-

The second one, domain is x and range is y.

Answer:

60 cm ( squared )

Step-by-step explanation:

you can find the area of the trapezoid ( by decomposing it into other shapes ) by separating two triangles, and using the formula to find the area of triangles, which is A= 1/2 ( b x h ) and add the answer to those together ( 16 cm squared and 4 cm squared ), and after that, you can find the area to the rectangle by multiplying the l x w, which is 10 x 4 ( after separating the triangles.). That equals 40, and when you add them all together ( 16 + 4 + 40 ) it equals 60 cm (squared).

Answer:

Sophie in 9 days and Susan in 12 days

Step-by-step explanation:

This question is very vague and the answer in clearly in front of your eyes.

The average value of F(x, y, z) = z over the region bounded below by the xy-plane, on the sides by the sphere \(x^2 + y^2 + z^2 = 36\), and bounded above by the cone ϕ = (pi/3) is -ρ\(^4 / 2304.\)

To find the average value of the function F(x, y, z) = z over the given region, we need to compute the triple integral of F(x, y, z) over the region and divide it by the volume of the region.

The region is bounded below by the xy-plane, on the sides by the sphere \(x^2 + y^2 + z^2 = 36\), and bounded above by the cone φ = (π/3).

In spherical coordinates, the sphere can be represented as ρ = 6, and the cone can be represented as φ = (π/3).

To set up the integral, we need to determine the limits of integration for each variable. Since the region is symmetric with respect to the xy-plane, we can integrate over one-half of the region and multiply the result by 2.

Let's integrate over the region in spherical coordinates:

0 ≤ ρ ≤ 6

0 ≤ φ ≤ (π/3)

0 ≤ θ ≤ 2π

The integral to compute the average value is:

2 * ∫∫∫ F(ρsin(φ)cos(θ), ρsin(φ)sin(θ), ρcos(φ)) ρ\(^2 sin\)(φ) dρ dφ dθ

Now, we substitute F(x, y, z) = z into the integral:

2 * ∫∫∫ ρcos(φ) ρ\(^2sin\)(φ) dρ dφ dθ

Evaluate the innermost integral first:

∫[0 to 6] ρ\(^3cos\)(φ)sin(φ) dρ = (1/4)ρ\(^4cos\)(φ)sin(φ)

Now, integrate with respect to φ:

∫[0 to π/3] (1/4)ρ\(^4cos\)(φ)sin(φ) dφ = (1/4)ρ\(^4[-(cos\)(φ))\(^2]\) [0 to π/3]

                                                      = (1/4)ρ\(^4(-1/4)\)

                                                      = -ρ\(^4/16\)

Now, integrate with respect to θ:

∫[0 to 2π] -ρ\(^4/16\) dθ = -ρ\(^4/16\) * 2π

                               = -πρ\(^4/8\)

Finally, we divide this result by the volume of the region to find the average value:

Volume of the region = (1/2) * Volume of the sphere

                                   = (1/2) * (4/3) * π * (\(6^3\))

                                   = 288π

Average value = (-πρ\(^4/8\)) / (288π)

                        = -ρ\(^4 / (2304)\)

Therefore, the average value of F(x, y, z) = z over the given region           is -ρ\(^4 / 2304.\)

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Answer:

34.77

Step-by-step explanation:

To reverse the order of integration in the integral i = z 8 0 z x/2 0 f(x, y) dy dx, we need to first draw the region of integration.

From the limits of integration, we see that the region is a right triangular pyramid with base in the xy-plane and height z.
To reverse the order of integration, we can integrate with respect to z first, and then with respect to x and y. Thus, the new integral becomes:
i = ∫0^8 ∫0^(2z) ∫0^x/2 f(x, y) dy dx dz
Note that we have reversed the limits of integration for x and z. This is because the limits of integration for x depend on the value of z. We have also kept the limit for y as it is since it is independent of z.
However, we have made no attempt to evaluate either integral, as requested in the question.

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Answer:

All of them are real numbers

Step-by-step explanation:

They are all considered real numbers it is a trick question. have a great day :)

It will take 16 seconds to get to your class.

\(\bold{Distance}=\bold{Speed }\times \bold{Time}\)

\(200m = 1.5m\div s \times t\)

\(24=1.5\times t\) (We want to get t by itself, so lets get rid of the \(\times1.5\) by dividing both sides by 1.5)

\(t = 16 \ \text{seconds}\)

Therefore, it will take 16 seconds to get to your class.

Answer:

x = -4

y = -1

Step-by-step explanation:

-5x+12y=8

2x-8y=0

We multiply the first equation by 2 and the second equation by 5

-10x + 24y = 16

10x - 40y = 0

-16y = 16

y = -1

Now put -1 back in for y and solve for x

-5x + 12(-1) = 8

-5x - 12 = 8

-5x = 20

x = -4

Let's check

-5(-4) + 12(-1) = 8

20 - 12 = 8

8 = 8

So, x = -4 & y = -1 is the correct answer.