What is the domain of the function f(x)=2x^2+5x-12

The height of the picture frame rounded to the nearest tenth is 13.4 inches.

In order to determine the height of the picture frame, we would have to apply Pythagorean's theorem.

In Mathematics and Geometry, Pythagorean's theorem is represented by the following mathematical equation (formula):

x² + y² = z²

Where:

x, y, and z represents the length of sides or side lengths of any right-angled triangle.

By substituting the side lengths of this rectangle, we have:

z² = x² + y²

18² = 12² + y²

324 = 144 + y²

y² = 324 - 144

y² = 180

y = √180

y = 13.4 inches.

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(a) The net force exerted on the test charge q by the two 2.00μC charges is 0 N.

(b) The electric field at the origin due to the two 2.00μC charges is 0 N/C.

(c) The electric potential at the origin due to the two 2.00μC charges is 0 V.

(a) To find the net force exerted on the test charge q, we need to calculate the individual forces between the charges and q using Coulomb's law. Coulomb's law states that the force between two charges is given by the equation:

\(\[F = \dfrac{k \cdot |q_1 \cdot q_2|}{r^2}\]\)

where F is the force, k is the electrostatic constant (k ≈ 9.0 × 10^9 N·m^2/C^2), \(q_1\) and \(q_2\) are the charges, and r is the distance between the charges.

Let's denote the charge at x = 0.8 m as \(q_1\) and the charge at x = -0.8 m as \(q_2\). The distances between the charges and the test charge q are 0.8 m and -0.8 m, respectively.

Calculating the forces:

\(\[F_1 = \dfrac{k \cdot |2.00\mu C \cdot 1.28\times10^{-18} C|}{(0.8m)^2}\]\)

\(\[F_2 = \dfrac{k \cdot |2.00\mu C \cdot 1.28\times10^{-18} C|}{(-0.8m)^2}\]\)

Substituting the values and evaluating the expressions:

\(\[F_1 = \dfrac{(9.0\times10^9 N \cdot m^2/C^2) \cdot (2.00\times10^{-6} C) \cdot (1.28\times10^{-18} C)}{(0.8 m)^2}\]\)

\(\[F_2 = \dfrac{(9.0\times10^9 N \cdot m^2/C^2) \cdot (2.00\times10^{-6} C) \cdot (1.28\times10^{-18} C)}{(-0.8 m)^2}\]\)

Simplifying the expressions:

\(\[F_1 = 2.304 N\]\)

\(\[F_2 = -2.304 N\]\)

The net force, \(F_{net}\), is the vector sum of these forces:

\(\[F_net = F_1 + F_2 = 2.304 N - 2.304 N = 0 N\]\)

Therefore, the net force exerted on the test charge q by the two 2.00μC charges is 0 N.

(b) The electric field at the origin due to the two 2.00μC charges can be calculated by dividing the net force by the magnitude of the test charge q. Using the formula:

\(\[E = \dfrac{F_net}{|q|}\]\)

Substituting the values:

\(\[E = \dfrac{0 N}{1.28\times10^{-18} C}\]\)

Simplifying the expression:

\(\[E = 0 N/C\]\)

Therefore, the electric field at the origin due to the two 2.00μC charges is 0 N/C.

(c) The electric potential at the origin due to the two 2.00μC charges can be found using the formula:

\(\[V = \dfrac{k \cdot (q_1/r_1 + q_2/r_2)}{|q|}\]\)

Substituting the values:

\(\[V = \dfrac{(9.0\times10^9 N \cdot m^2/C^2) \cdot [(2.00\mu C/0.8 m) + (2.00\mu C/-0.8 m)]}{1.28\times10^{-18} C}\]\)

Simplifying the expression:

\(\[V = 0 V\]\)

Therefore, the electric potential at the origin due to the two 2.00μC charges is 0 V.

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Rounding to the nearest thousand, the population after 11 years will be 742,000.

What is exponential growth ?

Exponential growth is a mathematical concept that describes a process in which the quantity or size of something increases at a constant rate proportional to its current value. In other words, exponential growth occurs when a quantity grows at an increasing rate over time, so that the amount of growth is itself growing exponentially.

For example, if a population of bacteria doubles every hour, then the rate of growth is proportional to the current population size, and the population will grow exponentially over time. Exponential growth can also occur in financial investments, where the interest earned on an investment is reinvested and earns additional interest, leading to exponential growth in the value of the investment.

According to the question:
a. We can use the formula for exponential growth to write an exponential function that represents the population after t years:

\(y = ab^t\)

where y is the population after t years, a is the initial population, b is the growth factor, and t is the time in years.

Since the population y increases by 5% each year, the growth factor b is 1 + r, where r is the growth rate expressed as a decimal. In this case, r = 5% = 0.05, so b = 1 + 0.05 = 1.05.

The initial population a is 435,000, so we have:

\(y = 435,000(1.05)^t\)

b. To find the population after 11 years, we substitute t = 11 into the exponential function we found in part a:

\(y = 435,000(1.05)^{11}\)

Using a calculator, we get:

y ≈ 741,536.72

Rounding to the nearest thousand, the population after 11 years will be 742,000.

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Answer:

4 avocados

Step-by-step explanation:

$3.74/$0.89 = 4.2, but you can't have 4.2 avocados so you round down to 4

The sides of the quadrilateral arranged from longest to shortest are CD, AB, DA, and BC.

We have,

To arrange the length of the sides of the quadrilateral from longest to shortest, we need to calculate the length of each side of the quadrilateral using the distance formula:

Distance Formula:

If (x1, y1) and (x2, y2) are two points in a plane, then the distance between them is given by:

d = √((x2 - x1)² + (y2 - y1)²)

Using the distance formula, we can calculate the length of each side of the quadrilateral as follows:

AB = √((4 - (-5))² + (5 - 5)²) = 9

BC = √((2 - 4)² + (0 - 5)²) = √(29)

CD = √((-5 - 2)² + (-2 - 0)²) = √(74)

DA = √((-5 - (-5))² + (5 - (-2))²) = 7

Therefore,

The sides of the quadrilateral arranged from longest to shortest are CD, AB, DA, and BC.

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The legend chart element will tells the category of data that each line represents the lines.

Lines:

Lines refers a one-dimensional figure, which has length but no width.

Given,

suppose that a line chart includes several lines.

Here we need to identify the chart element will tell you the category of data that each line represents.

Basically, chart is a visual representation of numeric data in a worksheet. And it helps you to identify trends, make comparisons, and recognize patterns in the numbers.

In order to get the clear information that appears in your chart, you can add a chart title, axis titles, and data labels.

The element legend or data table is used to represents the category of the data.

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Answer:

Given a function f, a new function g ( x ) = f ( x − h ) \displaystyle g\left(x\right)=f\left(x-h\right) g(x)=f(x−h), where h is a constant, is a horizontal shift of the function f. If h is positive, the graph will shift right. If h is negative, the graph will shift left.

Step-by-step explanation:

Answer:

1.4375

Step-by-step explanation:

\(\frac{10 + (2 x 3)^{2} / (4)(1)}{2^{3}} \\\)

\(\frac{10 + (6)^{2} /4}{8} \\\)

\(\frac{10 + 36 / 4}{8} \\\)

\(\frac{46 /4}{8} \\\) = \(\frac{11.5}{8} \\\)

C) the equation can be written as:y = mx + b. D) The slope can be interpreted as a measure of the association between the use of marijuana and other drugs.

c) Write the equation you would use to estimate the percentage of teens who use Other Drugs from the percentage who have used Marijuana.The equation to estimate the percentage of teens who use Other Drugs from the percentage who have used Marijuana is given by the formula:y = mx + bwhere y represents the estimated percentage of teens who use Other Drugs and x represents the percentage of teens who have used Marijuana.

The slope, m, represents the proportion of teens who have used other drugs after using marijuana, and b represents the percentage of teens who use Other Drugs when the percentage who have used Marijuana is 0.

Therefore, the equation can be written as:y = mx + b

Where x represents the percentage of teens who have used Marijuana, m represents the proportion of teens who have used other drugs after using marijuana, and b represents the percentage of teens who use Other Drugs when the percentage who have used Marijuana is 0.

d) Explain in context what the slope of this line means.The slope of this line represents the proportion of teens who have used other drugs after using marijuana. That is, if a certain percentage of teens have used marijuana, the slope of the line estimates the percentage of teens who have used other drugs.

In other words, the slope indicates how much more likely teens are to use other drugs after using marijuana. A positive slope would indicate that more teens use other drugs after using marijuana, while a negative slope would indicate that fewer teens use other drugs after using marijuana.

The slope can be interpreted as a measure of the association between the use of marijuana and other drugs.

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Answer:

1.94 mm

Step-by-step explanation:

V = pi(r^2)h

V/pi(h) = r^2

r = sqrt(V/pi(h))

r = sqrt(200/pi(17))

r = 1.94 mm

Answer:

To solve the given system of equations using the substitution method, we need to solve one equation for one variable and then substitute that expression into the other equation for that same variable. Let's solve the second equation for y.

-x + y = 4

y = x + 4

Now we can substitute this expression for y into the first equation and solve for x.

-2x + 2(x + 4) = 7

-2x + 2x + 8 = 7

8 = 7

The equation 8 = 7 is not true, which means the system of equations has no solution. We can see this visually by graphing the two lines. They are parallel and will never intersect, which means there is no point that satisfies both equations.

Therefore, the solution to the system of equations is "No solution."

Note: Please be sure to double-check your work to avoid mistakes.

Step-by-step explanation:

Hope this helps you!! Have a wonderful day/night!!

Answer:

x < -7/6

Step-by-step explanation:

In a equation that show a greater than or less than sign can be a equal sign .

Answer:

Begin by finding the area of the square, 24x22. This would equal 528. Then, we need to find the area of each circle using the area formula, \(\pi\)\(r^{2}\). We can plug in the numbers to get \(\pi\)\(3^{2}\). Multiply 3x3 to get 9\(\pi\). Because there are 4 circular burners, we need to multiply 9\(\pi\) by 4 to get 36\(\pi\) or 113.04. Now, we can subtract 528 with 113.04 to result with 414.96 or 415, when rounded. So, the answer would be 415 \(in.^{2}\)

The area of the shaded sector is 4π square units.

To find the area of the shaded sector, we need to calculate the central angle formed by the sector. In this case, we are given that the angle JIK is 90 degrees, which means it forms a quarter of a full circle.

Since a full circle has 360 degrees, the central angle of the shaded sector is 90 degrees.

Next, we need to determine the radius of the circle. The line segment IJ represents the radius of the circle, and it is given as 4 units.

The formula to calculate the area of a sector is A = (θ/360) * π * r², where θ is the central angle and r is the radius of the circle.

Plugging in the values, we have A = (90/360) * π * 4².

Simplifying, A = (1/4) * π * 16.

Further simplifying, A = (1/4) * π * 16.

Canceling out the common factors, A = π * 4.

Hence, the area of the shaded sector is 4π square units.

Therefore, the area of the shaded sector, expressed as a fraction times π, is 4π/1.

In summary, the area of the shaded sector is 4π square units, or 4π/1 when expressed as a fraction times π.

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The fan blades will have rotated 180 degrees when vertex D reaches the point where vertex C is now.

When the two fan blades in the shape of equilateral triangles rotate clockwise around point P, the vertex D will reach the point where vertex C is now.
To determine the number of degrees the blades will have rotated, we need to know the number of degrees in a full rotation. A full rotation consists of 360 degrees.
Since both blades rotate together, they will cover the same number of degrees. Therefore, when vertex D reaches the point where vertex C is now, the blades will have rotated by half of a full rotation, which is 180 degrees.

In summary, the fan blades will have rotated 180 degrees when vertex D reaches the point where vertex C is now.

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Steps to solve:

-(1 + 4x) = 4(1 - x) - 5

~Distribute both sides

-1 - 4x = 4 - 4x - 5

~Combine like terms on the left side

-1 - 4x = -1 - 4x

~Add 4x to both sides

-1 = -1

~Add 1 to both sides

0 = 0

Therefore, all real numbers are solutions.

Best of Luck!

The coordinates of the meeting place are approximately (-4.3, -4.3).

Option D is the correct answer.

We have,

Now,

Midpoint between cities A and B:

(((-16+1)/2), ((-1+6)/2)) = (-7.5, 2.5)

Midpoint between cities A and C:

(((-16+1)/2), ((-1-18)/2)) = (-7.5, -9.5)

Midpoint between cities B and C:

(((1+1)/2), ((6-18)/2)) = (1, -6)

Now we can find the intersection of the three lines formed by these midpoints.

One way to do this is to use the point-slope form of the equation of a line.

y - y1 = m(x - x1)

where (x1, y1) is a point on the line and m is the slope of the line.

The line passing through (-7.5, 2.5) and (-7.5, -9.5):

x = -7.5

The line passing through (-7.5, 2.5) and (1, -6):

y = (-8/9)x + 35/9

The line passing through (-7.5, -9.5) and (1, -6):

y = (3/5)x - 33/5

Solving for the intersection of these lines.

x = -4.3

y = -4.3

Therefore,

The coordinates of the meeting place are approximately (-4.3, -4.3).

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The income statement should include all sources of revenue and deduct all applicable expenses to calculate the net income or loss for the period. To create a balance sheet gather information about the company's assets, liabilities, and shareholders' equity as of that specific date. To determine whether there has been an increase or decrease compare the net income figure from a previous period with the net income figure from the current period

1) To prepare a projected income statement for the year ending November 20, sora, you would need to gather information about the revenues and expenses expected during that period. The income statement should include all sources of revenue and deduct all applicable expenses to calculate the net income or loss for the period.

2) To create a balance sheet as of November 30, 2oya, you will need to gather information about the company's assets, liabilities, and shareholders' equity as of that specific date. The balance sheet provides a snapshot of the company's financial position, showing what it owns, owes, and the remaining equity.

3) To determine whether there has been an increase or decrease in the amount of net income, you would need to compare the net income figure from a previous period (presumably November 20, sora) with the net income figure from the current period (ending November 30, 2oya). If the net income has increased, it means the company has generated more profit during the current period compared to the previous one. Conversely, if the net income has decreased, it indicates a decline in profitability.

Overall, the task involves preparing a projected income statement and balance sheet and analyzing the change in net income to assess the company's financial performance.

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Answer:

\({ \tt{ {27}^{3} \times {9}^{2} \times 3 }} \\ = { \tt{ {3}^{3} \times {3}^{2} \times {3}^{1} }} \\ = { \tt{ {3}^{(3 + 2 + 1)} }} \\ { \tt{ = {3}^{6} }}\)

Given:

The distance y (in meters) that runner A travels on a track in x minutes is represented by the equation

\(y=130x\)

To find:

How many meters per minute is runner A traveling.

Solution:

We have,

\(y=130x\)            ...(i)

Where, y is the distance in meters and traveling x minutes.

We need to find the slope of the above equation to find the number of meters  traveling by the runner per minute.

The slope intercept form of a line is:

\(y=mx+b\)           ...(ii)

Where, m is the slope and b is the y-intercept.

On comparing (i) and (ii), we get

\(m=130\)

Therefore, the runner is traveling 130 meters per minute.

Answer:

first blank: 15

second blank: 90

Step-by-step explanation:

Obviously, sin and cos are related, but they are not the same thing. In order for them to be equal:

sin(____) = cos(75)

the angles have to add up to 90 (complementary)

What + 75 is 90?

Do a tiny calc:

90 - 75 is 15

The second question is stating the rule generically.

x + (90 - x) is 90

Answer:

V = pi*r^2*h

V = 150 m^3

h = 8 m

150 = pi*r^2*8

Solve for r (the radius) then multiply by 2 to obtain the diameter.Only, this is a cone, not a cylinder.

V = 1/3 pi r^2 h

Diameter of the cone is 15 m. So, option D is correct.

Solid shapes are defined as the three-dimensional objects that are described by the three dimensions length, breadth and height.

Here,

Volume of the cone is given by,

 V = 150\(\pi\) m³

Height of the cone, h = 8 m

We know, the equation for the volume of a cone is,

V = 1/3\(\pi\)r²h

where r is the radius and h is the height of the cone.

So,

(1/3) \(\pi\)r²h = 150\(\pi\)

r²x 8 = 3 x 150 = 450

r² = 450/8

r² = 56.25

r = 7.5 m

Therefore, diameter of the cone,

d = 2r

d = 2 x 7.5

d = 15 m

Hence,

Diameter of the cone is 15 m.

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Answer:

a=9/3,b=15/2 using some postulate you will get answer like sss,sas,aa.

Answer:

60

Step-by-step explanation:

The given function is:

The average rate of change of h(t) from t=a to t=b is given by:

We can rewrite this function as:

The maximum height of the rocket is 231 and it occurs at t=3.75

The initial launch occurs at: t=0

and

The average rate of change from the initial launch to the maximum height is

The average rate of change from the initial launch to the maximum height is 59.21 ft/s.

We have a equation that represents the Rocket path.

We have to find the average rate of change from the initial launch to the maximum height.

A time varying quantity is the quantity whose absolute value change with time. For example - y = f(t) = 2t - 1 , where y is the displacement and it varies as y = 2t - 1 with time.

According to the question, we have -

Equation →  \(h(t) = -16t^{2} +120t+6\)

Height of podium → 6 feet.

Initial velocity (u) = 0

Now -

\(h(t) = - 16t^{2} +120t+6\)

Differentiating w.r.t time, we get →

\($\frac{dh}{dt} = - 32t + 120\)

For maximum height → \($\frac{dh}{dt} = 0\)

-32t + 120 = 0

32t = 120

t = 3.8 seconds

This means that at t = 3.8 seconds the rocket will reach its maximum height. Therefore, the maximum height will be -

h(t) = - 16 x 3.8 x 3.8 + 120 x 3.8 + 6

h(t) = - 231.04 + 456 + 6

h(t) = 224.96 + 6

h(t) = 230.96 = 231

The maximum height reached by the rocket is 231 feet's.

Now -

Initial height = 6 feet

Initial time = 0 s

Final height (max) = 231

Time at maximum height = 3.8

Therefore, the average rate of change from the initial launch to the maximum height will be -

\($v_{avg} = \frac{231-6}{3.8-0}=59.21\)

v (avg) = 59.21 ft/s

Hence, the average rate of change from the initial launch to the maximum height is 59.21 ft/s

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Answer:

it could either be 8C or -2C

Step-by-step explanation:

Answer:

Step-by-step explanation:

If it is 3c and it changes to 5c, then that means it increased.

Answer: -2c

nearly 3 pounds of salmon she bought spending $19.32.

What is division?

A division is one of the fundamental mathematical operations that divides a larger number into smaller groups with the same number of components. How many total groups will be established, for instance, if 20 students need to be separated into groups of five for a sporting event? The division operation makes it simple to tackle such issues. Divide 20 by 5 in this case. 20 x 5 = 4 will be the outcome. There will therefore be 4 groups with 5 students each. By multiplying 4 by 5 and receiving the result 20, you may confirm this value.

At the neighborhood grocery 0. 5 pounds of salmon cost $3. 45

So in $1 she will get 0.5/3.45 pound

For 19.32 she will be get = 0.5/3.45 * 19.32  = 2.8 pounds

Hence, nearly 3 pounds of salmon she bought spending $19.32.

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Answer:

The proof of Pythagorean Theorem in mathematics is very important. In a right angle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. States that in a right triangle that, the square of a (a²) plus the square of b (b²) is equal to the square of c (c²).

Answer: 3(x+4)

Step-by-step explanation:

Let's start with what we know. To factor problems, we just find a common divisor. Here, the common divisor is 3 so:

3(x+4)

The statement "the San Gabriel Mountains are 60 miles lengthy, 24 miles wide, and more or less 10,000 feet high (at their highest)" is true.

The San Gabriel Mountains are a mountain range positioned in Southern California, walking east-west across los angeles County. They stretch for approximately 60 miles from the Cajon bypass inside the east to the San Fernando Valley inside the west and are around 24 miles wide.

The best peak within the range is Mount San Antonio, also referred to as Mount Baldy, that is kind of 10,000 ft high. The San Gabriel Mountains are a famous destination for out of doors sports consisting of hiking, camping, and snowboarding, and are an vital supply of water for the los angeles place.

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