A towns population has been decreasing at a constant rate. In 2010 the population was 7,900. By 2012 the population had dropped to 7,700. assume this trend continues. Identify the year in which the population will reach 0. Show work.

(a) OIne critical number that is x = 1

(b) Function is decreasing on the interval (-∞,1) and increasing on the interval (1,∞).

(c) at x = 1, this critical number corresponds to a relative minimum.

(d) The graph is given in the attachment.

The rate change of the function at a specific point

a) The values of x where the derivative of the function equals zero or does not exist.

f'(x) = -4x + 4

Setting f'(x) equal to zero gives:

-4x + 4 = 0

-4x = -4

x = 1

So the critical number is x = 1.

(b) we need to examine the sign of the derivative on either side of the critical number.

When x < 1, f'(x) is negative, indicating that the function is decreasing.

When x > 1, f'(x) is positive, indicating that the function is increasing.

Therefore, the function is decreasing on the interval (-∞,1) and increasing on the interval (1,∞).

(c) all relative extrema, we examine the sign of the derivative in the neighborhood of the critical number x = 1. Since f'(x) changes sign at x = 1, this critical number corresponds to a relative minimum.

(d) The graph is given in the attachment.

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Answer:

multiply all of them then add all of them then divide by the lowest number

12:1 is the scale factor

3.5 ÷ 3.5 = 1 and 142 ÷ 3.5 =123.5 so 42:123.5 ratio simplified is 12:1

Looking at the question, to find the scale factor we are going to divide 42 by 3.5 which is 12. To check our work we will do 1 times 3.5 which is 42.

Why is it not 147:1? Well, scale factoring means that in two similar geometric figures, the scale factor is the ratio of their corresponding sides, dividing the two corresponding lengths of the sides will gives the ratio

To check go to:

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Please remember to revise this and make it in your own words if you want! I hope this helps you. -Doodle

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The product of  -4a and 3a-2b+4c is calculated as: -12a²+8ab-16ac.

Sums of terms of the form kxn, where k is any quantity as well as n is a positive integer, make up polynomials. For instance, the polynomial 3x+2x-5. a description of polynomials.

Have used FOIL method, Box method, and distributive property, multiply two polynomials. To multiply polynomials, you can employ one of three methods.

The polynomial's zeros must be located using a method of your choice, and the linear expression that produce those zeros must then be combined in order to describe the polynomial like a product of linear factors. After factoring, you will have to filter through the third degree polynomial.

The given polynomials are-

-4a and 3a-2b+4c

Formulation of rectangular array:

                  3a          -2b          4c

-4a  :     -4a*3a      -4a*(-2b)   -4a*(4c)

                -12a²         8ab           -16ac.

Thus, the product of  -4a and 3a-2b+4c is calculated as: -12a²+8ab-16ac.

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The area of the figure is approximately 86.325 square centimeters.

A triangle is a shape with three sides and three angles. It is one of the basic shapes in geometry. Triangles can be classified according to the lengths of their sides as equilateral, isosceles and scalene triangles, and also according to their internal angles as right, acute and obtuse triangles.

To find the area of the trapezoid triangle , we need to first find the length of the other diagonal

Since the center line is perpendicular to both diagonals, it divides the trapezoid triangle into two right triangles, ABC and ABD.

Using the Pythagorean theorem, we can find the length of BD:

BD = [tex]\sqrt{(AB^2 + AD^2)}[/tex]

BD = [tex]\sqrt{(10.2^2 + 7.5^2)}[/tex]

BD = 12.654

Now, we can use the formula for the area of a trapezoid:

A = (1/2) * (AB + CD) * h

where h is the height of the trapezoid, which is the distance between the parallel sides AB and CD.

To find h, we can use the formula for the area of a triangle:

A = (1/2) * b * h

where b is the base of the triangle and h is its height.

We can use triangle ABD, which is a right triangle, to find the height h:

h = AD = 7.5

Now we can substitute the values into the formula for the area of a trapezoid:

A = (1/2) * (AB + CD) * h

A = (1/2) * (10.2 + 15.3) * 7.5

A = 86.325

Therefore, the area of the trapezoid triangle ABC is approximately 86.325 square centimeters.

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Answer:

Step-by-step explanation:

Without the graph or any additional information, it is not possible to determine the formula for the quadratic function f(x). The graph provides visual information about the shape and characteristics of the function, but not enough details to determine the exact coefficients of the quadratic expression.

To find the formula for a quadratic function, we need to know three coefficients: a, b, and c. These coefficients are determined by the specific shape and features of the graph, such as the vertex, intercepts, and symmetry.

If you can provide more information about the graph, such as the coordinates of some key points or any additional characteristics, I can help you find the formula for the quadratic function f(x).

After addressing the issue at hand, we can state that As a result, x equals  triangle 180 degrees.

A polygon is a triangle with four or more sections. It is rectangular in shape. The edges of a triangle ABC are A, B, and C. Euclidean geometry yields a single plane and cube when the sides are not collinear. A polygon is formed when a triangle has three components and three angles. The corners of a triangle are the points at which the three edges meet. Triangle sides add up to 180 degrees.A polygon is a triangle with four or more sections. It is rectangular in shape. The edges of a triangle ABC are A, B, and C. Euclidean geometry yields a single plane and cube when the sides are not collinear. A polygon is formed when a triangle has three components and three angles. The corners of a triangle are the points at which the three edges meet. Triangle sides add up to 180 degrees.

To calculate x, we must use the fact that the sum of a triangle's interior angles is 180 degrees.

First, determine the size of angle B. Angle A is 60 degrees, and angle C is 75 degrees. So,

angle B = 180 minus angle A A - angle C angle B = 180 - 60 - 75 angle B = 45

D = 360 minus angle angle A angle B angle C angle D = 360° - 60° - 45° - 75° D is equal to 180 degrees.

angle E stands for angle. D\sangle E is equal to 180 degrees.

As a result, the value of x is:

x = the angle 180 degrees = E x

As a result, x equals 180 degrees.

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Step-by-step explanation:

To calculate the amount of wood needed to create a raised bed, you will need to know the dimensions of the bed.

Assuming the raised bed is rectangular, you will need to know the length and width of the bed, as well as the height of the bed.

Once you have these dimensions, you can calculate the surface area of the raised bed by multiplying the length and width of the bed together. This will give you the area of the bottom of the bed.

To calculate the total surface area of the bed, including the sides, you will need to multiply this area by 2 (since there are two sides) and add this to the area of the bottom.

So the formula for calculating the total surface area of the raised bed is:

Total surface area = (2 x length x height) + (2 x width x height) + (length x width)

Once you have this total surface area, you can then calculate how much wood you need by multiplying it by the thickness of the wood.

For example, if the total surface area of the bed is 100 square feet and you plan to use 2-inch-thick boards, you would need 200 cubic feet of wood.

It's worth noting that this calculation assumes that the raised bed has straight sides and right angles. If the bed has a more complex shape, the calculation will be more difficult.

Therefore , the solution of the given problem of equation comes out to be x = 100,003 is the value of x that fulfils the equation  log(x-3) = 5.

It is standard practise in mathematical formulas to employ a single variable term to ensure agreement between competing claims. Equations, which are mathematical statements, are used to demonstrate the equality of many academic expression numbers. Instead of dividing 12 into 2 parts in this instance, the normalise technique adds b + 6 to use the data from

y + 6.

Here,

By utilising the characteristics of logarithms, we can find x.

Beginning with the expression provided:

=>  log(x-3) = 5

It can be rewritten in exponential form as follows:

=> 10^5 = x - 3

When we simplify this solution, we obtain:

=> x = 10^5 + 3

We can calculate that 105 = 100,000 by using a calculator, so:

=> x = 100,000 + 3 = 100,003

As a result, x = 100,003 is the value of x that fulfils the equation

log(x-3) = 5.

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Answer idek

Step-by-step explanation: why

Answer:

C

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

The difference of –3.2 and the sum of a number and 19.1 is given as:

|-3.2 - (x + 19.1)| ≤ 14.2

Simplifying the left side of the inequality:

|-22.3 - x| ≤ 14.2

The absolute value of a number is always greater than or equal to 0, so we can split the inequality into two cases:

Case 1: -22.3 - x ≤ 14.2

-36.5 ≤ x

Case 2: -22.3 - x ≥ -14.2

-8.1 ≥ x

Combining the two cases, we get:

-36.5 ≤ x ≤ -8.1

Therefore, the correct option is:

A: Negative 3.2 minus (x + 19.1) less-than-or-equal-to 14.2.

The fοrmula fοr the circumference (C) οf a circle with radius (r) is C = 2πr.

The perimeter οf a circle οr ellipse is its circumference. That is, if the circle were οpened up and straightened οut tο a line segment, the circumference wοuld be the length οf the arc.

The equatiοn C/d = π relates the circumference (C) οf a circle tο its diameter (d) using the cοnstant pi (π).

we can use the relatiοnship between the diameter and the radius:

d = 2r

We can substitute 2r fοr d in the equatiοn C/d = π, giving us:

C/(2r) = π

We can then multiply bοth sides by 2r tο isοlate C:

C = 2πr

Therefοre, the fοrmula fοr the circumference (C) οf a circle with radius (r) is C = 2πr.

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Answer:

Step-by-step explanation:

a. Journal Entries:

i. Budget Approval:

Debit: Appropriations - Salaries - Br. 800,000

Debit: Appropriations - Utilities - Br. 50,000

Debit: Appropriations - Equipment - Br. 85,000

Credit: Estimated Revenues - Property Taxes - Br. 850,000

Credit: Estimated Revenues - Licenses and Fees - Br. 70,000

Credit: Estimated Revenues - Investment Income - Br. 5,000

ii. Property Tax Levy:

Debit: Property Taxes Receivable - Br. 850,000

Credit: Property Taxes Revenue - Br. 850,000

iii. Collection of Revenues:

Debit: Cash - Br. 910,000

Credit: Property Taxes Receivable - Br. 840,000

Credit: Licenses and Fees Revenue - Br. 70,000

iv. Investment in CD:

Debit: Cash - Br. 50,000

Credit: Investments - Br. 50,000

v. Purchase of Police Sedans:

Debit: Equipment - Br. 80,000

Credit: Cash - Br. 80,000

vi. Payment for Police Sedans:

Debit: Equipment - Br. 2,000

Credit: Cash - Br. 82,000

vii. Payment of Salaries and Utility Bills:

Debit: Salaries Expense - Br. 770,000

Debit: Utilities Expense - Br. 45,000

Credit: Cash - Br. 815,000

b. Statement of Revenues, Expenditures, and Changes in Fund Balance:

Revenues:

Property Taxes Revenue - Br. 850,000

Licenses and Fees Revenue - Br. 70,000

Investment Income - Br. 2,000

Total Revenues - Br. 922,000

Expenditures:

Salaries Expense - Br. 800,000

Utilities Expense - Br. 50,000

Capital Outlay - Br. 82,000

Total Expenditures - Br. 932,000

Net Change in Fund Balance:

Revenues - Expenditures - Br. 10,000

Fund Balance:

Beginning Fund Balance - Br. 50,000

Net Change in Fund Balance - Br. 10,000

Ending Fund Balance - Br. 40,000

c. Balance Sheet:

Assets:

Cash - Br. 58,000

Investments - Br. 50,000

Property Taxes Receivable - Br. 10,000

Equipment - Br. 85,000

Total Assets - Br. 203,000

Liabilities:

None

Fund Balance:

Unassigned - Br. 40,000

Total Liabilities and Fund Balance - Br. 203,000

The simple rate of return for the investment (rounded to the nearest tenth of a percent) is: 0.1572 or 15.7%.

Simple rate of return is a financial metric used to measure the profitability of an investment, calculated as the ratio of net income to the initial investment.

To calculate the simple rate of return for the investment, we need to first calculate the average annual net cash inflow.

Annual net cash inflow = Annual cash inflows - Annual depreciation expense

The annual depreciation expense can be calculated as:

Depreciation expense = (Initial cost - Salvage value) / Life of investment

Depreciation expense = ($34,000 - $0) / 15 years = $2,266.67 per year

Therefore, the average annual net cash inflow is:

Annual net cash inflow = $7,600 - $2,266.67 = $5,333.33

The simple rate of return can now be calculated as:

Simple rate of return = Average annual net cash inflow / Initial investment

Simple rate of return = $5,333.33 / $34,000 = 0.1572 or 15.7% (rounded to the nearest tenth of a percent)

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Answer:

$3,280.72

Step-by-step explanation:

300(1 + [tex]\frac{.08}{12}) ^{(12x30)}[/tex] = 3280.72

Helping in the name of Jesus.

That the gradient gives the direction of steepest ascent, so the negative of the gradient gives the direction of steepest descent.

To find the slope of the tangent in the positive y-direction to the surface z = 3x + 2y − 4exy at (6, 0, 14), we need to find the partial derivative of z with respect to y and evaluate it at the point (6,0):

∂z/∂y = 2 - 4ex(6)

At (6,0), this becomes:

∂z/∂y = 2 - 4e(36) = -646.158

So the slope of the tangent in the positive y-direction at (6,0,14) is -646.158.

To find the following for z = x2 + 5x − 3y3:

a) The partial derivative of z with respect to x:

∂z/∂x = 2x + 5

b) The partial derivative of z with respect to y:

∂z/∂y = -9y2

c) The gradient of z:

∇z = (2x + 5)i - 9y2j

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No, Kiran is incorrect. -2 is actually greater than -5, so the correct statement is -5 < -2.

A number line is an image of numbers plotted on a straight line, either horizontally or vertically. We can compare numbers and execute simple arithmetic operations on them easily by writing the numbers down on a number line. The starting point of a number line is often regarded as zero (0). The numbers to the left of zero are all negative whereas the numbers on the right of zero are all positive. As a result, we may argue that on a number line, the value of numbers grows as we approach towards the right. The numbers on the right are thus greater than the ones on the left, according to this statement.

No, Kiran is incorrect. -2 is actually greater than -5, so the correct statement is -5 < -2.

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The circumference of the circle is 150.768 units.

The area of the circle is 1809.216 units squared.

The area and circumference of a circle can be found as follows:

Let's find the circumference of the circle as follows:

circumference of a circle =  2πr

where

Therefore,

circumference of a circle = 2πr

r = 24 units

π = 3.141

Hence,

circumference of the circle = 2 × 3.141 × 24

circumference of the circle =  150.768 units

Let's find the area of the circle as follows:

area of the circle = πr²

area of the circle = 3.141 × 24²

area of the circle = 1809.216 units squared

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Answer:

Step-by-step explanation:

its 10.7

1x1 *why is that ok  ut number

Answer:

x ≤ 4

Step-by-step explanation:

5x-12 ≤3x-4

collect like terms

5x - 3x ≤ -4 + 12

2x ≤ 8

2x/2 ≤ 8/2

x ≤ 4

Answer:

x [tex]\leq[/tex] 4

Step-by-step explanation:

5x - 12 [tex]\leq[/tex] 3x - 4  Subtract 3x from both sides

2x - 12 [tex]\leq[/tex] -4  Add 12 to both sides

2x [tex]\leq[/tex] 8  Divide both sides by 2

x [tex]\leq[/tex] 4

Helping in the name of Jesus.

The expression that represents the product of t and 9 is 9t

The product of t and 9 can be represented by the following expressions:

All three of these expressions represent the same thing: the result of multiplying t and 9 together.

The expression "t * 9" uses the multiplication operator (*) to indicate that t and 9 are being multiplied.

The expression "9 * t" is equivalent, as multiplication is commutative and the order of the factors doesn't affect the result.

The expression "9t" is a shorthand way of writing the product, using the distributive property of multiplication.

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Answer:

Download 15 songs cost £22.50

Download 45 songs cost £67.50

Step-by-step explanation:

We know

Downloading 30 songs from a music website costs £45.

45 / 30 = £1.5 for 1 song

Download 1 song = £1.50

How much does it cost to download 15 songs?

1.5 x 15 = £22.50

How much does it cost to download 45 songs?

1.5 x 45 = £67.50

So,

Download 15 songs cost £22.50

Download 45 songs cost £67.50

By using scale and prοpοrtiοn, the dimensiοns οf the actual painting are 144 inches² by 216 inches².

Scale refers tο the relatiοnship between the dimensiοns οf a scaled οbject and the cοrrespοnding dimensiοns οf the οriginal οbject. If an οbject is scaled dοwn tο half its οriginal size, then the dimensiοns οf the scaled οbject will be half οf the dimensiοns οf the οriginal οbject.

Prοpοrtiοn, οn the οther hand, refers tο the relatiοnship between twο οr mοre quantities that have the same ratiο. In οther wοrds, if twο quantities are in prοpοrtiοn, then their ratiο is cοnstant.

Tο find the dimensiοns οf the actual painting, we need tο "undο" the 6:1 scale.

If the scaled painting is 6 times smaller than the actual painting, then the actual painting is 6 times larger than the scaled painting.

Sο we can find the actual dimensiοns by multiplying the scaled dimensiοns by 6:

Actual width = 24 inches x 6 = 144 inches

Actual height = 36 inches x 6 = 216 inches

Therefοre, the dimensiοns οf the actual painting are 144 inches² by 216 inches².

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Answer:

One example of an irrational number between 5.25 and 5.26 is:

√139 ≈ 11.78982612...

Since the decimal representation of √139 goes on forever without repeating, it is an irrational number.

Step-by-step explanation:

Twο statement for this graph are true -

O The functiοn is increasing οn the interval (-∞, 0).

O The functiοn is increasing οn the interval (0, ∞).

A functiοn's parameters are a grοup οf values that can be plugged intο the dοmain οf the functiοn. This set οf data cοntains the x values fοr a functiοn like f. (x).

The term "range" refers tο the set οf numbers that the functiοn cοnsiders tο be valid. The functiοn οutputs this string οf values in respοnse tο the insertiοn οf an x value.

The functiοn h(x) = 3x is a linear functiοn (straight line) with a slοpe οf 3, and a y-intercept οf 0.  The cοnstant, pοsitive slοpe means that h(x) will increase οver the interval (-∞, ∞).

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The complete question is -

Given the function h(x)=3x, which statement is true about h(x)?

O The function is decreasing on the interval (-∞, 0).

O The function is increasing on the interval (-∞, 0).

O The function is decreasing on the interval (0, ∞).

O The function is increasing on the interval (0, ∞).

The linear function that represents the above scenario is given as follows:

y = 6 + 2.5x.

The number of days needed to run 41 miles is given as follows:

14 days.

The slope-intercept representation of a linear function is given by the equation presented as follows:

y = mx + b

The coefficients of the function and their meaning are described as follows:

The parameters in the context of the problem have the values given as follows:

Hence the function is modeled as follows:

y = 2.5x + 6.

The number of days needed to run 41 miles is given as follows:

2.5x + 6 = 41

x = 35/2.5

x = 14 days.

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Answer:

405$

Step-by-step explanation:

First we need to find out what is the price of one unit:

330 units - 495$

1 unit - x $

Use the property of proportion to find x:

x = 1 × 495 / 330 = 1,5$ (for one unit)

Then multiply this price by 270 (since it's the new quantity of units):

270 × 1,5 = 405$

The end behavior of the function f(x) = -1/x - 4 is given as follows:

As x -> ∞, f(x) -> -4.

The end behavior of a function refers to the behavior of the function as the input variable (usually denoted as "x") approaches positive or negative infinity. To obtain the end behavior of a function, we look at the highest degree term in the function, which will determine the general shape of the graph.

The function for this problem is defined as follows:

f(x) = -1/x - 4.

As x goes to infinity, the term 1/x goes to zero, hence the end behavior of the function is defined as follows:

f(x) = 0 - 4

f(x) = 4.

The problem is incomplete, hence I found the end behavior of the function f(x) = -1/x - 4.

You should use the same procedure to find the end behavior of the function in your problem.

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Answer:

Step-by-step explanation:

To simplify the expression 24 + b/b + 24 x 53.72,

we first need to substitute the given value of b into the expression.

For example, if b is equal to 5, we can replace all instances of b with 5 to get 24 + 5/5 + 24 x 53.72.

Next, we can simplify the division by evaluating 5/5, which equals 1.

Then, we can multiply 24 and 53.72 to get a product of 1288.28.

Finally, we can add the simplified terms to get a final result of 1312.28.

Therefore, the simplified expression, given that b is equal to 5, is 1312.28.

Answer:

The formula gives the area of a parallelogram:

Area = base x height

Substituting the given values, we get:

Area = 7.5 cm x 12.2 cm

Area = 91.5 cm^2

Therefore, the area of the parallelogram is 91.5 square centimeters.

Step-by-step explanation:

Answer:

91.5 sq cm

Step-by-step explanation:

A=bh=7.5·12.2=91.5