What is 25^(2x-3)=125^(x+1)?

Answer:

a. The amount borrowed is $95,000. The annual interest rate is 5%. The number of payments per year is 12 (monthly payments). The loan term in years is 25, and the payment amount is $450.

b. The loan requires a total of 25 x 12 = 300 payments over the full term.

To calculate the total amount paid over the full term of the loan, we can use the formula for the present value of an annuity:

PV = PMT x [(1 - (1 + r)^-n) / r]

Where PV is the present value (the amount borrowed), PMT is the payment amount, r is the monthly interest rate (5% / 12 = 0.004167), and n is the total number of payments (300).

Plugging in the values, we get:PV = $95,000

PMT = $450

r = 0.004167

n = 300PV = $450 x [(1 - (1 + 0.004167)^-300) / 0.004167] = $144,781.92

Therefore, the total amount paid over the full term of the loan is $144,781.92.

Answer:

- 4

Step-by-step explanation:

(f + g)(3) = f(3) + g(3)

f(3) = - 5

g(3) = 1

f(3) + g(3) = - 5 + 1 = -4

Using the graph of the line, we can see that the inequality, including the line which is the boundary of inequality, is:

 y + 2x ≥ -3

What is meant by inequality?

An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa. Literal inequalities are relationships between two algebraic expressions that are expressed using inequality symbols.

Given that the boundary line of equality has points (4,5) and (1,-1) on it.

So we can write the equation of the line.

Slope m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex] = -1-5 / 1-4 = 2

Equation of the line:

y - y1 = m (x-x1)

y - 5 = 2(x - 4)

y - 5 = 2x - 8

y = 2x - 3

y + 2x = -3

Point (−3, −5) makes the inequality false.

Substituting,

-5 + 2 * -3 = -5 - 6 = -11

y + 2x should not be -11

When graphing the line it should not include the point (−3, −5).

This point is present on the lower portion of the line.

So the upper portion of the line should be the inequality including the line itself.

Therefore using the graph of line, we can see that the inequality, including the line which is the boundary of inequality, is:

 y + 2x ≥ -3

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The area of the figure can be expressed using the formula A = (x + 1)2.

Area is a quantity that measures the size of a two-dimensional surface or shape. It is expressed in square units such as square centimetres (cm2), square metres (m2) or square kilometres (km2). Area is used to describe the size of a garden, a house, a room, a city and much more. It can also be used to calculate the amount of material required for a project, such as paint, carpet or tiles. Knowing the area of a shape can help to calculate costs, and to make sure that enough materials are ordered.

This formula is derived from the fact that the figure is a square with sides of length x + 1. Since a square is a special type of rectangle, the area of a square is simply equal to the product of its two sides, or (x + 1)2.

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Answer:

Step-by-step explanation:

The expression "X divided by 5 multiplied by 12" can be written as:

( X / 5 ) * 12

To simplify this expression, we can first multiply 12 by X/5, which gives:

( X / 5 ) * 12 = X * (12/5)

So the simplified expression is:

X * (12/5)

or

(12/5)X

which is equivalent to "12/5 times X".

Answer:you did not give us anyting for us to answer

Step-by-step explanation:

Answer:

16Ft

Step-by-step explanation:

We can use proportions to solve this problem.

Let's let "x" be the height of the flagpole. We know that the sign is 4 feet high, and it casts a shadow of 1 1/4 feet. So we can set up the proportion:

4/1.25 = x/5

Simplifying the left side of the equation, we get:

4/1.25 = 16/5

Substituting into the original equation, we have:

16/5 = x/5

Multiplying both sides by 5, we get:

16 = x

Therefore, the height of the flagpole is 16 feet.

Answer:

W = 8cm

L = 19cm

Step-by-step explanation:

The first step to solving these problems is always writing the information that is given into 2 equations.

Piece of info #1: Length is 5cm less than 3 times the width

Piece of info #2: Perimeter (of the rectangle, which has 4 sides) is 54cm

Turing these into equations...

Equation 1) L = 3*W - 5

Equation 2a) L+L+W+W = 54

Let's simplify that second equation:

Equation 2b) 2L+2W = 54

Now, we just solve the system of two equations by substitution. Take the known value of L from equation 1 and substitute it in for the value of L in equation 2b:

2*(3*W-5)+2W = 54

Now we solve for W:

6W - 10 + 2W = 54

8W - 10 = 54

8W = 64

W = 64/8

W = 8 cm

Now that we know W, we can substitute its value into either equation 1 or equation 2 to find L. Here, I'll randomly choose equation 1.

Equation 1) L = 3*W - 5

L = 3*8 - 5

L = 24-5

L = 19 cm

Answer:

Step-by-step explanation:

up to beyond hald a milimeter in length

2mm

we need to mix milk and water in the ratio of 1:5 to gain a profit of 25% when selling the mixture at cost price.

What is ratio ?

Ratio can be defined as given value divided by total value.

Let's assume that we have x liters of milk and y liters of water. We want to find the ratio in which water must be mixed with milk to gain 25% on selling the mixture at cost price.

If we sell the mixture at cost price, we will not make any profit or loss. So, let's first calculate the cost price of the mixture.

Assuming that the cost price of milk is the same as the cost price of water, the cost price of x liters of milk and y liters of water is:

Cost price = Cost price of milk + Cost price of water

= x * cost price of milk + y * cost price of water

Since we are not making any profit or loss, the selling price of the mixture will be the same as the cost price.

Now, to gain a profit of 25%, the selling price must be 125% of the cost price. So, we have:

Selling price = 125% of cost price

= 1.25 * (x * cost price of milk + y * cost price of water)

We know that the mixture contains only milk and water, so the total volume of the mixture is x + y liters.

Now, we can set up an equation to find the ratio of water to milk:

y/x = (1 - 1.25) / (1.25 - 0)

y/x = -0.2

Simplifying this equation, we get:

y = -0.2x

This means that for every 1 liter of milk, we need to mix it with 0.2 liters of water in order to gain a 25% profit when selling the mixture at cost price.

In terms of ratio, the ratio of water to milk is:

0.2 : 1

or

1 : 5 (by simplifying the ratio by multiplying both sides by 5)

Hence, we need to mix milk and water in the ratio of 1:5 to gain a profit of 25% when selling the mixture at cost price.

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The opportunity cost of receiving a 90 on the statistics exam is 17  points on the economics exam.

Two or more expressions with an Equal sign is called as Equation.

The Opportunity cost in this case is the amount of points that Jose has to forgo for picking one alternative.

If Joe had picked strategy B which would give Jose 90 points on statistics then that means that Jose would not have picked strategy A which gave a 94 in Economics.

Therefore instead of getting a 94, Jose would get a 77. The opportunity cost is therefore;

= 94 - 77

= 17 points

Hence, the opportunity cost of receiving a 90 on the statistics exam is 17  points on the economics exam.

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Answer:

The answer to this question would be A

Step-by-step explanation:

I took the test one time before .

The measure of angle 1 and the measure of angle 2 are 45° and 90°.

A square is a two-dimensional closed shape with 4 equal sides and 4 vertices. Its opposite sides are parallel to each other.

Given is a square,

We are asked to find the missing angles,

We know that, The diagonals of the square bisect each other at 90°,

The diagonal of a square bisects its internal angle,

Therefore, the measure of angle 1 = 45°

And,

The measure of angle 2 = 90°

Hence, the measure of angle 1 and the measure of angle 2 are 45° and 90°.

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By integration of monthly revenue we will get total revenue of the shop for a year is $51,600.

What is integration ?

Integration is a fundamental operation in calculus that involves finding the area under a curve, or the antiderivative of a function. It is the reverse operation of differentiation, which is used to find the rate of change of a function.

Integration is represented by the symbol ∫ (the integral sign), and the result of the operation is called the indefinite integral or antiderivative of the function. The antiderivative is a family of functions that differ only by a constant, known as the constant of integration.

Given by the question:

The monthly revenue can be calculated by multiplying the unit price and the quantity of goods sold in a given month. Therefore, the monthly revenue function is:

[tex]R(t) = P(t) * Q(t) = (t^2 + 9t + 36) * (t + 12)[/tex]

To find the total revenue over a year, we need to integrate the monthly revenue function over the interval [0,12] (since we are considering a year):

[tex]Total revenue = \int\limits^a_0 {R(t)} \, dt[/tex]

= [tex]\int\limits^a_b (t^2 + 9t + 36) * (t + 12) } \, dt[/tex]

= [tex]\int\limits^a_b {(t^3 + 21t^2 + 132t + 432) } \, dt[/tex]

=[tex][t^4/4 + 7t^3/3 + 66t^2 + 432t][/tex]evaluated from 0 to 12

=[tex](20736/4 + 12096 + 9504 + 5184) - (0 + 0 + 0 + 0)[/tex]

= [tex]51600[/tex]

Therefore, the total revenue of the shop for a year is $51,600.

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Refer to the attached images.

The marginal revenue is 2752 dollar per unit of revenue function is given by R(q)=-7q²+400g.

The variance in the number of units sold is multiplied by the total change in revenue to determine marginal revenue. Here is how marginal revenue is determined: The difference between total income and output is the marginal revenue. Because it measures the increase in revenue from the sale of extra goods and services, marginal revenue is crucial. The law of diminishing returns, which asserts that any increase in production will result in smaller increases in output, has an impact on marginal revenue. The perfect level has been obtained as a result.

To find the marginal revenue, we obtain ,

R(q)=-7q²+400g.

q= 8

Marginal revenue= R(q)

MP(8)=-7(8)²+400×8

          =-7×64+3200=2752dollar per unit.

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The percentage of the normal oxygen level after 4 weeks is 52.2%

At week 4, the percentage of the normal oxygen level in the pond is increasing at a rate of 96% per week.

The percentage of the normal oxygen level after 5 weeks is 41.9%

At week 5, the percentage of the normal oxygen level in the pond is increasing at a rate of 60% per week.

What is the increasing rate of a function?

The increasing rate of a function is the rate at which the function is increasing at a specific point in its domain. It tells us how fast the function is increasing, or how quickly its output values are getting larger, at that particular point.

The increasing rate can be determined using the derivative of the function. Specifically, if the derivative of a function is positive at a certain point, then the function is increasing at that point, and the magnitude of the derivative gives us the rate of increase. If the derivative is negative at a point, then the function is decreasing at that point, and the magnitude of the derivative gives us the rate of decrease.

In general, the sign of the derivative indicates the direction of change of the function, while the magnitude of the derivative indicates the rate of change. So, when we take the derivative of a function, we can use it to analyse how the function is changing and how quickly it is changing at each point in its domain.

The given model is:

o(t) = [0.6t² - t + 2] / [t² + 2]

(a) To find the percentage of the normal oxygen level after 4 weeks, we need to evaluate o(4) and multiply it by 100:

o(4) = [0.6(4²) - 4 + 2] / [4² + 2] = 9.4 / 18 = 0.522

So the percentage of the normal oxygen level after 4 weeks is:

0.522 * 100% = 52.2%

(b) To find how quickly the percentage of the normal oxygen level is changing after 4 weeks, we need to find the derivative of o(t) with respect to t and evaluate it at t = 4:

o'(t) = [1.2t(t²+ 2) - (2t)(0.6t² - t + 2)] / (t² + 2)²

o'(4) = [1.2(4)(4² + 2) - (2)(4)(0.6(4²) - 4 + 2)] / (4² + 2)² = 0.96

So the rate of change of the percentage of the normal oxygen level after 4 weeks is:

0.96 * 100% per week = 96% per week

This means that at week 4, the percentage of the normal oxygen level in the pond is increasing at a rate of 96% per week.

(c) To find the percentage of the normal oxygen level after 5 weeks, we need to evaluate o(5) and multiply it by 100:

o(5) = [0.6(5²) - 5 + 2] / [5² + 2] = 11.3 / 27 = 0.419

So the percentage of the normal oxygen level after 5 weeks is:

0.419 * 100% = 41.9%

(d) To find o'(5), we can use the same formula for the derivative of o(t) that we found in part (b), but evaluate it at t = 5:

o'(5) = [1.2(5)(5² + 2) - (2)(5)(0.6(5²) - 5 + 2)] / (5² + 2)² = 0.60

So at week 5, the percentage of the normal oxygen level in the pond is increasing at a rate of 0.60 * 100% per week, which is approximately 60% per week.

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Answer:

Graph                 Function?

Graph 1                 No

Graph 2                No

Graph 3                Yes

Graph 4                Yes

Graph 5                No

Graph 6                No

Step-by-step explanation:

For a graph to represent a function, for a single value of x there can be one and only one value of y

When examining the graph of a function, use the vertical line test to see if the graph represents a function.

Vertical Line Test

The vertical line test is helpful to find if the given equation represents a function or not. The vertical line test states that a vertical line needs to cuts the graph of a function(equation) at only one point, for it to represent a function. If the graph of the equation represented in the coordinate axis, is cut by the vertical line at more than one point, then the graph is not a function.

Determine whether a curve in the plane represents the graph of a function by visually examining the number of intersections of the curve with vertical lines. and, as a result, any vertical line in the plane can intersect the graph of a function at most once.

For the given graphs, here are the results of the vertical line test

Graph #                      Vertical Line Test Result
Graph 1                        Fails
Graph 2                       Fails
Graph 3                       Succeeds
Graph 4                       Succeeds (vertical line intersects only one point)
Graph 5                       Fails
Graph 6                       Fails (vertical line through x =1 intersects 2 points)

Answer:

57%

Step-by-step explanation:

Let's consider the total number of students as 100%.

60% of all students are senior, which means that the rest (40%) are juniors.

Out of all senior students, 45% have school meals.

To find the percentage of senior students who have school meals, we should do the following:

[tex]\ \frac{45\% \times60\%}{100\%} = 27\%[/tex]

This is the percentage of students who are senior and have school meals.

We need to repeat the same procedure with junior students.

To do that, we need to find the 75% of 40% out of total, which is 100%.

[tex] \frac{75\% \times 40\% }{100\%} = 30\%[/tex]

This is the percentage of junior students who have school meals.

Finally we need to add up the percentages to find the total percentage of students who have school meals.

[tex]27\% + 30\% = 57\%[/tex]

The equation for the graphed function is [tex]y=\frac{8\left(x-1\right)^2}{5\left(x-2\right)^2\left(x+2\right)}[/tex]

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

The graph

On the graph, we have the following asymptotes

x = -2 and x = 2

This means that the denominator of the function is

(x + 2) and (x - 2)²

(x - 2) is squared because the graph appears to turn (not intersect) at the zeros of x = 1 (close to x = 2)

So, we have

y = a/(x + 2)(x - 2)²

Where a is a real value

The zero is x = 1 with a multiplicity of 2 (because the curve turns at x = 1)

So, we have

y = a(x - 1)²/(x + 2)(x - 2)²

The y-intercept is (0, 0.2)

This means that

0.2 = a(0 - 1)²/(0 + 2)(0 - 2)²

So, we have

0.2 = a/8

Evaluate

a = 1.6

So, we have

a = 8/5

The function becomes

y = 8(x - 1)²/5(x + 2)(x - 2)²

Express properly

[tex]y=\frac{8\left(x-1\right)^2}{5\left(x-2\right)^2\left(x+2\right)}[/tex]

Hence, the equation is [tex]y=\frac{8\left(x-1\right)^2}{5\left(x-2\right)^2\left(x+2\right)}[/tex]

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Therefore, the coordinates of point P are(-3+√(2), -5-√(2)).

A coordinate is a set of values that specifies the position of a point or an object in a geometric space. In two-dimensional Euclidean space (i.e., on a plane), the most common coordinate system is the Cartesian coordinate system, which consists of two axes, the x-axis and the y-axis, that intersect at a point called the origin. Any point in the plane can then be uniquely identified by its x-coordinate (its horizontal distance from the origin) and its y-coordinate (its vertical distance from the origin).

Here,

To find the coordinates of point P, we need to use the ratio given to divide the line segment AB into two parts.

Let's first find the coordinates of point A and B:

A = (-3, -5)

B = (1, -9)

The ratio given is 1:3, which means that AP:PB is also 1:3. Let's call the coordinates of point P (x, y).

We can use the midpoint formula to find the coordinates of the midpoint M of line segment AB:

M = ((-3+1)/2, (-5-9)/2) = (-1, -7)

Now, we can use the fact that AP:PB is 1:3 to set up the following equation:

AP/PB = 1/3

We can rewrite this as:

AP = (1/4) AB

where AB is the distance between A and B:

AB = √((1-(-3))²  + (-9-(-5))²)

= √(16+16)

=4√(2)

So, we have:

AP = (1/4) AB = (1/4) * 4√(2)

= √(2)

We also know that the vector AP is in the same direction as the vector AM, which goes from A to M:

AM = (-1-(-3), -7-(-5))

= (2, -2)

To find the vector AP, we can scale AM to have length sqrt(2):

AP = (√(2)/||AM||) AM

= (√(2)/2) (2, -2)

= (√(2), -√(2))

Finally, we can find the coordinates of point P by adding AP to the coordinates of A:

P = A + AP

= (-3, -5) + (√(2), -√(2))

= (-3+√(2), -5-√(2))

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Answer:

Step-by-step explanation:

$1.49 = 149 cents

149 / 42 = ~4

4 cents per fork

The area of quadrilateral KECF is greater than area of triangle.

A triangle is a three-sided polygon that consists of three edges and three vertices.

Given that ABCD is a square.

points E and F are midpoints of sides BC and CD, respectively

Line segments AE and BF intersect each other at point K

k is the midpoint of the square.

We need to find whether the area of triangle AKF or the area of quadrilateral KECF is greater.

then the area of quadrilateral will be greater.

Hence, the area of quadrilateral KECF is greater than area of triangle.

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The sequence of transformations that maps triangle ABC onto triangle A”B”C” is: First the triangle is rotated by 90 degrees thus following the transformation rule (x, y) → (y, -x) and then dilation.

The scale factor is defined as the difference in size between the new and old images. An established location in the plane is the centre of dilatation. The dilation transformation is determined by the scale factor and the centre of dilation.

The image stretches when the scaling factor exceeds 1.

When the scale factor is between 0 and 1, the image gets smaller.

The resulting image and the original image are identical if the scale factor is 1.

The coordinates of the triangle ABC are:

A(0, -1)

B (0, 1)

C (0, 1.8)

First the triangle is rotated by 90 degrees thus following the transformation rule:

(x, y) → (y, -x)

The new coordinates are:

A(0, -1) → A (1, 0)

B (0, 1) → B (-1, 0)

C (0, 1.8) → C (1.8, 0)

Then, the rotated figure is dilated using a scale factor of:

SF = 6/2 = 3

Hence, the sequence of transformations that maps triangle ABC onto triangle A”B”C” is: First the triangle is rotated by 90 degrees thus following the transformation rule (x, y) → (y, -x) and then dilation.

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The equations used to calculate the cost of a single tire patch are 22.2 - 4x = 1.9 and 4x + 1.9 + 22.2.

The statistic is said to be in its simplistic definition when divided into its smallest equivalent portion. How to further find the most basic form. Identify common factors in the denominator and the numerator. Verify a fractional integer to verify if it qualifies as a prime number. A remark having two quadrilateral and an identical sign in the middle is called an equation in mathematics. The general form of any issue contains the degrees of all the components in descending order. The basic form of a system of equations is an x + b = 0. The general form of a linear function with two variables is an x + b y + c = 0. (or something similar). Mathematics can be categorized as identity or conditional equations. An identity stands true regardless of the value given to the variables.

given

equations  4x + 1.9 + 22.2

22.2 - 4x = 1.9

It should all total up to $22.20 if you use the undetermined cost of the four tire patches as x, or $1.90 if you're deducting it.

The equations used to calculate the cost of a single tire patch are 22.2 - 4x = 1.9 and 4x + 1.9 + 22.2.

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Answer:

y = x + 3 --- 1

y = 4x + 9 --- 2

By combining 1 and 2, we have

x + 3 = 4x + 9

3-9 = 4x-x

-6 = 3x

x = -2

Sub x = -2 into 1

y = (-2) + 3 = 1

Intersection = (-2,1)

So the equation that can be used to find the number of cars that Mr. Diaz sold, c, is:

34c - 8 = 28

In algebra, a statement of mathematics that proves the equality of two mathematical expressions is known as an equation. Consider the equation 3x + 5 = 14, where the word "equal" is used to denote the relationship between the terms 3x + 5 and 14.

Let c be the number of cars that Mr. Diaz sold.

According to the problem statement, Ms. Wong sold 8 fewer cars than 34 times the number of cars Mr. Diaz sold, which can be written as:

Ms. Wong's cars sold = 34c - 8

We also know that Ms. Wong sold 28 cars, so we can set this expression equal to 28 to get:

34c - 8 = 28

To solve for c, we can add 8 to both sides and then divide both sides by 34:

34c - 8 + 8 = 28 + 8

34c = 36

c = 36/34

So the equation that can be used to find the number of cars that Mr. Diaz sold, c, is:

34c - 8 = 28

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The measure of the segment OD is same as OE. Hence , OD = DE.

A straight line that only touches a circle once is said to be tangent to it. The term "point of tangency" refers to this point. At the point of tangency, the tangent to a circle is perpendicular to the radius.

Given: XY is the tangent to the circle with centre O at A and

∠CAX=∠BAY=60°

By Alternate Segment Theorem

∠BCA=∠BAY=60°

Similarly,

∠ABC=∠CAX=60°

Therefore, ΔABC is an equilateral triangle circumscribing the circle with centre O.

Thus, centre O is also the centroid.

⇒OA:OD=2:1

Also,

OA=OE            (Radii)

∴ OD=DE

Hence , OD = DE

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