ABC~DEF. Find the length of median CP

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.

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 key features of this rational function include the following:

Domain: (-∞, -2) ∪ (-2, ∞)

Range: (-∞, -1) ∪ (-1, ∞)

Y-intercept: -5/2.

X-intercept: -5.

Vertical asymptote: x = -2.

Horizontal asymptote​: y = -1.

In Mathematics, a rational function simply refers to a type of function  which is expressed as a fraction. This ultimately implies that, a rational function is composed of two (2) main parts and these include the following:

Additionally, the vertical extent of any graph of a rational function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.

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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]

Refer to the attached images.

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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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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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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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:

- 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

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

Step-by-step explanation:

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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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: D = √2

(please respond if im wrong)

Step-by-step explanation:

The fold is made along BE. A folds onto A′.

A′B = AB =√2 ⇒ A′C = 1

(by Pythagoras)

ΔA′BC

is therefore a right-angled isosceles triangle.

⇒∠BA′C=45∘ ⇒∠EA′D=45∘

⇒ ED = A′D = √2−1

The solution for the table has been provided below. It has been obtained by using arithmetic operations.

What are arithmetic operations?

Mathematicians claim that all real numbers may be described using the four basic operations, also referred to as "arithmetic operations." The four mathematical operations that produce quotient, product, sum, and difference, respectively, are divide, multiply, add, and subtract.

We are given a table of the number of crafts x and the number of ounces y.

x        4          9         7            6            5           5            4           8

y        19        46       30          31          23         28          21         42

xy     76       414      210        186        115         140        84         336

x²       16       81         49         36         25          25         16          64

y²       361     2116     900      961        529        784       441        1764

Hence, the table has been completed.

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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)

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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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:

1,800 grams

Step-by-step explanation:

Answer:

180,000

Step-by-step explanation:

if you add 80+40+60=180kg

180kg is equal to 180,000g

sorry if it is wrong.

Answer:

pooooooooooooooooooooooooooop hope this helps

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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The transformation from to f(x) = -√(x - 4) involves reflecting the function across the x-axis and shifting it 4 units to the right.

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

f(x) = -√(x - 4)

The parent function is

f(x) = -√x

The transformation is represented as

f'(x) = (x - 4, -y)

This represents a reflection across the x-axis and a translation 4 units right

The transformed function is added as an attachment

From the graph, we have

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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:

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)

Answer:

11.2

Step-by-step explanation:

S(6, −2) to V(−4, 3)

d = sqrt[(-4 - 6)² + (-2 - 3)²]

d = 11.18

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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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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Answer:

Step-by-step explanation:

$1.49 = 149 cents

149 / 42 = ~4

4 cents per fork