1 let (sn) and (tn) be sequences and suppose there exists n0 such that sn ≤ tn for all n>n0. show lim inf sn ≤ lim inf tn and lim sup sn ≤ lim sup tn. hint: use definition 10.6 and exercise 9.9(c).

Answer:

Triangle P' Q' R' is half the size of the original triangle.

-The scale factor is probably 1/3.

Part B: P'(1, −2), Q'(0, 3), and R'(−1, 0).

Part C: No, the triangles are not congruent. If the second triangle didn't have a dilation, and instead have a reflection of the first triangle, then it would be congruent.

Step-by-step explanation:

:)

60+55=y

y=115

now x=180-Y( as being liner pair)

therefore=x=180-115=65

Step-by-step explanation:

two interior angles are equal to exterior angle

so 60+55=y

y=115

now x=180-Y( as being liner pair)

therefore=x=180-115=65

Data triangulation is a research method that involves using multiple data sources or methods to gather and analyze information, enhancing the validity and comprehensiveness of findings.

Data triangulation is a research method that involves using multiple sources or methods to gather and analyze data on a particular topic or research question. By combining different data sources, researchers aim to enhance the validity, reliability, and comprehensiveness of their findings.

Two real-world examples of data triangulation are:

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The center of a circle that circumscribes a triangle is known as the circumcenter of the triangle.

The circumcenter is the point of intersection of the perpendicular bisectors of the sides of the triangle. This point is equidistant from the three vertices of the triangle, which means that it lies on the perpendicular bisector of each side.

The circumcenter plays an important role in the geometry of triangles. One of its properties is that it is also the center of the circle that passes through the three vertices of the triangle, which is why it is called the circumcenter. This circle is known as the circumcircle of the triangle.

The circumcircle is a unique circle that can be drawn around any triangle, and its center is always the circumcenter. This circle has several important properties, such as:

The circumcircle passes through the three vertices of the triangle.

The circumcircle is centered at the circumcenter of the triangle.

The circumcircle has a radius that is equal to the distance from the circumcenter to any vertex of the triangle.

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Answer:

The vertex is located at (3,5)

The axis of symmetry is x = 3

The plot is in the image attached

Step-by-step explanation:

First we need to find the vertex of the quadratic function. We can find the x-coordinate of the vertex using the formula:

x_v = -b / 2a

Where 'a' and 'b' are coefficients of the quadratic equation in the model:

ax^2 + bx + c = 0

Then we need to expand the terms of f(x):

f(x) = (x-3)^2 + 5

f(x) = x^2 - 6x + 9 + 5

f(x) = x^2 - 6x + 14

So we have a = 1 and b = -6

Then the x-coordinate of the vertex is:

x_v = 6 / 2 = 3

We can use this value in f(x) to find the y-coordinate of the vertex:

f(x_v) = 3^2 - 6*3 + 14 = 5

So the vertex is located at (3,5)

The axis of symmetry is the vertical line traced in the vertex, so it is x = 3

The plot is in the image attached. The circle at (3,5) is the vertex, and the blue line is the axis of symmetry.

Answer:

How do you find volume when given surface area?

Since the base area is given, simply multiply the area of the base times the height to calculate the volume. *Reminder: Volume is measured in cubic units. The volume of the square prism is 225 cubic feet.

Step-by-step explanation:

The volume of the given cube is \(\frac{A^{\frac{3}{2} } }{216^{\frac{1}{2} } }\).

Given that, the surface area of a cube = A m².

The volume of a cube is defined as the total number of cubic units occupied by the cube completely. Volume is nothing but the total space occupied by an object. The formula to find the volume of cube = a³, where a= edge of the cube.

We know that, the surface area of a cube =6a²

So, 6a² = A m²

⇒ a² = A/6

⇒ a= √(A/6)

Now, volume = (√(A/6))³

= \(\frac{A^{\frac{3}{2} } }{6^{\frac{3}{2} } }\)

= \(\frac{A^{\frac{3}{2} } }{216^{\frac{1}{2} } }\)

Therefore, the volume of the given cube is \(\frac{A^{\frac{3}{2} } }{216^{\frac{1}{2} } }\).

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Answer:Any number that we can write as a decimal number, between 1.0 and 10.0, multiplied by a power of 10, is said to be in standard form. 1.23 × 108; If you observe carefully, 1.23 is a decimal number between 1.0 and 10.0 and so we have the standard form of 123,000,000 as 1.23 × 10 8.

Step-by-step explanation:

P.S i am emo

The first derivative of the function `g(u) = u(2u - 3)^3` is `g'(u) = 6u(2u - 3)^2 + (2u - 3)^3`. The second derivative of the function is `g''(u) = 12(u - 1)(2u - 3)^2`.

Given function: `g(u)

= u(2u - 3)^3`

To find the first derivative of the given function, we use the product rule of differentiation.`g(u)

= u(2u - 3)^3`

Differentiating both sides with respect to u, we get:

`g'(u)

= u * d/dx[(2u - 3)^3] + (2u - 3)^3 * d/dx[u]`

Using the chain rule of differentiation, we have:

`g'(u)

= u * 3(2u - 3)^2 * 2 + (2u - 3)^3 * 1`

Simplifying:

`g'(u)

= 6u(2u - 3)^2 + (2u - 3)^3`

To find the second derivative, we differentiate the obtained expression for

`g'(u)`:`g'(u)

= 6u(2u - 3)^2 + (2u - 3)^3`

Differentiating both sides with respect to u, we get:

`g''(u)

= d/dx[6u(2u - 3)^2] + d/dx[(2u - 3)^3]`

Using the product rule and chain rule of differentiation, we have:

`g''(u)

= 6[(2u - 3)^2] + 12u(2u - 3)(2) + 3[(2u - 3)^2]`

Simplifying:

`g''(u)

= 12(u - 1)(2u - 3)^2`.

The first derivative of the function `g(u)

= u(2u - 3)^3` is `g'(u)

= 6u(2u - 3)^2 + (2u - 3)^3`. The second derivative of the function is `g''(u)

= 12(u - 1)(2u - 3)^2`.

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The first derivative of g(u) is g'(u) = (2u - 3)³ + 6u(2u - 3)², and the second derivative is g''(u) = 12(2u - 3)² + 12u(2u - 3).

First, let's find the first derivative:

g'(u) = (2u - 3)³ * d(u)/du + u * d/dx[(2u - 3)³]

Using the chain rule, we can differentiate (2u - 3)³ and u as follows:

d(u)/du = 1

d/dx[(2u - 3)³] = 3(2u - 3)² * d(2u - 3)/du

= 3(2u - 3)² * 2

Plugging these values back into the equation for g'(u), we have:

g'(u) = (2u - 3)² + u * 3(2u - 3)² * 2

= (2u - 3)³ + 6u(2u - 3)²

Simplifying the expression, we have:

g'(u) = (2u - 3)³ + 6u(2u - 3)²

Now, let's find the second derivative:

g''(u) = d/dx[(2u - 3)³ + 6u(2u - 3)²]

Using the chain rule and product rule, we can differentiate each term:

d/dx[(2u - 3)³] = 3(2u - 3)² * d(2u - 3)/du

= 3(2u - 3)² * 2

d/dx[6u(2u - 3)²] = 6(2u - 3)² + 6u * d/dx[(2u - 3)²]

= 6(2u - 3)² + 6u * 2(2u - 3)

Plugging these values back into the equation for g''(u), we have:

g''(u) = 3(2u - 3)² * 2 + 6(2u - 3)² + 6u * 2(2u - 3)

= 6(2u - 3)² + 6(2u - 3)² + 12u(2u - 3)

= 12(2u - 3)² + 12u(2u - 3)

Simplifying the expression further, we have:

g''(u) = 12(2u - 3)² + 12u(2u - 3)

Therefore, the first derivative of g(u) is g'(u) = (2u - 3)³ + 6u(2u - 3)², and the second derivative is g''(u) = 12(2u - 3)² + 12u(2u - 3).

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To solve for x, we just need to compute the inverse of A (if it exists) and multiply it by b. If A is invertible, then this method will give us the unique solution to the linear system Ax=b.

To solve a linear system of the form Ax=b using inverse matrices, we can first find the inverse of matrix A (if it exists) and then multiply both sides of the equation by \(A^-1\), giving us:

\(A^-1Ax = A^-1b\)

Since\(A^-1A\) is the identity matrix I, we can simplify the left-hand side to just x:

\(x = A^-1b\)

However, it's worth noting that computing the inverse of a matrix can be computationally expensive, particularly for large matrices.

So, while using inverse matrices can be a useful technique for solving small systems, it may not be the most efficient approach for larger systems. In those cases, other techniques such as Gaussian elimination or LU decomposition may be more appropriate.

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Answer:

The mean is 67

Step-by-step explanation:

Lawnco should produce 300 bags of grade a, 400 bags of grade b, and 200 bags of grade c fertilizer in order to meet the given nutrient requirements.

Let x, y, and z denote the number of 100-lb bags of grade a, b, and c fertilizer respectively.
Then, we can create the following system of equations based on the given information:
16x + 20y + 24z = 26200 (total nitrogen)
6x + 4y + 3z = 4700 (total phosphate)
7x + 4y + 6z = 6600 (total potassium)
Solving this system of equations, we get:
x = 300 (number of bags of grade a)
y = 400 (number of bags of grade b)
z = 200 (number of bags of grade c)
To find out how many 100-lb bags of each of the three grades of fertilizers Lawnco should produce, we need to set up a system of linear equations using the given information and solve for a, b, and c.
Equation 1 (nitrogen): 16a + 20b + 24c = 26,200
Equation 2 (phosphate): 6a + 4b + 3c = 4,700
Equation 3 (potassium): 7a + 4b + 6c = 6,600
Solving this system of linear equations will give you the number of bags of grade A, B, and C fertilizers Lawnco should produce to use all available nutrients.

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Answer:

the answer is -8x^8

Step-by-step explanation:

..........

Answer:

(x+15)+(3x-17)=90

4x-2=90

x=92/4=23

Answer:

101

Step-by-step explanation:

41+38=79

180-79=101

Answer:

• (a)80 mg

• (c)f(t)=80(0.5)^t

• (d)0.625 mg

Explanation:

Part A

From the point (0, 80), we see that the person took 80 mg of the medicine at the start.

Part B

From the graph:

From points (0,80) and (2,20); and (2,20) and (4,5)

• After 2 hours, the amount of medicine has been reduced by a factor of 1/4.

Therefore, after 1 hour, the amount of medicine is reduced by a factor of 1/2.

The completed table is attached below:

Part C

An exponential function is written in the form:

Since the amount of medicine is halved every 1 hour:

The rate of decrease = 1/2

The starting amount, Ao = 80 mg

Therefore, an equation that defines f is:

Part D

After 7 hours, when t=7

After 7 hours, 0.625 mg of medicine remains in the person's body.

Answer:

The answer is 17

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

\( {x}^{2} - 12x + 23 = 0\)

\( {x}^{2} - 12x = - 23\)

\( {x}^{2} - 12x + 36 = 13\)

\( {(x - 6)}^{2} = 13\)

x - 6 = +√13

x = 6 + √13

An equation is formed when two equal expressions. There are 21 $20 bills and 24 $5 bills.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Let the number of $5 bills be x, while the number of $20 bills be y.

Given there were 3 more $5 bills than $20 bills. Therefore, this can be represented as

x = y + 3

Also, The total worth of the dominations is $540. Therefore, we can write,

5x + 20y = 540

Substitute the value of x form the first equation,

5x + 20y = 540

5(y+3) + 20y = 540

5y + 15 + 20y = 540

25y = 525

y = 21

Substitute the value of y in the first equation,

x = 21 + 3

x = 24

Hence, there are 21 $20 bills, and 24 $5 bills.

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Answer:

the first one is 10

the second one is 12.65

Step-by-step explanation:

hope this will help u

Hello there!

Here, we want to use the Pythagorean Theorem: \(a^{2} + b^{2} = c^{2}\).

For problem number 7, we plug 6 and 8 in for a and b. Like this:

\(6^{2} + 8^{2} = c^{2}\)

Now we solve. \(6^{2}\) is 36. \(8^{2}\) is 64.

64 + 36 = 100

Then, we take the square root of 100 to get c.

\(\sqrt{100} = 10\)

(There's something special about this triangle. If you want I'll tell you about it in the comments.)

For problem number 8, we do the same exact thing.

\(4^{2} + 12^{2} = c^{2}\)

\(4^{2} = 16\)  and  \(12^{2} = 144\)

\(144 + 16 = 160\)

\(\sqrt{160} = 8\sqrt{10}\)

I hope this helps!!

Based on the calculations, Sofia has 17 nickels and 8 dimes.

In order to determine the number of dimes and nickels, we would assign a variables to the unknown numbers and then translate the word problem into algebraic equation as follows:

Since you have a total number of 25 coins, an equation which models this situation is given by;

d + n = 25     ....equation 1.

Note: 1 nickel is equal to 0.05 dollar and 1 dime is equal to 0.1 dollar.

Additionally, the coins are worth 1.65 dollars;

0.1d + 0.05n = 1.65     ....equation 2.

Solving both equations simultaneously, we have:

0.1(25 - n) + 0.05n = 1.65

2.5 - 0.1n + 0.05n = 1.65

2.5 - 0.05n = 1.65

0.05n = 0.85

n = 0.85/0.05

n = 17 nickels.

For the number of dimes;

d = 25 - n

d = 25 - 17

d = 8 dimes.

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In the equation y = $7.20x + $790, "y" represents the total cost. An equation is a mathematical statement that shows the relationship between two or more variables. In this equation, there are two variables - "x" and "y". The variable "x" represents the number of units produced or sold, while "y" represents the total cost.

The coefficient of "x" in the equation, which is 7.20, represents the variable cost per unit. This means that for each unit produced or sold, there is an additional cost of $7.20. The constant term, which is $790, represents the total fixed costs. Fixed costs are those costs that do not vary with the number of units produced or sold.To find the total cost of producing or selling a certain number of units, we can plug in the value of "x" into the equation and solve for "y". For example, if we want to find the total cost of producing 100 units, we can substitute x=100 into the equation:
y = $7.20(100) + $790
y = $720 + $790
y = $1510
Therefore, the total cost of producing 100 units is $1510. In summary, "y" represents the total cost in the given equation, which is determined by both fixed and variable costs.
In the equation y = $7.20x + $790, "y" represents option C: total costs. This equation has two components: "$7.20x" represents the variable costs per unit, where x is the number of units, and "$790" represents the total fixed costs. By adding these two components together, you get the total costs (y) for producing x units.

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Answer:

a constant is a data item whose value cannot change during the program execution just as its name implies that the value is constant a variable is a data item whose value can change during the program's execution . Thus as its name implies the the value can vary

The inequality to represent how much Jessica can spend on a T-shirt =

$59 + $x ≤ $75

By utilizing the "equal to" symbol in mathematics, equations are not necessarily balanced on both sides. Occasionally it can be about a "not equal to" relationship, meaning that something is superior to or inferior to another. A relationship between two numbers or other mathematical expressions that yields an unfair comparison is referred to as an inequality in mathematics.

Given, Jessica spent the following amount out of $75 =

Bracelet = $8

Sunglasses = $15

Beach towel = $12

Hat = $10

Sandals = $14

So, the total amount spent = 8 + 15 + 12 + 10 + 14 = $59

Let Jessica spends x dollars on T-shirt.

Certain algebraic mathematical expressions are referred to as inequalities.

Now, using inequalities we can represent the amount Jessica can spend on a T-shirt:

= $59 + $x ≤ $75

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Applying one of the properties of a parallelogram, the value of x is 10°, then 6x=60° and 12x=120°.

There are different quadrilaterals, for example square, rectangle, rhombus, trapezoid, and parallelogram.  Each type is defined accordingly to its length of sides and angles. For example, a parallelogram presents some properties that are presented below.

The figure of the exercise shows two adjacent angles. From the property: the adjacent angles are supplementary, you have:

6x+12x=180

18x=180

x=10°

Therefore, 6x= 6*10=60° and 12x=12*10=120°.

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Answer:

Suppose we add up alternate Fibonacci numbers, Fn-1 + Fn+1; that is, what do ... L(1)=1 and L(3)= 4 so their sum is 5 whereas F(2)=1; L(2)=3 and L(4)= 7 so their ... What is the relationship between F(n-2), and F(n+2)? You should be able to find a ... Fib(N); K (an EVEN number!), Lucas(K) and Fib(K) in each expression like ...

i

Step-by-step explanation:

The triangle when dilated by a scale factor of -1/2 the final image is at the coordinates:

A' = (6, 3)

B' = (6, 5.5)

C' = (5, 4)

The coordinates of the preimage are

(-3, 3), (-3, -2), and (-1, 1)

this is achieved using the formula

=  (k(x - a) + a, k(y - b) + b)

(a, b) is the center of dilation and k is the scale factor

the dilation is done as follows

preimage      dilation                                         image

(-3, 3)         (-0.5(-3 - 3) + 3, -0.5(3 - 3) + 3)        (6, 3)

(-3, -2)       (-0.5(-3 - 3) + 3, -0.5(-2 - 3) + 3)       (6, 5.5)

(-1, 1)          (-0.5(-1 - 3) + 3, -0.5(1 - 3) + 3)          (5, 4)

The final coordinates are (6, 3), (6, 5.5) and (5, 4)

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Answer:

6 baskets

Step-by-step explanation:

The mode of a set of a data is the value which appears the most often. Here, we can see from the line plot that 6 shows more than any other value.