Triangle XYZ ​ is a right triangle with ZQ¯¯¯¯¯⊥XY¯¯¯¯¯¯ . A right triangle with vertices labeled X, Y, and Z. Side Y Z is the base. Angle Z is marked as a right angle. Side X Y contains a midpoint labeled Q. A line segment is drawn through vertex Z to the point Q that bisects angle X Z Y into two parts. Angle X Q Z is marked as a right angle. Side Z X is labeled as a. Side Y Z is labeled as b. Side X Y is labeled as c. Segment X Q is labeled as f. Segment Q Y is labeled as e. Segment Q Z is labeled as d. Drag and drop a correct answer into each box to complete the proof of the Pythagorean theorem. Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. By the angle-angle similarity postulate, △YXZ∼△YZQ and △YXZ∼△ZXQ. Since similar triangles have Response area sides, ac=fa and bc=eb . Solving the equation for a² and b² gives a2=cf and b2= Response area. Adding these together gives a2+b2=cf+ce. Factoring out the common segment gives a2+b2=c(f+e). Using Response area gives a2+b2=c(c), which simplifies to a2+b2=c2 .

The correct answer is thus Quantity A is greater. To compare Quantity A (4) and Quantity B (2π).

we need to convert both to a common unit of measurement. As the maximum area of a triangle that can be entirely drawn within a circle with a radius of 2 is 4, it can be concluded that 4 > 2π.

The maximum area of a triangle that can be entirely drawn within a circle with a radius of 2 is 4. This is accomplished by sketching an equilateral triangle with sides equal to the circle's diameter (4).


This triangle's area is 43, which is more than the area of the circle, which is 2. 4 > 2 is the right answer. To maximise the area, the triangle must be equilateral and have sides equal to the diameter of the circle. This guarantees that the triangle's vertices meet the circle, resulting in the greatest possible area.

To learn more about Area of Triangle:

https://brainly.com/question/21735282

#SPJ4

The correct question is:

The circle C has a radius of 2.from Quantity A and Quantity B which has greatest possible area of traingle that can be drawn completely within circle C?

Arithmetic operations provide meaningful results for variables that c. are quantitative.

For all real numbers, the four fundamental arithmetic operations in mathematics are: Finding the sum in addition ('+') Subtraction (Difference-finding; "-" Multiplication (Identifying the result; "" Finding the quotient in division (")

The commutative laws of addition and multiplication, such as a + b = b + a and ab = ba, the associative laws of addition and multiplication, such as a + (b + c) = (a + b) + c and a(bc) = (ab)c, as well as the distributive law, which links addition and...

Therefore, option C is correct.

Learn more about variables at:

https://brainly.com/question/25223322

#SPJ1

The value of the 5 number summery are minimum 1 , Q1 is 4, median is 4.5, Q2 is 5.5 and Maximum is 6.5

A box plot is a visual representation of the localization, dispersion, and skewness of a collection of numerical data through its quartiles.

The center "box" denotes the group's middle 50% of points. The inter-quartile range is the range of scores from the lower to higher quartile. The interquartile range encompasses the middle 50% of the scores. 75 percent of the scores are lower than the highest quartile.

When doing descriptive analyses or conducting an initial analysis of a sizable data set, a five-number summary is particularly helpful. The maximum and minimum values in the data set, the lower and upper quartiles, and the median make up a summary's five values.

The data set (20 datas)

1, 1.5, 2.5, 3, 4, 4, 4.5, 4.5, 4.5, 4.5, 4.5, 5, 5, 5.5, 5.5, 5.5, 6, 6, 6.5, 6.5

The Minimum is 1

The maximum is 6.5

The value of Q1 of first 10 datas = (4 + 4 )/2 = 4

The median of the data set (20 datas) = (4.5+ 4.5)/2 = 4.5

The value of Q2 of second 10 datas = (5.5+ 5.5)/2 = 5.5

The value of the 5 number summery are minimum 1 , Q1 is 4, median is 4.5, Q2 is 5.5 and Maximum is 6.5

To learn more about BoxPlot refer to :

https://brainly.com/question/29137531

#SPJ1

Work Shown:

xy + 2x + 3x^2 = 4

d/dx[ xy + 2x + 3x^2 ] = d/dx[4]

d/dx[ xy ] + d/dx[ 2x ] + d/dx[ 3x^2 ] = d/dx[4]

y + xy' + 2 + 6x = 0

xy' = -6x-y-2

y' = (-6x-y-2)/x

y' = (-6x-y-2)/x

The point that lies on the line is: (3, 2).

The slope is: 2/3.

The equation of a line in point-slope form is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line.

Given the graph of a line is represented by the equation, y - 2 = 2/3(x - 3), in point-slope form, we have:

Point (x1, y1) = (3, 2)

Slope (m) = 2/3.

The graph is shown in the image below.

Learn more about the point-slope form on:

https://brainly.com/question/24907633

#SPJ1

The derivative of the logarithm function y = ln |e^z| with respect to z is equal to 1/z, assuming each branch of the logarithm function is analytic.

The Chain Rule formula computes the derivative of the combination of two or more functions.

For composite functions, the chain rule in differentiation is defined. If f and g are functions, the chain rule expresses the derivative of their combination.

d/dx [f(g(x))] = f'(g(x)) g'(x)

The chain rule states that if y = f(u) and u = g(x), then the derivative of y with respect to x is given by:

dy/dx = df/du * du/dx

Let f(z) = ln |z| and let g(z) = e^z.

Then, for the composition y = f(g(z)),

we have:

u = g(z) = e^z

f(u) = ln |e^z| = ln |u|

du/dz = e^z

df/du = 1/u = 1/e^z

Now, we can use the chain rule to find the derivative of y with respect to z:

dy/dz = df/du * du/dz

= (1/e^z) * e^z

= 1/z

For more questions on Chain rule

https://brainly.com/question/30329626

#SPJ4

Table A represents a function, but Table B does not represent a function.

Table must meet the following requirements in order to qualify as a function (see the.jpeg picture attached with this response):

The tables below show the values of y corresponding to different values of x: Table A x 3 2 1 y 1 0 0 Table B x 3 5 4 y − 2 1 1

1. Requirement: Each element in the first circle must be linked to at least one element in the second circle.

2. Requirement: There CANNOT be more than one relationship between items in the first circle and those in the second circle.

Table A is in fact a function because it meets BOTH of these requirements.

Table B is not a function since it meets the FIRST criteria but not the SECOND condition.

so

Table A represents a function, but Table B does not represent a function.

To learn more about values of y refer to:

https://brainly.com/question/1389658

#SPJ1

The value of AD is  2.4cm

We have to find [tex]$\mathrm{AD}=$[/tex] ?

Since,

[tex]$$\mathrm{DB}=7.2 \mathrm{c} . \mathrm{m} .$$[/tex]

[tex]$$\mathrm{AE}=1.8 \mathrm{c} . \mathrm{m} .$$[/tex]

[tex]$$\mathrm{EC}=5.4 \mathrm{c} \cdot \mathrm{m} .$$[/tex]

So, We know that (using Thales Theorem)

[tex]\frac{\mathrm{AD}}{\mathrm{DB}}=\frac{\mathrm{AE}}{\mathrm{CE}}[/tex]

Then,

[tex]$\frac{\mathrm{AD}}{7.2}=\frac{1.8}{5.4}$[/tex]

[tex]$\mathrm{AD}=\frac{1.8 \times 7.2}{5.4}$[/tex]

[tex]$\mathrm{AD}=\frac{7.2}{3}$[/tex]

[tex]$\mathrm{AD}=2.4 \mathrm{~cm}$[/tex].

[tex]$\mathrm{EC}=5.4 \mathrm{~cm}$[/tex].

The complete question is,

In [tex]$\triangle \mathrm{ABC} \mathrm{DE} \| \mathrm{BC}$[/tex]Find [tex]$\mathrm{AD}$[/tex] if [tex]$\mathrm{DB}=7.2 \mathrm{~cm}, \mathrm{AE}=1.8 \mathrm{~cm}$[/tex], and

To learn more about Thales Theorem refer to:

https://brainly.com/question/14417137

#SPJ1

Answer:

70 cases will be needed, and with 70 cases, there will be 4 water bottles left over.

Step-by-step explanation:

844 / 12 = 70.333

0.333 = 4 bottles

When revolved over the {x} axis will occupy more volume as compared to when revolved over the {y} axis.

Given is that one bag of pebbles covers 5 ft² and costs $8.99​​.

Refer to the image attached. The reflection over the {x} axis will occupy more volume as compared to the reflection over the {y} axis. The figure generated in both the cases would be a cuboidal prism structure.

Therefore, when revolved over the {x} axis will occupy more volume as compared to when revolved over the {y} axis.

To solve more questions on algebraic expressions, visit the link below-

brainly.com/question/1041084

#SPJ1

The value of P(t) is [tex]\frac{dP}{dt} = k \cdot \sqrt{P}[/tex]  and there will be approximately 220 fish in the lake after 1.6 years.

(a) This is a separable differential equation and can be solved using the separation of variables. We have:

[tex]\frac{dP}{dt}[/tex] = k * [tex]\sqrt{P}[/tex]

[tex]\frac{dP}{\sqrt{P}}[/tex] = k * dt

Integrating on both sides:

2 * [tex]\sqrt{P}[/tex] = k * t + C1

where C1 is a constant of integration. Solving for P, we have:

P(t) = [tex](k * t + C1)^2[/tex] / 4

Using the initial condition P(0) = C, we can solve for C1:

C = [tex](C1)^2[/tex] / 4

C1 = 2 * [tex]\sqrt{C}[/tex]

Therefore, we have:

[tex]\frac{dP}{dt} = k \cdot \sqrt{P}[/tex]

(b) There will be approximately 220 fish in the lake after 1.6 years.

Using the values given, we have:

C = 102

t = 7 months = 7/12 years = 0.5833 years

P(7 months) = 155

We can use this information to solve for k:

[tex]155 =[/tex] [tex]\frac{(k * 0.5833 + 2 *\sqrt{102})^2}{4}[/tex]

[tex]k = \frac{(4 * 155 - 4 * 2^2 *\sqrt{102})}{0.5833^2}[/tex]

Now that we have k, we can find P(1.6 years):

[tex]P(t) = \frac{\left( k \cdot t + 2 \cdot \sqrt{C} \right)^2}{4}[/tex]

By solving, the final value of k is approximately = 10.04

Substituting the value of k, we get:

P(1.6 years) = [tex]\frac{\left( 10.04 \cdot 1.6 + 2 \cdot \sqrt{102} \right)^2}{4}[/tex]

By evaluating the expression, we get:

P(1.6 years) = 220.72

So, there will be approximately 220 fish in the lake after 1.6 years.

To learn more about differential equations:

https://brainly.com/question/1164377

#SPJ4

Answer:

Yes

Step-by-step explanation:

Since they want 10% off EVERY item, this makes it easier.

Instead of having to do them one of a time, we can add all these prices together, find 10%, and see if it's less than $60.

Let's start off with adding all the items

1.25+2.50+1.50+2.00+5.00+12.50+4.50+1.00 = 30.25

Multiplying by 2 because he wants two of everything

$60.50

Now we take 10% of that $60.50

10% in decimal form is 0.10, so we multiply

(60.50)(.10) = $6.05

Lastly, we subtract that $60.50 and $6.05

$60.50 - $6.05 = $54.45

Sales Tax is 9%

So again, we will multiply then add that sales tax

.09 is 9%

(54.45)(.09) = 4.9

Adding that together

54.45 + 4.9 = $59.35

So yes, he would have enough

The arc length is 18.43 cm and the area of the sector of a circle is 64.53 cm².

The arc is a portion of the circumference of a circle.

The formula for calculating the arc states that:

Arc length = 2πr (θ/360)

Where r = the radius of the circle,

π = pi = 3.14

θ = the angle (in degrees) subtended by an arc at the center of the circle.

360 = the angle of one complete rotation.

A sector of a circle of diameter 14 cm has a central angle of 151°.

Here r = 14/2 = 7 cm, and θ = 151°

Substitute the values in the above formula, and we get

Arc length = 2π(7) (151°/360)

Arc length ≈ 18.43 cm

As we know the area of a sector of a circle = θ/360 × πr², where r is the radius of the circle and θ is the central angle.

Substitute the values in the formula to get:

Area of sector of a circle = (151°/360) × π(7)²

Area of sector of a circle ≈ 64.53 cm²

Learn more about the arc of the circle here:

brainly.com/question/1577784

#SPJ1

Answer:

Step-by-step explanation:

Given this information, we can determine the maximum number of units of each product (A, B, and C) that can be produced with the given quantity of resources (M1, M2, and M3). To do this, we can use the formula:

Maximum number of units of product = Minimum of (available quantity of resource / resource required per unit of product)

For example, to find the maximum number of units of product A that can be produced, we take the minimum of the following three values:

(71,000 units of M1 / 3 units of M1 per unit of A) = 23,666.67 units of A

(81,000 units of M2 / 2 units of M2 per unit of A) = 40,500 units of A

(92,000 units of M3 / 6 units of M3 per unit of A) = 15,333.33 units of A

So the maximum number of units of A that can be produced is 15,333.33 units.

Similarly, we can find the maximum number of units of B and C that can be produced:

(71,000 units of M1 / 3 units of M1 per unit of B) = 23,666.67 units of B

(81,000 units of M2 / 2 units of M2 per unit of B) = 40,500 units of B

(92,000 units of M3 / 4 units of M3 per unit of B) = 23,000 units of B

So the maximum number of units of B that can be produced is 23,000 units.

(71,000 units of M1 / 5 units of M1 per unit of C) = 14,200 units of C

(81,000 units of M2 / 7 units of M2 per unit of C) = 11,571.43 units of C

(92,000 units of M3 / 4 units of M3 per unit of C) = 23,000 units of C

So the maximum number of units of C that can be produced is 11,571.43 units.

It is important to note that these calculations are based on the assumption that all resources are used fully and no resources are left over.

Answer:2

Step-by-step explanation:

just because

Answer:

5/4 or C

Step-by-step explanation:

First, it's important to know that the equation is written in slope-intercept form. Slope intercept form is y=mx+b, where m is the slope and b is the y-intercept. So, whatever is in front of x, when the equation is in slope intercept form, is the slope. Since 5/4 would be the value of b, the slope is 5/4, or C.

If this answer helped you, please leave a thanks or a Brainliest!!!

Have a GREAT day!!!

The correct matching is given below.

A. (x, y)= (-y, x) represents the reflection.

B. (x, y) = (x + 9,y - 2) represents the translation.

C. (x, y) = (x - 9,y + 2) represents the translation.

D. (x, y) = (-x, y) represents the reflection.

A spatial transformation is each mapping of feature space to itself and it maintains some spatial correlation between figures.

The translation does not change the shape and size of the geometry. But changes the location.

The reflection does not change the shape and size of the geometry. But flipped the image.

A. (x, y) = (-y, x), this represents the reflection over the line y = -x.

B. (x, y) = (x + 9,y - 2), this represents the translation.

C. (x, y) = (x - 9,y + 2), this represents the translation.

D. (x, y) = (-x, y), this represents the reflection over the y-axis.

More about the transformation of a point link is given below.

https://brainly.com/question/27224339

#SPJ1

Answer: (x' , y') = (x - 9, y + 2)

Step-by-step explanation:

I took the test

Given matrix [tex]\left[\begin{array}{cccc}1&7&3&-4\\0&1&-1&3\\0&0&0&2\\0&0&1&1\end{array}\right][/tex], so the solution set is empty.

Correct option: c

Mathematicians analyze matrices as a subject of study in a field called matrix theory. It started out as a branch of linear algebra but quickly expanded to cover topics in graph theory, algebra, combinatorics, and statistics. When it's necessary to summarise an infinite or limited collection of objects grouped in rows and columns, matrices are utilised. The initial set of a matrix's attributes are those of its constituent entities. Solving linear equations is made easier by it. Matrices are incredibly priceless items that are used in a variety of contexts. In addition to mathematical applications, matrices are employed in a wide range of scientific disciplines.

Given that,

[tex]\left[\begin{array}{cccc}1&7&3&-4\\0&1&-1&3\\0&0&0&2\\0&0&1&1\end{array}\right][/tex]

now exchange R₄ ↔ R₃

[tex]\left[\begin{array}{cccc}1&7&3&-4\\0&1&-1&3\\0&0&1&1\\0&0&0&2\end{array}\right][/tex]

Therefore, rank of main matrix = 3

rank of Augmented matrix = 4

So, rank of main matrix < rank of Augmented matrix

Thus, there is no solution.

Also we can say, the solution set is empty.

correct option: c

To know more about matrix refer to:

https://brainly.com/question/28060752

#SPJ1

When the b-component of the equation is 2, the y-intercept for y = 6x + 2 is (0,2).

An equation is a formula in mathematics that expresses the equivalence of two expressions by linking them with the equals symbol =. In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical equation that depicts the connection between two expressions on opposite sides of the sign. It generally consists of one variable and one equal to symbol. 2x - 4 = 2 is an example.

Here,

y = 6x + 2

y-intercept=(0,2)

The y-intercept for y = 6x + 2 is (0,2) when the b-component of equation is 2.

To know more about equation,

https://brainly.com/question/2228446

#SPJ1

Answer:

In 2020, the baseball card will be worth $1,072.50.

I hope this helps!

Step-by-step explanation:

The maximum acceleration attained on the interval [0,3] by the particle whose velocity is given by: v(t) = t3 – 3t2 + 12t + 4 is 21

The correct answer is an option (a)

The velocity function is given by,

v(t) = t³ – 3t² + 12t + 4

We differentiate above function to get the acceleration function which will be

a(t) = v'(t)

a(t) = 3t² - 6t + 12 + 0

a(t) = 3t² - 6t + 12

Consider the interval [0,3]

We find the value of acccleration function at the end of the intervals.

For t = 0,

a(0) = 3(0)² - 6(0) + 12

a(0) = 0 - 0 + 12

a(0) = 12

And for t = 3,

a(3) = 3(3)² - 6(3) + 12

a(3) = 27 - 18 + 12

a(3) = 21

This means, the function a(t) is increasing and the maximum value of function a(t) would be at t = 3.

Therefore, the maximum acceleration attained on the interval [0,3] is 21

Learn more about the function here:

https://brainly.com/question/28193995

#SPJ4

Answer:

971.92 square inches of wrapping paper.

Step-by-step explanation:

Please find the attachment for detail

a) The differential equation which

stating that the instantaneous rate of change of y with respect to t is directly proportional to the square root of y is

dy/dt = c√y .

b) The value of constant of proportionality, c is equals to the -3/4.

I fill up a tall topless tin can with water and punch a hole near the bottom with an ice pick. As a results of it water leakage is started. Due to water leakage, the depth of water in tin start decreasing. According to Torricelli's Law, the rate of change of the volume V of water in a draining tank with respect to time is dirctly proportional to the square root of the water's depth. Let the depth of water in tin be "y".

a) Now, the instantaneous rate of change of y with respect to t is directly proportional to the square root of y. A differential equation which states the above condition is represented as

dy/dt ∝ √y

to remove the proporationalty sign we use a constant c which is known as constant of proportionality.

=> dy/dt = c√y

This is the required differential equation.

b) Now, we have at t = 0 minute, y = 16cm

and rate of change of y with respect to time, dy/dt = - 3 cm/ min. We have to calculate the value of constant c . So, plugging all known values in above differential equation,

=> dy/dt = c√y

=> -3 = c√16

=> -3 = c×4

=> c = -3/4

Hence, required constant is -3/4.

To learn more about constant of proportionality, visit :

https://brainly.com/question/1835116

#SPJ4

Complete question :

Suppose you till a tall topless tin can with water, and then punch a hole near the bottom with an ice pick. The water leaks quickly at first, then more slowly as the depth of the water decreases. In engineering or physics. you will learn that the rate at which water leaks out is directly proportional to the square root of its depth. y. a. Write a diferential equation stating that the instantaneous rate of change of y with respect to t is directly proportional to the square root of y

b. Suppose at time t=0 minutes. the depth y is 16 cm and dy/dt =-3 cm / min. Find the constant of di proportionality c.

The value of each unknown emoji is as shown below:

1) 3

2) 3

3) 4

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

Take x and y for each symbols and solve as shown:

1) x+y=8

y=5

x+5=8

=> x=8-5=3

2) 2x+y=10

    y=4

2x+4=10

2x=10-4=6

=> x=6/2 = 3

3) 3x+2y=18

  y=3

3x+2(3)= 18
3x+6=18

=> 3x=18-6 = 12

=> x=12/3 = 4

To learn more about the solution of an equation from the given link

https://brainly.com/question/22688504

#SPJ1

The final price for the members after the discount is $395.52.

What is meant by discount price?

Discounts are price reductions that store owners offer on items or services that are otherwise priced as marked. This portion of the rebate is typically provided to boost sales or get rid of excess inventory. The price of an item as stated by the manufacturer or seller, without any price reduction, is known as the List price or Marked Price. After any discounts or price reductions from the list price, the selling price is the final price at which an item is actually sold.

Given,

  The cost price of the computer = $370.80

 The selling price at first = $618

a) The markdown percentage = 20%

The selling price after this markdown = 618 - (618 * 20/100)

                                                              = 618 - 123.6 = $494.4

b) Additional discount for the members of the store's loyalty club = 20%

  The final selling price for the members = 494.4 - (494.4 * 20/100)

                                                                    = 494.4 - 98.88 = $395.52

Therefore the final price for the members after the discount is $395.52.

To learn more about discounts, follow the link.

https://brainly.com/question/1548141

#SPJ1