Drag and drop an answer to each box to correctly explain the derivation of the formula for the volume of a pyramid.

P and Q are endpoints, so the center of the circle would be the midway point.

A. The midpoint is found using:

(x1 + x2 /2 , y1 +y2 /2)

-10 + 4 = -6 /2 = -3

-2 + 6 = 4 /2 = 2

The center of the circle is at (-3,2)

B) The radius would be the distance from the midpoint to an end point.

Using the distance formula:

√((x2-x1)^2 + (y2-y1)^2)

√(4 - -3^2 + 6-2^2)

√(7^2 + 4^2)

√(49+16)

√65

C) Using the circle equation form of (x-h)^2 + (y-k)^2 = r^2

H,K is the center point found in part A and r is the radius found in part B.

The equation becomes (x-(-3))^2 + (y -2)^2 = √65^2

Which simplifies to: (x+3)^2 + (y-2)^2 = 65

For this case we have the variable [tex]x = -3[/tex]:

[tex]A) 6x = 6 (-3) = - 18\\B) 4x = 4 (-3) = - 12\\C) -3x = -3 (-3) = + 9\\D) -7x = -7 (-3) = + 21[/tex]

Now, matching each expression with its value we have:

A goes with 4

B goes with 3

C goes with 2

D goes with 1

ANswer:

A goes with 4

B goes with 3

C goes with 2

D goes with 1

Answer:

True

Step-by-step explanation:

∠4 and ∠5 are congruent and alternate angles, hence

A and B  are parallel lines

Answer:

In conclusion, dreams are the driving theme and characterization in the novel. They help explain each character's motivation for the actions they take and the way they feel. All of the characters have a obstacles in their life stopping them from reaching their goal. Authors use dreams to give their characters something to live for and strive for. Without the character's dreams and goals for the future, the characters would have nothing to work towards and they would be much less complex  

A conclusion for an essay on dreams in 'Of Mice and Men' should discuss the portrayal of the elusive American Dream, the use of dreams as a literary device, and the reflection of societal constraints and collective unconscious.

When crafting a conclusion for an essay about the theme of dreams in Of Mice and Men, you must strive to encapsulate the essence of the theme and its impact on the characters and the reader's understanding of the novel's message. The unattainable nature of the American Dream is vividly portrayed through the characters' struggles, symbolizing the universal experience of aspiration and loss. While each character harbors personal ambitions, the novel ultimately reveals the harsh reality of shattered dreams and the perseverance of hope, despite life's unpredictable and often tragic course. Understanding the role of dreams as a literary tool employed by John Steinbeck deepens one’s appreciation for his exploration of the human psyche and the societal constraints of the time period. Dreams in Steinbeck’s work reflect a combination of the characters' inner desires and the collective unconscious that connects them to the broader human experience, as Carl Jung would suggest.

By the law of sines,

[tex]\dfrac{\sin m\angle A}a=\dfrac{\sin m\angle B}b\implies\sin m\angle B=\dfrac{33.7\sin75^\circ}{51.2}[/tex]

We get one solution by taking the inverse sine:

[tex]m\angle B=\sin^{-1}\dfrac{33.7\sin75^\circ}{51.2}\approx39^\circ[/tex]

In this case there is no other solution!

To check: suppose there was. The other solution is obtained by recalling that [tex]\sin(180-x)^\circ=\sin x^\circ[/tex] for all [tex]x[/tex], so that

[tex]180^\circ-m\angle B=\sin^{-1}\dfrac{33.7\sin75^\circ}{51.2}\implies m\angle B\approx141^\circ[/tex]

But remember that the angles in any triangle must sum to 180 degrees in measure. This second "solution" violates this rule, since two of the known angles exceed 180: 75 + 141 = 216 > 180. So you're done.

This triangle is not a right triangle. How do we solve this then? You will use the law of sine with is shown below:

[tex]\frac{sin A}{a} =\frac{sin B}{b} = \frac{sinC}{c}[/tex]

What we know is shown in the image attached below:

Plug what you know into the law of sine

[tex]\frac{sin75}{51.2} =\frac{sinB}{33.7}[/tex]

To solve for sinB cross multiply

sin75*33.7 = sinB * 51.2

32.55 = sinB*51.2

Divide 51.2 to both sides to isolate sinB

32.55 / 51.2 = sinB / 51.2

0.63577 = sinB

To find B you must use arcsin:

[tex]sin^{-1} 0.63577[/tex]

39.477

^^^This is your rough estimate but you can simply keep it to 39 degrees

This means that your answer is correct!

Hope this helped!

Answer:

Correct choice is  C. Similar AA.

Step-by-step explanation:

We have been given a picutre of the triangles. Using those information we need to find the correct choice.

Consider triangle FGH and triangle JKL.

∠F≅∠J  {Both are equal to 30°}

∠H≅∠L  {Both are equal to 50°}

Then triangle  FGH is similar to the triangle JKL by AA - similarity of the triangle. Because we are getting two congruent angle pairs.

Hence correct choice is  C. Similar AA.

Answer:

1.2 cm

Step-by-step explanation:

Quadrilateral circumscribing a circle is a quadrangle whose sides are tangent to a circle inside it (see attached diagram).

The area of circumscribed quadrilateral is

[tex]A=p\cdot r,[/tex]

where [tex]p=\dfrac{a+b+c+d}{2}[/tex] is semi-perimeter and r is radius of inscribed circle.

In your case, [tex]A=12\ cm^2[/tex]

If a quadrilateral is circumscribed over the circle, then the sum of opposite sides is equal, so

[tex]a+c=b+d=10\ cm,[/tex]

so

[tex]P=10+10=20\ cm\\ \\p=\dfrac{20}{2}=10\ cm[/tex]

Now

[tex]12=10\cdot r\Rightarrow r=\dfrac{12}{10}=1.2\ cm[/tex]

Answer:

360

Step-by-step explanation:

Answer:

360

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Plotting the points in a sketch quickly shows that the vertices are not at right angles to each other, thus excluding rectangle and square whose vertices are at right angles.

The best selection is a rhombus

Answer:

Step-by-step explanation:

This is the pre-calculus version of the arc length problem.  The formula we need for this is:

[tex]s=r\theta[/tex]

where s is the arc length (here, the distance she has to travel to get the gum off the tire), r is the radius, and theta is the angle given (the angle here always always has to be in radians!!!)  Filling in accordingly, we get

[tex]s=(6.5)(\frac{37\pi }{90})[/tex]

Do the math.  You need the answer rounded to the nearest inch, so that means you have to multiply in the pi (I used 3.1415):

s = 8 inches

Answer:

8

Step-by-step explanation:

Answer:

310

Step-by-step explanation:

62 percent of 500 is 310

Hope this helps :)

Answer:

Option D, 310

Step-by-step explanation:

In the given graph 500 people were surveyed.

Now we have to calculate the number of individuals who have a college degree or some college.

Now from the given pie chart.

College degree individuals = 25% of 500

                                             = 0.25 × 500

                                            = 175

Individual with some college = 27% of 500

                                                = 0.27 × 500

                                               = 135

So the total of college dgree + some college = 135 + 175 = 310

Option D 310 is the answer.

if you shift it down 7, the new equation would be

g(x)=x-7

hope this helps

Answer:

B

Step-by-step explanation:

An upward shift or a downward shift is reflected in the +k or -k (k being some real number).  If there is a number "stuck" to the x, that reflects the steepness (slope) of the line.  The slope of this line is 1, and the y-intercept (where it goes through the y-axis) is down 7 from the origin. B is your answer.

Hello there!

Answer:

The slope is 9, and the y-intercept is –2

Step-by-step explanation:

The equation is y = 9x - 2

This follows the equation y = mx + b

Where as:

m = slope

b = y-intercept

When you know this, you would figure out that 9 is in the same place as m, and -2 is in the same place as b.

The y-intercept would not be a positive 2 because when there's a minus sign next to the number in the y-intercept spot, then you would have to bring that over to the number. We can also say the minus sign belongs to the 2, making it a -2.

With the information we know now, we can say that the slope of the equation is 9, and the y-intercept would be -2.

Therefore, giving your answer as "The slope is 9, and the y-intercept is –2"

Final answer:

The slope of the linear function represented by y=9x-2 is 9, and the y-intercept is -2. This is determined by comparing the equation to the slope-intercept form y = mx + b.

Explanation:

The slope and y-intercept of the linear function represented by the equation y=9x-2 can be identified by comparing it to the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept. In the given equation, 9 is the coefficient of x, which means it is the slope of the line. The constant term, -2, is the y-intercept because it indicates the point at which the line crosses the y-axis.

Answer:

(x - 3)² + (y - 2)² = 17

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r the radius

here (h, k) = A(3,2), thus

(x - 3)² + (y - 2)² = r²

The radius is the distance from the centre to a point on the circle

Calculate r using the distance formula

r = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (3, 2) and (x₂, y₂ ) = (- 1, 1) ← point on circle

r = [tex]\sqrt{(-1-3)^2+(1-2)^2}[/tex] = [tex]\sqrt{(-4)^2+(-1)^2}[/tex] = [tex]\sqrt{17}[/tex]

Hence r² = ([tex]\sqrt{17}[/tex] )² = 17

(x - 3)² + (y - 2)² = 17 ← equation of circle

Area = length times width

Length = x + 4

Width = 4_2/5, which we can write as the improper fraction 22/5.

Area is given to be 28_3/5, which can be written as 143/5.

Here is the set up:

(143/5) = (x + 4)(22/5)

Take it from here.

Answer:

Choice B

Step-by-step explanation:

We can perform a least squares regression model in Ms. Excel to determine the equation of the line of best fit for the data given;

The first step is to enter the data into any two adjacent columns of an excel workbook. Next, click on the Data ribbon followed by the Data Analysis tool pack. We then proceed to select regression from the pop-up window. The final step is to select the y range and the x range of values from our data.

Once we click ok, Excel returns our least squares regression model as shown in the attachment below.

The coefficient of X variable 1 is our slope.

Answer:

b

Step-by-step explanation:

Answer:

V = 400

Step-by-step explanation:

The volume (V) of the pyramid is

V = [tex]\frac{1}{3}[/tex] area of base × perpendicular height (h)

Consider a right triangle from the vertex to the midpoint of the base across to the slant height, with hypotenuse of 13

Using Pythagoras' identity on the right triangle, then

h² + 5² = 13²

h² + 25 = 169 ( subtract 25 from both sides )

h² = 144 ( take the square root of both sides )

h = [tex]\sqrt{144}[/tex] = 12

Area of square base = 10² = 100, thus

V = [tex]\frac{1}{3}[/tex] × 100 × 12 = 4 × 100 = 400

For this case we have that the volume of the figure is composed of the volume of a prism and the volume of a pyramid:

The volume of the prism is given by:

[tex]V = A_ {b} * h[/tex]

Where:

[tex]A_ {b}[/tex]: It is the area of the base

h: It's the height

Substituting:[tex]V = 6 * 6 * 6\\V = 216 \ units ^ 3[/tex]

The volume of the pyramid is given by:

[tex]V = \frac {1} {3} * L ^ 2 * h[/tex]

Where:

[tex]L ^ 2:[/tex]It is the area of the base

h: It's the height

Substituting:

[tex]V = \frac {1} {3} * 6 ^ 2 * 5\\V = \frac {1} {3} * 36 * 5\\V = 60units ^ 3[/tex]

We add and we have:

[tex]V = 276 \ units ^ 3[/tex]

ANswer:

Option D

Answer:

x = -2 and y = -3

Step-by-step explanation:

It is given that,

-8x + 3y =7    ----(1)

13x - 3y =-17   -----(2)

To find the value of x and y

eq(1) + eq(2) ⇒

-8x + 3y = 7    ----(1)

13x -  3y = -17   -----(2)

 5x +    = -10

x = -10/5 = -2

Substitute value of x in eq (1)

-8x + 3y =7    ----(1)

-8 * -2  + 3y = 7

16 + 3y = 7

3y = 7 - 16 = -9

y = -9/3 = -3

Therefore x = -2 and y = -3

For this case we must solve the following system of equations:

[tex]-8x + 3y = 7\\13x-3y = -17[/tex]

If we add both equations we have:

[tex]-8x + 13x + 3y-3y = 7-17\\5x = -10\\x = \frac {-10} {5}\\x = -2[/tex]

We find the value of the variable "y":

[tex]3y = 7 + 8x\\y = \frac {7 + 8x} {3}\\y = \frac {7 + 8 (-2)} {3}\\y = \frac {7-16} {3}\\y = \frac {-9} {3}\\y = -3[/tex]

Thus, the solution of the system is (-2, -3)

ANswer:

(-2, -3)

Answer:

The right answer is figure B

Step-by-step explanation:

* Lets talk about the complex number

- The complex number z = a + bi consists of two part:

# a is the real part and represented graphically by the x-axis

# b is the imaginary part and represented graphically by the y-axis

- We can add and subtract them by adding or subtracting the real parts

 together and the imaginary parts together

# Ex: if z1 = 2 + 3i and z2 = -1 - i

∴ z1 + z2 = (2 + -1) + (3 + -1)i = 1 + 2i

∴ z1 - z2 = (2 - -1) + (3 - -1)i = (2 + 1) + (3 + 1)i = 3 + 4i

* Now lets solve the problem

- Let find from the graph z1 , z2 and point A

- Look to the any graph and find z1 through the axes

- We moved 6 units on the x-axis (real part) and 7 units up

 (imaginary part)

∴ z1 = 6 + 7i

- Similarly find z2 through the axes

- We moved 5 units on the x-axis (real part) and 2 units down

 (imaginary part)

∴ z2 = 5 - 2i

* Now lets solve z1 - z2

∵ z1 = 6 + 7i and z2 = 5 - 2i

∴ z1 - z2 = (6 + 7i) - (5 - 2i) = (6 - 5) + (7 - -2)i = 1 + 9i

* Lets find in which figure the coordinates of A are (1 , 9)

∵ In figure A point A is (1 , 6)

∵ In figure B point A is (1 , 9)

∵ In figure C point A is (11 , 5)

∵ In figure D point A is (11 , 9)

∴ The right answer is figure B

Answer:

The Angles of △SPT are

[tex]m\angle STP=35\°[/tex]  

[tex]m\angle SPT=126\°[/tex]

[tex]m\angle PST=19\°[/tex]

Step-by-step explanation:

step 1

Find the measure of angle PET

we know that

The inscribed angle is half that of the arc it comprises.

[tex]m\angle PET=\frac{1}{2}(arc\ PT)[/tex]

substitute the given values

[tex]m\angle PET=\frac{1}{2}(70\°)[/tex]

[tex]m\angle PET=35\°[/tex]

step 2

Find the measure of angle PTE

we know that

The sum of internal angles of a triangle must be equal to 180 degrees

In the triangle PET

[tex]m\angle PET+m\angle EPT+m\angle PTE=180\°[/tex]

substitute the given values

[tex]35\°+54\°+m\angle PTE=180\°[/tex]

[tex]m\angle PTE=180\°-89\°=91\°[/tex]

step 3

Find the measure of angle STP  

we know that

The inscribed angle is half that of the arc it comprises.

[tex]m\angle STP=\frac{1}{2}(arc\ TP)[/tex]

substitute the given values

[tex]m\angle STP=\frac{1}{2}(70\°)=35\°[/tex]

step 4

Find the measure of angle SPT

we know that

[tex]m\angle SPT+m\angle EPT=180\°[/tex] ----> by supplementary angles

[tex]m\angle SPT+54\°=180\°[/tex]

[tex]m\angle SPT=180\°-54\°=126\°[/tex]

step 5

Find the measure of angle PST

we know that

The sum of internal angles of a triangle must be equal to 180 degrees

In the triangle SPT

[tex]m\angle STP+m\angle SPT+m\angle PST=180\°[/tex]

substitute the given values

[tex]35\°+126\°+m\angle PST=180\°[/tex]

[tex]m\angle PST=180\°-161\°=19\°[/tex]

Answer:

The equation that represents the instantaneous velocity at any given time, t is:

[tex]v (t) = 8t -2[/tex]

Step-by-step explanation:

In physics, the equation that describes the instantaneous velocity of an object is the derivative of the position of this object as a function of time.

In this problem we have the function that describes the position of the object at a time t.

[tex]f (t) = 4t ^ 2-2t[/tex]

Therefore to obtain the instantaneous velocity we derive f (t) with respect to time

[tex]\frac{df(t)}{dt} = 2(4)t-2\\\\\frac{df(t)}{dt} = 8t-2 = v (t)[/tex]

Finally the equation of velocity is:

[tex]v (t) = 8t -2[/tex]

Answer: C.

Step-by-step explanation: popcorn are made out of corn

Answer is D (: !!!!!!!!!!

Answer:

23.

Using Thales theorem, we have:

AP/BP = AQ/CQ

=> 8/40 = x/45

=> x = (45 · 8)/40 = 9

24.

Also using Thales theorem, we have:

5/6 = (x - 1)/12

x - 1 = (12 · 5)/6 = 60/6 = 10

x     = 10 + 1 = 11

25.

Because we already have the bisector, we know that:

x/6.9 = 18.3/6.2

x        = (6.9 · 18.3)/6.2 ≈ 20.4

Hopefully all of them are correct

To calculate the conditional probability, we need to find the probability of transferring two red balls and two blue balls from Bowl I to Bowl II and the probability of selecting a blue ball from Bowl II which is 0.0923

To calculate the conditional probability, we need to find the probability of transferring two red balls and two blue balls from Bowl I to Bowl II and the probability of selecting a blue ball from Bowl II.

First, we calculate the probability of transferring two red balls and two blue balls from Bowl I to Bowl II. There are 14 balls in Bowl I, so the probability of transferring a red ball on the first draw is 8/14. After transferring one red ball, there are now 13 balls in Bowl I, so the probability of transferring another red ball is 7/13. Similarly, the probability of transferring a blue ball on the first draw is 6/14, and the probability of transferring another blue ball is 5/13. To find the overall probability, we multiply these probabilities: (8/14) * (7/13) * (6/14) * (5/13).

Next, we calculate the probability of selecting a blue ball from Bowl II. After transferring four balls from Bowl I, there are now 10 balls in Bowl II, with 6 blue balls. The probability of selecting a blue ball is therefore 6/10.

Finally, we calculate the conditional probability by dividing the probability of transferring two red balls and two blue balls from Bowl I to Bowl II by the probability of selecting a blue ball from Bowl II:

= (8/14) * (7/13) * (6/14) * (5/13) / (6/10)

= 0.0923 (rounded to four decimal places).

https://brainly.com/question/32171649

#SPJ12

The answers are:

C) [tex](3+xz)(-3+xz)[/tex]

D) [tex](y^2-xy)(y^2+xy)[/tex]

F) [tex](64y^2+x^2)(-x^2+64y^2)[/tex]

To know which of the products results in a difference of square, we need to remember the difference of squares from:

The difference of squares form is:

[tex](a+b)(a-b)=a^{2}-b^{2}[/tex]

So, discarding each of the given options in order to find which products result in a difference of squares, we have:

[tex](x-y)(y-x)=xy-x^{2}-y^{2} +yx=-x^{2} -y^{2}[/tex]

So, the obtained expression is not a difference of squares.

[tex](6-y)(6-y)=36-6y-6y+y^{2}=y^{2}-12y+36[/tex]

So, the obtained expression is not a difference of squares.

[tex](3+xz)(-3+xz) =(xz+3)(xz-3)=(xz)^{2}-3xz+3xz-(3)^{2}\\\\(xz)^{2}-3xz+3xz-(3)^{2}=(xz)^{2}-(3)^{2}[/tex]

So, the obtained expression is a difference of squares since it matches with the form of the difference of squares.

[tex](y^2-xy)(y^2+xy)=(y^{2})^{2}+y^{2}*xy-y^{2}*xy-(xy)^{2} \\\\(y^{2})^{2}+y^{2}*xy-y^{2}*xy-(xy)^{2}=(y^{2})^{2}-(xy)^{2}[/tex]

So, the obtained expression is a difference of squares since it matches with the form of the difference of squares.

[tex](25x-7y)(-7y+25x)=-175xy+(25x)^{2}+49y^{2}-175xy\\\\-175xy+(25x)^{2}+49y^{2}-175xy=(25x)^{2}+49y^{2}-350xy[/tex]

So, the obtained expression is not a difference of squares

[tex](64y^2+x^2)(-x^2+64y^2)=(64y^2+x^2)(64y^2-x^2)\\\\(64y^2+x^2)(64y^2-x^2)=(64y^{2})^{2} -(x^{2}*64y^{2})+(x^{2}*64y^{2})-(x^{2})^{2}\\ \\(64y^{2})^{2} -(x^{2}*64y^{2})+(x^{2}*64y^{2})-(x^{2})^{2}=(64y^{2})^{2}-(x^{2})^{2}[/tex]

So, the obtained expression is a difference of squares since it matches with the form of the difference of squares.

Hence, the products that result in a difference of squares are:

C) [tex](3+xz)(-3+xz)[/tex]

D) [tex](y^2-xy)(y^2+xy)[/tex]

F) [tex](64y^2+x^2)(-x^2+64y^2)[/tex]

Have a nice day!

Answer:

{x = 3 , y = -3 thus the answer is A

Step-by-step explanation:

Solve the following system:

{5 x + 2 y = 9 | (equation 1)

{2 x - 3 y = 15 | (equation 2)

Subtract 2/5 × (equation 1) from equation 2:

{5 x + 2 y = 9 | (equation 1)

{0 x - (19 y)/5 = 57/5 | (equation 2)

Multiply equation 2 by 5/19:

{5 x + 2 y = 9 | (equation 1)

{0 x - y = 3 | (equation 2)

Multiply equation 2 by -1:

{5 x + 2 y = 9 | (equation 1)

{0 x+y = -3 | (equation 2)

Subtract 2 × (equation 2) from equation 1:

{5 x+0 y = 15 | (equation 1)

{0 x+y = -3 | (equation 2)

Divide equation 1 by 5:

{x+0 y = 3 | (equation 1)

{0 x+y = -3 | (equation 2)

Collect results:

Answer:  {x = 3 , y = -3

Answer:

A) 5x+2y=9

B) 2x-3y=15

Multiply A) by 1.5

A) 7.5x +3y = 13.5  then add it to B)

B) 2x-3y=15

9.5x = 28.5

x = 3

5*3 + 2y=9

2y = -6

y = -3

answer is A

Step-by-step explanation:

Answer:

x = 36

Step-by-step explanation:

The angles 3x - y and 2x + y form a straight angle and are supplementary, so

3x - y + 2x + y = 180

5x = 180 ( divide both sides by 5 )

x = 36

-----------------------------------------------

5y and 3x - y are vertical angles and congruent, hence

5y = 3x - y ( add y to both sides )

6y = 3x ← substitute x = 36

6y = 3 × 36 = 108 ( divide both sides by 6 )

y = 18