Answer:
24
Step-by-step explanation:
a circle is 360
we can divide 360 by 15
360 divided by 15 =
24
120
∑ (3n-6)
n=1
Find the sum.
Answer:
21300
Step-by-step explanation:
120∑n=13n−4
Split the summation into smaller summations that fit the summation rules.
120∑n=1 3n−4=3120∑n=1 n+120∑n=1 −4
Evaluate
3120∑n=1 n.
21780
Evaluate
120∑n=1 −4 −480
Add the results of the summations.
21780−480
Subtract 480 from 21780.
21300
Question 1
The prism shown in the diagram has a volume of 39 units. What is the volume of the pyramid? Explain your reasoning.
Question 2
Consider this cone and pyramid, which have the same height, h. Planes parallel to the base cut through each solid at equal
heights, as shown.
Part A
What is the approximate area of each cross section of the cone and pyramid?
Type the correct answer in each box. Use numerals Instead of words.
Part B
Consider your results from part A. What conclusion can you draw about the volumes of the cone and pyramid? Explain
your reasoning.
Part C
The volume of the pyramid is one-third of the area of its base multiplied by its height, which is 144/3 pi h cubic units. Using
this measurement and your answer from part B, derive a formula for the volume of a cone.
The volume of the cone and pyramid are the same.
Formula for volume of cone = ⅓(144π × h)
What is the Volume of a Triangular Pyramid and a Cone?Volume of cone = ⅓[πr² × height of cone)
Volume of triangular pyramid = ⅓[(½bh × height of pyramid)]
Also note the following:
Area of a circle = πr²
Area of a triangle = ½bh
Part A:
Area of circle 1 = πr² = π(12²) = 144π units²
Area of circle 2 = πr² = π(6²) = 36π units²
Area of circle 3 = πr² = π(3²) = 9π units²
Area of triangle 1 = ½(24)(12π) = 144π units²
Area of triangle 2 = ½(12)(6π) = 36π units²
Area of triangle 3 = ½(6)(3π) = 9π units²
Part B: Based on our results in part A, the volumes of the cone and pyramid, having the same height are the same.
Part C:
Volume of pyramid = ⅓(144π × h)
Using this measurement and our conclusion in part B:
Formula for the Volume of a cone = ⅓(144π × h)
Learn more about the volume of cone and pyramid on:
https://brainly.com/question/16017622
find the value of the variable
Answer:
x=5
Step-by-step explanation:
6:5
x:4, so x =5
The side also looks a little bigger than 4.
Hope it Helps
Is the solution shown below correct? explain. 9x 2=8x2 6x negative 8 x squared 3 x 2 = 0. x = startfraction negative 3 plus-or-minus startroot (3) squared minus (4) (negative 8) (2) endroot over negative 16 endfraction. x = startfraction negative 3 plus-or-minus startroot 9 minus (64) endroot over negative 16 endfraction. x = startfraction 3 plus-or-minus startroot 55 endroot i over 16 endfraction.
The correct solution of the given quadratic equation was found using the formula.
The given equation is:
[tex]9x+2=8x^{2} +6x[/tex]
[tex]8x^{2} +6x-9x-2=0[/tex]
[tex]8x^{2} -3x-2=0[/tex]....(1)
What is a quadratic equation?An equation of the form [tex]ax^{2} +bx+c=0[/tex] is called a quadratic equation where [tex]a\neq 0[/tex].
We can solve equation (1) by the formula
[tex]x=\frac{-b+-\sqrt{b^{2} -4ac} }{2a}[/tex]
So, [tex]x=\frac{3+-\sqrt{(-3)^{2} -4(8)(-2)} }{2(8)}[/tex]
[tex]x=\frac{-3+-\sqrt{73} }{16}[/tex]
Hence, the correct solution of the given quadratic equation was found using the formula.
To get more about quadratic equations visit:
https://brainly.com/question/1214333
what are the angle measures of X and Z?
Answer:
m∠Z=146
m∠X=34
Step-by-step explanation:
Since this is an Isosceles Trapezoid, we can assume that m∠Z=m∠Y, because an isosceles trapezoid has two pairs of congruent angles, therefore m∠Z=146.
Since angle Y and Angle X are same side interior and line ZY║WX, we can assume that m∠X+m∠Y=180. Substitute values:
[tex]146+X=180\\Y=34[/tex]
PLEASE HELP I WILL GIVE YOU 5 STARS AND BRAINLIEST
Answer:
224 ÷ 4 = 56
Step-by-step explanation:
14 × 4 = 56
56 × 4 = 224
224 ÷ 4 = 56
Solve the following:
Answer:
-25
Step-by-step explanation:
What is the Pythagorean triplet whose one member is 14
Answer:
14, 48 and 50
Step-by-step explanation:
plane leaves the airport at 9:15 p.m. and travels at 560 km/h. how far away will it be at midnight?
t=2 hrs-------so 2 hrs after the second plane leaves it will catch the first plane
CK
720+240*2=600*2
720+480=1200
1200=1200
A glider flies 8 miles south from the airport and then 15 miles east. Then it flies in a straight line back to the airport. What was the distance of the glider's last leg back to the airport?
Answer:
17
Step-by-step explanation:
This flight makes a right triangle
The sides are 8 and 15. The hypotenuse isnt know and that is the answer.
8^2 + 15^2 = c^2
c^2 = 289
c = 17
2. In the last quarter of a high school basketball game,
you team is behind by 34 points. A field goal is 2 points
and a foul shot is 1 point. The coach doesn’t want the team
shooting any 3-point shots.
- Let x represent the number of field goals scored.
Let y represent the number of foul shots scores.
- Write and graph an inequality that models the
different numbers of field goals and foul shots
your team could score to win or tie the game.
(Assume that the other team scores no more points.
The inequality of the expression is a greater than inequality, and the required inequality is 2x + y > 34
How to determine the inequality?From the question, we have the following representations:
x represents field goalsy represents foul shotsA field goal has 2 points, while a foul shot has 1 point.
So, the number of points in a game is:
Score = 2x + y
The team is behind by 34 points.
So, the team must attain above 34 points
This means that the score must be greater than 34.
So, the inequality is:
2x + y > 34
See attachment for the graph of the inequality
Read more about inequality at:
https://brainly.com/question/11234618
#SPJ1
a. YXZ
b. YZX
c. ZYX
d. XYZ
Answer:
The triangle which is congruent to triangle QRS is YXZ
If he is choosing one event and one time how many options does he have for his birthday party?
Answer:
6 options
Step-by-step explanation:
hes got 3 event options
and 2 time slots so
3 times 2 is 6
how much is 2.268 in dimes
Answer:
1 dime
Step-by-step explanation:
didvide 1 pound by the weight or the dime to get the answer
Select all of the equations that are equivalent to 3x+45=180
1. 3(x+45)=180
2. 3(x+15)=180
3. 3(x+15)=60
4. x+15=60
5. 3x=135
3. The curve C with equation y=f(x) is such that, dy/dx = 3x^2 + 4x +k
Where k is a constant.
Given that passes through the points (0, -2) and (2, 18).
a. Show that k = 2 and find an equation for C
b. Show that the line with equation y = x-2 is a tangent to C and find the coordinates of the point of contact.
a. Given that y = f(x) and f(0) = -2, by the fundamental theorem of calculus we have
[tex]\displaystyle \frac{dy}{dx} = 3x^2 + 4x + k \implies y = f(0) + \int_0^x (3t^2+4t+k) \, dt[/tex]
Evaluate the integral to solve for y :
[tex]\displaystyle y = -2 + \int_0^x (3t^2+4t+k) \, dt[/tex]
[tex]\displaystyle y = -2 + (t^3+2t^2+kt)\bigg|_0^x[/tex]
[tex]\displaystyle y = x^3+2x^2+kx - 2[/tex]
Use the other known value, f(2) = 18, to solve for k :
[tex]18 = 2^3 + 2\times2^2+2k - 2 \implies \boxed{k = 2}[/tex]
Then the curve C has equation
[tex]\boxed{y = x^3 + 2x^2 + 2x - 2}[/tex]
b. Any tangent to the curve C at a point (a, f(a)) has slope equal to the derivative of y at that point:
[tex]\dfrac{dy}{dx}\bigg|_{x=a} = 3a^2 + 4a + 2[/tex]
The slope of the given tangent line [tex]y=x-2[/tex] is 1. Solve for a :
[tex]3a^2 + 4a + 2 = 1 \implies 3a^2 + 4a + 1 = (3a+1)(a+1)=0 \implies a = -\dfrac13 \text{ or }a = -1[/tex]
so we know there exists a tangent to C with slope 1. When x = -1/3, we have y = f(-1/3) = -67/27; when x = -1, we have y = f(-1) = -3. This means the tangent line must meet C at either (-1/3, -67/27) or (-1, -3).
Decide which of these points is correct:
[tex]x - 2 = x^3 + 2x^2 + 2x - 2 \implies x^3 + 2x^2 + x = x(x+1)^2=0 \implies x=0 \text{ or } x = -1[/tex]
So, the point of contact between the tangent line and C is (-1, -3).
PLEASEE HELPPPPPPP!!!!!!!!!!!
Answer:
6
Step-by-step explanation:
[tex]h \sqrt{28 } \\ \sqrt{28} = \sqrt{4 \times 7} \\ \sqrt{28} = \sqrt{4} \times \sqrt{7} \\ 2 \sqrt{7} \\ 8 \sqrt{7} - 2 \sqrt{7} = 6 \sqrt{7} [/tex]
hope this helps :D have a good day
Please ANSWER
Amy is wrapping a present
that is a rectangular prism.
The height is 18 inches, the
width is 16 inches and the
length is 20 inches. What is the
least amount of wrapping
paper, in square inches, that
Amy needs to wrap the
present
The least amount of wrapping paper that Amy needs to wrap the present is 1936in².
What is Surface Area?Surface area is simply the amount of space covering the outside of a 3-dimensional object.
The surface area of a rectangular prism is expressed;
A = 2( wl + hl + hw )
Given the data in the question;
Height of the rectangular prism h = 18inWidth w = 16inLength l = 20inSurface area of the rectangular prism A = ?To determine the least amount of wrapping paper that Amy needs to wrap the present in the shape of a rectangular prism, we substitute our given values into the expression above.
A = 2( wl + hl + hw )
A = 2( (16in×20in) + (18in×20in) + (18in×16in) )
A = 2( 320in² + 360in² + 288in² )
A = 2( 968in² )
A = 1936in²
Therefore, the least amount of wrapping paper that Amy needs to wrap the present is 1936in².
Learn more about the surface area of a rectangular prism here: https://brainly.com/question/14987814
The vertices of PQR are P(6, 1), Q(3,5), and R(11, 11). The length of segment PR is √125 units. Use the coordinates and geometric reasoning to show that PQR is a right triangle.Explain your reasoning and show your work
Check the picture below, so hmm we know that much, and we can also more or less see that PR is the longest side, let's check the length of the other two sides
[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ P(\stackrel{x_1}{6}~,~\stackrel{y_1}{1})\qquad Q(\stackrel{x_2}{3}~,~\stackrel{y_2}{5})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ PQ=\sqrt{[3 - 6]^2 + [5 - 1]^2}\implies PQ=\sqrt{(-3)^2+4^2}\implies \boxed{PQ=5} \\\\[-0.35em] ~\dotfill\\\\ Q(\stackrel{x_1}{3}~,~\stackrel{y_1}{5})\qquad R(\stackrel{x_2}{11}~,~\stackrel{y_2}{11})~\hfill QR=\sqrt{[11 - 3]^2 + [11 - 5]^2} \\\\\\ QR=\sqrt{8^2+6^2}\implies \boxed{QR=10}[/tex]
if that's true, the triangle is indeed a right-triangle, then hmmmm most likely using the pythagorean theorem PR² = PQ² + QR², let's check
[tex](\sqrt{125})^2~~ = ~~5^2~~ + ~~10^2\implies 125=25+100\implies 125=125~~\textit{\Large \checkmark}[/tex]
HELP ME!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
[tex]y=-\dfrac 14 x~~....(i)\\\\x+2y = 4~~...(ii)\\\\\text{Substitute}~~ y= -\dfrac 14 x ~~ \text{in equation (ii):}\\ \\ \\x+2\left(-\dfrac 14 x \right) = 4\\\\\implies 4x -2x = 16~~~~;\left[\text{Multiply both sides by 4} \right]\\\\\implies 2x = 16\\\\\implies x =\dfrac{16}2 \\ \\\implies x =8\\\\\text{Substitute x = 8 in equation (i);}\\\\y= -\dfrac 14 \cdot 8 = -2\\\\\text{Hence,}~ (x,y) = (8,-2)[/tex]
Answer:
[tex]y = - \frac{1 }{4} x \\ [/tex]
[tex]x + 2y = 4 \\ [/tex]
[tex]x + 2( - \frac{1}{4} x) = 4 \\ [/tex]
[tex]x + ( - \frac{2}{4} x) = 4 \\ [/tex]
[tex]x - \frac{1}{2} x = 4 \\ [/tex]
[tex] \frac{2x - 1x}{2} = 4 \\ [/tex]
[tex]2x - x = 8[/tex]
[tex]x = 8[/tex]
[tex]x + 2y = 4 \\ [/tex]
[tex]8 + 2y = 4[/tex]
[tex]2y = 4 - 8[/tex]
[tex]2y = - 4[/tex]
[tex]y = - 2[/tex]
The width w is less than 10 inches
Answer:
w - 10
Step-by-step explanation:
Substract 10 from W --> w - 10
What is the value of the expression when a = 3 and b = 5?
3a+b−4
4
7
10
34
How to solve and the answer.
Answer:
The answer is 20
Step-by-step explanation:
There's two ways in which you can do this. The first one, and the simpliest one is finding the derivative of the equation P(x). After finding the derivative, set the dy/dx to be zero (so set the derivative to be zero). Then solve for x. This should give you the point at which there's no increase or decrease in the value of P, thus meaning the point at which its the maximum.
The second method is simply ploting a graph and finding the highest point.
i’ll mark Brainliest or whatever it is
Which expression is equivalent to m (n + p)?
O A. m X n + P
Ов. т Хр+п
OC, (m x n) + P
OD. (mx n) + (m xp)
m
O E. (m + n) x (m + p)
Answer:
A
Step-by-step explanation:
m( n+ p)
it's also known as m × n + p
Please help!!!
Danil, Gabriel and Hadley share some money in the ratios 3:5:9
The difference between the amount of money that Gabriel receives and the amount of
money that Hadley receives is 196 euros.
Work out the amount of money that Danil receives.
Answer:
Danil received 147 euros
Step-by-step explanation:
Let, Danil,Gabriel and Hardly share some money of 3x:5x:9x ratio then,
From the question,
9x - 5x= 196
or, 4x= 196
or, x = 196/4
or, x = 49 euros
Again,Danil received 3x share of money
=3*49
=147 euros
Answer:
Step-by-step explanation:
Ratio = 3 : 5 : 9
Money received by Danil = 3x
Money received by Gabriel = 5x
Money received by Hadley = 9x
Difference in the amount between Gabriel and Hadley = 196 euros
9x - 5x = 196
4x = 196
x = 196/4
x = 49
Money received by Danil = 3*49
= € 147
helppppp................................/
Answer:
pounds and ounces
Randomly pick 25 fish from the entire pond and weigh each of them
Step-by-step explanation:
Centimeters, feet and inches measure length, not weight.
To find the average weight of fish living in a large pond, the scientist will randomly pick 25 fish from all over the pond. Next, each fish will be weighed. The weight of all 25 fish will be added and the total will be divided by 25. This will give you the average weight of a fish living in the large pond.
Please help me
I will give brainlist
Answer:
69 degrees
Step-by-step explanation:
See attached image.
An item is regularly priced at $80. It is now priced at a discount of 70% off the regular price. What is the price now?
Answer:
$24
Step-by-step explanation:
PRICE=$80
DISCOUNT=70٪ OF $80=(70/100)×80=70×80/100=$56
HENCE DISCOUNT=$56
NOW THE PRICE=$80-$56=$24
I HOPE IT HELPED YOU
Answer: 24
Step-by-step explanation:
Multiply the original price by how much is being discounted.
80 x .70 = 56
Subtract the answer from the original price.
80 - 56 = 24
(2y^2 – 3y + 1) = (y - 2)
Answer:
see below
Step-by-step explanation:
Move R side to the L side to get
2y^2 -4y +3 = 0
Use quadratic formula to find y = 1 +- i sqrt (2) / 2
Write the slope-intercept form of equation.
9x + 3y = 27
slope intercept form: y = mx + b [ where m is slope and b is y-intercept ]
[tex]\dashrightarrow \ \sf9x + 3y = 27[/tex]
[tex]\dashrightarrow \ \sf 3y = 27 -9x[/tex]
[tex]\dashrightarrow \ \sf y = \dfrac{27 -9x}{3}[/tex]
[tex]\dashrightarrow \ \sf y = -3x + 9[/tex]
Here, the "slope is -3" and "y-intercept is 9"
Slope intercept form:-
y=mx+bNow convert
9x+3y=273y=-9x+273y=3(-3x+9)Cancel 3
y=-3x+9