This pyramid has the same base as the prism and its height is three times the height of the prism. What is the ratio of the volume of the
pyramid to the volume of the prism?
1
A} volume of Pyramid
volume of priam
B} volume of pyramid
volume of priuam
C} volume of pyramid
volume of priim
D} Volume of pyramid
volume of
prime
____________________________________________
volume of the prism
hi can someone help me here
Answer:
[tex]\left(x-\dfrac{7}{2}\right)^2+\left(y+\dfrac{7}{2}\right)^2=\dfrac{25}{2}[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{7.4 cm}\underline{Midpoint between two points}\\\\Midpoint $=\left(\dfrac{x_2+x_1}{2},\dfrac{y_2+y_1}{2}\right)$\\\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the endpoints.\\\end{minipage}}[/tex]
Given endpoints of the diameter of the circle:
(x₁, y₁) = A (7, -3)(x₂, y₂) = B (0, -4)To find the center of the circle, substitute the given endpoints into the midpoint formula:
[tex]\begin{aligned} \implies \textsf{Midpoint} & =\left(\dfrac{0+7}{2},\dfrac{-4-3}{2}\right)\\& =\left(\dfrac{7}{2},-\dfrac{7}{2}\right)\end{aligned}[/tex]
[tex]\boxed{\begin{minipage}{4 cm}\underline{Equation of a circle}\\\\$(x-a)^2+(y-b)^2=r^2$\\\\where:\\ \phantom{ww}$\bullet$ $(a, b)$ is the center. \\ \phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}[/tex]
Substitute the found center and one of the given points (0, -4) into the equation and solve for r²:
[tex]\implies \left(0-\dfrac{7}{2}\right)^2+\left(-4-\left(-\dfrac{7}{2}\right)\right)^2=r^2[/tex]
[tex]\implies \left(-\dfrac{7}{2}\right)^2+\left(-\dfrac{1}{2}\right)^2=r^2[/tex]
[tex]\implies \dfrac{49}{4}+\dfrac{1}{4}=r^2[/tex]
[tex]\implies \dfrac{50}{4}=r^2[/tex]
[tex]\implies r^2=\dfrac{25}{2}[/tex]
Therefore, the equation of the circle is:
[tex]\implies \left(x-\dfrac{7}{2}\right)^2+\left(y+\dfrac{7}{2}\right)^2=\dfrac{25}{2}[/tex]
The graph of the circle is attached.
Use the graph to find the AOS, Vertex, Zeros, Domain, and Range
In this problem
we have a vertical parabola open downward
so
the vertex is a maximum
Looking at the graph
The vertex is the point (0,4)
The axis of symmetry is x=0 (y-axis)
The zeros are x=-2 and x=2
The domain is all real numbers -----> interval (-infinity, infinity)
The range is all real numbers less than or equal to 4 ----> interval (-infinity,4]
The vertices of ΔABC are A(7, 3), B(−8, 6), C(0, −5). If ∆ABC is translated along the vector <−9, 5>, what are the coordinates of the vertices of ΔA'B'C' ?
Responses
A'(−2, 8), B'(−17, 11), C'(−9, 0)
A ' ( - 2 , 8 ) , B ' ( - 17 , 11 ) , C ' ( - 9 , 0 )
A'(8, −2), B'(11, −17), C'(0, −9)
A ' ( 8 , - 2 ) , B ' ( 11 , - 17 ) , C ' ( 0 , - 9 )
A'(12, −6), B'(−3, −3), C'(5, −14)
A ' ( 12 , - 6 ) , B ' ( - 3 , - 3 ) , C ' ( 5 , - 14 )
A'(16, −2), B'(1, 1), C'(9, −10)
The coordinates of the vertices of ΔA'B'C' after the transformation are (a) A'(-2, 8), B'(-17, 11), C'(-9, 0)
How to determine the vertices of ΔA'B'C'?The coordinates of the triangle are given as
ΔABC are A(7, 3), B(−8, 6), C(0, −5).
The transformation is given as
∆ABC is translated along the vector <−9, 5>
Mathematically, this can be represented as
(x, y) ⇒ (x - 9, y + 5)
When this is applied on ABC, we have:
ΔA'B'C' = A'(7 - 9, 3 + 5), B'(−8 - 9, 6 + 5), C'(0 - 9, −5 + 5)
Evaluate the computations
ΔA'B'C' = A'(-2, 8), B'(-17, 11), C'(-9, 0)
Hence, the image of the transformation is (a) A'(-2, 8), B'(-17, 11), C'(-9, 0)
Read more about transformation at
https://brainly.com/question/27224272
#SPJ1
If Patriciana has 4 more dimes than nickels and they have a combined value of 100 cents, how many of each coin does she have?
Patriciana has (20/9) nickels and (80/9) dimes of coins .
Evaluation for the number of dimes and nickels.There are 5 cents in a nickel and 10 cents in a dime.
Let the number of number of nickels be represented by the letter x, so that the number of dimes Patriciana has will be 4x.
So, 5x cents + 10 × 4x cents = 100 cents
5x cents + 40 cents = 100 cents
45x cents = 100 cents
divide through by the coefficient of x
x = 100cents/45cents
x = 20/9 by simplification,
and the number of dimes is calculated by putting 20/9 for x in 4x.
Hence, the number of dimes is 4(20/9) = 80/9 and that of nickels is 20/9.
Learn more about nickels and dimes here:https://brainly.com/question/9181464
#SPJ1
Enter the number in scientific notatlon. 65,978 Hint: Move the decimal left 4 places.
ANSWER
[tex]6.5978\cdot10^4[/tex]EXPLANATION
We are given the number 65,978.
To put it in scientific notation, we will need to put it in a format such that we have a number between 1 and 10 multiplying a power of ten.
So, to do that, we will move the decimal point from the end of the number (65978.) to just after the first number.
Then the number of times we move it will be the power of 10.
Since we will move it to the left, it will be a positive power.
So, we have that the number becomes:
[tex]6.5978\cdot10^4[/tex]The power is 4 because we moved the decimal four times.
Simone paid $13 for an initial year's subscription to a magazine. The renewal rate is $8 per year. This situation can be represented by the equation y = 8x + 13, where x represents the number of years the subscription is renewed and y represents the total cost, in dollars. Part 1 out of 4 Complete the table of values for this situation. x (number of years renewed) 0 1 2 3 4 y (total cost in dollars) Next
Data Input
Simone paid $13 for an initial year's
The renewal rate is $8 per year
Equation
y = 8x + 13
Table
x (number of years renewed) | (total cost in dollars)
0 -> 13 dollars
1 -> 21 dollars
2 -> 29 dollars
3 -> 37 dollars
4 -> 45 dollars
Divide…. Unit 2 test: scientific notation
Answer:
I do believe the answer for you is B. 2 x 10^14.
Step-by-step explanation:
4 x 10^4
Add four zeros to the original number since the exponent to the 10 is positive.
40,000/ 2 x 10^-10
Since the exponent here is a negative number, make 9 zeros behind the decimal point and the 2 at the end.
40,000/.0000000002
Using a calculator, you will get 2e14 which is equivalent to 2 x 10^14. Hope this helped!
Answer:
The answer is B
help meeeeeeeeeeeeeee pleaseeeeeee
Answer: 10.8 seconds
Step-by-step explanation:
[tex]-16t^2 + 170t+40=10\\\\16t^2 -170t-30=0\\\\t=\frac{-(-170) \pm \sqrt{(-170)^2 -4(16)(-30)}}{2(16)}\\\\t \approx 10.8 \text{ } (t > 0)[/tex]
Find the percent change from 32 to 60.
Answer:
87.50%
Step-by-step explanation:
You have to find the difference between the two numbers and divide the result by the first number which is 32. Multiply the answer by 100 to get the answer as a percentage!
Answer:32% of 60 = 87.5
Step-by-step explanation:
What is the equation of the line that passes
through the point (-6, -7) and has an
undefined slope?
A line with an undefined slope would be x=___, in which you would put the x value of the coordinate. So, the equation would be x = -6
Write an inequality that can be solved using the Subtraction Property of Inequality and has a solution of all numbers less than -3.
Answer:
90183
Step-by-step explanation:
A number is squared. This is added to fifteen and the product of eight and the number, to give zero.
A number is squared. This is added to fifteen and the product of eight and the number, to give zero.
the algebraic expression is
Let
x ----> the number
x^2+(15+8x)=0
therefore
x^2+8x+15=0
solve the quadratic equation
Solve by using calculator
x=-5 and x=-3
How can I solve the problem 3+4(10-8)
Find the slope and y-intercept of the line below
help!! ASAP!! 50 points too whoever helps!!
Answer:720
thats the answer 720
Which of the fractions is equivalent to 2/5
Answer:
all the fractions that are equivalent to 2/5 are 4/10, 6/15, 8/20
Step-by-step explanation:
this is all I can rember
Joey invented an electric light device to put on his 26-inch diameter bicycle
wheel. Every time the tire makes a full revolution, a wire touches a battery
contact and a light flashes on the back of the bike seat. How many times will
the light flash if he rides 50 yards?
π = 3.14
F
G
H
J
2 times
7 times
22 times
82 times
If he rides 50 yards then the light will flash 22 times.
Given,
Diameter of wheel =26 inch
Radius of wheel,r=[tex]\frac{26}{2}=13 inch[/tex]
Distance covered by bicycle =50 yards =50*36=1800 inch
First find the perimeter of wheel,
[tex]Perimeter =2\pi r\\\\Perimeter =2*3.14*13\\\\Perimeter =81.64[/tex]
This perimeter represents the distance covered for 1 revolution
Now, to find number of times of revolution,
[tex]\frac{Total\ distance\ covered }{distance\ covered\ for\ 1\ revolution}\\\\=\frac{1800}{81.64}\\\\=22.04[/tex]
So,it will take 22 revolutions to complete the whole distance.
Hence, the light will flash 22 times if he rides 50 yards.
To learn more about distance and time refer here
https://brainly.com/question/28540623
#SPJ1
40. If you want a poll to have a margin of error of 3.06%, how large will your sample have to be? Round your answer to the nearest whole number. people
Margin of Error:
[tex]=\pm\frac{100}{\sqrt[]{n}}[/tex]ANSWER: 1068
[tex]\begin{gathered} \text{Margin of Error}=\pm\frac{1}{\sqrt[]{n}} \\ 0.0306=\pm\frac{1}{\sqrt[]{n}} \\ \sqrt[]{n}\cdot0.0306=1 \\ \frac{\sqrt[]{n}\cdot0.0306}{0.0306}=\frac{1}{0.0306} \\ \sqrt[]{n}=32.67973856 \\ (\sqrt[]{n})^2=32.67973856^2 \\ n=1,067.965312 \end{gathered}[/tex]Albert bought 3 rolls of masking tape that cost the same amount of money and an extension cord that cost $5.50. Albert spent less than $10 altogether.Which inequality can be used to find the cost of each roll of masking tape?A.) 3m+5.50<10B.) 3m-5.50<10C.) 3m+5.50>10D.) 3m-5.50>10
Data:
m: cost of the masking tape
As the masking cost the same amount of money: 3m
Then, you add to the cost of the masking the 5.50, you get: 3m+5.50
The symbol to less than is <
You get:
[tex]3m+5.50<10[/tex]help meeeeeeeeeeeeeee pleaseeeeeee
Answer:
10.8 sec
Step-by-step explanation:
Setting [tex]h=10[/tex],
[tex]-16t^2+170t+40=10 \\ \\ 16t^2 -170t-30=0 \\ \\ 8t^2 - 85t-15=0 \\ \\ t=\frac{85 \pm \sqrt{(-85)^2-4(8)(-15)}}{2(8)} \\ \\ t \approx 10.8 (t>0)[/tex]
Someone please help me. I can't get the right answer
The required value of x will be 44°.
What is an Isosceles Triangle?An Isosceles Triangle is defined as a triangle with two sides of equal length is an isosceles triangle.
We have been given a triangle in the figure
According to the given figure, we can see that the triangle is an isosceles triangle
As per the property of the isosceles triangle, here two angles are the same.
Now, the sum of angles in a triangle as:
⇒ 68° + 68° + x = 180°
⇒ 136° + x = 180°
⇒ x = 180° - 136°
⇒ x = 44°
Therefore, the required value of x will be 44°.
Learn more about Isosceles Triangle here:
brainly.com/question/2456591
#SPJ2
Myra can fill 20 glasses with 2 containers of iced tea. How many glasses can she fill with 3 containers of tea?
Hint: Find the unit rate first!
Answer: 30 glasses
Step-by-step explanation:
Answer:
30 glasses
Step-by-step explanation:
2:20 = 1:10
1:10 x 3 = 3: 30
How to find Unit Rate:
https://brainly.com/question/20445093
Here's a similar question:
https://brainly.com/question/2461012?referrer=searchResults
20, 37, 68, --?--2. Solve.3. Sketch.V + F = E + 2IT V 12 andF = 8, find E.
V + F = E + 2
If V=12 and F=8 Find E:
We have to replace the values given of V and F IN THE EXPRESSION:
12 + 8 = E+2
Now, we simply have to solve for E:
12+8 -2 =E
18=E
E=18
Jose went to another store that has a sale of 25% off everything. He wants to buy jeans that cost $40. How much money will he save on the jeans?
Answer:
$30
Step-by-step explanation:
25% of $40 = $10
$10 is the discount price, i.e., $10 is 25% of $40
selling price - discount
= 40 - 10
= $30
THIS QUESTION IS WHAT I NEED ANSWERED
Answer: its 1 over 0 which equals B^-1
During a thunderstorm at a sports event, a detector activates to let participants know there is lightning in the area so people can seek shelter. The accuracy of the lightning detector is summarized in the table. Lightning detector activates Lightning detector does not activate Row Totals Lightning in area 88% 2% 90% No lightning in area 7% 3% 10% Column Totals 95% 5% 100% What is the ratio of true positives to false positives in this scenario? Round your answer to one decimal place. 0.1 1.5 12.6 44
The answer is 12.6
Step-by-step explanation:
The ratio is calculated with division.
This means we need to do this equation: 88/7.
The answer to 88/7 is 12.57. However, the question states: Round your answer to one decimal place.
This means we round 12.57 up to 12.6.
Answer: its (C) 12.6
Step-by-step explanation:
basically the first person already explained it
the positives are ( lighting detector activates ) column
the true positive its when the detector activates and there is lightning, so 88%
and false positive its when the detector activates but there's no lightning, so 7%
at the end you just divide 88% / 7%
which is 12.57 and you round it
-0.125 divided by (-0.5)
Help please
Answer:
Step-by-step explanation:
Since the numbers, we are given are fractions there is this ultimate rule when we divide fractions
the sign changes from division to multiplciation and the second fraction flips
so lets do this
-0.125 = -1/8
-0.5 = -1/2
Now lets put into into an equation
-1/8 * -2 = 1/4
8. Brendan ran a total of 88 miles over the course of 44 track practices.
How many track practices would it take for Brendan to run 1010 miles?
Solve using unit rate?
simple interest is computed by finding the product of the principal amount, p, and the interest rate, r, and the time t.translate each sentence into an formula
You have that simple interest is computed by the multiplication of p (principal amount), r (interest rate) and t (time).
The previoues sentence can be written algebraically as follow:
I = p x r x t you only have to multiply each factor
where I is the letter for simple interest.
help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Step-by-step explanation:
the question is about distance.
what do we use to measure distance ? things like feet, yards, meters, ...
definitely not square feet (areas) or cubic feet (volume).
it is a right-angled triangle. so Pythagoras applies
c² = a² + b²
c is the Hypotenuse (the side opposite of the 90° angle). in our case the 48 ft side.
a and b are the legs. in our case x and x+6.
the saved walking distance is the difference between 48 ft and the sum of the legs (which would be the walking distance, when they cannot get though the lot).
48² = x² + (x + 6)² = x² + x² + 12x + 36
2304 = 2x² + 12x + 36
1152 = x² + 6x + 18
x² + 6x - 1134 = 0
the solution for such a quadratic equation
ax² + bx + c = 0
is
x = (-b ± sqrt(b² - 4ac))/(2a) =
= (-6 ± sqrt(6² - 4×1×-1134))/(2×1) =
= (-6 ± sqrt(36 + 4536))/2 =
= (-6 ± sqrt(4572))/2 =
= -3 ± sqrt(4572/4) = -3 ± sqrt(1143) =
= -3 ± sqrt(9×127) = -3 ± 3×sqrt(127)
x1 = -3 + 3×sqrt(127) = 30.80828301...
x2 = -3 - 3×sqrt(127) = -36.80828301...
negative numbers for a distance don't make any sense, so
x = 30.80828301... is our solution.
that means the 2 legs are
30.80828301... ft
36.80828301... ft
in total they are
67.61656602... ft
and so they save
67.61656602... - 48 = 19.61656602... ft ≈
≈ 19.617 ft
by walking across the lot.
Answer: 19.6 feet
Step-by-step explanation:
Using the Pythagorean theorem,
[tex]x^2 +(x+6)^2 =48^2\\\\x^2 +x^2 +12x+36=2304\\\\2x^2 +12x-2268=0\\\\x^2 +6x-1134=0\\\\x=\frac{-6 \pm \sqrt{6^2 -4(1)(-1134)}}{2(1)}\\\\x \approx 30.8 \text{ } (x > 0)\\\\\implies x+(x+6) \approx 67.6\\\\\therefore (x+(x+6))-48 \approx 19.6[/tex]