Let's see
For initial cone
r=6h=9Volume
1/3πr²h1/3π(6)²(9)3(36)π108π units³For new cone
r=4(6)=24h=9Volume
1/3π(24)²(9)3(576)π1728πSo
1728π/108π16timesAnswer:
16 times
Step-by-step explanation:
[tex]\textsf{Volume of a cone}=\sf \dfrac{1}{3} \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}[/tex]
If only the radius is changed, the change in volume will be proportionate to the multiplicative factor squared.
[tex]\sf \implies Volume =\dfrac{1}{3} \pi (ar)^2h=\dfrac{1}{3} \pi (a^2)r^2h[/tex]
Therefore, if the cone is quadrupled (multiplied by 4), the volume of the larger cone will be 4² times greater than the volume of the smaller cone, so 16 times greater than the smaller cone.
ProofGiven:
radius = 6height = 9Substituting the given values into the formula:
[tex]\sf \implies Volume =\dfrac{1}{3} \pi (6)^2(9)=108 \pi \: \:cubic\:units[/tex]
If the radius is quadrupled:
radius = 6 × 4 = 24height = 9Substituting the new given values into the formula:
[tex]\sf \implies Volume =\dfrac{1}{3} \pi (24)^2(9)=1728 \pi \: \:cubic\:units[/tex]
To find the number of times greater the volume of the large cone is than the volume of the smaller cone, divide their volumes:
[tex]\sf \implies \dfrac{V_{large}}{V_{small}}=\dfrac{1728\pi}{108\pi}=16[/tex]
So the volume of the larger cone is 16 times greater than the volume of the smaller cone.
Which classification describes the following system of equations? inconsistent and dependent consistent and dependent consistent and independent inconsistent and independent.
The system of equations is consistent and independent and the solutions are x = 4, y = 5, and z = -1 option third is correct.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
We have three linear equations in three variables:
x - y - z = 0 ..(1)
2x - y + 2z = 1 ..(2)
x - y + z = -2 ..(3)
From the equation (1):
[tex]\rm x=y+z[/tex]
Plug this value in the equation (2) and (3):
[tex]\rm 2\left(y+z\right)-y+2z=1\\\\ y+z-y+z=-2[/tex]
After solving we get:
z = -1
y = 5
Plug the above two values in equation (1) we get:
x = 4
Thus, the system of equations is consistent and independent and the solutions are x = 4, y = 5, and z = -1 option third is correct.
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The circle has a diameter of 9 inches what is the circumference rounded to the nearest whole number
Answer:
28
Step-by-step explanation:
Circumference = 2*pi*r
r = 1/2*diameter = 4.5
pi = 3.14
Circumference = 2*(3.14)*(4.5) = 28.26 = 28
Suppose that the functions g and h are defined for all real numbers x as follows.
g(x) = 5x
h(x) = 4x-3
Write the expressions for (h+g)(x) and (h-g)(x) and evaluate (h-g) (4).
PLEASE HELP
The expressions for (h+g)(x) and (h-g)(x) and evaluate (h-g) (4) is 9x-3 , x+3 and 7
What is a Function ?A function is defined as the law that build relation between a dependent variable and an independent variable.
It is given that
functions g and h are defined for all real numbers x as follows.
g(x) = 5x
h(x) = 4x-3
the expressions for (h+g)(x)= ?
(h+g)(x)= 5x+4x-3
(h+g)(x)= 9x-3
and (h-g)(x) = ?
(h-g)(x) = 5x - 4x +3
(h-g)(x) = x+3
and evaluate (h-g) (4).
(h-g)(x) = x+3
at x = 4
(h-g)(4) = 4+3 = 7
Therefore the value for the functions have been determined.
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Mrs. Yamaguchi's class weighed the potatoes that they grew in their garden and recorded the data on a table. Determine how many dots are above each data value in a line plot of this data.
Weights of Potatoes (in pounds)
1
4
3
8
5
8
1
2
5
8
1
2
1
2
3
4
1
4
1
8
3
4
1
2
3
8
1
2
3
4
3
8
The value
1
8
will have
Choose...
dots above it.
The value
1
4
will have
Choose...
dots above it.
The value
3
8
will have
Choose...
dots above it.
The value
1
2
will have
Choose...
dots above it.
Using a dot plot, it is found that the number of dots of each point are given as follows:
The value [tex]\frac{1}{8}[/tex] will have one dot above it.The value [tex]\frac{1}{4}[/tex] will have two dots above it.The value [tex]\frac{3}{8}[/tex] will have three dots above it.The value [tex]\frac{1}{2}[/tex] will have five dots above it.The value [tex]\frac{5}{8}[/tex] will have two dots above it.The value [tex]\frac{3}{4}[/tex] will have three dots above it.What does a dot plot shows?The dot plot shows the number of times each measure appears in the data-set.
In this problem, one measure has a value of 1/8, hence:
The value [tex]\frac{1}{8}[/tex] will have one dot above it.
Two measures have a value of 1/4, hence:
The value [tex]\frac{1}{4}[/tex] will have two dots above it.
Three measures have a value of 3/8, hence:
The value [tex]\frac{3}{8}[/tex] will have three dots above it.
Five measures have a value of 1/2, hence:
The value [tex]\frac{1}{2}[/tex] will have five dots above it.
Two measures have a value of 5/8, hence:
The value [tex]\frac{5}{8}[/tex] will have two dots above it.
Three measures have a value of 3/4, hence:
The value [tex]\frac{3}{4}[/tex] will have three dots above it.
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Answer:
1 2 3 5 2 3
Step-by-step explanation:
A concert that features different singing groups will be held at a Municipal Hall. The concert will start with a solo performance, followed by a duet, then a trio, and so on with the last performance coming from a choir with 30 members. How many people will perform at the concert? (problem-solving)
Step-by-step explanation:
this is the problem to sum the numbers 1 ... n.
remember the old trick by adding
n + 1
n-1 + 2 = n + 1
n-2 + 3 = n + 1
...
and doing this n/2 times, giving us a sum
n×(n+1)/2
for n = 30 we get
30×31/2 = 15×31 = 465
so, 465 people will perform.
Chandler was a caretaker at the state zoo. He noticed that the number of animals adopted by the zoo increased at a constant rate every year since 2010.
Which of the following graphs shows the slowest rate at which the animals in the zoo were adopted?
A.
B.
C.
D.
what is the surface area of this design? 6in, 4in, 4in, 6in, 10in
Answer:
392
Step-by-step explanation:
hope this helps!!
what is the approximate solution of this system of equaltion y=x^2+3x+3 , y=x^2+x+2
Answer:
(B
The given system of equations are:
y=x^2+3x+3y=x
2
+3x+3 (1)
and y=x^2+x+2y=x
2
+x+2 (2)
Subtracting equation (2) from (1), we get
0=2x+10=2x+1
⇒2x=-12x=−1
⇒x={\frac{-1}{2}}x=
2
−1
⇒x=-0.5x=−0.5
Now, substituting the value of x=-0.5 in equation (2), we get
y=0.25-0.5+2y=0.25−0.5+2
⇒y=1.7y=1.7
Thus, the values of x and y are -0.5 and 1.7.
Therefore, the approximate solution of the given system of the equation is (-0.5, 1.7).
Hence, option (B) is correct.
Plot the value(s) on the number line where this function is equal to zero: f(x)= (x+5)(x-1).
A new car is for lease for $192 per month for 36 months, with a down payment of $358. the lease allows for 12,000 miles per year and includes a $0.29 per mile charge for miles driven in excess of that amount. at the end of the lease, the car has been driven a total of 45,425 miles. what is the cost for three years for this vehicle?
Answer:
2 733.25 + 7270 = 10 003.25
Step-by-step explanation:
192 * 36 = 6 912 +358 = 7 270
45425 - 36000 ( allowed miles for 3 years )
9 425 * 0.29 = 2 733.25
Which inequality has a solid boundary line when graphed?
Y<-x-9
y<1/9x+9
y>-1/9x
y >9x+9
Inequalities are expression not separated by an equal sign. None of the inequality is correct since there is absence of equal sign.
Graph of inequalitiesInequalities are expression not separated by an equal sign. According to the question, we ned the inequality's graph that will have a dashed boundary line.
An inequality that will have solid boundary line must include only the less than or equal to sign < or greater than or equal to > sign.
From the option given, none of the inequality is correct since there is absence of equal sign.
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what is 7.7 x 10 to the 8th power
solve w^2 + 7w - 18 = 0
with the steps pls
Answer:
w=2 w = -9
Step-by-step explanation:
w^2 + 7w - 18 = 0
We can factor this equation
What 2 numbers multiply to -18 and add to 7
9*-2 = -18
9+-2 = 7
(w-2) (w+9) = 0
Using the zero product property
w-2 = 0 w+9 =0
w=2 w = -9
Answer:
[tex]w_1=2\\w_2=-9[/tex]
Step-by-step explanation:
This is going to be solved using the quadratic formula.
1. Determine the quadratic equation’s coefficient [tex]a[/tex], [tex]b[/tex], and [tex]c[/tex].
Use the standard form, [tex]ax^2+bx+c=0[/tex] , to find the coefficients of our equation,
[tex]w^2+7w-18=0[/tex]:
a = 1
b = 7
c = -18
2. Plug these coefficients into the quadratic formula
The quadratic formula gives us the roots for [tex]aw^2+bw+c=0[/tex] , in which [tex]a[/tex], [tex]b[/tex], and [tex]c[/tex] are numbers (or coefficients), as follows:
[tex]w=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]
7 additional steps:
a = 1
b = 7
c = -18
[tex]w=\frac{-7\pm\sqrt{7^2=4*1*-18} }{2*1}[/tex]
Simplify exponents and square roots
[tex]w=\frac{-7\pm\sqrt{49-4*1*-18} }{2*1}[/tex]
Perform any multiplication or division, from left to right:
[tex]w=\frac{-7\pm\sqrt{49-4*-18}}{2*1}\\w=\frac{-7\pm\sqrt{49--72}}{2*1}\\\\w=\frac{-7\pm\sqrt{49+72}}{2*1}\\w=\frac{-7\pm\sqrt{121}}{2*1}[/tex]
to get the result:
[tex]w=\frac{-7\pm\sqrt{49-4*-18}}{2}[/tex]
3. Simplify square root [tex]\sqrt{121}[/tex]
Simplify 121 by finding its prime factors:
121 ( 11 * 11)
The prime factorization of 121 is 11^2
Write the prime factors:
[tex]\sqrt{121}=\sqrt{11\cdot 11}[/tex]
Group the prime factors into pairs and rewrite them in exponent form:
'[tex]\sqrt{11\cdot 11}=\sqrt{11^2}[/tex]
Use the rule [tex]\sqrt{x^2=x}[/tex] to simplify further:
[tex]\sqrt{11^2}=11[/tex]
4. Solve the equation for w
[tex]w=\frac{-7\pm11}{2}[/tex]
The ± means two answers are possible.
Separate the equations:
[tex]w_1=\frac{(-7+11)}{2}[/tex] and [tex]w_2=\frac{-7-11}{2}[/tex]
[tex]w_1=\frac{-7+11}{2}[/tex]
[tex]w_1=\frac{4}{2}[/tex]
[tex]w_1=2[/tex]
[tex]w_2=\frac{-7-11}{2}[/tex]
[tex]w_2=\frac{-18}{2}[/tex]
[tex]w_2=-9[/tex]
---------------------
Why learn this
In their most basic function, quadratic equations define shapes like circles, ellipses and parabolas. These shapes can in turn be used to predict the curve of an object in motion, such as a ball kicked by football player or shot out of a cannon. When it comes to an object’s movement through space, what better place to start than space itself—with the revolution of planets around the sun in our solar system. The quadratic equation was used to establish that planets’ orbits are elliptical, not circular. Determining the path and speed an object travels through space is possible even after it has come to a stop: the quadratic equation can calculate how fast a vehicle was moving when it crashed. With information like this, the automotive industry can design brakes to prevent collisions in the future. Many industries use the quadratic equation to predict and thus improve their products’ lifespan and safety.---------------
Terms and topics
Solving quadratic equations using the quadratic formulaSimplifying radicalsFind prime factors-----------
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Identify the center and the Radius of a circle that has a diameter with endpoints at (-5,9) and (3,5)
Answer:
See below
Step-by-step explanation:
The CENTER will de directly between the two given points
h, k = -1,7
so...so far the circle eq is
(x+1)^2 + ( y-7)^2
the RADIUS is 1/2 of the distance between the given points
1/2 d = (using distance formula) = 1/2 sqrt 80 = 4.472
then the equation of the circle in standard form
(x+1)^2 + (y-7)^2 = 20
I need help with my math it’s in the image
Answer:
3.5x10^4 is 50 times larger than 7x10^2
Step-by-step explanation:
3.5x10^4 is 35,000 (move decimal 4 places to the right)
7x10^2 is 700 (7.0 move decimal 2 places to the right)
700x50=35,000 which shows that 35,000 is 50 times larger than 700
Are the equations -3(2x+9)=12 and 2x+9=-4 equivalent?
15 Which point is a solution to the system below?
2y < -12x + 4
y <- 6x +4.
A (1,1)
B (0,6)
C (-1/2,5)
D (-3,2)
The attached graph shows that the system of equation has no solution since there is no point of intersection
Solution to system of equationsInequalities are expressions not separated by an equal sign
Given the following inequalities
2y < -12x + 4
y <- 6x +4
_________________
2y < -6x + 4
y <- 6x +4.
Find the y-intercept. When x = 0
y < -6(0) + 4
y < 4
Plot the graphs and determine the point of intersection
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20 ft
The ceiling of Stacy's living room is a square that is 20 ft long on each side. Stacy
knows the diagonal of the ceiling from corner to corner must be longer than 20 ft.
but she doesn't know how long it is.
Solve for the length of the diagonal of Stacy's ceiling in two ways:
(a) Using the Pythagorean Theorem.
(b) Using trigonometry.
Round each answer to the nearest whole number and make sure to show all your
work. (Hint: the answers should be the same!)
The value of the diagonal will be equal to 20√2.
What is the Pythagorean theorem?Pythagorean theorem states that in the right angle triangle the hypotenuse square is equal to the square of the sum of the other two sides.
The value of the diagonal by the Pythagorean theorem.
H² = B² + P²
H² = 20² + 20²
H² = 400 + 400
H = √800
H = 20√2
Therefore the value of the diagonal will be equal to 20√2.
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1 tablespoon is equivalent to _____ ml.
Answer:
14.7868 ml are equal to 1 tablespoon
Step-by-step explanation:
1 tablespoon is equivalent to __14.7868___ ml.
Hope This Helped
Answer:
14.7868ml or 15 ml
Step-by-step explanation:
it can be either one since 14.7686 is close to 15
Solve the proportion (write it as a whole number or decimal)
2/3 - 3/q
so q =__
1 1/2 + 1 x 2 + 1 1/2
Answer:
5.Step-by-step explanation:
From left to right:
1 1/2 + 1 * 2 + 1 1/2= (1 1/2) + (1 * 2) + (1 1/2)= 1 1/2 * 2= 3 1/2 + 1 1/2= 5.Hence, 5 is your answer.(don't listen to the other ways. this should be correct).
(Just g o o g l e it).
Charlotte surveyed 400 of the students in her school about their favorite color. 392 students said their favorite color was purple. What percentage of the surveyed students said their favorite color was purple?
Monica earned twice as much Samuel walking dogs. The amount Samuel earned was $7 more than Kara earned. Suppose Monica earned $48.50. Write and solve an equation to find the amount Kara earned. What is the difference between the greatest amount earned and the least amount earned walking dogs?
Answer:
Always include the steps and/or background required to get to the final answer. Let’s help other people understand and solve future problems on their own.
Step-by-step explanation:
There are 1,486 souvenir paperweights that need to be packed in boxes. Each box will hold 16 paperweights. How many boxes will be needed?
Answer: 93 boxes will be needed
Step-by-step explanation:
If each box holds 16 paperweights, and 1,486 need to be packaged, we will divide 1,486 by 16.
1,486 / 16 = 92.875
We will assume you cannot have 0.875 of a box, so we will round up to:
93 boxes will be needed
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An item costs $490 before tax, and the sales tax is $44.10.
Answer:
The item has a 9% sales tax.
Step-by-step explanation:
Given the following question:
We are given an item that costs 490 dollars before tax, the sales tax of the item is $44.10, which means the item will cost $534.10 in total. Assuming what you are asking is to find the percentage of the sales tax we will use the formula to calculate percentages, and then add that answer to our before cost to confirm our answer.
Formula to calculate percentages:
[tex]\frac{p\times n}{100}[/tex]
[tex]p=9[/tex]
[tex]\frac{9\times490}{100}[/tex]
[tex]9\times490=4410[/tex]
[tex]4410\div100=44.1=44.10[/tex]
[tex]490+44.10=534.10[/tex]
[tex]=534.10[/tex]
Our sales tax percentage is 9%.
Hope this helps.
In the coordinate plane below, the xxx-axis represents the number of hours before or after noon. For example, -1−1minus, 1 would represent 11 \text{ a.m.}11 a.m.11, start text, space, a, point, m, point, end text The yyy-axis represents the temperature in degrees Celsius. The points (-1, 6)(−1,6)left parenthesis, minus, 1, comma, 6, right parenthesis and (7,6)(7,6)left parenthesis, 7, comma, 6, right parenthesis represent two temperatures at different times of the day.
The points mean that the temperature at 11 am and 7 pm is 6 degree Celsius
How to represent the points on the coordinate plane?The given parameters are:
x represent the number of hours before/after noony represents the temperatureThe points are given as:
(x, y) = (-1,6) and (7,6)
-1 represents 11 am and 7 represents 7 pm.
The points mean that:
The temperature at 11 am and 7 pm is 6 degree Celsius
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solve for x !
[tex]x {}^{2} + 5x + 6 = 0[/tex]
ty! ~
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
Let's solve for x ~
[tex]\qquad \sf \dashrightarrow \: {x}^{2} + 5x + 6 = 0[/tex]
[tex]\qquad \sf \dashrightarrow \: {x}^{2} + 3x + 2x + 6 = 0[/tex]
[tex]\qquad \sf \dashrightarrow \: {x}^{}( x+ 3) + 2(x + 3)= 0[/tex]
[tex]\qquad \sf \dashrightarrow \: {}^{}( x+ 2)(x + 3)= 0[/tex]
[tex] \begin{cases} \sf \: x = - 2 \: \: \: \: \: \: \: \sf if \: (x + 2) = 0 \\ \\ \sf \: x = - 3 \: \: \: \: \: \: \: if \: (x + 3) = 0\end{cases} [/tex]
I hope that helps ~
(a) Charlie bought 10 pounds of sugar for $6.
How many dollars did he pay per pound of sugar?
dollars per pound
Answer:
$0.60 per pound
Step-by-step explanation:
Dollars per pound :
No. of dollars / No. of pounds$6 / 10 pounds$0.60 per poundQuestion 9 (5 points)
Which is the equation of the line for the points in the given table?
X
-4 2 6
y
13 -5 -17
On y= -2x-1
OB) y = -2x+5
OC) y = -2x - 5
OD) y=-3x + 1
to get the equation of any straight line, we simply need two points off of it, let's use those two points from the table in the picture below.
[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{13})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{-17}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-17}-\stackrel{y1}{13}}}{\underset{run} {\underset{x_2}{6}-\underset{x_1}{(-4)}}} \implies \cfrac{-30}{6 +4} \implies \cfrac{ -30 }{ 10 }\implies -3[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{13}=\stackrel{m}{-3}(x-\stackrel{x_1}{(-4)}) \\\\\\ y-13=-3(x+4)\implies y-13=-3x-12\implies y=-3x+1[/tex]
Maria's car has a gas mileage of 31 miles per gallon. How many miles can Maria travel on 9 gallons of gas?
Answer:
279 miles
Step-by-step explanation:
31 miles/gal * 9 gallons = 279 miles