if a cone and cylinder share the same radius and height what would be the volume of a cylinder if the volume of the cone is 30 cm
step 1
Volume of the cone is equal to
[tex]\begin{gathered} V=\frac{1}{3}\cdot B\cdot h \\ 30=\frac{1}{3}\cdot B\cdot h \\ 90=B\cdot h \end{gathered}[/tex]where
B is the area of the base and h is the height of cone
step 2
the volume of cylinder is equal to
[tex]V=B\cdot h[/tex]Which of the following graphs shows the solution for the inequality y+3<2/3(x-9)?
Explanation
We are to select the best option that represents the graph of the inequality
[tex]y+3\leq-\frac{2}{3}(x-9)[/tex]From the above, we have the slope as -2/3
Also, we have the x-intercept as 9/2 or 4.5
Then we have the y-intercept as 3
Thus
the graph is
Does the graph show an increasing or decreasing linear function?A) IncreasingB) Decreasing
The values of the y-variable decrease as the values of the x-variable increase, then the graph shows a decreasing liner function
Given f(x) = Vx+1, which graphs represents | 1(2)?yA.B.cC.D.Select one:O a. AObBОс. СO d. D.
Given:-
[tex]\sqrt[3]{x+1}[/tex]To find:-
The graph of,
[tex]f^{-1}(x)[/tex]To find the required value, first we convert it.
[tex]y=\sqrt[3]{x+1}[/tex]By solving the above equation. we get,
[tex]x=y^3-1[/tex]Now we sketch the graph of,
[tex]x=y^3-1[/tex]By sketching. we get,
So this is the required graph.
So the correct option is A.
f(x)=4x^2+7x-18 find f(-9)
To find f(-9) you have to replace x = -9 into f(x) as follows:
f(x)=4x²+7x-18
f(-9) = 4(-9)² + 7(-9) - 18
f(-9) = 4(81) - 63 - 18
f(-9) = 324 - 63 - 18
f(-9) = 243
In Livingston, the use of landlines has been declining at a rate of 20% every year. of there are 23,000 landlines this year, many will there be in 6 years?? if necessary, round your answer to the nearest whole number
In 6 years there are
Apply N1= 230000
N = N1 - N1•20/100 - N1• (20/100)^2 - N1•(20/100/^3 - N1•(20/100)^4 - N1(20/100)^5 - N1•(20/100) ^6
Then replace 20/100= 1/5
N= 23000 - 23000 • ( 1/5 + 1/25 + 1/125/ + 1/625 + 1/3125 + 1/15625 )
N= 23000 - 5750 = 17250
Then answer is
In 6 years there will be 17250 landlines
Ben and Jerry’s sells 3 times more ice cream cones ($2) than shakes ($9). If last month’s sales totaled $9,600, how many of each were sold?
It is given that the sales of ice cream is three times as shakes.
Let x be the number of ice creams and y be the number of shakes,
So x=3y.
Also the total sales if ice cream is $2 and shake is $9 is $9600 so it follows:
[tex]\begin{gathered} 2x+9y=9600 \\ 2\times3y+9y=9600 \\ 15y=9600 \\ y=640 \end{gathered}[/tex]Since x=3y so it follows that x=1920.
So Number of shakes sold is 640 and number of ice cream cones sold is 1920.
What is the remainder when x^2 + 5x - 24 is divided by x - 6?
Given:
The dividend is,
[tex]x^2+5x-24[/tex]The divisor is,
[tex]x-6[/tex]To find: The remainder
Explanation:
Let us take,
[tex]p(x)=x^2+5x-24[/tex]Using the remainder theorem,
Let p(x) be any polynomial of degree greater than or equal to one and let a be any real number.
If p(x) is divided by the linear polynomial x - a, then the remainder is p(a).
Here,
[tex]a=6[/tex]Substitute the value of a in the above polynomial.
[tex]\begin{gathered} p(6)=6^2+5(6)-24_{} \\ =36+30-24 \\ =42 \end{gathered}[/tex]Hence, the remainder is 42.
Final answer: The remainder is 42.
what are the ordered pairs of the solutions for this system of equations?f (x)=x^2-2x+3;f (x)=-5x+1
we get:
[tex]\begin{gathered} x^2-2x+3=-5x+1\rightarrow \\ x^2+3x-2=0\rightarrow x=\frac{-3+\sqrt[]{17}}{2},x=\frac{-3-\sqrt[]{17}}{2} \end{gathered}[/tex]so the pairs are,
[tex](\frac{-3+\sqrt[]{17}}{2},\frac{15-5\sqrt[]{17}}{2}+1),(\frac{-3-\sqrt[]{17}}{2},\frac{15+5\sqrt[]{17}}{2}+1)[/tex]can you do the check part too? so i can understand. thank you!
12 is dividing on the left, then it will multiply on the right.
[tex]\begin{gathered} 9+t=(-3)\cdot12 \\ 9+t=-36 \end{gathered}[/tex]9 is adding on the left, then it will subtract on the right
t = -36 - 9
t = -45
To check the answer, replace the value found into the original equation, as follows:
[tex]\frac{9-45}{12}=\frac{-36}{12}=-3[/tex]X - y = 0X + y = - 4
We are given the following system of equations:
[tex]\begin{gathered} x-y=0,(1) \\ x+y=-4,(2) \end{gathered}[/tex]We are asked to determine the solution by graphing the system.
To do that we will graph each of the equations. We will solve for "y" in equation (1), to do that we will add "y" to both sides:
[tex]\begin{gathered} x-y+y=y \\ x=y \end{gathered}[/tex]Switching the direction of the equation we get:
[tex]y=x[/tex]Now, we graph the equation. We notice that this is the equation of a line since it has the form:
[tex]y=mx+b[/tex]In this case, m = 1 and b = 0.
To graph a line we need to know two points in the line. We will determine those points by giving values to "x". We will substitute the value x = 0, we get:
[tex]y=0[/tex]Substituting "x = 1" we get:
[tex]y=1[/tex]Therefore, the two points are:
[tex]\begin{gathered} (x_1,y_1)=(0,0) \\ (x_2,y_2)=(1,1) \end{gathered}[/tex]Now we plot both points and join them with a line. The graph is the following:
Now we solve for "y" in equation (2). To do that we will subtract "x" from both sides:
[tex]y=4-x[/tex]Now, we graph using the same procedure as before. We will graph both lines in the same coordinate system and we will determine their interception point, like this:
The interception point is the solution of the system. Therefore, the solution is:
[tex](x,y)=(-2,-2)[/tex]What is the domain and range of the function? 15c
The first thing we have to know is that the Domain are all the values that x can take in the function and that the Range are all the values that the function takes in y
Taking this into account, the best way to see the domain and range is by graphing the function
[tex]\begin{gathered} f^{-1}(x)=3+\log _4(\frac{1-x}{3}) \\ f^{-1}(x)=3+\log _4(1-x)-\log _4(3) \end{gathered}[/tex]If you want to find the Domain we have to guarantee that what is inside the logarithm and have a x is greater than zero:
[tex]\begin{gathered} 1-x>0 \\ 1>x \end{gathered}[/tex]This means that the domain will only be those values less than 1
Instructions: Solve the triangle, find m
step 1
Find out the measure of angle A
we have that
In the given right triangle
[tex]\begin{gathered} cosA=\frac{17}{38}\text{ ----> by CAH} \\ \\ A=cos^{-1}(\frac{17}{38}) \\ A=63^o \end{gathered}[/tex]step 2
Find out the measure of angle C
Remember that
In the right triangle
A+C=90 degrees -----------> by complementary angles
[tex]\begin{gathered} 63^o+C=90^o \\ C=90^o-63^o \\ C=27^o \end{gathered}[/tex]Given parallelogram ABCD; ED=7x and BD=16x-38. Find BD. * B C E А D
For the given equation, enter the value of B when x= - 1/5B/x =20
Answer:
[tex]B=4[/tex]Step-by-step explanation:
To solve the following equation.
[tex]\begin{gathered} \frac{B}{x}=20 \\ \end{gathered}[/tex]Substitute x=-1/5, and use inverse operations to solve equations.
*Addition and subtraction are inverse operations, multiplication, and division too.
[tex]\begin{gathered} \frac{B}{\frac{1}{5}}=20 \\ 5B=20 \\ B=\frac{20}{5} \\ B=4 \end{gathered}[/tex]Which is more, 10 tons or 20,004 pounds?
A ton is equivalent to 2000 pounds. Then, 10 tons are 20,000 pounds.
Therefore, 20,004 pounds is more.
The angle of depression from d measures 25 if EF= 10 find De.
Step 1: You draw the diagram
The term angle of depression denotes the angle from the horizontal downward to an object. An observer's line of sight would be below the horizontal.
The angle of depression is equal to angle
Step 2: Apply trigonometric ratio to find the side DE.
[tex]\begin{gathered} \tan \theta\text{ = }\frac{Opposite}{\text{Adjacent}} \\ \theta\text{ = 25} \\ \text{Opposite DE = ?} \\ \text{Adjacent EF = 10 yd} \end{gathered}[/tex]Step 3: Substitute the values in the tangent equation to find side DE.
[tex]\begin{gathered} \tan 25\text{ = }\frac{DE}{10} \\ 0.4663\text{ = }\frac{DE}{10} \\ \text{Cross multiply} \\ DE\text{ = 10 x 0.4663} \\ DE\text{ = 4.663} \end{gathered}[/tex]Final answer
DE = 4.7 yard
SHORT ANSWERWhy is 3Vx + 4x2not a polynomial?Answer in complete sentences.Н.BI U SX2 x?E= = =ATXVXEnter your answer here
is not a polynomial because the power of the unknown for polynomials are always positive integers.
In this case, the power of x has 0.5
Find the values of each variable using sin, cos or sine
To obtain the value of x, substitute the values of the following.
[tex]\begin{gathered} \theta=70\degree \\ \text{opposite side}=x \\ \text{hypothenuse}=30 \end{gathered}[/tex]Thus, we obtain the following
[tex]\begin{gathered} \sin \theta=\frac{opposite\text{ side}}{hypothenuse} \\ \sin 70\degree=\frac{x}{30} \end{gathered}[/tex]Multiply both sides of the equation by 30 and then simplify.
[tex]\begin{gathered} 30\sin 70\degree=x \\ x\approx28.19 \\ x\approx28 \end{gathered}[/tex]Since the two sides are equal, the base angles must be equal. Thus, we obtain the following.
[tex]\begin{gathered} \theta=70\degree \\ \text{adjacent side}=y \\ \text{hypothenuse}=30 \end{gathered}[/tex]Substitute the values using the following equation.
[tex]\begin{gathered} \cos \theta=\frac{adjacent\text{ side}}{hypothenuse} \\ \cos 70\degree=\frac{y}{30} \end{gathered}[/tex]Multiply both sides of the equation by 30 and then simplify.
[tex]\begin{gathered} 30\cos 70\degree=y \\ y\approx10.26 \\ y\approx10 \end{gathered}[/tex]Therefore, the value of x is approximately 28.19 and the value of y is approximately 10.26.
The topic is solving radical equations, but im just confused on whether to squafe it or not[tex]2 \sqrt{n} = n - 3[/tex]
a We are given the following radical equation
[tex]2\sqrt[]{n}=n-3[/tex]To solve this equation we need to square both sides of the equation
[tex]\begin{gathered} (2\sqrt[]{n})^2=(n-3)^2 \\ 4n=(n-3)^2 \end{gathered}[/tex]Apply the squares formula on right-hand side of the equation
[tex](a-b)^2=a^2+b^2-2ab[/tex]So the equation will become
[tex]\begin{gathered} 4n=n^2+3^2-2(n)(3) \\ 4n=n^2+9-6n \\ 0=n^2+9-6n-4n \\ 0=n^2+9-10n \\ n^2-10n+9=0 \end{gathered}[/tex]So we are left with a quadratic equation.
The standard form of a quadratic equation is given by
[tex]ax^2+bx+c=0[/tex]Comparing the standard equation with our equation we get the following coefficients
a = 1
b = -10
c = 9
Now recall that quadratic formula is given by
so I have to make a table for the following equations and then graph them y= 2x+7
we have
y= 2x+7
this is the equation of the line
Make the table
For different values of x, calculate the values of y
so
For x=-1
y=2*(-1)+7
y=5
For x=0
y=2*(0)+7
y=7
For x=1
y=2*(1)+7
y=9
For x=2
y=2*(2)+7
y=11
therefore
we have the points
(-1,5) (0,7) (1,9) (2,11)
Plot the points and join them to graph the line
using a graphing tool
see the attached figure
please wait a minute
Hannah bought an emerald pendant online. It cost $751 plus 19% shipping and handling. What was the total cost? Round your answer to the nearest dollar: $
To find the shipping cost we can use the rule of three:
[tex]\begin{gathered} 751\rightarrow100 \\ x\rightarrow19 \end{gathered}[/tex]Then:
[tex]x=\frac{19\cdot751}{100}=\frac{14269}{100}=142.69[/tex]Therefore the total cost is $893.69
standing 200ft from the base of an antenna, Maria measures the angle of elevation to the top of the antenna to be 38 degrees. If her eye level is 5ft above the ground, what is the height of the antenna to the nearest foot?
Given: The bearing and distance of Maria and an antenna
To Determine: The height of the antenna from the given information
Solution
From the given information, the diagram below can be deduced
From the diagram above, the height of the antenna is TB
Using SOH CAH TOA
[tex]\begin{gathered} tan38^0=\frac{TC}{EC} \\ EC=BG=200ft \\ SO, \\ tan38^0=\frac{TC}{200} \\ TC=200\times tan38^0 \end{gathered}[/tex][tex]\begin{gathered} TC=156.257ft \\ TB=TC+CB \\ EG=CB=5ft \\ TB=156.257+5 \\ TB=161.257ft \\ TB\approx161ft \end{gathered}[/tex]Hence, the height of the antenna is 161ft
How do I do this math problem I’m kinda lazy
Choose the equation of the horizontal line that passes through the point (-5,9)
We are asked to find the equation of the horizontal line that passes through the point (-5, 9)
Recall that point-slope is given by
[tex]y-y_1=m(x_{}-x_1)[/tex]Where m is the slope of the line and x1 and y1 are the coordinates of the given point.
We know that the slope of a horizontal line is 0.
So let us substitute m = 0 and the given point into the above formula
[tex]\begin{gathered} y-9_{}=0\cdot(x_{}-(-5)_{}) \\ y-9=0 \\ y=9 \end{gathered}[/tex]Therefore, the equation of the line is y = 9
find the exact length of a circular Arc if the radius is 2 ft, with a angle of π/2 radian.
We get that
[tex]S=r\cdot\theta=2\cdot\frac{\pi}{2}=\pi[/tex]Find y given that x = -6: y = -6x - 3Select one:O a. 39O b. -9O c. 33Od. -3
Answer:
c. 33
Explanation:
Given the equation:
[tex]y=-6x-3[/tex]When x=-6:
[tex]\begin{gathered} y=-6(-6)-3 \\ =36-3 \\ =33 \end{gathered}[/tex]The value of y when x=-6 is 33.
Option C is correct.
Evaluate the expression when X = 2X to the second power -8x -3
Evaluate for x = 2:
[tex](2)^2-8(2)-3=4-16-3=4-19=-15[/tex]2. Rewrite by factoring the GCF from each expression.a) 8r + 12O 8 (r + 3)O 4 (2r + 3)O 4 (2r + 12)O 8 (r + 12)
We are asked to rewrite the given expression by factoring the GCF from the expression.
[tex]8r+12[/tex]GCF is the greatest common factor.
Factors of 8 = 1, 2, 4, 8
Factors of 12 = 1, 2, 3, 4, 6, 12
Notice that the greatest common factor is 4
So, take out 4 from the expression
[tex]8r+12=4(2r+3)[/tex]Therefore, the correct answer is
[tex]4(2r+3)_{}[/tex]Find a formula for P = f(t), the size of the population that begins in year t = 0 with 2070 members and decreases at a 3.9% annual rate. Assume that time is measured in years. P = f(t) =
Explanation
Step 1
let
[tex]P=f(t)[/tex]where P represent the population, and t represents the time in years
so,
when t=0, P=2070
[tex]\begin{gathered} P=f(t) \\ 2070=f(0) \end{gathered}[/tex]Step 2
if the population decrease 3.9% every year,in decimal form
[tex]\begin{gathered} \text{3}.9\text{ =3.9/100= 0.039} \\ \end{gathered}[/tex]so,after 1 year the population is
[tex]\begin{gathered} P_1=P(1-0.039)\rightarrow Eq1 \\ P_1=P(0.961) \\ P_1=2070(0.961) \\ P_1=1989.27 \end{gathered}[/tex]now, after the 2 years
[tex]\begin{gathered} P_2=P_1(1-0.039)=P(1-0.039)(1-0.039)=P(1-0.039)^2 \\ \end{gathered}[/tex]now, after 3 years
[tex]P_3=P_2(1-0.039)=P(1-0.039)(1-0.039)(1-0.39==P(1-0.039)^3[/tex]now, we can see the function
[tex]\begin{gathered} P(1-0.039)^t\rightarrow P_f=P(1-0.039)^t \\ f(t)=P(1-0.039)^t \end{gathered}[/tex]I hope this helps you
To avoid calculating difficult probabilities by hand, use aA. stimulationOB. simulcastOC. simulationD. stimulusReset SelectionNextto estimate the probability.
When probabilities are tedious, the method of of using hand is likely to produce errors. We can use simulation in this case. Thus, the correct option is