Pair A:
[tex]7x+11y,11y+7x[/tex]Remember that characteristic of the numbers is that, in general:
[tex]a+b=b+a[/tex]For any numbers a and b, this is always true. So, in our case:
[tex]\begin{cases}a=7x \\ b=11y\end{cases}\Rightarrow7x+11y=11y+7x[/tex]So the pair A is equivalent
As for pair B:
We are going to it by contradiction: if we suppose that the two equations are the same (one is equal to the other) and we found a pair of numbers (x,y) that produce a contradiction, then the two equations cannot be equivalent. Let me show you:
Suppose pair B is equivalent, then:
[tex]3x+3y=6xy[/tex]Now, suppose that x=0 and y=1, then:
[tex]3(0)+3(1)=6(0)(1)\Rightarrow3=0!![/tex]And of course, 3 is not equal to 0!
So, by supposing that the 2 equations are equivalent we reach a false implication, which means that the pair is NOT equivalent
As for pair C:
We can expand the expression 6(2x-y):
[tex]6(2x-y)=6(2x)-6(y)=12x-6y[/tex]Which is exactly the first expression! So the pair is equivalent!
=Solve this system of equations byusing the elimination method.4x + 2y = -6-3x – 2y = 7([?], []-=The ordered pair of solutionsis written in the format (x, y).
STEP - BY - STEP EXPLANATION
What to find?
The solution to the system of equations.
Given:
4x + 2y = -6
-3x – 2y = 7
To solve the given system using the elimination method, we will follow the steps below:
Step 1
Eliminate y by adding the first and second equation.
[tex]\lparen4x-3x)+\left(2y-2y\right)=-6+7[/tex][tex]x=1[/tex]Step 2
Substitute x=1 into the first equation.
[tex]4\left(1\right)+2y=-6[/tex]Step 3
Subtract 4 from both-side of the equation.
[tex]\begin{gathered} 2y=-6-4 \\ \\ 2y=-10 \end{gathered}[/tex]Step 4
Divide both-side of the equation by 2
[tex]\frac{2y}{2}=-\frac{10}{2}[/tex][tex]y=-5[/tex]Therefore, the solution in its ordered pair is (1, -5)
Two cyclists start at the same point and travel in opposite directions. One cyclists travels 3 km/h slower than the other. If the two cyclists are 183 kilometers apart after 3 hours, whats is the rate of each cyclists ? Rate of the slower cyclist:Rate of the faster cyclist:
Two cyclists start at the same point and travel in opposite directions. One cyclist travels 3 km/h slower than the other. If the two cyclists are 183 kilometers apart after 3 hours, whats is the rate of each cyclist?
Let
x ------> Rate of the slower cyclist
y ------> Rate of the faster cyclist
Remember that
In this problem the rate is the same that the speed
so
x=y-3 ------> equation 1
Let
d -----> distance from the start after 3 hours slower cyclist
183-d -----> distance from the start after 3 hours faster cyclist
speed slower cyclist
x=d/3
speed faster cyclist
y=(183-d)/3
substitute the values of speed in equation 1
d/3==(183-d)/3-3
solve for d
multiply by 3 on both sides
d=183-d-9
2d=183-9
2d=174
d=87 km
therefore
speed slower cyclist -----> 87/3=29 km/h
speed faster cyclist ----> (183-87)/3=32 km/h
The graph of the exponential function f(x)=5^x+2 is given with three points. Determine the following for the graph of f^-1(x).(1) graph f^-1(x)(2) find the domain of f^-1(x)(3) find the range of f^-1(x)(4) does f^-1(x) increase or decrease on its domain?(5) the equation of the vertical asymptote for f^-1(x) is?
If you don’t need further explanation on this question, we can end the session. Remember the answer of this question will be on your profile once we finish the session. I’d really appreciate you letting me know how I did by rating our session after you exit. Thanks and have a great day!
To find the inverse of a function, we need to replace f(x) for y and switch every x for a y, and every y for a x:
[tex]\begin{gathered} f(x)=5^{x+2} \\ y=5^{x+2} \\ x=5^{y+2} \\ \ln x=\ln 5^{y+2} \\ By\text{ properties of logarithms:} \\ \ln (x)=(y+2)\ln (5) \\ \frac{\ln(x)}{\ln(5)}=y+2 \\ y=\frac{\ln(x)}{\ln(5)}-2 \\ f^{-1}(x)=\frac{\ln(x)}{\ln(5)}-2 \end{gathered}[/tex]1. The graph of f^-1(x) would be:
2. Domain of a function is all the set x-values or input values of a function, so in this case:
As we can see in the graph the function goes from (0, ∞), then its domain:
[tex]D_{f^{-1}(x)}=(0,\text{ }\infty)^{}[/tex]3. Range is the set of y-values that the function can take or output values, in this case, we can see it goes from 0 to -∞, then its range would be:
[tex]R_{f^{-1}(x)}=(0,-\infty)[/tex]4. In the graph, we can see that from 0 to ∞, the function is increasing.
5. Vertical asymptotes are vertical lines which correspond to the zeroes of the denominator of a rational function, we can see that the asymptote would be x=0.
Merry buys t shirts for $6 each and marks up the price by 45%. How much profit bodies Merry make from each t shirt sold?
The original price of a t-shirt is $6. And Merry marks up the price by 45%.
We need to find how much is the profit, in other words, we need to find how much is that 45% that Merry marks up from the original price.
Calculating 45% of $6:
The general process to calculate a percentage is to take the quantity (in this case 6), divide it by 100, and then multiply by the percentage we want (in this case 45):
[tex]\frac{6}{100}\times45[/tex]Solving this expression:
[tex]\frac{6}{100}\times45=2.7[/tex]The profit she makes from each t-shirt sold is $2.7.
Answer: $2.7
Analytically determine what type(s) of symmetry, if any, the graph of the equation would possess. Show your work.23) 2x^2 -3 = 4|y|
Answer:
The graph is symmetric about the x-axis, the y-axis, and the origin
Explanation:
A graph can be symmetric about the x-axis, about the y-axis, and about the origin.
To know if the graph is symmetric about the x-axis, we need to replace y by -y and determine if the equation is equivalent. So,
If we replace y with -y, we get:
[tex]\begin{gathered} 2x^2-3=4|-y| \\ 2x^2-3=4|y| \end{gathered}[/tex]Therefore, the graph is symmetric about the x-axis.
The graph is symmetric about the y-axis if we replace x by -x and we get an equivalent equation. So:
[tex]\begin{gathered} 2(-x)^2-3=4|y| \\ 2x^2-3=4|y| \end{gathered}[/tex]Since both equations are equivalent, the graph of the equation is symmetric about the y-axis
The graph is symmetric about the origin if we replace x by -x and y by -y and we get an equivalent equation. So:
[tex]\begin{gathered} 2(-x)^2-3=4|-y| \\ 2x^2-3=4|y| \end{gathered}[/tex]Therefore, the graph is symmetric about the origin.
Don’t show work. It’s not necessary. I just need answers to check my doings. Directions in pic
What is equivalent to [tex] {5}^{3} \times {5}^{4} [/tex]A: [tex] {25}^{7} [/tex]B: [tex] {5}^{7} [/tex]C: [tex] {25}^{12} [/tex]D: [tex] {5}^{12} [/tex]
Given
[tex]5^3\times5^4[/tex]To find the equivalent, apply the indices product rule
That is
[tex]a^b\times a^c=a^{b+c}[/tex]This implies
[tex]5^3\times5^4=5^{4+3}[/tex]Simplify further
[tex]5^{4+3}=5^7[/tex]Therefore, the solution is option B
[tex]5^7[/tex]which of the following numbers are located eight units from zero on the number line? Select all that apply.
1) Given the numbers, and the position on the number line we can sketch it:
2) So, as we can see the numbers that are located at 8 units from zero, are -8 (to the left) and 8
Triangle ABC is dilated using a scale factor of 1/2.What are the new coordinates of point A'?A.) (-3, 3)B.) (-2, 2)C.) (-12, 12)
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
ABC
A = (-6 , 6)
factor of dilation = 1/2
A' = ?
Step 02:
A' = (-6 * 1/2 , 6 * 1/2 )
A' = ( -3 , 3 )
The answer is:
A' = ( -3 , 3 )
3) f(t) = -2t²+ 1; Find f(-9) A) -31 B) -71 C) -161 D) -97
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
f(t) = -2t²+ 1
f(-9) = ?
Step 02:
t = -9
f(-9) = -2(-9)² + 1
= -2(81) + 1
= - 162 + 1
= -161
The answer is:
f(-9) = -161
Find the surface area. Round to the nearest tenth.12 inI19 in
INFORMATION:
We have the next figure
And we must find its surface area
STEP BY STEP EXPLANATION:
The surface area of a cone is equal to the curved surface area plus the area of the base:
[tex]A=\pi r^2+\pi Lr[/tex]Where, r denotes the radius of the base of the cone, and L denotes the slant height of the cone.
Now, we must calculate L using the right triangle formed
We can use the Pythagorean theorem,
[tex]\begin{gathered} L^2=9^2+12^2 \\ L^2=81+144 \\ L^=\sqrt{225} \\ L=15 \end{gathered}[/tex]So, having r = 9 in and L = 15 in, we can replace the values in the formula
[tex]\begin{gathered} A=\pi\cdot9^2+\pi\cdot15\cdot9 \\ A=81\pi+135\pi \end{gathered}[/tex]Then, replacing π = 3.14
[tex]\begin{gathered} A=81(3.14)+135(3.14) \\ A=678.2\text{ }in^2 \end{gathered}[/tex]Finally, the surface area of the cone is 678.2 in^2
ANSWER:
678.2 in^2
If a triangle has sides of length 6cm and 8cm, what do you know about the length of the third side?
If a triangle has sides a, b, and c, then
The length of any one of them is the between the difference and the sum of the other 2 sides
[tex]a-bLet a = 8 cm and b = 6 cm, then[tex]\begin{gathered} 8-6The length of the third side must be greater than 2 and less than 14Evaluate the expression:5^3.2 = y
Given the following expression:
[tex]\text{ 5}^{3.2^{}}\text{ = y}[/tex]To expand the given exponential expression, we first convert 5.2 into an improper fraction.
We get,
[tex]3.2\text{ = 3}\frac{20}{100}\text{ = 3}\frac{1}{5}[/tex][tex]\text{ 3}\frac{1}{5}\text{ = }\frac{1\text{ + (3 x 5)}}{5}\text{ = }\frac{1\text{ + 15}}{5}[/tex][tex]\text{ = }\frac{16}{5}[/tex]Reconstructing the expression, we get:
[tex]\text{ 5}^{3.2}\text{ = y }\rightarrow5^{\frac{16}{5}}=\text{ y}[/tex]When the exponent is a fraction, the numerator remains the exponent of the base while the denominator becomes the degree of the root.
We get,
[tex]\text{ 5}^{\frac{16}{5}}\text{ = y }\rightarrow\text{ }\sqrt[5]{5^{16}}\text{ = y}[/tex][tex]undefined[/tex]3. The rectangle and the trapezoid have the same area. What is the length of the rectangle? 21 ft. 5 ft. 5 ft. e 9 ft.
The formula for determining the area of a trapezoid is expressed as
Area = 1/2(a + b)h
where
a and b are the length of the opposite sides of the trapezium
h is the height
From the information given,
a = 21
b = 9
h = 5
Area = 1/2(21 + 9)5 = 1/2(30)5
Area = 75 square feet
The area of a rectangle is expressed as
Area = length x width
Given that the rectangle and the trapezoid has the same area, it means that
75 = 5 x l
l = 75/5
l = 15
Thus, length of the rectangle is 15 ft
Kali and Asanji each improved their yards by planting daylilies and ornamental grass. They bought their supplies from the same store. Kali spent $132 on 6 daylilies and 12 bunches of ornamental grass. Asanji spent $83 on 14 daylilies and 3 bunches of ornamental grass. What is the cost of one daylily and the cost of one bunch of ornamental grass?
cost of one daylily= $4
cost of one bunch= $ 9
Explanation
Step 1
Let x represents the cost of one daylily
Let y represents the cost of one bunch
then
Kali spent $132 on 6 daylilies and 12 bunches of ornamental grass.
in math terms
[tex]132=6x+12y\text{ Equatino(1)}[/tex]and
Asanji spent $83 on 14 daylilies and 3 bunches of ornamental grass
[tex]83=14x+3y\text{ Equation(2)}[/tex]Step 2
solve for x and y
multiply equation (2) by -4 and add the result to equation(1)
[tex]\begin{gathered} 83=14x+3y\text{ Equation(2) multiplied by -4} \\ -332=-56x-12y\text{ Equation (3)} \\ \text{Now, add Eq(1) and (3)} \\ 132=6x+12y \\ -332=-56x-12y \\ \text{.}------------ \\ -200=-50x+0 \\ \text{divide both sides by -50} \\ \frac{-200}{-50}=\frac{-50x}{-50} \\ 4=x \end{gathered}[/tex]now, to find y, replace x equation (2) and isolate y
[tex]\begin{gathered} 83=14x+3y\text{ Equation(2)} \\ 83=14\cdot4+3y\text{ } \\ 83=56+3y \\ \text{subtract 56 in both sides} \\ 83-56=56+3y-56 \\ 27=3y \\ \text{divide both sides by 3} \\ \frac{27}{3}=\frac{3y}{3} \\ 9=y \end{gathered}[/tex]so
cost of one daylily= $4
cost of one bunch= $ 9
Emily had 5 tacos she gave 3 to her friends how much does she have
Answer
Emily has 2 tacos now after giving her friends the 3 tacos.
Explanation
Emily had 5 tacos.
She gave her friends 3 tacos.
Number of tacos that Emily has now
= (Initial number of tacos she had) - (Number of tacos she gave her friends)
Initial number of tacos she had = 5 tacos
Number of tacos she gave her friends = 3 tacos
Number of tacos that Emily has now
= (Initial number of tacos she had) - (Number of tacos she gave her friends)
= 5 - 3
= 2 tacos
Hope this Helps!!!
1 ptsQuestion 3Two angles are complementary. The smaller angle is 42 degrees less than the largerangle. What is the measurement of the smaller angle?Be precise in the measurement, including any decimal value. You only need toenter the value for the angle. No other symbols or unit information needed.
It is given that two angles are complementary.
Let x be the larger angle.
It is given that The smaller angle is 42 degrees less than the larger angle
[tex]\text{The smaller angle=}x-42^o[/tex]We know that the sum of the complementary angles is 90 degrees.
[tex]\text{the larger angle+ the smaller angle =}90^o[/tex]Substitute the larger angle =x and the smaller angle =x-42, we get
[tex]x+x-42^o=90^o[/tex][tex]2x-42^o=90^o[/tex]Transferring 42 to the right-hand side, we get
[tex]2x=90^o+42^o[/tex][tex]2x=132^o[/tex][tex]x=\frac{132^o}{2}[/tex][tex]x=66^o[/tex][tex]T\text{he larger angle=x=}66^o[/tex][tex]\text{The smaller angle =}x-42^o=66^o-42^o=24^o[/tex]Hence the given two complementary angles are
[tex]66^o,24^o[/tex]Which equation best fits the data, where x is the year and y is the population in thousands?
Verify each option
the answer is between option A and option B, because is not a linear equation
and option D is not the solution because the graph is a growth function, and the option D is a decay exponential function
we have that
For x=0 ------> y=1.5
option A ----> y=(0^2)+1.5=1.5 is ok
option B ----> y=1.5(1.25^0)=1.5 is ok
For x=1 ------> y is about 2
option A ----> y=(1^2)+1.5 =2.5
option B -----> y=1.5(1.25^1)=1.875 is ok
For x=3 ------> y is about 3
option A -----> y=(3^2)+1.5=10.5 is not ok
option B -----> y=1.5(1.25^3)=2.93 is ok
the answer is option BA coin is tossed, then aletter from the wordINDIANAPOLIS is selected atrandom. Find eachprobability.a) P(heads, then P)b) Pitails, then a vowel)c) P(tails, then N)d) P/heads, then D or I)
Answer
a) P(heads, then P) = (1/2) × (1/12) = (1/24) = 0.04167
b) P(tails, then a vowel) = (1/2) × (1/2) = (1/4) = 0.25
c) P(tails, then N) = (1/2) × (1/6) = (1/12) = 0.0833
d) P(heads, then D or I) = (1/2) × (1/3) = (1/6) = 0.1667
Explanation
First of, we need to define what the probability of an event is
[tex]\text{Probability of an event =}\frac{Number\text{ of elements in that event}}{Number\text{ of total elements in the sample space}}[/tex]And when two independent events (two events whose probabilities do not depend on each other) happen one after the other, the total probability is the product of the two probabilities. That is, if A and B are independent events,
P (A n B) = P(A) × P(B)
So, we can start answering now,
a) P(heads, then P)
First of, we calculate the probability of a head turning up in a coin toss.
Probability of heads turning up in a coin toss = P(heads) = ?
Number of elements in the event = Number of heads possible in one coin toss = 1
Number of total elements in the sample space = Number of possible outcomes in a coin toss = 2 (It's usually either heads or tails!)
Probability of heads turning up in a coin toss = P(heads) = (1/2) = 0.5
Now, we calculate the probability of selecting a P from INDIANAPOLIS
Probability of selecting a P from INDIANAPOLIS = P (P) = ?
Number of elements in the event = Number of P's that are in INDIANAPOLIS = 1
Number of total elements in the sample space = Total number of letters in INDIANAPOLIS = 12
Probability of selecting a P from INDIANAPOLIS = P (P) = (1/12) = 0.08333
Now, we calculate the total probability of obtaining a head from the coin toss and then selecting P from INDIANAPOLIS
P(heads, then P) = (1/2) × (1/12) = (1/24) = 0.04167
b) P(tails, then a vowel)
First of, we calculate the probability of a tail turning up in a coin toss.
Probability of tails turning up in a coin toss = P(tails) = ?
Number of elements in the event = Number of heads possible in one coin toss = 1
Number of total elements in the sample space = Number of possible outcomes in a coin toss = 2 (It's usually either heads or tails!)
Probability of tails turning up in a coin toss = P(tails) = (1/2) = 0.5
Now, we calculate the probability of selecting a vowel from INDIANAPOLIS
Probability of selecting a vowel from INDIANAPOLIS = P (vowel) = ?
Number of elements in the event = Number of vowels that are in INDIANAPOLIS = 6
Number of total elements in the sample space = Total number of letters in INDIANAPOLIS = 12
Probability of selecting a vowel from INDIANAPOLIS = P(vowel) = (6/12) = (1/2) = 0.5
Now, we calculate the total probability of obtaining a tail from the coin toss and then selecting a vowel from INDIANAPOLIS
P(tails, then a vowel) = (1/2) × (1/2) = (1/4) = 0.25
c) P(tails, then N)
First of, we calculate the probability of a tail turning up in a coin toss.
Probability of tails turning up in a coin toss = P(tails) = ?
Number of elements in the event = Number of heads possible in one coin toss = 1
Number of total elements in the sample space = Number of possible outcomes in a coin toss = 2 (It's usually either heads or tails!)
Probability of tails turning up in a coin toss = P(tails) = (1/2) = 0.5
Now, we calculate the probability of selecting N from INDIANAPOLIS
Probability of selecting N from INDIANAPOLIS = P(N) = ?
Number of elements in the event = Number of N's that are in INDIANAPOLIS = 2
Number of total elements in the sample space = Total number of letters in INDIANAPOLIS = 12
Probability of selecting N from INDIANAPOLIS = P(N) = (2/12) = (1/6) = 0.1667
Now, we calculate the total probability of obtaining a tail from the coin toss and then selecting N from INDIANAPOLIS
P(tails, then N) = (1/2) × (1/6) = (1/12) = 0.0833
d) P(heads, then D or I)
First of, we calculate the probability of a head turning up in a coin toss.
Probability of heads turning up in a coin toss = P(heads) = ?
Number of elements in the event = Number of heads possible in one coin toss = 1
Number of total elements in the sample space = Number of possible outcomes in a coin toss = 2 (It's usually either heads or tails!)
Probability of heads turning up in a coin toss = P(heads) = (1/2) = 0.5
Now, we calculate the probability of selecting a D or I from INDIANAPOLIS
Probability of selecting a D or I from INDIANAPOLIS = P(D or I) = ?
Number of elements in the event = Number of D's or I's that are in INDIANAPOLIS = 4 (Three I's and one D)
Number of total elements in the sample space = Total number of letters in INDIANAPOLIS = 12
Probability of selecting a D or I from INDIANAPOLIS = P(D or I) = (4/12) = (1/3) = 0.3333
Now, we calculate the total probability of obtaining a head from the coin toss and then selecting D or I from INDIANAPOLIS
P(heads, then D or I) = (1/2) × (1/3) = (1/6) = 0.1667
Hope this Helps!!!
Question 2 of 13To graph the inequality y < 2x-1, you would draw a dashed line.A. TrueB. False
A. True.
There are two types of inequality, either strict inequality, or mixed inequality.
The inequality including the possibility of equality is called as mixed inequality. This is represented by solid line.
The inequality excluding the possibility of eauality is called as strict ineq
Hello do you no have to do Hands on Equations?
Given that
Then,
[tex]\begin{gathered} x=8 \\ \chi=-8 \\ x+\chi+4x=16+2x \\ 8+(-8)+4(8)=16+2(8) \\ 0+32=16+16 \\ 32=32 \end{gathered}[/tex]The answer is 32=32
On Thursday afternoon at camp, Elise played basketball and went swimming before dinner.She spent 1 hour and 30 minutes playing basketball and 1 hour and 35 minutes swimming.Dinner lasted for 1 hour and 10 minutes. If dinner ended at 7:10 P.M., what time did Elisestart playing basketball?
On Thursday afternoon at camp, Elise played basketball and went swimming before dinner.She spent 1 hour and 30 minutes playing basketball and 1 hour and 35 minutes swimming.Dinner lasted for 1 hour and 10 minutes. If dinner ended at 7:10
SolutionWe need to start subtracting backwardStep 17 : 10p.m - 1: 10 = 6pmStep 26pm - 1:35= 4 : 25pmStep 34: 25 - 1 : 30 = 2: 55pmAlternatively(second method)Add all the time before dinner ended and then subtract from when dinner ended[tex]1\text{ :30 +1 : 35 +1 :10= 4 hours 15minutes}[/tex]Now
[tex]7:\text{ 10pm -4: 15= 2:55pm}[/tex]The Final answer Elise started playing basketball at 2: 55pmFill in the blanks below with the correct units.A) Laura poured about 9 _____ of medicine onto a spoon.A: MillilitersB: Liters B) The blade of grass was about 8 ____ wide.A: Millimeters B: centimeters C: meters D: Kilometers C) Aldo used a fork that had a mass of about 28 _____.A: grams B: kilograms
EXPLANATION
Filling in the blanks give us:
A) Laura poured about 9 mililiters of medicine onto a spoon.
B) The blade of grass was about 8 milimeters wide.
C) Aldo used a fork that had a mass of about 28 grams.
percy is going to the water slides and needs to figure out which deal is better he can pay$30 to go on the water slides as much as he wants or he can pay$15 to get in plus an additional $1 per trip down the water slides if percy goes on a certain number of trips down the water slides the two options are equvinlet in terms of cost what is the costwrite a system of equtions graph them and type the solution
Solution:
Let the first option be x and the second option be y.
Let the number of trips down the water slides be z.
Thus;
[tex]\begin{gathered} x=30 \\ \\ y=15+z \end{gathered}[/tex]When the two options are equivalent;
Find the tangent of ZS.S2-/11Q3-67-12R.Write your answer in simplified, rationalized form. Do not round.tan (S) =
we are asked to determine the tangent of angle S. To do that let's remember the definition of the tangent function:
[tex]\tan s=\frac{opposite}{adjacent}[/tex]Replacing the values we get:
[tex]\tan s=\frac{3\sqrt[]{6}}{2\sqrt[]{11}}[/tex]rationalizing the expression, by multiplying numerator and denominator by the square root of 11:
[tex]\tan s=\frac{3\sqrt[]{6}\times\sqrt[]{11}}{2\sqrt[]{11}\times\sqrt[]{11}}[/tex]Solving the operations:
[tex]\tan s=\frac{3\sqrt[]{6(11)}}{2(11)}[/tex][tex]\tan s=\frac{3\sqrt[]{66}}{22}[/tex]There was three-fourths of a gallon ofwhite paint left. There was also one-eighth of a gallon of blue paint. Howmuch more white paint was left?
Step 1: Let's review the information given to us to answer the problem correctly:
Paint we have: 3/4 of a gallon of white paint and 1/8 of a gallon of blue paint
Step 2: The paint is from different colors, therefore:
It was left 1/8 of a gallon of blue paint and 3/4 of a gallon of white paint.
Step 3: The question is asking this:
3/4 - 1/8 = ?
3/4 = 6/8
Therefore,
6/8 - 1/8 = 5/8 more white paint
Solve the following formula for the indicated variable.R=3(x - 11): solve for x
ANSWER:
[tex]\frac{5R}{3}+11[/tex]STEP-BY-STEP EXPLANATION:
We have the following equation:
[tex]R=\frac{3\cdot\mleft(x-11\mright)}{5}[/tex]We solve for x:
[tex]\begin{gathered} 5R=3(x-11) \\ x-11=\frac{5R}{3} \\ x=\frac{5R}{3}+11 \end{gathered}[/tex]Find the value of 64 ÷ 42·16
You have the following expression:
64 ÷ 42·16
In order to simplify the previous expression, first multiply the factors 42 and 16:
42·16 = 672
next, simplify the fraction 64/672:
64/672 divide by 2 both numerator and denominator
32/336 divide by 2
16/168 divide by 2
8/84 divide by 2
4/42 divide by 2
2/21
Hence, the simplied expression is 2/21
Identify the horizontal asymptote for the function belowОy= 4Oy=1.5Oy= -3O y= -2
ok
According to the graph the horizontal asymptote is y = -3, because the curve follows that line.
A sphere is inscribed in a right circular cylinder, such that it is tangent to both bases. What is the ratio of the volume of the sphere to the volume of the cylinder?
We are given that a sphere is inscribed is a right circular cylinder. This means that the diameter of the sphere is equivalent to the height of the cylinder. A front view of this is the following:
We notice that the radius of the sphere and the radius of the cylinder coincide.
Now, we are asked to determine the ratio of the volume of the sphere to the volume of the cylinder. First, the volume of a sphere is given by:
[tex]V_S=\frac{4}{3}\pi r^3_{}[/tex]And the volume of a cylinder is given by:
[tex]V_c=\pi r^2h[/tex]Now, the ratio is the quotient between the volumes, therefore, we have:
[tex]\frac{V_s}{V_c}=\frac{\frac{4}{3}\pi r^3_{}}{\pi r^2h}[/tex]We can cancel out pi:
[tex]\frac{V_s}{V_c}=\frac{\frac{4}{3}r^3_{}}{r^2h}[/tex]We can also cancel out the square of the radius:
[tex]\frac{V_s}{V_c}=\frac{\frac{4}{3}r^{}_{}}{h}[/tex]Now, We know that the height "h" of the cylinder is equivalent to the diameter, this means that the height if equivalent to two times the radius, that is:
[tex]h=2r[/tex]Substituting in the ratio we get:
[tex]\frac{V_s}{V_c}=\frac{\frac{4}{3}r^{}_{}}{2r}[/tex]Now we cancel out the radius:
[tex]\frac{V_s}{V_c}=\frac{\frac{4}{3}}{2}[/tex]Simplifying the fraction we get:
[tex]\frac{V_s}{V_c}=\frac{4}{6}[/tex]Therefore, the ratio is 4/6.