Graph the exponential function.G(x)=(1/3)^xPlot five point on the graph of the function.
Answers
Graph the function:
[tex]G(x)=(\frac{1}{3})^x[/tex]We'll use the following values of x: {-2, -1, 0, 1, 2}.
Substituting:
[tex]G(-2)=(\frac{1}{3})^{-2}=3^2=9[/tex][tex]G(-1)=(\frac{1}{3})^{-1}=3^1=3[/tex][tex]G(0)=(\frac{1}{3})^0=1[/tex][tex]G(1)=(\frac{1}{3})^1=0.333[/tex][tex]G(2)=(\frac{1}{3})^2=0.111[/tex]The graph of the function is shown below:
Related Questions
what sentence represent the number of poins in the problem below
Answers
hello
to solve this question, we can write out two sets of equation and solve them
let the short answers be represented by x
let the multiple-choice questions be represented by y
we know that the test has 60 points
multiple-choice carries 2 points
short answers carries 5 points
[tex]2x+5y=60[/tex]now we have a total of 15 questions which comprises of multiple-choice questions and short answers
[tex]x+y=15[/tex]now we have two set of equations which are
[tex]\begin{gathered} 2x+5y=60\ldots\text{equ}1 \\ x+y=15\ldots\text{equ}2 \end{gathered}[/tex]now let's solve for x and y
from equation 2, let's make x the subject of formula
[tex]\begin{gathered} x+y=15 \\ x=15-y\ldots\text{equ}3 \end{gathered}[/tex]put equation 3 into equation 1
[tex]\begin{gathered} 2x+5y=60 \\ x=15-y \\ 2(15-y)+5y=60 \\ 30-2y+5y=60 \\ 30+3y=60 \\ \text{collect like terms} \\ 3y=60-30 \\ 3y=30 \\ \text{divide both sides by the coeffiecient of y} \\ \frac{3y}{3}=\frac{30}{3} \\ y=10 \end{gathered}[/tex]now we know the value of y which is the number of multiple-choice question. we can use this information to find the number of short answer through either equation 1 or 2
from equation 2
[tex]\begin{gathered} x+y=15 \\ y=10 \\ x+10=15 \\ \text{collect like terms} \\ x=15-10 \\ x=5 \end{gathered}[/tex]from the calculations above, the number of short answers is equal to 5 and multiple-choice questions is equal to 10.
The answer to this question is option C
The distance to the grocery store is 13.456 miles round this distance to the nearest tenth
Answers
Answer:
Your answer is 13.50
in the graphs state wether these represent a function or not. PLEASE HELP !!
Answers
Answer:
graph 1 is a function
graph 2 is not
graph 3 is not
graph 4 is not
graph 5 is not
graph 6 is a function
Step-by-step explanation:
The measures of the angles of a triangle are shown in the figure below. Solve for x.
Answers
Answer:
x = 9
Step-by-step explanation:
87 + 36 = 123
180 - 123 = 57
6x + 3 = 57
57 - 3 = 54
54/6 = 9
I need help with this problem. The table below shows that the number of miles driven by Samuel is directly proportional to the number of gallons he used. \text{Gallons Used}Gallons Used \text{Miles Driven}Miles Driven 3030 10411041 4646 1596.21596.2 4848 1665.61665.6 \text{What is the rate of gas usage, in miles per gallon?} What is the rate of gas usage, in miles per gallon?
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The rate of gas usage, in miles per gallon is 34.7 miles per gallon.
What is a direct proportion?A direct proportion is used to show the constant of proportionality.
In this case, at 30 gallons, the miles used was 1041. Therefore the rate of gas usage will be:
= Miles travelled / Number of gallons
= 1041 / 30
= 34.7 miles per gallon
This shows the rate.
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Sammi had a total of 25 ft of ribbon. She cut off 13 ½ feet to keep, the remaining fabric she cut into 3 inch sections to make ribbons. How many ribbons would she be able to make?
Answers
First, find the total length of the remaining fabric by substracting 13 1/2 from 25:
[tex]\begin{gathered} 25-13\frac{1}{2} \\ =25-13-\frac{1}{2} \\ =12-\frac{1}{2} \\ =11\frac{1}{2} \end{gathered}[/tex]Since one feet equals 12 inches, multiply 11 1/2 by 12 to find the total length of the remaining fabric in inches:
[tex]\begin{gathered} 11\frac{1}{2}\times12=11\times12+\frac{1}{2}\times12 \\ =132+\frac{12}{2} \\ =132+6 \\ =138 \end{gathered}[/tex]Since each ribbon takes 3 inches, divide 138 over 3 to find the total amount of ribbons that can be made:
[tex]\frac{138}{3}=46[/tex]Therefore, Sammi is able to make 46 ribbons.
Helena is watching a movie on television she notices that there are 9 1/4 min of commercial for every 1/2 hour of the movie
Answers
If Helena watches a movie that shows a commercial for 9 1/4 mins of every 30 minutes (half hour), then the unit rate of commercials per hour is derived as;
[tex]\begin{gathered} \text{Com /30 mins=9}\frac{1}{4} \\ \text{Com /60 mins=9}\frac{1}{4}\times2 \\ \text{Com /hour=}\frac{37}{4}\times2 \\ \text{Com /hour=}\frac{37}{2} \\ Com\text{ /hour=18}\frac{1}{2} \end{gathered}[/tex]The unit rate of commercials per hour is 18 1/2 minutes (eighteen and half minutes)
. Find the Value of x. SHOW YOUR WORK OR NO CREDITIMI
Answers
we can use pythagoras to solve the triangle
[tex]a^2+b^2=h^2[/tex]where a and b are sides and h the hypotenuse on this case we use half triangle to make a rigth triangle and apply pythagoras
a is 9, b is 20 and h the x
so replacing
[tex]\begin{gathered} 9^2+20^2=x^2 \\ \end{gathered}[/tex]solve for x
[tex]x=\sqrt[]{9^2+20^2}[/tex]and do the operatios
[tex]\begin{gathered} x=\sqrt[]{81+400} \\ x=\sqrt[]{481}\approx21.93 \end{gathered}[/tex]the value of x is 21.93 units
A 17 m guy wire attached to the top of a tower (the height of the tower is not yet known) is anchored on the ground, 8 m away from the base of the tower. A second guy wire needs to be attached to the centre of the tower and then anchored to the same ground-anchor as the first wire.Draw and label a diagram.How long does the second guy wire need to be?Determine the measure of the angle formed between the two wires.
Answers
Solution
Step 1:
Draw the diagram to illustrate the information.
Step 2:
Use the Pythagoras theorem to find the height of the pole.
[tex]\begin{gathered} 17^2\text{ = h}^2\text{ + 8}^2 \\ 289\text{ = h}^2\text{ + 64} \\ h^2\text{ = 289 - 64} \\ h^2\text{ = 225} \\ h\text{ = }\sqrt{225} \\ \text{h = 15m} \end{gathered}[/tex]Step 3
b) The height of the second guy wire = d
[tex]\begin{gathered} \text{Apply the pythagoras theorem} \\ d^2=\text{ \lparen}\frac{15}{2}\text{\rparen}^2+\text{ 8}^2 \\ d^2\text{ = 56.25 + 64} \\ d^2\text{ = 120.25} \\ \text{d = }\sqrt{120.25} \\ \text{d = 10.97m} \end{gathered}[/tex]c)
[tex]\begin{gathered} sin(\theta\text{ + }\alpha)\text{ = }\frac{Opposite}{Hypotenuse} \\ sin(\theta\text{ + }\alpha)\text{ = }\frac{15}{17} \\ \theta\text{ + }\alpha\text{ = sin}^{-1}(\frac{15}{17}) \\ \theta\text{ + }\alpha\text{ = 61.9}^o \end{gathered}[/tex][tex]\begin{gathered} sin\alpha\text{ = }\frac{7.5}{10.97} \\ \alpha=\text{ sin}^{-1}(\frac{7.5}{10.97}) \\ \alpha\text{ = 43.1} \end{gathered}[/tex]The angle between the two guys' wires = 61.9 - 43.1
Measure of the angle formed between the two wires = 18.8
Stores on the verbal Graduate Record Exam (GRE) have a mean of 462 and a standard deviation of 119. Scores on the quantitative GRE have a mean of 584 and a standard deviation of 151. Assuming the scores are normally distributed, what quantitative scores are required for an applicant to score at or above the 90th percentile
Answers
We need Z-score here.
The formula is:
[tex]z=\frac{x-\mu}{\sigma}[/tex]A normal curve (with 90th percentile), looks like the one below:
We need a standard normal table to move further.
When we go to the table, we find that the value 0.90 is not there exactly, however, the values 0.8997 and 0.9015 are there and correspond to Z values of 1.28 and 1.29, respectively
(i.e., 89.97% of the area under the standard normal curve is below 1.28).
The exact Z value holding 90% of the values below it is 1.282.
--------------- Now, we work backwords and find the value of x:
Verbal GRE:
[tex]\begin{gathered} \mu=462 \\ \sigma=119 \\ z=\frac{x-\mu}{\sigma} \\ 1.282=\frac{x-462}{119} \\ x-462=1.282(119) \\ x=614.558 \end{gathered}[/tex]So, a 90th percentile on Verbal GRE is a score above 614.56
Quantitative GRE:
[tex]\begin{gathered} z=\frac{x-\mu}{\sigma} \\ 1.282=\frac{x-584}{151} \\ x=777.582 \end{gathered}[/tex]So, a 90th percentile on Quantitative GRE is a scoer above 777.58
A four sided residential lot that measures 112.7 ft, 85.3 ft, 110.8 ft, and 98.5 ft is to be fenced. How many feet of fencing are required?
Answers
307.3 feet is the perimeter of fencing that is required to fence a four sided residential lot that measures 112.7 ft, 85.3 ft, 110.8 ft, and 98.5 ft.
What is perimeter?The distance around a shape or space is measured by its perimeter. The length of a shape's outline is what it is, simply put.
Children may have an easier time understanding this new term if they are given an analogy like walking completely around a shape or erecting a fence around a field.
When determining the size of a space, such as a garden or a room in your home, the perimeter is frequently used. The distance around your living room or garden, for instance, would be necessary if you wanted a new carpet or garden fence.
We need to simply find the perimeter of the polygon lot to find measure of fencing required.
Perimeter = sum of sides
= 12.7 + 85.3 + 110.8 + 98.5
= 307.3 ft
Thus, 307.3 feet of fencing are required to fence a four sided residential lot that measures 112.7 ft, 85.3 ft, 110.8 ft, and 98.5 ft.
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3 feeding 54C 3. What is the constant of proportionality? What does it tell us about the situation? day 4. If we switched the columns in the table, what would be the constant of proportionality? Explain your reasoning. 5. Use d for number of days and f for amount of food in grams that a shrimp eats to write two equations that represent the relationship between d and f. 6. If a tank has 10 shrimp in it, how much food is added to the tank each day? 7. If the aquarium manager has 300 grams of shrimp food for this tank of 10 shrimp, how many days will it last? Explain or show your reasoning.
Answers
3) 0.6 grams per day
4) 1.67 grams per day
5) f = kd
k = f/d
Explanation:3) y = kx
where k = constant of proportionality
from the table, let x = number of days
y = food in grams
when x = 1, y = 0.6
we find k:
0.6 = k(1)
0.6 = k
Hence, the constant of proportionality is 0.6
It means the rate at which the shrimp is fed is 0.6grams per day
4) if columns are switched, the number of days = y
food in grams = x
let's use the same values but it will be interchanged:
when x = 0.6, y = 1
y = kx
1 = k(0.6)
1 = 0.6k
k = 1/0.6
k = 1.67 or 5/3
The rate at which the shrimp is fed is 1.67 grams per day
Here the rate is higher than the previous result. This is because the y value is greater then the x value.
5) if f = amount of food in grams
d = number of days
Since the relationship between the amount of food and number of days is proportional (it has beeen established previously), we would use the proportional equation:
y = f = amount of food in grams
x = d = number of days
f = kd (one equation)
it can also be written as:
f = kd
k = f/d (2nd equation)
the statement below always sometimes or never true give at least two examples to support your reasoning the LMC of two numbers is the product of the two numbers discuss with a partner
Answers
After filling the ketchup dispenser at the snack bar where she works, Kelley measures the level of ketchup during the day at different hourly intervals.
Complete parts a to c.
Question content area bottom
Part 1
a. Assuming the ketchup is used at a constant rate, write a linear equation that can be used to determine the level of ketchup in the dispenser after x hours. Let y represent the level of ketchup in inches.
y equals negative five eighths x plus 15
(Type an equation.)
Part 2
b. How can the equation from part a be used to find the level of ketchup when the dispenser is full?
A.
Identify the slope of the line represented by the equation.
B.
Find the difference between the slope and the y-intercept of the line represented by the equation.
C.
Substitute 0 for x in the equation and solve for y. Equivalently, find the y-intercept.
D.
Substitute 0 for y in the equation and solve for x. Equivalently, find the x-intercept.
Part 3
c. If Kelley fills the ketchup dispenser just before the snack bar opens and the snack bar is open for 18 hours, will the dispenser need to be refilled before closing time? Explain.
If the ketchup is used at a constant rate, then the equation from part a indicates the dispenser will become empty
enter your response here hours after the snack bar opens. This means that the dispenser
▼
will become empty before closing time,
will become empty exactly at closing time,
still has ketchup in it at closing time,
and so it
▼
will not
will
need to be refilled before closing time.
Answers
Answer:
Answers
Step-by-step explanation:
Got it from SAVVAS
Please help!! College Algebra. Need answer fast!!
Answers
On the graph of y=25-x², a rectangle has four corners: one at the origin. The area of the rectangle is A=25x-x³.
Given that,
On the graph of y=25-x², a rectangle has four corners: one at the origin, one in quadrant I, one in the positive y-axis, and one in the positive x-axis. Refer to Figure.
We have to find as a function of x, express the rectangle's area A.
The area occupied by the rectangle within its perimeter can be calculated using the formula for the area of a rectangle.
The area of rectangle is A=xy
A=x(25-x²)
A=25x-x³
Therefore, the area of the rectangle is A=25x-x³.
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of the arithmetic sequence -10, -25, -40, ...
Find the 81st term
Answers
The 81st term of the arithmetic sequence -10, -25, -40, ... is -1210
Here is a step-by-step explanation The common difference in this sequence,
d = a2 -a1
let a2 = -25 and a1 = -10
d= -25 - (-10)
d = -15
the common difference (d) = -15
To find the n term we use :
an= a1+ (n-1)d
Therefore,
a81 = -10 + (81-1)(-15)
= -1210
The 81stterm of the arithmetic sequence -10, -25, -40, ... -1210
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Which relation is a function? 4 15 O -6- 7 C fy 0 -H O O O -2 -4
Answers
The most appropriate choice for functions will be given by -
Third option is correct
Third relation is a function.
What is a function?
A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.
There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.
Here,
For a function a point in the domain has a unique image.
Here values of x axis represents domain and values of y axis represents the range
For the first option,
x = -1 has two images, y = -1 and y = 3
so x = -1 do not have a unique image
So the first relation is not a function
For the second option,
x = 0 has two images, y = -1 and y = 2
so x = 0 do not have a unique image
So the second relation is not a function
For the third option,
Every point of the domain has a unique image
So the third relation is a function
For the fourth option,
x = -2 has two images, y = 1 and y = -2
so x = -2 do not have a unique image
So the fourth relation is not a function
so, Third option is correct
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Mimstoon started with at most 2 boondins (y). Every day (x), he
bought at most 1/2 more of them.
Write an inequality to model this relationship.
Answers
Step-by-step explanation:
y <= x/2 + 2
the maximum is to have 2 boondins and add 1/2 boondin every day.
but every time Mimstoon did not use the max. possible, the resulting total sum of boodins stays smaller that the maximum, and is therefore a valid data point.
(6, 7) is not in the inequality relationship.
because the max. boondins after 6 days is 2 (from the beginning) and 1/2 every day = 2 + 1/2 × 6 = 2 + 3 = 5.
but the data point shows 7 as y value (which is larger than the allowed max. of 5).
therefore the inequality is false for this data point, and therefore the data point is not in the inequality relationship.
if you can't read it, it says : Add -7d-3 and 10d-6. Show all steps
Answers
-7 d - 3 + 10d - 6
First step
Group in parenthesis and
Add both letter terms
(-7d + 10d)= -3d
Second step
Group and add numbers only
(-3 - 6) = -9
Now add both results
=-3d - 9
Answer is -3d - 9
Keywords Key Concept The total area of all surfaces, or faces, of a solid is called the surface area of the solid. Think of painting all the faces of a toy box for a baby's room. The paint covers the surface area of the toy box. net prism pyramid surface area Area of each face combined - surface area You can use the net of a three-dimensional figure, like a prism or pyramid to find the surface area of the solid. A soild can be unfolded into a net made up of polygons. The polygons within the net are the faces of the solld. You can use formulas to find the area of the pol zons vithin the net and find the sum of these areas. The sum equals the surface area of the solid
Answers
Solution
The solution is given in the image below
Brief Explanation
Let the sides of the cube be x
Each sides are squares
[tex]Area=x^2[/tex]Therefore, the surface area is
[tex]Surface\text{ }Area=6x^2[/tex]The Jacksons bought a $276,000 condominium. They made a down payment of S43,000 and took out a mortgage for the rest. Over the course of 30 years theymade monthly payments of $1396.96 on their mortgage until it was paid off.Х$?(a) What was the total amount they ended up paying for the condominium(including the down payment and monthly payments)?si(b) How much interest did they pay on the mortgage?si
Answers
(a) What was the total amount they ended up paying for the condominium
(including the down payment and monthly payments)?
We need to calculate the total monthly payments, plus the down payment.
[tex]=1396.96\cdot30\cdot12+43000=545905.60[/tex]So, the total amount they ended up paying was $545,905.60
(b) How much interest did they pay on the mortgage?
The interest they pay is: $269,905.60
[tex]=545905.60-276000.00=269905.60[/tex]Determine the sum of the measure of the interior angle of the specified polygon (octagon)A/720B/900C/1080D/1440
Answers
Solution:
The sum of interior angles of a polygon is calculated using the formula below
[tex]=(n-2)\times180[/tex]Since the polygon is an octagon,
[tex]n=8[/tex]By substituting the values, we will have
[tex]\begin{gathered} (n-2)\times180 \\ (8-2)\times180 \\ =6\times180 \\ =1080^0 \end{gathered}[/tex]Hence,
The final answer is
[tex]\Rightarrow1080^0[/tex]OPTION C is the right answer
A train goes at a constant speed. If it covers 150 miles in 2 1/2 hours, a What distance would it cover in 7 hours
Answers
how do I solve Tan-1(0.577)?
Answers
In the given fexpressionwe have,
Tan-1(0.577)
[tex]\begin{gathered} \text{Tan}^{-1}(0.577) \\ \text{Let x = Tan}^{-1}(0.577) \\ \text{Multiply both side by Tan} \\ \text{Tan x=0.577} \\ \text{ From the trignometric table find at what degr}e\text{ the tangent will be 0.577} \\ \text{ SO, }from\text{ Trignometric table we have, Tan 29.98}=0.577 \\ So,Tan^{-1}(0.577)\text{ = 29.98} \end{gathered}[/tex]Answer : 29.98 degress
Can you help me solve the problem by multiplying or dividing.
Answers
Given:
The width (w) of a rectangular swimming pool is
[tex]w=7x^2[/tex]The area (A) of the pool is
[tex]A=7x^3-42x^2[/tex]Required:
The expression for the length (l) of the pool.
Answer:
Let us find the expression for the length (l) of the pool.
The area (A) of the rectangular swimming pool is,
[tex]\begin{gathered} A=l\times w \\ 7x^3-42x^2=l\times7x^2 \\ l=\frac{7x^3-42x^2}{7x^2} \\ l=\frac{7x^3}{7x^2}-\frac{42x^2}{7x^2} \\ l=x-6 \end{gathered}[/tex]Final Answer:
The expression for the length (l) of the pool is,
[tex]l=x-6[/tex]Which set of expressions are not equivalent?(4 1\2 a + 2) + 3 and 5 + 4 a18 a + 14 and 6 a + 12 + 2 + 1 2a0.5 a + 3.5 + 4 a and 3.5 + 4.5 a3 a + 7 +2 a and 7 a + 5
Answers
Solution:
Solution:
To find which of given expressions are equivalent
For the first expressions
[tex](4\frac{1}{2}a+2)+3\text{ and 5}+4\frac{1}{2}a[/tex]Solving the expression
[tex]\begin{gathered} 4\frac{1}{2}a+2+3=5+4\frac{1}{2}a \\ 5+4\frac{1}{2}a=5+4\frac{1}{2}a \end{gathered}[/tex]The expressions are equivalent
For the second expression
[tex]18a+14\text{ and 6a}+12+2+12a[/tex]Solving the expression
[tex]\begin{gathered} 18a+14=6a+12a+12+2 \\ 18a+14=18a+14 \end{gathered}[/tex]The expressions are equivalent
For the third expression
[tex]0.5a+3.5+4a\text{ and 3.5}+4.5a[/tex]Solving the expression
[tex]\begin{gathered} 3.5+0.5a+4a=3.5+4.5a \\ 3.5+4.5a=3.5+4.5a \end{gathered}[/tex]The expressions are equivalent
For the fourth expression
[tex]3a+7+2a\text{ and 7a}+5[/tex]Solving the expression
[tex]\begin{gathered} 3a+2a+7=7a+5 \\ 5a+7\ne7a+5 \end{gathered}[/tex]The expressions are not equivalent.
Hence, the set of expressions that are not equivalent is
[tex]3a+7+2a\text{ and 7a}+5[/tex]Suppose you choose four booksto read from a summer readinglist of 12 books. How manydifferent combinations of booksare possible?Note: nCrn!r!(n-r)!
Answers
Answer
495 different combinations of books are possible.
Explanation
The different combinations of books possible can be known using the given formula
[tex]_nC_r=\frac{n!}{r!(n-r)!}[/tex]Choosing four books to read from a list of 12 books means r = 4 and n = 12
Therefore
[tex]\begin{gathered} _nC_r=\frac{n!}{r!(n-r)!}=\frac{12!}{4!(12-4)!}=\frac{12!}{4!\times8!}=\frac{12\times11\times10\times9\times8!}{4\times3\times2\times8!}=495 \\ \\ \end{gathered}[/tex]Hence, there are 495 different combinations of books are possible
it is presentation day in class and your instructor is drawing names from a hat to determine the order of the presentations. If there are 19 students in the class, what is the probability that the first 3 presentations will be by Mika, Todd and Kelly? Express your answer as a fraction.
Answers
The probability of an event is the number of outcomes in which the event happens divided by the number of total outcomes.
The outcome we want is that the first 3 will be Mika, Todd and Kelly, in this order.
For this, we can thing in picks:
The first pick we can only pick Mika, so there is 1 possibilitie1:
[tex]1[/tex]For the second pick, we can pick only Todd, so 1 possibility:
[tex]1\times1[/tex]And for the third there is only Kelly, so 1 possibility:
[tex]1\times1\times1[/tex]For the following pick, we can pick any of the 16 students left, so 16 possibilities:
[tex]1\times1\times1\times16[/tex]And for the next we have one less, so 15 and so on until we picked everyone:
[tex]1\times1\times1\times16\times15\times14\times13\times12\times11\times10\times9\times8\times7\times6\times5\times4\times3\times2\times1[/tex]We don't need to multiply all of this, because some of them will cancel afterwards.
Let's go the all possible outcomes. In this case, the first pick can be any of the 19 students:
[tex]19[/tex]And the next we have one less, and so on:
[tex]19\times18\times17\times16\times15\times14\times13\times12\times11\times10\times9\times8\times7\times6\times5\times4\times3\times2\times1[/tex]The probability will be the number of outcomes of the event we want over the number of total outcomes, so:
[tex]P=\frac{1\times1\times1\times16\times15\times14\times13\times12\times11\times10\times9\times8\times7\times6\times5\times4\times3\times2\times1}{19\times18\times17\times16\times15\times14\times13\times12\times11\times10\times9\times8\times7\times6\times5\times4\times3\times2\times1}[/tex]Notice that all from 16 down will cancel out, so:
[tex]P=\frac{1\times1\times1}{19\times18\times17}=\frac{1}{5814}[/tex]So, the probability is 1/5814.
Solve |3x +18| = 6x
Please help
Answers
Answer: x = 2, 6
Step-by-step explanation:
To solve, we will isolate the variable. Since this deals with absolute value, we can assume we'll have two answers.
|3x + 18| = 6x
3x + 18 = 6x 3x + 18 = - 6x
18 = 3x 18 = 9x
6 = x 2 = x
x = 2, 6
which trig function should you pick ? solve for x
Answers
To find the value of x and according to the given information, it is necessary to use cosine, which is the ratio between the adjacent side and the hypotenuse.
In this case the given angle is 43, it means that cos 43 is the ratio between 36 (adjacent side) and x (hypotenuse). Solve for x, this way:
[tex]\begin{gathered} \sin 43=\frac{36}{x} \\ x=\frac{36}{\sin 43} \\ x=52.8 \end{gathered}[/tex]x has a value of 52.8 (approximately).
