Answer:
[tex]x=5, \\x=-1[/tex]
Step-by-step explanation:
Given [tex](x-2)^2=9[/tex], to solve for [tex]x[/tex], our goal is to isolate [tex]x[/tex].
Take the square root of both sides:
[tex]x-2=\pm\sqrt{9},\\x-2=\pm 3[/tex](recall that [tex]3^2=(-3)^2=9[/tex]).
Therefore, we have two cases:
[tex]\begin{cases}x-2=3,x=\boxed{5} \\x-2=-3, x=\boxed{-1}\end{cases}[/tex]
Element X is a radioactive isotope such that its mass decreases by 73% every
hour. If an experiment starts out with 680 grams of Element X, write a
function to represent the mass of the sample after t hours, where the rate of
change per minute can be found from a constant in the function. Round all
coefficients in the function to four decimal places. Also, determine the
percentage rate of change per minute, to the nearest hundredth of a percent.
Mi
Answer:
Step-by-step explanation:
The element decay percentage rate of change 2.22% per minute.
What is radioactive isotope?
Radioisotope, radionuclide, or radioactive nuclide, any of several species of the same chemical element with different masses whose nuclei are unstable and dissipate excess energy by spontaneously emitting radiation in the form of alpha, beta, and gamma rays.
Here, mass decreases by 73% every hour.
Weight of element X is 680 grams.
According to question,
f(t) = 680 (1 - 73%)ⁿ
f(t) = 680 (1 - 0.73)ⁿ
f(t) = 680 X 0.27ⁿ
f(t) = 680 X 0.9778ⁿ
f(t) = 680 X (1 - 0.02322)ⁿ
Thus, the element decay percentage rate of change 2.22% per minute.
Learn more about radioactive isotope from:
https://brainly.com/question/1907960
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D
Solving Systems of Linear Equations Algebraically - Qutz - Level H
Question 7
Solve.
3
b=0
a + b = 21
a = 20
a = 12
a = 20
a = 37
b = 11
0 = 371
%
b = 9
b = 15
b = -16
ET
6:26
the number 3.14063 written correct to 3 decimal places is
Answer:
3.141
Step-by-step explanation:
3 decimals is .xxx, and you round the last digit up, so it becomes 3.141
Answer:
3.141
Step-by-step explanation:
since the forth number behind the decimal place is bigger than 5 we round up the third number.
I hope this helps in anyway.
Find the median and mean of the data set below:
48,32,5, 13, 11, 22, 2
Answer:
the median is 13 and the mean is 13
What is my answer if I Add
-9+84+(-2)
Answer:
73
Step-by-step explanation:
-9+84+(-2) =
-9+82 =
= 73
Hope this helps
2x+5y=20 y=-0.4x-1 i really need help over here
Answer:
x=6.25 and y=1.5
Step-by-step explanation:
Given equation
2x+5y=20
y=0.4x-1
Putting the value of y in above equation
2x+5(0.4x-1)=20
2x+2x-5=20
4x-5=20
4x=20+5
4x=25
x=6.25
Now,
y=0.4x-1( Given)
Putting the value of x=6.25 in above equation y
y=0.4(6.25)-1
y=2.5-1
y=1.5
A high school has 32 players on the football team. The summary of the players' weights is given in the box plot. Approximately, what is the percentage of players weighing greater than or equal to 233 pounds
Answer:
[tex]\% = 11.96\%[/tex]
Step-by-step explanation:
Given
See attachment for box plot
Required
Percentage greater than or equal to 233
From the box plot, the maximum is:
[tex]Max = 244[/tex]
The minimum is:
[tex]Min = 152[/tex]
Percentage greater than 233 is calculated as:
[tex]\% = \frac{Max - 233}{Max - Min}[/tex]
[tex]\% = \frac{244 - 233}{244-152}[/tex]
[tex]\% = \frac{11}{92}[/tex]
Express as percentage
[tex]\% = \frac{11}{92}*100\%[/tex]
[tex]\% = \frac{1100}{92}\%[/tex]
[tex]\% = 11.96\%[/tex]
Leila buys candy that costs 8 dollars per pound. She will spend more than 40 dollars on candy. What are the possible numbers of pounds she will buy?
Answer:
She must buy more than 5 lbs
Step-by-step explanation:
First write the inequality
cost per pound * number of pounds > total cost
8 * lbs > 40
Divide each side by 8
8 lbs /8 > 40/8
lbs > 5
She must buy more than 5 lbs
what is equivalent to 7w +7w
Answer:
14w
Step-by-step explanation:
Hope this helps
HELP TIMER Write the equation of a hyperbola centered at the origin with x-intercept +/- 4 and foci of +/-2(squareroot 5)
Given:
x-intercepts of the hyperbola are ±4.
The foci of hyperbola are [tex]\pm 2\sqrt{5}[/tex].
Center of the hyperbola is at origin.
To find:
The equation of the hyperbola.
Solution:
The general equation of a hyperbola:
[tex]\dfrac{(x-h)^2}{a^2}-\dfrac{(y-k)^2}{b^2}=1[/tex] ...(i)
Where, (h,k) is the center of the hyperbola, ±a are x-intercepts, [tex](\pm c,0)[/tex] are foci.
Center of the hyperbola is at origin. So, h=0 and k=0.
x-intercepts of the hyperbola are ±4. So,
[tex]\pm a=\pm 4[/tex]
[tex]a=4[/tex]
The foci of hyperbola are [tex]\pm 2\sqrt{5}[/tex].
[tex]\pm c=\pm 2\sqrt{5}[/tex]
[tex]c=2\sqrt{5}[/tex]
We know that,
[tex]a^2+b^2=c^2[/tex]
[tex](4)^2+b^2=(2\sqrt{5})^2[/tex]
[tex]16+b^2=20[/tex]
[tex]b^2=20-16[/tex]
[tex]b^2=4[/tex]
Taking square root on both sides, we get
[tex]b=\sqrt{4}[/tex] [b>0]
[tex]b=2[/tex]
Substituting [tex]h=0,k=0,a=4,b=2[/tex] in (i), we get
[tex]\dfrac{(x-0)^2}{4^2}-\dfrac{(y-0)^2}{2^2}=1[/tex]
[tex]\dfrac{x^2}{4^2}-\dfrac{y^2}{2^2}=1[/tex]
Therefore, the correct option is (d).
PLS HELP TYSMMMM <33333333333333333333333333
Answer:
dvide 54 by 6 then the answer you get subrtact it by 3 then the answer you get multiply iy by 2 then thats will be your answer
Step-by-step explanation:
remember always use PEMDAS always add or subract wich ever comes first and if theres none of that then do Multiply or devide wich ever comes first ( btw your answer is ( 3 )
An English teacher needs to pick 4 books to put on his reading list for the next school year. He has narrowed down his choices to 8 novels and 6 plays.
a. How many different ways can he choose the books to put on the list if he wants to include at least two plays?
b. Find the standard deviation.
Answer:
A) 3 ways
B) sorry don't know.
Step-by-step explanation:
2 P and 2 N
3P and 1 N
4P
So 3 ways.
How do you solve a system of linear equations by graphing?
9514 1404 393
Explanation:
This is a self-answering question: you solve it by graphing the equations.
The solution is where the lines intersect. The point of intersection of the lines is the point that satisfies all the equations for the lines, hence is a solution to the system. If they do not intersect, there are no solutions. If the lines are coincident, there are an infinite number of solutions.
__
The equations can be graphed by any of a number of methods. (My favorite is to let a graphing calculator do it.) The method of choice depends on the coefficients and the form the equations are given in. Methods of graphing are a topic for a more lengthy discussion.
High School Dropouts
Number of Dropouts
1990
2000
Male
Female
MAMD.M.D.3: Which of the
following is true about the graph?
Answer:
There are more females dropping than males each year and that there are more females than males
Help ASAP please!!
For a proof by induction of the math statement below,
identify the correct step for proving the theorem is true
for n=k+1
2+4+6+...+2n=n(n+1)
Answer:
2+4+6+...+2k+2(k+1) = k(k+1) + (k+1)(k+1)
Step-by-step explanation:
Proved case for n
2+4+6+...+2n = n(n+1) ................(1)
for n = k + 1, we replace n by k and add n = k+1 on both sides (
2+4+6+...+2k+2(k+1) = k(k+1) + 2(k+1))
rearrange by factoring the right-hand-side
2+4+6+...+2k+2(k+1) = (k+1)(k+2)
which if we substitute n=k+1, we get back
2+4+6+...+2(n-1) + 2(n) = n(n+1) ...............(2)
This means that equation (1) is applicable to case n+1, and the proof by induction is completed.
How many Egyptian numerals (total) are needed to represent the following problem?
Which graph represents the function f(x)=|x|-4?
See the graph in the attached image.
Rewrite each mixed number as a sum of two signed numbers,
3 1/5
-7 3/8
Answer:
31/5 as a mixed number: 6 and 1/5
-73/8 as a mixed number:-9 and 1/8
Step-by-step explanation:
Rewriting each mixed number as a sum of two signed numbers 3 1/5 and -7 3/8 are 3 and 1/5 and -8 and 5/8 respectively
The mixed number to rewrite as a sum of two signed numbers are as follows:
3 1 / 5-7 3 / 8Rewriting as a sum of the two signed numbers can be represented as follows;
3 1/5 = 16 / 5
-7 3/ 8 = - 59 / 8
Therefore,
3 1/5 will be 3 and 1/5
-7 3/ 8 will be -8 and 5/8
Note
3 + 1/5 = 3 1/5
-8 + 5/8 = -7 3/8
learn more on fraction here: https://brainly.com/question/24645582
13. Find the area of the parallelogram.
Answer:
Step-by-step explanation:
make it 1 triangle and trapezium
1) 1/2 x 7 x 8 = 28 in2
Answer:
56 in^2
Step-by-step explanation:
A = b* h
A = (8) * (7)
A = 56
A = 56 in ^2
Hope this helps!
A local salesman has forty-five stacks of magazines. If the salesman plans to sell three-fifths of the stacks, how many stacks will he have left?
Answer:
2
Step-by-step explanation:
Answer:
2
Step-by-step explanation:
Determine if each proportion on the left is True or False. Answer options on the right side may be used more than once.
True
False
28/16=14/8
3/5=9/15
4/32=10/78
3/4=12/16
Answer:
28/16=14/8 true
3/5=9/15 true
4/32=10/78 false
3/4=12/16 true
Step-by-step explanation:
DID IT ON BRIDGE
Find the volume in the shape
Answer:
1205.76 m^3
Step-by-step explanation:
given:
radius = 8m
height = 18 m
volume of a cone = πr2h/3
=3.14 * (8)^2 * 18/3
=3.14 *64 *18/3
=3617.28/3
=1205.76 m^3
The perimeter of the rectangle is 80 cm. The area of the rectangle is acm2 . (i) show that x 2 40x + a = 0.
Answer:
Proved
Step-by-step explanation:
Given
[tex]p = 80[/tex] ---- perimeter
[tex]a \to area[/tex]
Required
[tex]x^2 + 40x + a = 0[/tex]
The perimeter is calculated as:
[tex]p = 2(x + y)[/tex]
Where
[tex]x,y \to[/tex] the rectangle dimension
So, we have:
[tex]2(x + y) = 80[/tex]
Divide by 2
[tex]x + y = 40[/tex]
Make y the subject
[tex]y = 40 - x[/tex]
The area of the rectangle is:
[tex]a = xy[/tex]
[tex]a = x * (40 -x)[/tex]
[tex]a = 40x -x^2[/tex]
Equate to 0:
[tex]x^2 - 40x + a = 0[/tex]
If function f has zeros at -3 and 4, which graph could represent function f?
Answer:
A
Step-by-step explanation:
f has zero means that f(x)=0
if f(x)=0 we have to look intersection point or points in the graph on the x-axis.
for A
y=0
x=-3, x=4
for B
y=0
x=-4, x=3
for C
y=0
x=-4, x=-3
for D
y=0
x=3, x=4
Given m||n, find the value of x
Answer:
The answer is 104 degrees.
Step-by-step explanation:
M is equivalent to N, which means x is also 104 degrees.
A square dancing contest has 245 teams of 4 pairs each. How many dancers are participating in the contest?
Answer:
1960 dancers
Step-by-step explanation:
your are on "ace" level and need help here ?
a pair is 2 people
4 pairs is therefore 4×2 people = 8
245 teams of 4 pairs or 8 people each means
245×8 = 1960 people
32,131 round this to two decimal places
Answer:
Is 32,13
Step-by-step explanation:
Because one is not bigger than five so it disappears.
Dan has an old lawn mower! It takes him 1 hour to mow the whole lawn. How many square yards does Dan cut in one minute? Hints: There are 60 minutes in 1 hour. To find the unit rate divide the area of the lawn by the amount of time it takes Dan to mow the whole lawn.
40 square yards per minute
400 square yards per minute
2400 square yards per minute
240 square yards per minute
Answer: You didnt mention how much Dan mows in 1 hour, but just do that divided by 60
Step-by-step explanation:
A spinner with 8 equal-size sections labeled as shown is spun 200 times. What is the sample
space for this experiment?
Answer:
hiiooioudzzxuxojxoufxodyzufxufxyfxuoxudr tztdxhxfuoxir d and
m) Factorise:
x2/9+1+9/x2
Answer:
Cannot be factored
Step-by-step explanation:
Given
[tex]\frac{x^2}{9} + 1 + \frac{9}{x^2}[/tex]
Required
Factorize
Take LCM
[tex]\frac{x^2}{9} + 1 + \frac{9}{x^2} = \frac{x^4+9x^2+81}{9x^2}[/tex]
The expression cannot be factored