Question:
Simplify:
[tex](12a^2b-8a+5a^2b-2ab)-(4ab^2-6ab+2a+3ab)[/tex]
Answer:
[tex]17a^2b - 4ab^2 - 10a + ab[/tex]
Step-by-step explanation:
Given
[tex](12a^2b-8a+5a^2b-2ab)-(4ab^2-6ab+2a+3ab)[/tex]
Required
Simplify
[tex](12a^2b-8a+5a^2b-2ab)-(4ab^2-6ab+2a+3ab)[/tex]
Open brackets
[tex]12a^2b-8a+5a^2b-2ab-4ab^2+6ab-2a-3ab[/tex]
Collect Like Terms
[tex]12a^2b + 5a^2b - 4ab^2 - 8a - 2a + 6ab - 3ab- 2ab[/tex]
[tex]17a^2b - 4ab^2 - 10a + ab[/tex]
What constant term should be added to both sides to complete the square on the left side?
x^2 - 3/4x + _____ = 10
Answer:
9/64Step-by-step explanation:
Given
x² - 3/4x + _____ = 10Need to complete square on the left side of equation
The square should be in the form of:
(a + b)² = a² + 2ab + b²We see a = x therefore
2b = -3/4, so b = -3/8 and b² = (-3/8)² = 9/64So the missing constant term is 9/64
Given functions f (x) and g (x), the x-coordinate of the point of intersection of two functions is a solution of the equation f (x) = g (x).
A. The statement is true because when you substitute the x-coordinate of the point of intersection in the equation f (x) = g(x), a false statement results.
B. The statement is false because when you substitute the x-coordinate of the point of intersection in the equation f (x)=g(x), a true statement results.
C. The statement is true because, when you substitute the x-coordinate of the point of intersection in the equation f (x) = g(x), a true statement results
D.The statement is false because when you substitute the x-coordinate of the point of intersection in the equation f (x) = g (x), a false statement results.
The answe is C.
Explenation:
I did the question and
Answer:
C. The statement is true because, when you substitute the x-coordinate of the point of intersection in the equation f (x) = g(x), a true statement results
solve for x. solve for x. solve forx.
Answer: I think your answer should be x=7, please mark me as brainliest! :D
Step-by-step explanation:
3. The sequence 6, 18, 54, 162, … shows the number of pushups Kendall did each week, starting with her first week of exercising. (a) What is the recursive rule for the sequence? (b) What is the iterative rule for the sequence?
Answer:
Please check the explanation.
Step-by-step explanation:
(a) What is the recursive rule for the sequence?
Given the sequence
6, 18, 54, 162,...
Please note that each successive term is 3 times the previous term.
i.e. 18 = 6×3, 54 = 18×3, 162 = 54×3
Here, r = 3 is the common multiplier
In other words, every next term can be obtained by multiplying the previous term by a number 'r', using the recursive formula
[tex]a_n=a_{n-1}\times r[/tex]
Here, aₙ is r times the previous term aₙ₋1.
For example, in order to determine the 2nd term a₂, just put n=2 in the recursive formula
[tex]a_n=a_{n-1}\times r[/tex]
so substituting r = 3, and n = 1 in the recursive formula
[tex]a_2=a_{2-1}\times 3[/tex]
[tex]a_2=a_1\times \:3\:\:\:\:\:\:[/tex]
as
a₁ = 6
so
[tex]a_2=6\times \:3\:\:\:\:\:\:[/tex]
[tex]a_2=18[/tex]
(b) What is the iterative rule for the sequence?
Given the sequence
6, 18, 54, 162,...
A geometric sequence has a constant ratio 'r' and is defined as
[tex]a_n=a_1\cdot r^{n-1}[/tex]
[tex]\frac{18}{6}=3,\:\quad \frac{54}{18}=3,\:\quad \frac{162}{54}=3[/tex]
The ratio of all the adjacent terms is the same and equal to, so
r = 3
as
a₁ = 6
so substituting r = 3 and a₁ = 6 in the nth term of the sequence
[tex]a_n=a_1\cdot r^{n-1}[/tex]
[tex]a_n=6\cdot \:3^{n-1}[/tex]
Thus, the iterative rule for the sequence is
[tex]a_n=6\cdot \:3^{n-1}[/tex]a) The recursive rule for the sequence is [tex]a_n=3a_{n-1}[/tex]
b) The iterative rule for the sequence is [tex]a_n=2(3^n)[/tex]
The given sequence is:
6, 18, 54, 162, …
The common ratio, r = 18/6
r = 3
Let the last term be [tex]a_n[/tex]
Let the preceding term be [tex]a_{n-1}[/tex]
The recursive rule for the sequence is given as:
[tex]a_n=a_{n-1}r\\\\a_n=3a_{n-1}[/tex]
b) The iterative rule is gotten by using the formula:
[tex]a_n=ar^{n-1}[/tex]
Substitute a = 6 and r = 3 into the formula above
[tex]a_n=6(3)^{n-1}\\\\a_n=\frac{6}{3}(3^n )\\\\a_n=2(3^n)[/tex]
Learn more on sequence here: https://brainly.com/question/6561461
Merry Christmas please help
Answer:
All Of The Number At The Top
Step-by-step explanation:
Like Said, The Tables Functions f
So, Basically It's A Challenge,
All Of The Numbers In Row X From Above Table
I Hope You Found This Answer Helpful
Good Day
You'll Get 100% Don't Stress It✨
By: LocalLesMara
A class trip to a beach has been planned for your senior trip. The lifeguard is only on duty when the temperature is between 70 degrees and 105 degrees. There is room for 60 people on your trip. Write the constraints to represent this real-world problem, where x is the temperature and y is the number of people on your trip.
x > 70 and y 70
70 < x < 105 and 0 < y ≤ 60
Answer:
70 < x < 105 and 0 < y ≤ 60
Step-by-step explanation:
The constraints that represent this real-world problem are; 70 < x < 105 and 0 < y ≤ 60 where x is the temperature and y is the number of people on your trip.
What is inequality?Inequality is defined as the relation which makes a non-equal comparison between two given functions.
Given:
The Range of temperature is between 70 and 105 degrees.
So, x lies between these two temperatures so x must be greater than 70 degrees but less than 105 degrees.
Therefore, x > 70and x < 105.
On combining these two inequalities we get,
70 < x < 105
Now, number of people that can come for the trip is 60.
y represents the number of people for the trip. So, y can be at most 60.
Or, y ≤ 60 must be less than or equal to 60 and is given as:
Hence, the constraints are:
70 < x < 105 and 0 < y ≤ 60
The constraints that represent this real-world problem are; 70 < x < 105 and 0 < y ≤ 60 where x is the temperature and y is the number of people on your trip.
Learn more about inequality ;
brainly.com/question/14164153
#SPJ2
A new window costs $600 plus VAT 20%. How much is the total bill?
Answer:
720
Step-by-step explanation:
600*.2=120
120+600
720
Answer:
720 dollars
Step-by-step explanation:
find 20% of 600 dollars
[tex]\frac{20}{100} * 600[/tex]
= 120 dollars
600 + 120
= 720
I hope this helped!
please mark me as brainliest
what times 64 equals 32
Which explains why the graph is not a function?
Answer:
the points are not joined hence not a function
Answer:
Imma say its option 2 thats the only one that makes any sense good luck
Step-by-step explanation:
WHAT IS THE ANSWER FOR THIS PLZ!!! I WILL MARK BRAINLIEST!!!
Answer:
-54+17= -37 LESS
35+(-61)= -26
Step-by-step explanation:
plz mark B R A I N L I E S T :P
These points are linear. Find the slope.
Answer:
5
Step-by-step explanation:
To find the slope of a line, you need to find the [tex]\frac{rise}{run}[/tex] between two points. I will be calculating the slope using the two points (2, 10) and (3, 15).
Slope = [tex]\frac{rise}{run}[/tex]
= [tex]\frac{15-10}{3-2}[/tex]
= 5
"simplify 3/5+(-1/4) ÷ 7/10" How can you answer this question. and what's the answer, can you help me out please
Answer:
s
Step-by-step explanation:
Answer:
17/70
Step-by-step explanation:
First use PEMDAS which is the order to solve questions like these.
Parenthesis
Exponents
Multiplication
Division
Addition
and Subtraction
There is one parenthesis which has a (-1/4) so let's start with that, we know that when there is a negative and a positive sign the negative out rules the positive
3/5-1/4 divided by 7/10 (Sorry I don't have the division sign on my device)
There are no exponents or multiplication but there is division
-1/4 divided by 7/10 is -5/14
3/5-5/14 is 17/70
Thus, our answer is 17/70
What is the volume of the rectangular prism?
What is the answer to 3/4x1/7
Answer:0.1072
Step-by-step explanation:
Siri
Evaluate 32 divided by 1.6
show work
Answer:
20
Step-by-step explanation:
32/1.6= 20
How do you want me to show the work? Long division?
Answer:
20
Step-by-step explanation:
Idk how you want me to show the work, sorry. The formatting will be weird unless I attach a pic or something
which of the following does the extrema represent
A. A turning point of the function
B. The minimum value of a function
C. Either a maximum or a minimum value of a function
D. The maximum value of a function
Answer:
A
Step-by-step explanation:
Solve for x.
Round to the nearest hundredth if necessary.
Answer:
4.24
Step-by-step explanation:
By geometric mean property
[tex] {x}^{2} = 6 \times 3 \\ \\ {x}^{2} = 18 \\ \\ x = \pm\sqrt{18} \\ \\ x = \pm 4.24264069 \\ \\ \because \: x \: can \: not \: be \: - ve \\ \\ \therefore \: x = 4.24 \: units \\ [/tex]
Quinn is baking cookies for the bake sale at her school using her grandmother recipe. She uses 12.5 cups of flour to make 5 dozen cookies.
Find the constant of proportionality
A bicyclist is in the exact middle of a straight trail that has endpoints at coordinates (11, 2) and (13, 5)on a map. Each unit of the grid is equal to 1 mile. What are the coordinates of the bicyclist on the map? *
6.5, 9)
(12, 3.5)
(13, 18)
(24, 7)
What is the slope of the line through the points (-2, -1) and (4, 3)?
Group of answer choices
2/3
3/2
5/2
2/5
12. Isabel created a scale model of her dad's truck. On the scale model, the length of
the truck is 51 inches. The length of the actual truck is 17 feet long.
Which scale did Isabel use to create the scale model of her dad's truck?
Answer:
11
Step-by-step explanation:
32.50-7.50=25
225/25=11
. If a random variable x has a discrete uniform distribution
1
fx(x) = 2
for x = 1,2, ..., 2k; 0 Otherwise.
Derive p.g.f. of X and Compute E(2X + 3)
16 is what percent of 20?
Answer:
3.2
Step-by-step explanation:
Which of the following numerical expressions results in a negative number?
A.
(−18)÷(−3)
B.
(−57)+(−60)
C.
(−18)−(−20)
D.
(−4)×(−5)
42. Which of the following is TRUE about the princal square riot
number?
A. always positive
C. sometimes positive
B. always negative
I sometimes negative
Answer:
a. always positive
Step-by-step explanation:
Alex learning?
A random Gaussian process x has a mean of 2.5 and variance of 0.36. Calculate the probability of the random variable having a value less than 3.
Answer: 0.79758
Step-by-step explanation:
Given that :
Mean (m) = 2.5
Variance = 0.36
Thw standard deviation = sqrt(variance) = sqrt(0.36) = 0.6
The probability of the random variable having a value less than 3 is obtained by:
P(x < 3)
Using the relation to obtain the standardized Zscore :
Z = (x - m) / s
Z = (3 - 2.5) / 0.6
Zscore = 0.8333333
p(Z < 0.833) = 0.79758 ( Z probability calculator)
Daniel plays two games in the casino. The first game he believes he has 60% chance to win. If he wins the first game, he will win the second game with 25% chance, if he loses the first game, he will win the second game with 75% chance. The winning prices for the first and second game are $1 and $2 respectively
A. What is the probability that he wins the second game?
B. If he wins the second game, what is the probability that he also won the first game?
C. What is the expected value for the price he wins from the two games? What is the variance of it?
Answer:
1) the probability that he wins the second game is 0.45
2) the probability he wins the first game given that he won the second game is 0.333
3) Expected Value is $ 1.5 and the variance is 0.75
Step-by-step explanation:
Given the data in the question;
Let Win1 represent first game victory
and Loss1 represent first game loss
Let Win2 denote second game victory
and Loss2 denote second game loss
now from the Tree diagram of Daniel;
P ( Win1 ) = 0.6
P ( Loss1 ) = 0.4
P ( Win2 | Win1 ) = 0.25
P ( Loss2 | Win1 ) = 0.75
P ( Win2 | Loss1 ) = 0.75
P ( Loss2 | Loss1 ) = 0.25
1) probability that he wins the second game will be;
P ( Win2 ) = [P ( Win1 ) × P ( Win2 | Win1 )] + [P ( Loss1 ) × P ( Win2 | Loss1 ) ]
we substitute
= [0.6 × 0.25] + [0.4 * 0.75] = 0.45
Therefore the probability that he wins the second game is 0.45
2)
If he wins the second game, what is the probability that he also won the first game will be;
{From Bayes' Theorem}
P ( Win1 | Win2 ) = P ( Win1 ) × P ( Win2 | Win1 ) / P ( Win2 )
= 0.6 × 0.25 / 0.45 = 0.333
Therefore the probability he wins the first game given that he won the second game is 0.333
c)
winnings probability
$0 0.4 × 0.25 = 0.1
$1 0.6 × 0.75 = 0.45
$2 0.4 × 0.75 = 0.3
$3 0.6 × 0.25 = 0.15
so Expected Value = ∑( winnings × individual win probability)
= (0 × 0.1) + (1 × 0.45) + (2 × 0.3) + (3 × 0.15)
= 0 + 0.45 + 0.6 + 0.45
= $ 1.5
Variance = ∑( X² ) - (∑(X))²
∑( X² ) = Summation of ( Winnings² × Probability of Each Win )
so
Variance = 0 × 0 × 0.1 + 1 × 1 × 0.45 + 2 × 2 × 0.3 + 3 × 3 × 0.15 - ( 1.5 )²
Variance = 0 + 0.45 + 1.2 + 1.35 - 2.25
Variance = 3 - 2.25
Variance = 0.75
Therefore Expected Value is $ 1.5 and the variance is 0.75
Find the quotient.
415 ÷ −3.4=
Answer:
415 ÷ 3.4 = 122.058
Step-by-step explanation:
The ratio for 2 batches of recipe
Answer:
The ratio of that is 2:1
Step-by-step explanation:
Thats all
need an answer showing work thax!
Answer:
Option (a) [tex]\sum_{k=1}^{\infty} \dfrac{3}{k(k+1)}[/tex]
Step-by-step explanation:
The given expression is :
[tex]\dfrac{3}{1{\cdot} 2}+\dfrac{3}{2{\cdot} 3}+\dfrac{3}{3{\cdot} 4}+\dfrac{3}{4{\cdot} 5}+....[/tex]
We need to rewrite the sum using sigma notation.
The numerator is 3 in all terms.
At denominator, in first term (1)(2), in second term (2)(3) and so on.
A general term for the denominator is k(k+1).
Sigma notation is :
[tex]\sum_{k=1}^{\infty} \dfrac{3}{k(k+1)}[/tex]
Hence, the correct option is (A).