Answer:
If m(x) = x^3 - x^2 - 5x - 3 then x - 3 is a factor.
Step-by-step explanation:
By the Factor Theorem if (x - a) is a factor of f(x) then f(a) = 0.
m(x) = x^3 - x^2 - 5x - 3
m(3) = 27 - 9 - 15 - 3 = 0
- so x - 3 is a factor
Simplify this expression √x4y12
Answer:
4[tex]\sqrt{3xy}[/tex]
Step-by-step explanation:
4 is a perfect square. We can pull 2 out from under the square root symbol.
The prime factor of 12 is 2.2.3. We can pull another 2 outside of the square root symbol. 2 x2 is 4 that will be outside of the square root symbol and the x, y and 3 will be left under the symbol.
Geometry: complete this proof, ASAP!!!
Answer:
1. Given
2. Triangle Interior Angle Sum Theorem
3. Substitution Property of Equality
4. Subtraction Property
5. Definition of Complementary Angles
Directions: Simplify the following expressions using the imaginary number.
1. V-5
2. √-49
3. -3√-9
4. -8√-64
5. -√-50
6.-2√-12
7.5√-12
8. V-8
9. 3√-7
10. -3√-200
Answer:
1 i(sqrt5)
2 7i
3 -9i
4 -64i
5 -5i(sqrt2)
6 -4i(sqrt3)
7 10i(sqrt3)
8 2i(sqrt2)
9 3i(sqrt7)
10 -30i(sqrt2)
Step-by-step explanation:
i is the square root of (-1). We can simplify each one as such.
Please this is urgent!
The perimeter of a regular octagon is
8 times the length of one side.
Dexter has plotted the line shown in red.
What is the slope of the line?
-8-6-4-2
CA
€
10
O
Answer:
-1/3
Step-by-step explanation:
1:make y the subject.
2:slope of line is the coefficient of x
To gain a pass a student needs to achieve a mean of at least 60% in eight tests. In the first seven
tests the student achieved a mean of 54%. What percentage must the student achieve in test eight
if they are to pass the course?
Step-by-step explanation:
the mean value is the sum of all data points divided by the number of data points.
first we have 7 tests and their mean value :
(t1 + t2 + t3 + t4 + t5 + t6 + t7) / 7 = 54
that means
(t1 + t2 + t3 + t4 + t5 + t6 + t7) = 54 × 7 = 378
in order for the mean value to be at least 60% after 8 tests, we need to add a t8, so that
(t1 + t2 + t3 + t4 + t5 + t6 + t7 + t8) = 60 × 8 = 480
because only then we have
(t1 + t2 + t3 + t4 + t5 + t6 + t7 + t8) / 8 = 60
and the student passes.
so,
(t1 + t2 + t3 + t4 + t5 + t6 + t7) + t8 = 480
378 + t8 = 480
t8 = 480 - 378 = 102%
the student would have to achieve 102% on the 8th test.
which would be normally impossible, but maybe the tests involve some bonus points.
June and Angad have played 30 tennis matches.
June has won 14 times.
Angad won the rest.
a) Estimate the probability that June wins.
b) Estimate the probability that Angad wins
Answer:
The file contains the solution to the question
In your own words, define the unit rate in an equation of proportional relationship y= kx.
Answer:
hdchyf
Step-by-step explanation:
fhyrb ufgfyg hchybgvtct ugh
The go fish game tank contains 30 fish the probability of catching a purple fish is 1/3 the probability of catching a green fish
Answer:
2/3
Step-by-step explanation:
since they are just two colors of fish inside, since the probability is always 1.. so we have to minus 1/3 from 1,which is 1-1/3=2/3
How to factorise completely please help this is algebra
(a) (x-12)(x+11)
(b) x³-4x=x(x²-4)=x(x-2)(x+2)
What is the answer please
Answer:
m∠RSU = 10x - 9 = 10(14) - 9 = 140 - 9 = 131
m∠RST = 2x = 2(14) = 28
m∠TSU = 2x + 75 = 2(14) + 75 = 28 + 75 = 103
Step-by-step explanation:
m∠RSU = m∠RST + m∠TSU
10x - 9 = 2x + (2x + 75)
10x - 9 = 2x + 2x + 75
10x - 9 = 4x + 75
-4x +9 -4x +9
6x = 84
x = 14
m∠RSU = 10x - 9 = 10(14) - 9 = 140 - 9 = 131
m∠RST = 2x = 2(14) = 28
m∠TSU = 2x + 75 = 2(14) + 75 = 28 + 75 = 103
help please. which one is right?
Answer: B
Step-by-step explanation: If it goes through a point, flip that point around and that is the point of the inverse. Do that for multiple points to get your answer, which is B
Please help !!! Need help !!!
If the first two angles of a triangle measure 45° and 111°, what does the third angle measure?
Answer:
third angle measures 24°
Step-by-step explanation:
triangles are 180°
add up the first two angles and subtract the sum from 180°
45° + 111° = 156°
180 - 156 = 24
A 6 character computer password is made up of 4 numbers followed by 2 letters. How many different passwords are possible?
Answer: 6,760,000
Step-by-Step Explanation:
Three hens lay 3 eggs any 3 days. in how many days will 3n hens lay at this rate 9nk eggs
Answer: is 48 eggs .
Step-by-step explanation:
3 hens gives 3 eggs in 3 days
Therefore , 1 gives 1 egg in 3 days
So
3days = 1egg
After that 12 days\/3 times = 4 eggs (in 12 times )
So 1 hen offers 4 eggs in 12 days after that
12 hens x 4 eggs = 48 eggs (in 12 days by 12 hens)
the graph of y=-3x+ 2 is:
The coefficient of determination, r, is the amount of variation in _______ that is explained by the regression line.
The coefficient of determination, r, is the amount of variation in the observed values of the response variable that is explained by the regression line.
About Coefficient of Determination:
When forecasting the result of an event, the coefficient of determination is a statistical measurement that looks at how variations in one variable may be explained by differences in a second variable.
In other words, the coefficient of determination, r, which is more frequently used to refer to the strength of a linear relationship between two variables, is a crucial tool for researchers when undertaking trend analysis.
For illustration, this coefficient of determination might be used to consider the possibility that a woman would give birth to her child on a specific date in the future if she became pregnant on a specific day. This metric's objective in this situation is to determine the relationship between the connected occurrences of conception and birth.
Learn more about coefficient of determination here:
https://brainly.com/question/16258940
#SPJ4
help me with this please
Answer:
48
Step-by-step explanation:
The area of this circle is
[tex]\pi( {4}^{2} ) = 16\pi = 50.27[/tex]
about 50.27 square centimeters. So 48 square centimeters seems reasonable here since 3 is used for π.
Graph f(x) = 2 sin x.
Use 3.14 for π.
Please see the picture below
Ebony's bank balance 1st reached $400 on Day 4. The last day her balance was $400 was Day 8.
(a) Determine
B(5), B(6), and B(7). Explain how you determined these amounts.
Explain how you determined these amounts.
(b) Estimate
B(1), B(2), and B(3)
(c) Jade said that the amount of money Ebony took out of her account each day between Day 8 and Day
12 was the same amount of money she put into her account each day between Day 0 and Day 4.
Recall that Day 12 is when the balance first reached $0. Without doing any calculations, how could
you show Jade why that cannot be true?
Ebony’s bank balance is $400 was Day 8 and this can be explained below.
How to explain the information?Jade cannot be true because for every transaction made during withdraws, a little amount of money is collected and as such the amount will never remain $400.
Note that the scenario for the above to occur is:
On day 4, her balance = $400
On day 5, her balance = $40
On day 6, her balance = $400
On day 7, her balance = $400
On day 8, her balance = $400
Another fact is that since she deposited 400 at first, on day 8, there will be a 0 increase so the amount will still be 400.
Therefore, if the above is the case, one can deduce the fact that her balance will still be $400.
Learn more about estimation on:
brainly.com/question/107747
#SPJ1
Given the domain {-4, 0, 5}, what is the range for the relation 12x 6y = 24? a. {2, 4, 9} b. {-4, 4, 14} c. {12, 4, -6} d. {-12, -4, 6}
The domain of the function 12x + 6y = 24 exists {-4, 0, 5}, then the range of the function exists {12, 4, -6}.
How to determine the range of a function?Given: 12x + 6y = 24
Here x stands for the input and y stands for the output
Replacing y with f(x)
12x + 6f(x) = 24
6f(x) = 24 - 12x
f(x) = (24 - 12x)/6
Domain = {-4, 0, 5}
Put the elements of the domain, one by one, to estimate the range
f(-4) = (24 - 12((-4))/6
= (72)/6 = 12
f(0) = (24 - 12(0)/6
= (24)/6 = 4
f(5) = (24 - 12(5)/6
= (-36)/6 = -6
The range exists {12, 4, -6}
Therefore, the correct answer is option c. {12, 4, -6}.
To learn more about Range, Domain and functions refer to:
https://brainly.com/question/1942755
#SPJ4
When comparing the f(x) = –x2 + 2x and g(x) = log(2x + 1), on which interval are both functions positive?
(–∞, 0)
(0, 2)
(2, ∞)
(∞, ∞)
Considering their graphs, the interval in which both functions are positive is:
(0, 2)
When are the functions positive?A function is positive when it's graph is positioned above the x-axis.
Looking at the graph, the functions are positive for x between 0 and 2, hence the interval in which both functions are positive is stated as follows:
(0, 2)
More can be learned about functions at https://brainly.com/question/25537936
#SPJ1
. f(x) = Square root of quantity x plus eight. ; g(x) = 8x - 12 Find f(g(x)). (1 point) f(g(x)) = 2 Square root of quantity two x plus one. f(g(x)) = 8 Square root of quantity x plus eight. - 12 f(g(x)) = 2 Square root of quantity two x minus one. f(g(x)) = 8 Square root of quantity two x plus one.
Answer:
[tex]f(g(x))[/tex] = [tex]\sqrt{8x - 4}[/tex]
Step-by-step explanation:
• [tex]f(x) = \sqrt{x + 8}[/tex]
• [tex]g(x) = 8x - 12[/tex]
[tex]f(g(x))[/tex] is the combination of the functions [tex]f(x)[/tex] and [tex]g(x)[/tex] such that [tex]g(x)[/tex] is the input to the function [tex]f(x)[/tex] .
This means, we have to replace the original input of [tex]f(x)[/tex], which is [tex]x[/tex], with the function [tex]g(x)[/tex].
∴ [tex]f(g(x))[/tex] = [tex]f(8x - 12)[/tex]
⇒ [tex]\sqrt{8x - 12 + 8}[/tex]
⇒ [tex]\sqrt{8x - 4}[/tex]
What is 0.08 written as a fraction in simplest form?
Answer:
[tex]\frac{2}{25}[/tex]
Step-by-step explanation:
Each "place" in the decimal, can be represented with a base 10 in the numerator.
For example the "tenths" place can be represented as: [tex]\frac{a}{10^1}[/tex] where a=decimal.
The hundredths place can be represented as: [tex]\frac{a}{10^2}[/tex]
The thousandths place can be represented as: [tex]\frac{a}{10^3}[/tex]
and so on...
In this case, we have a decimal in the hundredths place which can be represented as: [tex]\frac{8}{10^2} = \frac{8}{100}[/tex]. Now to simplify this fraction, you simply divide both sides by 4 (greatest common factor of 8 and 100), or in other words multiply it by 0.25/0.25 which is just 1, so the value is the same. [tex]\frac{8}{100} * \frac{0.25}{0.25} = \frac{2}{25}[/tex]
A population has a mean of 94 and a standard deviation of 18. A sample of 36 observations will be taken. The probability that the sample mean will be between 89.17 and 101.05 is _____. a. 0.9463 b. 0.4369 c. 0.0094 d. 0.9369
The probability that the sample mean will be between 89.17 and 101.05 is: 0.940091407
A sample mean is a data set's average. A data set's central tendency, standard deviation, and variance may all be calculated using the sample mean.
The sample mean may be used to calculate population averages, among other things.
What is the calculation that supports the above answer?The information given are as follows:
μ = 94,
σ = 18
Where Χ = Sample Mean
hence P (89.17 < X< 101.05) =
P [[tex]\frac{89.17 -94}{18/\sqrt{36} } \leq \frac{X -mu}{sd/\sqrt{xn} } \leq \frac{101.5-94}{18/\sqrt{36} }[/tex]]
= P [ -1.61 ≤ Z ≤ 2.5]
= P (Z ≤ -1.61) - P (Z ≤ 2.5)
= NORMSIDST (-1.61) - NORMSDIST (2.5)
= 0.053698928 - 0.993790335
= -0.940091407
Since probability cannot be negative,
The probability that the sample mean will be between 89.17 and 101.05 is: 0.940091407
Learn more about sample mean at;
https://brainly.com/question/7597734
#SPJ1
need help finding x.
Answer:
x = 6
Step-by-step explanation:
• the diagonals of a parallelogram bisect each other , then
5x + 11 = 4x + 17 ( subtract 4x from both sides )
x + 11 = 17 ( subtract 11 from both sides )
x = 6
Since it's divided equally diagonally, 4x+17 and 5x+11 are equal.
Let's set them equal to each other and solve.]
[tex]4x+17=5x+11[/tex]
Subtract 4x from both sides to combine like terms.
[tex]17=x+11[/tex]
Now subtract 11 from both sides to isolate the variable and solve for x.
[tex]6=x[/tex]
Flip the equation to put in standard form and now you have x :)
[tex]x=6[/tex]
hope this helped!
How many solutions can be found for the equation 4z 2(z − 4) = 3z 11? none one two infinitely many
There is only one solution for the equation 4z + 2(z -4) = 3z + 11 because the exponent for the power of z is 1.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
What is the Solution?A solution is any value of a variable that makes the specified equation true.
According to the given information:
4z + 2(z-4)= 3z+11
Solve the equation,
4z+2z-8=3z+11
6z-3z=11+8
3z =19
z=
Hence,
Number of solution that can be found for the equation 4z + 2(z-4)= 3z+11 is option(2) one
To know more about Equations and Solutions visit:
https://brainly.com/question/545403
#SPJ4
Solve this inequality and write the solution using interval notation:
The solution to the inequality in discuss involving a rational expression as indicated in the task content is; t (9, infinity).
What is the solution to the inequality as indicated in the task content in which case, the solution is expressed using interval notation?The inequality given in the task content as evident is; (2t +22)/(2t +2) <= 2.
On this note, the inequality can be solved by cross-multiplication as follows;
2t +22 <= 4t +4
Hence, we have;
-2t <= -18
t >= 9.
Hence, when expressed as an interval notation, we have; t (9, infinity).
Read more on inequalities;
https://brainly.com/question/11613554
#SPJ1
The university theatre department is selling tickets to their
upcoming performance. Three senior citizen tickets and one
student ticket were sold for $38. Three senior citizen ad two
student tickets were sold for $52. Determine the cost of a
senior citizen ticket, x and the price of a student ticket, y. Write
your answer as an ordered pair (x,y).
Answer:
(8,14)
Step-by-step explanation:
3x+2y=52
3x+1y=38 Subtract these equations using elimination method to get y=14
Then substitute y=14 to either equation
the bottom one is easier so
3x+1(14)=38 distribute 1 to 14 and any number times one is 1
3x+14=38 Subtract 14 from both sides
3x=24 Divide by 3
x=8 so check now
3(8)+1(14)=38
24+14=38?
38=38? yes