If a polynomial function has integer coefficients, the every rational zero of the function has the form p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.
The rational zero theorem says that if a polynomial has integer coefficients then any rational zeros must be of the form p/q where p is the factor of the constant term and q is the factor pf the leading coefficients.
The rational zero theorem is used to determine the rational roots of a polynomial function.
Rational Zero Theorem statement:-
The rational zero theorem states that each rational zero(s) of a polynomial wit integer coefficients
f(x) = anxⁿ + an-1xⁿ⁻¹ + ... + a₂x² + a₁x + a₀ is of the form p/q where,
p is a factor of the constant a₀,
q is a factor of the leading coefficient an,
and p and q are relatively prime.
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please help ASP WIIL GIVE Brilliance
Answer:
2. Definition of Midpoint
3. Vertical Angles Theorem
Step-by-step explanation:
Definition of Midpoint is the middle point of a line segment
Vertical Angles Theorem is proving angles that are opposite each other and formed by two intersecting straight lines, are congruent.
Need answer will mark Brainliest
Answer:
see explanation
Step-by-step explanation:
from the table we can obtain that
f(x ) = 6x³ + 8x - 12 ( 6 0 8 - 12 , being the coefficients of the polynomial )
f(x) is divided by (x + 7) , since evaluated at - 7
the quotient is
6x² - 42x + 302 ( 6 - 42 302, are the coefficients of the quotient )
with remainder - 2126
Solve using quadratic formula: 5x^2+9=4x+5
Answer:
No real solutions.
Step-by-step explanation:
No real solutions.
If both dimensions are doubled then which of the following statements about it’s perimeter will be true
Refer to this rectangle
4mm
9mm
The new perimeter will be 3 times larger then the old perimeter
The new perimeter will be 2 times larger then the old perimeter
The new perimeter will be 1/3 times larger then the old perimeter
The new perimeter will be 4. Times larger then the old perimeter
The new perimeter will be 2 times larger then the old perimeter, if both dimensions of rectangle are doubled.
What is perimeter ?The length of a shape's outline is its perimeter. You must add the lengths of all four sides of a rectangle or square to determine its perimeter. In this instance, x represents the rectangle's length and y its width.
The figure's length is essentially revealed by the perimeter. Assume that the perimeter of a square with equal sides will be four times that square's sides. The perimeter of a circle, which is determined by its radius, is known as its circumference.
The new dimensions of rectangle = 4mm and 9mm
The original dimension = 2mm and 4.5 mm
Perimeter of rectangle = P=2(l+w) = 2 (4.5 +2 ) = 13 mm
Perimeter of rectangle after doubled dimension = 2 (9 + 4) = 26
So, the new perimeter will be 2 times larger then the old perimeter
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19. The amount of money in a savings account increases from $ 250 to $ 270 in one month. If the percent increase is the same for every month, how much money will be in the account at the end of the next month?
(A) $ 291.60
(B) $ 295
(C) $ 289.60
(D) $ 300
Answer:
the answer will be the options A
Solve the following equation. Answer as a reduced, mixed number.
9(x − 6) = 8(x + 6)
The value of x in the equation 9(x − 6) = 8(x + 6) is 102.
How to calculate the equation?An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.
It should be noted that from the information given, the equation is illustrated as:
9(x − 6) = 8(x + 6)
9x - 54 = 8x + 48
Collect the like terms
9x - 8x = 48 + 54
x = 102
The value of x is 102.
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Which statement is true about the diagram?
R
S
يحة
Ο Δ QRC ~Δ SCU
O ARQCA SUC by SSS
O A CRQA CSU by SAS
O No triangles are congruent
U
Answer:
[tex]\triangle CRQ \cong \triangle CSU[/tex] by SAS
Step-by-step explanation:
[tex]\angle QCR \cong \angle SCU[/tex] because of vertical angles.
Solve.
9^(3x+1) = 27^2x
Answer: the equations has no solution
Step-by-step explanation:
[tex]9^{3x+1}=27^{2x}\\\\(3^2)^{3x+1}=(3^3)^{2x}\\\\3^{2(3x+1)}=3^{3(2x)}\\\\3^{6x+2}=3^{6x}\\\\Hence,\\\\6x+2=6x\\\\6x+2-6x=6x-6x\\\\2\neq 0\\\\Thus,\ the\ equations\ has\ no\ solution[/tex]
Mrs.Barrera learned that 21 of her 25 students ride the school bus every morning.What percent of her students ride the school bus every morning?
The percentage of her students that ride the school bus every morning would be = 84%
What is percentage expression?A percentage expression is an representation of a data set to a fraction of 100.
The total number of students = 25 students
The number of students that ride the school bus = 21
To calculate the percentage of the students that ride the bus the following is done;
= 21/25 × 100
= 2100/25
= 84%
Therefore, the percentage of her students that ride the school bus every morning is 84%
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During summer, the height of the water in Scott's pool decreases by 4 inches each week, due to evaporation. How many weeks does it take for the water to decrease by 20 inches?
Responses
A −5
B 5
C 20
D −20
Answer:
5 weeks
Step-by-step explanation:
20 inches / ( 4 inches/week ) = 5 weeks
Find the inverse function to y=f(x)= 8-9x/5-4x
x=g(y)=
Therefore , the inverse function to y=f(x)= 8-9x/5-4x is 8-5x /-4x+9 .
A function is what?In mathematics, a function from a set X to a set Y assigns each item in X exactly one element in the other set. The sets X and Y represent the function's domain and codomain, respectively.
Here,
Given :
function :8-9x/5-4x
To find the inverse ,
Inverse of 8-9x. 8-5x 5 4x -4x+9
Steps Function Inverse definition A function g is the inverse of function F if for y=√(x), x=g(v)
y= 8-9x 5-4x
Replace x with y
x = 8-9y/ 5-4y
Solve for y,
x = 8-97/ 5-4y
=>8-5x /-4x+9
Therefore , the inverse function to y=f(x)= 8-9x/5-4x is 8-5x /-4x+9 .
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The replacement set for an equation is {10, 24, 25, 36}.
The equation is represented by the sentence, "5/6 of a number is 30."
What is the solution set of the equation?
options:
Responses
{10}
{24}
{25}
{36}
ill give brainleist
{25} is the solution set of the equation {10, 24, 25, 36}.
What is an equation?An equation is a combination of different variables, in which two mathematical expressions are equal to each other.
The given set of equation is {10, 24, 25, 36}
Since, The equation is represented by the sentence that is 5/6 of a number is 30.
So the required solution,
5/6 of the number 30 = 25
The solution set of the equation is {25}.
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is 2/5 equivalent to 25
Answer:
2/5 ≠ 25
Step-by-step explanation:
Given question,
→ Is 2/5 equivalent to 25?
Let's check the problem,
→ 2/5 = 25
→ 0.4 ≠ 25
The equivalent fractions of 2/5 are,
→ 2/5 = 4/10
→ 2/5 = 6/15
→ 2/5 = 8/20
→ 2/5 = 10/25
Hence, 2/5 is not equivalent to 25.
The local weather forecast has been accurate for 25 of the past 37 days. Based on this fact, what is the relative frequency probability that the
forecast for tomorrow will be accurate?
The relative frequency probability that the forecast for tomorrow will be accurate = 16/33.
What is probability?
Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means.P(A) = Number of accurate days/ Total number of days
Here, the number of accurate days is 25 and total number of days is 37.
Substitute the above values as follows:
P(A) = 25/37
Hence, the relative frequency probability that the forecast for tomorrow will be accurate = 16/33.
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how many tens are in 7x30 or 30x7
There are 3 tens in 7x30 or 30x7.
What is an equation?
A mathematical statement is referred to as an equation when two expressions are connected by the equal sign. A mathematical equation serves as the connection between two expressions on each side of the sign. Usually, there is only one variable and an equal sign.
Equations can be categorized as identities or conditional equations. An identity holds true regardless of the value given to the variables. A conditional equation's variables can only have specific values that produce the truth.
An equation is created by joining two expressions with an equal sign. The solution to an equation is a number that may be used as the variable to generate a true number statement.
Here, we have
7x30 = 7 x 10 x 10 x 10
The value of 7x30 = 210
Hence, there are 3 tens in 7x30 or 30x7.
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Suppose Colleen works two jobs. At job A, Colleen’s monthly earnings can be described by the distribution N(2100, 200) and at job B, her monthly earnings can be described by the distribution N(550, 70). Assuming that her earnings are independent,
1) What is the mean and standard deviation of the TOTAL amount of money she earns in a month? (this will use knowledge from prior units)
2) What is the probability that she earns more than $2750 in a given month?
1) The mean and the standard deviation of the total amount of money that she earns in a month are of:
Mean: 2650.Standard deviation: 211.9.2) The probability that she earns more than $2750 in a given month is of: 0.3192 = 31.92%.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.When two variables are added, the mean is given by the sum of the means, hence:
[tex]\mu = 2100 + 550 = 2650[/tex]
The standard deviation is given by the square root of the sum of the variances, hence:
[tex]\sigma = \sqrt{200^2 + 70^2} = 211.9[/tex]
The probability that she earns more than $2750 in a given month is one subtracted by the p-value of Z = 2750, hence:
Z = (2750 - 2650)/211.9
Z = 0.47
Z = 0.47 has a p-value of 0.6808.
1 - 0.6808 = 0.3192 = 31.92%.
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Determine how many digits are to the right of the decimal point in the answer from multiplying: 0.3568 x 0.042
Responses
A. 5
B. 9
C. 7
D. 3
The number of the digits after the decimal point is 7. The correct option is C.
What is a number system?A numeral system is a way of writing numbers; it's a way of mathematically notating a collection of numbers by utilizing a consistent set of digits or other symbols. In several numeral systems, the same set of symbols may represent various numbers.
Given that the numbers are 0.3568 and 0.042. The multiplication of the two numbers will be done as,
P = 0.3568 x 0.042
P = 0.0149856
The number of the digits after the decimal is 7.
Therefore, the number of the digits after the decimal point is 7. The correct option is C.
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Write the equation of the line which passes
through the point (2. −3) and has a slope of -2/5
A. 2x + 5y = 4
C. 2x+ 5y = −11
B. 2x+5y = −9
D. 2x-5y = −16
Show work for this question please & thank u
y = -2/5 x -11/5 is the equation of line with slope -2/5 that passes through the point (2, -3).
What is the equation of line?The slope of the line is the rise to run ratio, or the rise divided by the run. It expresses the slope of a line in the coordinate plane.
The standard form of an equation is y = mx+c.
Here given,
A line with a slope of -2/5 that passes through the point (2, -3).
Simplify y = mx+c with m=2/5 and (x, y)=(2, -3). That is to say,
-3 = -2/5 (2)+c
⇒ -3 = -4/5 +c
⇒ c = -3 + 4/5
⇒ c = (-15 + 4) / 5
=> c = -11/5
When m = -2/5 and c = -11 /5 are substituted in y = mx+c, we get
y = -2/5 x -11/5
As a result, an equation for a line with a slope of -2/5 that passes through the point (2,-3) is y = -2/5 x -11/5.
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Answer:
C. 2x+ 5y = −11
Step-by-step explanation:
You want the equation of the line with slope -2/5 through point (2, -3).
Point-slope equationThe equation of a line with slope m through point (h, k) can be written as ...
y -k = m(x -h)
Then the equation of the line with slope -2/5 through point (2, -3) will be ...
y +3 = -2/5(x -2)
Standard formWe can put this in standard form by ...
5(y +3) = -2(x -2) . . . . . multiply by 5
5y +15 = -2x +4 . . . . . . eliminate parentheses
2x +5y = -11 . . . . . . . . . add 2x-15 to both sides
The desired equation is 2x +5y = -11.
help meeeeeeeeeee pleaseee
The pressure of 28 inches of mercury occurs about 6 miles from the eye of the hurricane. We get this from the given algebraic expression.
What is an expression?An expression is formed by variables, constants, and algebraic operations. Since the operation among them is an algebraic or arithmetic operation, it is said to be an algebraic expression.
Calculation:It is given that the algebraic expression that relates the barometric pressure and the eye of the hurricane as
f(x) = 0.48 ln(x+2) + 27
Here x is the distance in miles from the eye of the hurricane.
f(x) is the pressure of the mercury in a barometer in inches
So, the required distance from the eye of the hurricane when the pressure of 28 inches of mercury in the meter is
(Here f(x) = 28)
f(x) = 0.48 ln(x+2) + 27
⇒ 28 = 0.48 ln(x+2) + 27
⇒ 0.48 ln(x+2) = 28 - 27
⇒ ln (x+2) = 1/0.48
⇒ ln(x+2) = 2.0833
Applying exponential base "e" on both sides, we get
(x+2) = [tex]e^{2.0833}[/tex]
⇒ x + 2 = 8.0309
⇒ x = 8.0309 - 2 = 6.0309
When the result is rounded to the nearest whole number, we get x = 6 miles.
Thus, for the pressure of 28 inches of mercury, the eye of the hurricane is 6 miles far from the barometer.
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how do i find x? please help me, I tried everything :(
In how many ways can a person order one ice cream cone with 3 different
flavors of ice cream if there are 14 flavors to choose from and it matters to
the person how the 3 flavors are stacked on the one cone? That is, which
flavor is on the top, middle, and bottom.
Answer:
2184
Step-by-step explanation:
You want to know the possible number of ways 3 flavors can be chosen from 14 when order matters.
PermutationsThe number of permutations of 14 flavors taken 3 at a time is ...
14 × 13 × 12 = 2184
There are 14 ways to choose the bottom flavor, then 13 ways to choose a different middle flavor, and finally 12 ways to choose a different top flavor. Each flavor can go with any combination of the others, so the total number is the product of 14·13·12, or 2184.
The formula for the number of n things taken k at a time is ...
P(n, k) + n!/(n-k)!
For n=14, k=3, this is the product shown above.
ANALYZE PROBLEMS The midpoints of the sides of a triangle are located at (a, 0),(2 a, b) and (a, b). If one vertex is located at the origin, what are the
coordinates of the other vertices?
,( ______0) and (______,______)
The coordinates of the other vertices of the triangle are (2a, 0), (2a, b), and (a, b).
What are the coordinates of the vertices of the triangle?
The coordinates of the vertices of a triangle are (x1,y1), (x2,y2), and (x3,y3). The line joining the first two is divided in the ratio l:k and the line joining this point of division to the opposite angular point is then divided in the ratio m:k+l.
To find the coordinates of the other vertices of the triangle, you can use the fact that the midpoint of a line segment is located at the average of the coordinates of the endpoints of the segment.
If the midpoint of one side of the triangle is located at (a, 0), then the coordinates of the two endpoints of this side must be (a, 0) and (2a, 0). The coordinates of one of the vertices is (2a, 0), and since this vertex is not the one located at the origin, the coordinates of the other vertex must be the origin, or (0, 0).
If the midpoint of another side of the triangle is located at (2a, b), then the coordinates of the two endpoints of this side must be (2a, b) and (2a, 0). One of the endpoints is (2a, 0), which we already know is a vertex of the triangle. The other endpoint, (2a, b), is also a vertex of the triangle.
Finally, if the midpoint of the third side of the triangle is located at (a, b), then the coordinates of the two endpoints of this side must be (a, b) and (0, 0). One of the endpoints is (0, 0), which we already know is a vertex of the triangle. The other endpoint, (a, b), is also a vertex of the triangle.
Hence, the coordinates of the other vertices of the triangle are (2a, 0), (2a, b), and (a, b).
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Help with this plsss !!!
Answer:
:))
Step-by-step explanation:
The maximum value is 22 as the last small line (end of the "whisker") is marked at 22. Hope this helps!! Pls mark as brainliest and lots of points, help ya girl out!!!
3) Juakali used Kingo's computer to type a report document which had 123 pages, and
each page occupied by 70 lines. 36 of 70 lines had 14 words while the remaining lines
had 18 words each. He wanted to take the document with him, and he had only a flash
disk with 256 KB as free space. Can he successfully save the document on the device?
Why?
To determine whether Juakali can successfully save the document on the flash disk, you can calculate the total number of words in the document and compare it to the amount of free space on the flash disk.
First, calculate the total number of lines in the document by multiplying the number of pages by the number of lines per page:
Total number of lines = 123 pages * 70 lines/page
= 8610 lines
Next, calculate the number of lines with 14 words by multiplying the total number of lines by the proportion of lines with 14 words:
Number of lines with 14 words = 8610 lines * 36/70
= 4380 lines
Calculate the total number of words in the lines with 14 words by multiplying the number of lines by the number of words per line:
Total number of words in lines with 14 words = 4380 lines * 14 words/line
= 61320 words
Calculate the number of lines with 18 words by subtracting the number of lines with 14 words from the total number of lines:
Number of lines with 18 words = 8610 lines - 4380 lines
= 4230 lines
Calculate the total number of words in the lines with 18 words by multiplying the number of lines by the number of words per line:
Total number of words in lines with 18 words = 4230 lines * 18 words/line
= 76140 words
Finally, add the total number of words in the lines with 14 words and the total number of words in the lines with 18 words to find the total number of words in the document:
Total number of words = 61320 words + 76140 words
= 137,460 words
To determine whether Juakali can successfully save the document on the flash disk, you can compare the total number of words in the document to the amount of free space on the flash disk. Since the flash disk has 256 KB of free space and there are 137,460 words in the document, Juakali will not be able to save the document on the flash disk. This is because the document is larger than the amount of free space available on the flash disk.
It is important to note that the capacity of a storage device is usually measured in bytes, and 1 KB is equal to 1024 bytes.
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lake front company is considering investing in a new dock that will cost 560,000 the company expects to use the dock for 5 years after which it will be sold for 300,000 lake front aticipates annual cash flows of 110,000 resulting from the new dock the companys borrowing rate is 8% while its cost of capital is 10% calculate the net present value of the dock and indicafe whether lake front should make the investment
The lakefront company should make the investment as in 5 years they'll have a profit of 10000.
What is simple interest?We know simple interest (SI) is given by SI = (p×r×t)/100, where
p = principle, r = rate in percentage, and t = time in years.
Given, the lakefront company is considering investing in a new dock that will cost 560,000.
So, a Capital cost of 10% is (560000/10) = 56000
The company's borrowing rate is 8%.
∴ SI = (560000×8×5)/100.
SI = 5600×8×5.
SI = 224000.
So, The total cost is (560000 + 56000 + 224000) = 840000.
After 5 years they can sell it for 300000.
And has a cash flow of 110000, so in 5 years it is 550000.
So, total earnings is (300000 + 550000) = 850000.
Total profit is (850000 - 840000) = 10000 so it is profitable.
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Question 10
What is the equation of the line shown?
does it want the answer in a specific form?
slope intercept form; y = mx + b
slope = 2
b = -1
plug the values in
y = 2x -1 or y = 2/1x -1
raphael drives to his office which is 75km away from his house what is his speed if it takes him 1 hour and 15 minutes to get to his office
Answer:
1km\h
Step-by-step explanation:
like in physics, the calculation of speed is total distance divided by total time, you should do the same in math, and so you do 1 hour (60 minutes) + 15 minutes which gives you 75 minutes, and then you divide 75 km by the time so it should look something like this:
[tex]\frac{75 km}{75 minutes}[/tex] which gives you 1
so raphael is going 1 km\h
Answer:
[tex]\huge\boxed{\sf v = 60\ km/hr}[/tex]
Step-by-step explanation:
Given:Distance = S = 75 km
Time = t = 1.25 hours
Required:Speed = v = ?
Formula:v = S/t
Solution:v = 75/1.25
v = 60 km/hr
[tex]\rule[225]{225}{2}[/tex]
The length of a rectangle is 3 less than twice the width. If the perimeter of the rectangle is 78 inches, find the dimensions (length and width) of the rectangle.
Length of the rectangle is 25 and width of the rectangle is 14.
What do you mean by algebraic expression?
A combination of terms through addition, subtraction, multiplication, division, and other operations is known as an algebraic expression (or variable expression). An algebraic expression is composed of various parts.
Any algebraic expression's variables, constants, terms, and coefficients.
A variable is a symbol that doesn't have a set value. Any value may be used.
It is given that the length of a rectangle is 3 less than twice the width and the perimeter of the rectangle is 78 inches.
Let the width of the rectangle be x
Length of the rectangle become 2x - 3
Perimeter of rectangle = 2(length + width)
78 = 2(2x - 3 + x)
78 = 2(3x - 3)
78 = 6x - 6
78 + 6 = 6x
84 = 6x
x = 84/6
x = 14
length of the rectanle is 2x - 3 = 2(14) - 3 = 28 - 3 = 25
Width of the rectangle is x = 14
Therefore, length of the rectangle is 25 and width of the rectangle is 14.
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am i doing well on this
Answer:
The last option is the correct answer.
Step-by-step explanation:
The graph of g(x) is a transformation of the graph of f(x) = 2².
Enter the equation for g(x) in the box. g(x) =