The rational function is (x + 2)/(x - 3)(x + 2) which has a vertical asymptote at X = 3, and a removable discontinuity at x = -2.
Function
The function is referred as a mathematical expression that defines a relationship between one variable and another variable.
Given,
Here we need to construct a rational function that has a vertical asymptote at x = 3 and a removable discontinuity at x = -2.
Through the given question, we have been given that the rational function that has a vertical asymptote at x = 3, and a removable discontinuity at x = -2.
Here the x = 3 is a vertical asymptote.
So the one factor in the denominator is (x - 3),
And the discontinuity at x = - 2 can be removed, so the another common factor in the numerator and denominator is x+2.
Therefore, the rational function would be :
f(x) = (x + 2)/(x - 3)(x + 2)
So, the rational function would be (x + 2)/(x - 3)(x + 2).
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Convert 0.8 grams to grains
Answer:
12.3459 grains
Step-by-step explanation:
Answer:
12.346 grains
Step-by-step explanation:
for an approximate result, multiply the mass value by 15.432
( which is basically 0.8 times 15.432)
Lena took out a $9000 loan for 7 months and was charged simple interest. The total interest she paid on the loan was $336.
The loan given has a rate of 0.53%
Simple InterestSimple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time. In simple interest, the principal amount is always the same, unlike compound interest where we add the interest of previous years principal to calculate the interest of the next year.
The formula of simple interest is given as;
S.I = P(1 + RT)
S.I = Simple interestP = principalR = rateT = timeSubstituting the values into the formula;
(9000 + 336) = 9000(1 + r * 7)
9336 = 9000 + 63000r
Collecting like terms
336 = 63000r
r = 0.0053
r = 0.0053 * 100
r = 0.53%
The rate on the loan is 0.53%
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Emma learned in science class that fruit fly populations can increase by about 30% each day. She found 7 fruit flies on a rotten banana today, and she is curious how many fruit flies could be on the banana in a few days. You can use a function to approximate the number of fruit flies on the banana after x days.
The exponential function that approximates the number of fruit flies on the banana after x days is y = 7 x 1.3ˣ.
What is an exponential function?An exponential function is a mathematical function form of y = aⁿ or y = abˣ, where b is a constant or the base of the function, a is a variable, and n is the variable exponent.
Exponential functions must always contain an exponent, which is an integer raised to some power.
When the exponent is positive, it implies the function is increasing in value and vice versa.
Percentage increase per day = 30%
The number of fruit flies found = 7
The number of days = x days
Let the number of flies after x days = y
y = 7 x 1.3ˣ
Thus, an exponential representation of the function which Emma can use to model the number of fruit flies after x days is y = 7 x 1.3ˣ.
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9.
A.O
B.
1 12
Genevieve's
Function
Gary and Genevieve both plot lines on a coordinate grid. Gary plots the function y=2x-5, and Genevieve plots the function y=-3x + 4. Which of these represents their lines as well as the solution of the system?
The coordinate plane that represents both lines as well as the solution of the system is shown in the diagram below.
What is the Solution of a System of Equations?The solution to a system of equations is the value of x and y that will make the equations of the system true if they are plugged in into either of the two equations in the system.
Thus, when the equations or functions are plotted as a line on a coordinate grid, the system intersect at a point The coordinates of this point is the solution of the system of equations.
The function for Gary, y = 2x - 5, would be a line that has a slope of 2 and cuts the y-axis at -5, while that of Genevieve y = -3x + 4 will have a slope of -3, and will intercepts the y-axis at 4.
The red line in the coordinate grid in the image below is Gary's function y = 2x - 5, while the blue line is that of Genevieve y = -3x + 4. They bot intersect at (1.8, -1.4).
The solution is: (1.8, -1.4).
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Simplify these expressions
a) ххххххуху
b) 2 xx x x x 3 xyxyxy
A certain number is multiplied by 7, and 4 is taken from the product. Finally, the difference is divided by 9, resulting in 5. Find the initial number.
Alex house is 15 blocks from school. Carlene lives 7 blocks from Alex's house. Which equation represents the location of Carlene's house in relation to the school?
|x+7|=15
|x-7|=15
|x+15|=7
|x-15|=7
Answer:
Answer is b
Step-by-step explanation:
Because
|x-7|=15--->x=15+7, x=22(-42n+28p)(-1/4) simplify. Assume that no denominator equals zero
The value of (-42n+28p)(-1/4) is 249n/4
What are fractions?A fraction represents a part of a whole or, more generally, any number of equal parts. A fraction describes how many parts of a certain size there are, for example, one-half, three-fifths, three-quarters.
A fraction has a denominator and numerator. There are three types of fraction. Proper, improper and mixed fraction
Opening the parentheses of the equation
(-42n+ 28p)(-1/4).
= -42n× -1/4+ 28× -1/4
= (42n×-7)/4
= -294n/4
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What is the slope of this line
Answer: Slope is 0
Step-by-step explanation
the graph's points doesn't change its value on the y - values but the x values change by 1 meaning the slope is 0/1 meaning there is no slope
Assume that a hat contains four bills: a $1, a $5, a $10,
and a $20 bill. Two bills are to be selected at random with
replacement. Find the probability that both bills are $20 if
the first selected is a $20 bill?
The probability that both bills are $20 if the first selected is
a $20 bill is
(Simplify your answer. Type an integer or a fraction.)
The probability that both bills are $20 if the first selected is a $20 bill is 1/16.
What is probability ?The probability formula is as defined as the possibility of any event to happen which comes to be equal to the ratio of the number of favourable outcomes and the total number of outcomes.
Probability of event to occur P (E) =
[tex]\frac{Number of favourable outcomes}{ Total number of outcomes }[/tex]
Hat contains four bills: a $1, a $5, a $10, and a $20 bill.
Probability(P1) of Getting $20 bill in 1st selection = 1/4 ;
After Replacement,
Probability(P2) of Getting $20 bill in 2nd selection = 1/4 ;
So, the probability that both bills are $20 if the first selected is
a $20 bill = 1/4 * 1/4 = 1/16,
Hence we get 1/16 as the probability of getting both bills of $20.
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Am I correct? Did I do this right?
Answer:
Step-by-step explanation:
Yes, you did it right.
Exercise 4.3
1. Given f=x^2 y; the change in for the total differential of fis given by df = Pdx+Qdy.
Find P, Q at x=1 and y=-1
(Ans: P= -2; Q=1)
Question one
By using the concept of differentiation, it can be calculated that
value of P is -2 and value of Q is 1
What is differentiation?
Differentiation is the process where the instantaneous rate of change of function can be calculated based on one variable. Differentiation is a very important tool in calculus
Here differentiation is used
f(x) = [tex]x^2y[/tex]
[tex]df = 2xydx+x^2dy[/tex]
Here P = 2xy, Q = [tex]x^2[/tex]
At x = 1, y = -1
P = 2(1)(-1) = -2
Q = [tex](-1)^2[/tex] = 1
So value of P is -2 and value of Q is 1
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Do the measurements 15,17,22 make up a right triangle? Yes or no explain??
answer me fast
The measurements 15, 17, 22 do not form a right triangle.
In this question, we have the measurements 15, 17, 22
We check whether the measurements 15, 17, 22 is Pythagorean triple.
22^2 = 484
15^2 = 225
17^2 = 289
15^ + 17^2 = 225 + 289
= 514
≠ 484
i.e., 15^ + 17^2 ≠ 22^2
This means, these measurements do not form a right triangle.
Therefore, the measurements 15, 17, 22 do not form a right triangle.
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Use the number line to plot –3, 1, and 3.
Which statements are true
Select all that apply.
–3 > 1
–3 = 3
1 < 3
–3 < 1
The number line with the numbers -3, 1 and 3 is shown by the image at the end of the answer.
The correct statements regarding the number line are given as follows:
1 < 3.–3 < 1.How to plot an integer number on the number line?Integer numbers are numbers that do not have decimal parts, they are either positive or negative, but exact.
These numbers are plotted marking a symbol such as a X or a circle on the number line.
The number line is increasing, so the negative numbers appear before the positive numbers.
This means that if a number a is to the left another number b, the number a is less than b, hence:
1 < 3–3 < 1.As the order in which the numbers appear is given as follows:
-3, 1 and 3.
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About 53% of adults in the US have traveled with a commercial airline. A random sample of 400 adults was selected
and whether they have traveled with a commercial airline was recorded.
Calculate the standard deviation of the sampling distribution of
O 0.00062
O 0.00086
* 0.00125
O 0.02495
B
M
B
1
■
▬
T
U
Done
♥
The standard deviation of the sampling distribution is 0.01767.
What is a standard deviation?Standard deviation is a measure of the amount of variability or spreads in a set of data.
It is calculated as the square root of the variance and is often denoted by the symbol σ (sigma) for a population and s for a sample.
We have,
Given that the sample size is sufficiently large (n=400) and the population proportion is known, we can use the formula for the standard deviation of the sampling distribution of the sample proportion, which is:
[tex]\sigma_{\hat{p}} = \sqrt((p (1 - p)) / n)[/tex]
where p is the population proportion and n is the sample size.
In this case,
p = 0.53 (as given in the problem) and n = 400.
Substituting these values into the formula, we get:
[tex]\sigma_{\hat{p}} = \sqrt((0.53 (1 - 0.53)) / 400)\\\sigma_{\hat{p}} = \sqrt((0.53 0.47) / 400)\\\sigma_{\hat{p}} = \sqrt(0.0003121)\\\sigma_{\hat{p}} = 0.01767[/tex]
(rounded to five decimal places)
Therefore,
The standard deviation of the sampling distribution is 0.01767.
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Select the correct answer from each drop-down menu. Using the image below, select the best answer from each pull-down to complete the statements. The measure of ∠FED is ? °. ∠CBD and ∠ ? are complementary angles. Please help. thank you
The value of ∠FED is 120° and ∠CBD is complementary to ∠FDE
What are complementary angles?Complementary angles are two angles that sum up to 90°
For example 60° and 30° are complementary.
Either angle is called the complement of the other angle.
∠FED, ∠FDE and ∠DFE are in a triangle.
so,
∠FED + ∠FDE + ∠DFE = 180°
16x - 8 + 2x + 9 + 35 = 180 ( sum of angles in a triangle)
18x +36 = 180
18x = 180 - 36
18x = 144
x = 144/18
x = 8
so ∠FED = 16x - 8
Substitute x = 8 into the equation above we have
16(8) - 8 = 128 - 8 = 120°
∠FDE = 2x + 9
∠FDE = 2(8) + 9 = 25°
∠BED = 6x + 12
∠BED = 6(8) + 12
∠BED = 48 + 12
∠BED = 60°
∠CBD = -2x + 81
∠CBD = -2(8) + 81
∠CBD = 65°
so since ∠CBD = 65° and 90 - 65 = 25°
∠CBD is complementary to ∠FDE
In conclusion, ∠FED is 120° and ∠CBD is complementary to ∠FDE
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A bag contains 3 gold marbles, 5 silver marbles, and 26 black marbles. Someone offers to play this game: You randomly select one marble from the bag. If it is gold, you win $3. If it is silver, you win $2. If it is black, you lose $1. What is your expected value if you play this game?
The expected value if you play this game will be -$0.205.
Let the number of gold, silver, and black marbles be P1, P2, and P3, respectively.
Given, The bag contains,
Number of gold marbles (P1) = 3
Number of silver marbles (P2) = 5
Number of black marbles (P3) = 26
Also given,
The winning value if a gold marble is selected = $3
The winning value if a silver marble is selected = $2
The losing value if a black marble is selected = $1
Probability = Expected value/ Sum of the total number of events
Probability of picking a gold marble,
P1 = 3/ (3+ 5+ 26)
= 3/34.
Probability of picking a silver marble,
P2 = 5/ (3+ 5+ 26)
= 5/34.
Probability of picking a black marble,
P3 = 26/ (3+ 5+ 26)
= 26/34.
The expected value if you play the game will be,
Value = ($3) P1 + ($2) P2 + (-$1) P3
= ($9/34) + ($10/34) - ($26/34)
= - ($7/34)
= -$ 0.205
Thus, you will face a loss of 0.205 cents.
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Which statements are always true regarding the diagram? Select three options. m∠5 + m∠3 = m∠4 m∠3 + m∠4 + m∠5 = 180° m∠5 + m∠6 =180° m∠2 + m∠3 = m∠6 m∠2 + m∠3 + m∠5 = 180°
The valid equations are written below. Then the correct options are C, D, and E.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180 °.
The sum of the two interior angles is equal to the exterior angle of the third angle.
The sum of the supplementary angle will be 180°.
From the diagram, the equations are written as,
m∠5 + m∠6 = 180° (Supplementary angle)
m∠2 + m∠3 = m∠6 (Exterior angle)
m∠2 + m∠3 + m∠5 = 180° (Angle sum of triangle)
Then the correct options are C, D, and E.
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The complete question is attached below.
Mr. Harris is adding tiles to his patio area. On Monday, he tiled 1/3 of his patio, and on Tuesday, he tiled 1/2 of the patio area. How much would he have left to tile on Wednesday?
Responses
On Wednesday 1/6 of the patio area is left to tile
Let the patio area be x
On Monday, he tiled 1/3 of his patio = 1/3 x
on Tuesday, he tiled 1/2 of the patio area = 1/2 x
The area left to tile on Wednesday
= x - (1/3 x + 1/2 x)
x - 1/3 x - 1/2 x
(6x - 2x - 3x)/6
= 1/6 x
The area left to tile on Wednesday is 1/6 of the patio area
Therefore, 1/6 of the patio area is left to tile on Wednesday
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5x + y = 8
2x + y = 5
Answer:
x=1 y=3
Step-by-step explanation:
By looking at the equations, you can use substitution
Set the equation equal to y
y=-5x+8
y=-2x+5
Then put equation together
-5x+8=-2x+5
Move numbers over
3x=3
x=1
Put x back into equation
5+y=8
2+y=5
y=3
A bus ticket used to cost $2.50
Today, 1 bus ticket costs $2.75
The increase in cost is?
The percent increase is?
Tiana is looking up her county's census data for a school project. Her county conducts a census every decade. She finds that the population was about 641,000 the year she was born, and that it had decreased to about 634,590 a decade later. Tiana reads that the population of the county is expected to continue decreasing each decade.
Write an exponential equation in the form y=a(b)x that can model the county population, y, x decades after Tiana was born.
Use whole numbers, decimals, or simplified fractions for the values of a and b.
y =
How many decades after Tiana was born will the county population fall below 600,000?
decades
The exponential function that can model the county population, y, x decades after Tiana was born, is:
[tex]y = 641000(0.99)^x[/tex]
The population will fall below 600,000 in 6.6 decades after Tiana was born.
What is an exponential function?The definition of the exponential function is presented as follows:
[tex]y = a(b)^x[/tex]
In which the parameters of the exponential function are presented as follows:
a is the initial value.b is the rate of change.In the context of this problem, the values of these parameters are given as follows:
a = 641000, which is the initial population.b = 634590/641000 = 0.99.Hence the function is:
[tex]y = 641000(0.99)^x[/tex]
The population will fall below 600,000 when y = 600000, hence:
[tex]y = 641000(0.99)^x[/tex]
[tex]600000 = 641000(0.99)^x[/tex]
[tex](0.99)^x = \frac{600000}{641000}[/tex]
[tex]\log{(0.99)^x} = \log{\left(\frac{600000}{641000}\right)}[/tex]
[tex]x\log{0.99} = \log{\left(\frac{600000}{641000}\right)}[/tex]
[tex]x = \frac{\log{\left(\frac{600000}{641000}\right)}}{\log{0.99}}[/tex]
x = 6.6 decades.
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which ones bigger -1.35 or -1 4/9 by the way 4/9 is a fraction
Answer:
[tex]-1.35[/tex] is bigger (larger)
Step-by-step explanation:
[tex]-1\frac{4}{9}=-1.\overline{44}[/tex]
Therefore, because [tex]-1.35[/tex] is less negative than [tex]-1.\overline{44}[/tex],
[tex]-1.35[/tex] is bigger (larger).
What is the mode for test scores 84,76,95,66,87,91,79,88,81,87?
Answer: mode is 94
Step-by-step explanation:
Considering the following statements, what is X → Z? X → Y: If the sum of the interior angles of a shape is 180°, then it's a triangle. Y → Z: If a shape is a triangle, then it has three sides. Question 4 options: A) X → Z: If the sum of the interior angles of a shape is 180°, then it has three sides. B) X → Z: If a shape has three sides, then it's a triangle. C) X → Z: If a shape has three sides, then the sum of the interior angles of the shape is 180°. D) X → Z: If the sum of the interior angles of a shape isn't 180°, then it doesn't have three sides.
The correct statement that is a combination of both conditional statements is; X → Z: If the sum of the interior angles of a shape is 180°, then it has three sides.
How to interpret conditional statements?
A triangle is defined as a three-sided polygon that consists of three edges and three vertices. The most important property of a triangle is that the sum of the internal angles of a triangle is equal to 180 degrees.
We are given the conditional statements as;
X → Y: If the sum of the interior angles of a shape is 180°, then it's a triangle.
Y → Z: If a shape is a triangle, then it has three sides.
Now, transitive property states that “if two quantities are equal to a third quantity, then we can say that all the quantities are equal to each other”.
Thus, applying transitive property to our given statements we can say that; X → Z: If the sum of the interior angles of a shape is 180°, then it has three sides.
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The population of a city can be modeled using the formula P=100,000e^(0.05t), where t is the number of years after 2012 and P is the city's population. Which of the following equations can be used to find the number of years after 2012 that the population will triple to 300,000?
Group of answer choices
t=3/(0.05e)
t=ln3/0.05
t=(ln200,000)/0.05
t=log3/0.05
The equation that can be used to find the number of years after 2012 that the population will triple to 300,000 is option B t = ln(3) / 0.05
Given,
The population of a city can be modeled using the formula P=100,000e^(0.05t)
t is the number of years after 2012
P is the population of the city
We have to find the equation that can be used to find the number of years after 2012 that the population will triple to 300,000.
Here,
Substitute 300000 in for P and solve for t
300000=100000e^0.05t
Divide both sides by 100000:
We get,
3 = e^0.05t
Multiply both sides by the natural log (ln)
Then,
ln(3) = 0.05t
Now, divide 0.05 on both sides to get t by its self
t = ln(3) / 0.05
Therefore,
The equation that can be used to find the number of years after 2012 that the population will triple to 300,000 is option B t = ln(3) / 0.05
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A family has two cars. During one particular week, the first car consumed 30 gallons of gas and the second consumed 40 gallons of gas. The two cars drove a combined total of 1600 miles, and the sum of their fuel efficiencies was 45 miles per gallon. What were the fuel efficiencies of each of the cars that week?
If the fuel efficiencies of each of the cars that week is 20 gallons of gas and 25 gallons of gas.
How to find the efficiencies?Let x represent the gallons consumed by car 1
Let y represent gallons consumed by car 2
Formulate an equation:
30x+40y = 1600 equation 1
x+y = 45 equation 2
Substituting equation 2 into equation 1,
30x+40(45-x) = 1600
30x+ 1800-40x = 1600
-10x+1800 = 1600
-10x = -200
Divide both side by -10x
x = -200/-10
x = 20
Substitute value of x into equation 2
x+y = 45
20+y = 45
y = 25
Hence,
Car 1 consumes 20 gallons of gas and Car 2 consumes 25 gallons of gas.
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Please help please and thank you..
The value of x for the triangle by the mid point theorem is obtained as 5.
What is defined as the mid-point theorem?The line segment of a triangle connecting the midpoint in two the triangle's sides is thought to be parallel to that third side and also half the length of the third side, according to the midpoint theorem. A location that is at, close, or equally far both from ends of a line segment is referred to as the midpoint. To put it another way, the midpoint is indeed the place in a fact where the beginning and the conclusion meet.For the given diagram in the question.
As, the sides of the triangle is divided in equal parts.
By the mid -point theorem-
(1/2)24 = x + 7
12 = x + 7
x = 12 - 7
x = 5
Thus, the value of x for the triangle by the mid point theorem is obtained as 5.
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What is the y-intercept of a line that has a slope of 2 and ( - 2, 3 ) is a point on the line?
The y-intercept of the line will be equal to 7.
What is an equation of the line?An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.
The general form of the equation of the line:-
y = mx + c
m = slope
c = y-intercept
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given that a line that has a slope of 2 and ( - 2, 3 ). The y-intercept of the line will be calculated as,
y = mx + c
3 = (-2 x 2 ) +c
3 = -4 + c
c = 4 + 3
c = 7
Therefore, the y-intercept of the line will be equal to 7.
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f(x) = x + 2
g(x) = 3x² - 5
Find (f.g)(x).
OA. (f g)(x) = 3x³ - 10
OB. (f g)(x) = 3x³ + 6x² - 5x - 10
OC. (f. g)(x) = 3x³ + 10
OD. (f g)(x) = 3x³ + 6x² + 5x + 10
SUBMIT
Answer:
It's option B, (f • g)(x) = 3x^3 + 6x^2 - 5x - 10
Step-by-step explanation:
In this problem, we are dealing with a branch of functions called composite functions. What the difference is between normal and composite functions is that we instead of defining a value for f(x), take two functions, f(x) and g(x), in the form of f and g. For instance, h(x) = g.
• Take the products of both functions.
f(x)g(x) = 3x²+5 • x-2
• Next, expand the functions. We expand by combining like terms.
= 3x^3 - 6x^2 + 5x - 10
Since the function cannot be simplified further, this leads to option B being our answer.
Hope this helps!
