Answers
Answer: Option (2)
Step-by-step explanation:
There is a double root at x=-1, so there is a factor of [tex](x+1)^2[/tex].
Eliminate options (1) and (3).Also, as x approaches both positive and negative infinity, the graph approaches negative infinity, so the leading coefficient is negative.
Eliminate (4).Related Questions
18. For the following exercises, use the descriptions of each pair of lines given below to find the slopes of Line 1 and Line
2. Is each pair of lines parallel, perpendicular, or neither?
18. Line 1: Passes through (0, 6) and (3, -24 Line 2: Passes through (-1, 19) and (8, -71)
Answers
Answer:
The given lines are parallel.
Step-by-step explanation:
In the question, two lines are given as line 1 passes through (0,6) and (3,-24). Whereas, line 2 passes through (-1,19) and (8,-71).
It is required to find the slope of given lines and figure out whether they are perpendicular, parallel or neither.
To solve this question, first find the slope of both lines. Check if their product is equal to -1, then they are perpendicular. If the slopes are equal the lines are parallel
Step 1 of 2
Find the slope of first line.
[tex]$$\begin{aligned}&m_{1}=\frac{-24-6}{3-0} \\&m_{1}=\frac{-30}{3} \\&m_{1}=-10\end{aligned}$$[/tex]
Step 2 of 2
Find the slope of first line.
[tex]$$\begin{aligned}&m_{2}=\frac{-71-19}{8-(-1)} \\&m_{2}=\frac{-90}{9} \\&m_{2}=-10\end{aligned}$$[/tex]
Since, both slopes are equal.
Therefore, the lines are parallel.
A machine can pump 15 litres of water in one minute.
How long does it take to pump 900 litres of water
Answers
Answer:
900 liters of water is pumped in 1 hour
Step-by-step explanation:
Time taken to pump 15 liters of water = 1 minute.
Time taken to pump 1 liters of water = 1/15 minute
[tex]\sf \text{Time taken to pump 900 liters of water=$\dfrac{1}{15}*900$}[/tex]
= 60 minutes
= 1 hour
classify the decimal form of the given rational number into terminating and non terminating type
Answers
19 : 125 = 0.152, and because there is a finite amount of digits after the decimal, this is a terminating decimal. (if anything's wrong just message)
hi hermes
the graph of f(x)=3x what is the value of x when f(x)=9
Answers
Answer:
[tex]\{3\}[/tex]
Step-by-step explanation:
Strictly speaking, we need to know the point of [tex]f(x) = 3x[/tex] intersecting [tex]f(x) = 9[/tex]. In other words, we need to solve the equality:
[tex]3x = 9; \\ x = \frac{9}{3}; \\ x = 3[/tex]
Here it is.
The graph of f(x) =[tex]2^{x+3}[/tex] shifts 10 units to the right when it is replaced with the graph of f(x) = [tex]2^{x-k}[/tex]. What is the value of k? 3 7 10 13
Answers
Answer:
7
Step-by-step explanation:
Whenever you shifting an exponential function to the left/right, you're going to generally have the equation: [tex]y=2^{x-k}[/tex] where k is the shift. So in this case we can think of x+3 as x and k as 10, since the shift is 10. This gives you the equation: (x+3) - 10, which simplifies to x-7, meaning the k value in this case is going go be 7. You can also think of it as already being shifted 3 units to the left, and you shift it 10 units to the right, that means this new function will be shifted 7 units to the right relative to the origin. This means the k=7.
The midpoint of AB is M (5, 6). If the coordinates of A are (3, 8), what are the
coordinates of B?
Answers
Answer:
(7, 4)
Step-by-step explanation:
[tex]\text{Let the coordinates of B } = x_{B} , y_{B} \\\text{Let the coordinates of A} = x_{A} , y_{A} \\\text{Let the coordinates of midpoint M} = x_{M} , y_{M}[/tex]
By the midpoint formula,
[tex](x_{M},y_{M}) = (\frac{x_{A} + x_{B}}{2} , \frac{y_{A} + y_{B}}{2} )[/tex]
[tex]x_{M} = \frac{x_{A} + x_{B}}{2} \\y_{M} = \frac{y_{A} + y_{B}}{2} \\[/tex]
We have coordinates of midpoint as (5, 6) and coordinates of A as (3,8)
So
[tex]5 = \frac{3 + x_{B}}{2} \\\\\\textrm{Cross-multiplying } 10 = 3 + x_{B}} \textrm{ or } x_{B} = 10-3 = 7\\[/tex]
[tex]6 = \frac{8 + y_{B}}{2} \\\\\\\\textrm{Cross-multiplying } 12 = 8 + y_{B}} \textrm{ or } y_{B} = 12-8 = 4\\[/tex]
So coordinates of B are (7,4)
6.7 Section 6.7 Integer Exponents and Scientific Notation
Convert from Decimal Notation to Scientific Notation
In the following exercises, write each number in scientific notation.
740. 8,500,000
Answers
Answer:
The decimal number 8,500,000 has been converted to its corresponding scientific notation, which is [tex]$8.5 \times 10^{6}$[/tex].
Step-by-step explanation:
Given: The decimal number 8,500,000.We need to convert the number to its corresponding scientific notation.Dissociate the number into the multiples of 10.Adjust the coefficient such that it lies between 1 and 10.Use the format [tex]$a \times 10^{b}$[/tex] to write the final answer.Step 1 of 1
Remember that the decimal lies at the end of 8,500,000. Move the decimal next to 8 such that the result is greater than 1 and less than 10 . So the decimal point will move 6 places to the left.
As 8,500,000 is greater than 1 so the power of 10 will have an exponent of 6 .
So,
[tex]$$8,500,000=8.5 \times 10^{6}$$[/tex]
Verifying the result we can see that
[tex]$$10^{6}=1,000,000$$[/tex]
when multiplied by 8.5 will result in 8,500,000.
un bibliotecario de la biblioteca "Amauta" coloca libros de aritmética y álgebra en un estante, notando que la relación de libros de aritmética y el total de libros es de4 a 9. respectivamente Si sabe que coloca 10 libros de álgebra en el estante
¿Cuántos libros de aritmética coloca la bibliotecaria?
Answers
Concluimos que hay 8 libros de aritmética.
¿Cuántos libros de aritmética coloca la bibliotecaria?
Sabemos que la relacion entre el número de libros de aritmetica y el total de libros es de 4 a 9.
Es decir, sí el número total de libros es N, entonces (4/9)*N de esos libros son de aritmética.
Sea X el número de libros de aritmética. Sabemos que hay 10 libros de algebra, entonces el número total N es:
N = 10 + X
Y usando la relación de arriba, podemos escribir:
X = (4/9)*N = (4/9)*(10 + X)
Ahora podemos resolver esto para X.
X*(9/4) = 10 + X
X*(9/4) - X = 10
X*(5/4) = 10
X = (4/5)*10 = 8
Concluimos que hay 8 libros de aritmética.
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Given ƒ(x) = x + 10, find ƒ(x + 1).
Answers
Work Shown:
f(x) = x + 10
f(x+1) = x+1 + 10 .... replace every x with x+1
f(x+1) = x + 11
Solve for y 3x+3-x+ (-7) > 6 o a. x > (-5) b. x<5 ) cy>5 ) d. x > 2.5
Answers
The value of x for the inequality 3x+3-x+ (-7) > 6 is x > 5. This a can be obtained by solving the linear inequality by taking terms with x to one side of the inequality similar to solving of linear equation.
What is the value of x?Given that
3x + 3 - x + (-7) > 6
3x - x > 6 + 7 - 3
2x > 10
x > 5
Hence the value of x for the inequality 3x+3-x+ (-7) > 6 is x > 5. The correct option is c.
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3) A woman buys 3 dezen eggs. Later she discovers that x of them are broken. How many mang eggs are not broken 3 ) A woman buys 3 dezen eggs . Later she discovers that x of them are broken . How many mang eggs are not broken
Answers
Answer:
36 - xStep-by-step explanation:
A woman buys 3 dezen eggs. Later she discovers that x of them are broken. How many mang eggs are not broken
3 = 3
Dozen = 12
x = broken eggs
3 * 12 - x =
36 - x
Please help me find the answers to all the questions whoever answers all the question I will mark the brainlest.
Answers
Answer:
[tex]\textsf{a)} \quad \textsf{Recursive Rule}: \quad a_n=5n-2[/tex]
[tex]\textsf{Explicit Rule}: \quad \begin{cases}a_1=3\\a_n=a_{n-1}+5\end{cases}[/tex]
b) 4998
c) explicit rule (see below for explanation)
d) see below
Step-by-step explanation:
An explicit formula for an arithmetic sequence allows you to find the nth term of the sequence.
A recursive formula for an arithmetic sequence allows you to find the nth term of the sequence provided you know the value of the previous term in the sequence.
Part aExplicit Formula
[tex]a_n=a+(n-1)d[/tex]
where:
[tex]a_n[/tex] is the nth terma is the first termn is the number of the termd is the common differenceGiven sequence: 3, 8, 13, 18, 23, ...
To find the common difference, subtract one term from the next term.
Therefore:
a = 3d = 8 - 3 = 5Substituting the found values of a and d into the formula to create a explicit rule for the given sequence:
[tex]\implies a_n=3+(n-1)5[/tex]
[tex]\implies a_n=3+5n-5[/tex]
[tex]\implies a_n=5n-2[/tex]
Recursive Formula
[tex]a_n=a_{n-1}+d \quad \textsf{for }n\geq 2[/tex]
where:
[tex]a_n[/tex] is the nth term[tex]a_{n-1}[/tex] is the term immediately before the nth termd is the common differenceWe already know the common difference our previous calculations.
Therefore:
[tex]\implies a_n=a_{n-1}+5[/tex]
When giving a recursive rule we also have to define the first term of the sequence, as it is not part of the formula. Therefore, the full recursive rule for the given sequence is:
[tex]\begin{cases}a_1=3\\a_n=a_{n-1}+5\end{cases}[/tex]
Part bTo find the 1000th term of the sequence, use the explicit rule and substitute n = 1000:
[tex]\implies a_{1000}=5(1000)-2[/tex]
[tex]\implies a_{1000}=5000-2[/tex]
[tex]\implies a_{1000}=4998[/tex]
Therefore, the 1000th term of the sequence is 4998.
Part cWe used the explicit rule to find the 1000th term as this rule allows us to find the nth term of the sequence without having to know any previous terms.
Part dThe disadvantage of a recursive rule when compared to an explicit rule is that we need to know the previous term to find the nth term, whereas the explicit rule doesn't need this information.
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The function below models the correlation
between the number of hours a plant is kept in
sunlight (x) and the height (y), in mm, to which it
grows:
y = 2 + 4x
What does the y-intercept of this function
represent?
The original height of the plant was 4 mm.
The original height of the plant was 2 mm.
The height of the plant increases by 2 mm for
every hour of sunlight it receives.
The height of the plant increases by 4 mm for
every hour of sunlight it receives.
Answers
hallar el valor de ab datos: bc= 4,5 cm de= 2cm ef= 3 cm
Answers
The measure of ab and df are 3cm and 7.5cm respectively
Similarity theorem of shapesIn order to determine the missing sides, we need to take the ratio of the similar sides as shown:
1) ab/de = ac/df
ab/de = ab+bc/df
Substitute the given values
ab/2 = ab+4.5/2+3
ab/2 = ab+4.5/5
2(ab+4.5) = 5ab
2ab+9=5ab
3ab = 9
ab = 3cm
Hence the measure of ab is 3cm
2) ae/ce = bf/df
24/9 = 20/df
24df =. 9(20)
24df = 180
df = 7.5cm
Hence the measure of ab and df are 3cm and 7.5cm respectively
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Marcus was going up 10 stairs in his office. Write an absolute value expression for the given statement.
1. -10
2. |10|
3. |-10|
4. ±10
Answers
The absolute value expression for the given statement is |10|
What is absolute value?The absolute value (or modulus) | x | of a real number x is the non-negative value of x without regard to its sign
Marcus was going up stairs in his office. Therefore, he was ascending .
This means the 10 staircase will be added since there is an increase.
Hence, the absolute value expression for the given statement is as follows:
absolute value = |10|
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A measure of the strength of the relationship between two variables is referred to as the.
Answers
A measure of the strength of the relationship between two variables is referred to as the correlation coefficient.
What is the correlation coefficient?To gauge the strength of the linear link between two variables, correlation coefficients are used.
A value of correlation coefficient less than zero denotes a negative association, while a value greater than zero denotes a positive relationship.
A zero correlation coefficient means there is no correlation between the two variables under comparison.
A crucial idea in building diversified portfolios that may better resist portfolio volatility is the concept of a negative correlation, often known as an inverse correlation.
Since calculating the correlation coefficient takes time, it is frequently done by entering data into a calculator, computer, or statistics application.
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A translation is shown on the grid below. On a coordinate plane, triangle A B C has points (negative 4, 2), (negative 4, negative 2), (negative 1, negative 2). Triangle A prime B prime C prime has points (1, 5), (1, 1), (4, 1). Which are true statements about the translation? Select 3 options. The sides of the image and pre-image are congruent. The image is turned 90°. The angles in the image are different from the angles in the pre-image. The image is a slide of the pre-image. The image has a different shape than the pre-image. Each point has moved in a different direction. Each point has moved the same number of units.
Answers
Based on the translated image and the original triangle ABC, the true statements are:
The sides of the image and pre-image are congruent.The image is a slide of the pre-image.Each point has moved the same number of units.What can be said of the translation?The pre-image of triangle ABC and the image are shown to have sides that are congruent because they are exactly the same. This is why triangle A¹B¹C¹ is a slide of triangle ABC.
In order to form the image, the translation must have been such that each point of the preimage moved the same number of units.
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Answer:
a, d, g
Step-by-step explanation:
i took da test
Determine whether the given sequence could be geometric, arithmetic, or neither. If possible, identify either the common ratio or the common difference.
9, 13, 17, 21,....
Answers
What is the 6th term of the geometric sequence where a1 = −4,096 and a4 = 64
Answers
The 6th term of the sequence is 4
How to determine the 6th term?The given parameters are:
a1 = -4096
a4 = 64
The nth term of the sequence is:
a(n) = a1 * r^(n-1)
So, we have:
a4 = a1 * r^3
This gives
r^3 = a4/a1
Substitute the known values
r^3 = 64/-4096
Evaluate
r^3 = -1/64
Take the cube roots
r = -1/4
The 6th term is
a(6) =a1 * r^5
This gives
a(6) = -4096 * (-1/4)^5
Evaluate
a(6) = 4
Hence, the 6th term of the sequence is 4
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Members of a lacrosse team raised $1307.50 to go to a tournament. They rented a bus
for $812.50 and budgeted $41.25 per player for meals. Determine the number of
players the team can bring to the tournament.
Answers
Answer:12
Step-by-step explanation:(1307.50-812.50)/41.25 = 12
The lacrosse team can bring 12 players to the tournament.
How to determine the number of players the team can bring to the tournament.Let's assume the number of players on the lacrosse team is "n."
The total amount raised by the team is $1307.50, and they rented a bus for $812.50. The remaining amount after renting the bus is available for meals.
Amount available for meals = Total amount raised - Bus rental cost
Amount available for meals = $1307.50 - $812.50
Amount available for meals = $495
Now, the budgeted amount per player for meals is $41.25. To find the number of players the team can bring to the tournament, we need to divide the total amount available for meals by the budgeted amount per player:
Number of players = Amount available for meals / Budgeted amount per player
Number of players = $495 / $41.25
Number of players = 12
So, the lacrosse team can bring 12 players to the tournament.
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If a store sold 25 pairs of socks, making a 25% profit (i.e., percent of sales) of $150, how much did they charge for each pair
Answers
The store charged $24 for each pair of socks as the selling price.
What is Profit?Profit is the financial gain that is earned by a business or an individual after deducting all expenses from revenue. In other words, it is the amount of money that remains after all costs of producing and selling a product or service have been subtracted from the total revenue earned.
What is Revenue?Revenue refers to the total amount of income earned by a business or an individual from the sale of goods or services during a specific period of time. It is the total amount of money that a business receives from its customers in exchange for its products or services.
In the given question,
Let's start by calculating the total revenue from the sale of 25 pairs of socks
Since the profit is 25% of the revenue, we can set up the equation:
Profit = 0.25 * Revenue
$150 = 0.25 * Revenue
Revenue = $150 / 0.25
Revenue = $600
The total revenue from selling 25 pairs of socks is $600.
To find the price per pair of socks, we can divide the revenue by the number of pairs:
Price per pair = Revenue / Number of pairs
Price per pair = $600 / 25
Price per pair = $24
Therefore, the store charged $24 for each pair of socks.
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Find the two straight lines represented by x² + 5xy - 6y² = 0
Answers
By factorizing, we have
[tex]x^2 + 5xy - 6y^2 = (x - y) (x + 6y) = 0[/tex]
so that
[tex]x - y = 0 \implies \boxed{y = x}[/tex]
or
[tex]x + 6y = 0 \implies \boxed{y = -\dfrac x6}[/tex]
If x+y=6,y+z=7, z+x=9 what is the average or x, y and z
Answers
Step-by-step explanation:
so in this case
x-4
y-2
z-5
average=x+y+z/no of values
= 4+5+2/3
=11/3
=3.6
The plane flew over a beacon which is 280 miles from bristol. write down the gmt times when the plane flew over the beacon.
Answers
According to graph, GMT time when the plane flew over the beacon was 9:24.
While looking closely at the graph on x axis , one will notice that each hour is divided into 5 parts and hence each part has 12 minutes. looking at y axis, one may find that each part on y axis resembles 20miles. Hence at 280 miles away from Bristol, The GMT time is 9:24.
What is a graph?In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way.The relationships between two or more items are frequently represented by the points on a graph.The study of graphs, which are mathematical constructions used to represent pairwise relationships between things, is known as graph theory in mathematics. Vertices (also known as nodes or points) make up a graph in this sense, which are connected by edges (also called links or lines).Undirected graphs, in which edges connect two vertices symmetrically, are distinguished from directed graphs, in which edges connect two vertices asymmetrically. One of the main topics of study in discrete mathematics is graphs.Know more about graph numerical
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60. Cities A and B are on the same east-west line.
Assume that city A is located at the origin. If the
distance from city A to city B is at least 100 miles
and x represents the distance from city B to city A,
express this using absolute value notation.
Answers
Answer:
The expression for the statement using absolute value notation is [tex]|x|\geq 100[/tex]
Step-by-step explanation:
It is given in the question that the distance from city A to city B is at least 100 miles.
It is required to express the statement using absolute value notation.
To express the statement using absolute value notation, deduce the statement in the form of an equation.
x represents the distance from city B to A city .
Deduce the statement in the form of an equation
[tex]|x|\geq 100[/tex]
The Westminster Widget Company has an old machine that can produce 50 widgets in five hours. Now they have purchased a
new machine that can produce 30 widgets in two hours. Working together, how long will it take the two machines to produce
100 widgets?
4 hours
16 hours
hour
8 hours
Answers
Answer:
If they worked together it would take 4 hours for the machines to produce 100 widgets
Step-by-step explanation:
w = widgets hr = hour ph = per hour
Old machine - 50w = 5hr = 10ph
New machine - 30w = 2hr = 15ph
Old machine - 20w = 2hr
New machine - 30w = 2hr
Together - 50w = 2hr x 2 Final: 100w = 4hrI hope this helped!
i need help on this question for algebra
Answers
Answer:
36 miles and 10 miles
Step-by-step explanation:
area = length × width
A = LW
W = unknown = x
L = 26 ft more than width = x + 26
A = LW
360 = (x + 26)x
360 = x² + 26x
x² + 26x - 360 = 0
(x + 36)(x - 10) = 0
x + 36 = 0 or x - 10 = 0
x = -36 or x = 10
We discard the solution x = -36 since the width of a rectangle cannot be a negative number.
W = x = 10
L = x + 26 = 10 + 26 = 36
Answer: 36 miles and 10 miles
How many different ways
can you arrange the letters
in the word SMILE?
PLSSS HELP
Answers
Answer:
120 different ways
Step-by-step explanation:
The formula to count the permutation since the order the matters: nPr = n! / (n - r)!, where n is the total number and r is the total number of chosen.
1) Substitute values into the formula. SMILE has 5 letters, and we choose 5.
5P5 = 5! / (5 - 5)!
5P5 = 5! / 0!
Zero factorial (0!) is always 1.
So, 5P5 = 5! / 1
5! = 5 × 4 × 3 × 2 × 1
5! = 120
Therefore, 5P5 = 120 / 1, which is 120. We can arrange the word SMILE in 120 different ways.
Please help with a rational functions equation question.
Answers
Write y=x²-4x-1 in vertex form.
Answers
Answer:
y = (x - 2)² - 5
Step-by-step explanation:
y = x² - 4x - 1
using the method of completing the square
add/subtract ( half the coefficient of the x- term)² to x² - 4x
y = x² + 2(- 2)x + 4 - 4 - 1
y = (x - 2)² - 5 ← in vertex form