The solution to the questions are:
The expression that represents the factoring pattern is (a + b)(a² - ab + b²)The solutions of the equation x³ + 2x² - 9x = 18 are x = -3, x = 3 and x = -2The other roots are x = -3 and x = 2The result of subtracting the expressions is - x³ + x² + 2x - 2The largest multiplicity is 1Factoring pattern for the sum of cubesAs a general rule, the sum of cubes x³ and y³ is:
x³ + y³= (x+y)(x² - xy + y²)
Replace x with a and y with b
a³ + b³= (a + b)(a² - ab + b²)
Hence, the expression that represents the factoring pattern is (a + b)(a² - ab + b²)
The solutions of the polynomialThe equation is given as:
x³ + 2x² - 9x = 18
Subtract 18 from both sides
x³ + 2x² - 9x - 18 = 0
Factorize the expression
x²(x + 2) - 9(x + 2) = 0
Factor out x + 2
(x²- 9)(x + 2) = 0
Express x²- 9 as a difference of two squares
(x + 3)(x - 3)(x + 2) = 0
Split
(x + 3) = 0 or (x - 3) = 0 or (x + 2) = 0
Remove brackets
x + 3 = 0 or x - 3 = 0 or x + 2 = 0
Solve for x
x = -3, x = 3 and x = -2
Hence, the solutions of the equation x³ + 2x² - 9x = 18 are x = -3, x = 3 and x = -2
The other roots of the polynomialThe polynomial equation is given as:
0 = x³ + 2x² - 5x - 6
Rewrite as:
x³ + 2x² - 5x - 6 = 0
Factorize the expression on the left-hand side
(x + 3)(x + 1)(x - 2) = 0
Split
x + 3 = 0 or x + 1 = 0 or x - 2 = 0
Solve for x
x = -3 or x = -1 or x = 2
Hence, the other roots are x = -3 and x = 2
Subtract the expressionsThe expression is given as:
(x² - 1) - (x³ - 2x + 1)
Expand
x² - 1 - x³ + 2x - 1
Collect like terms
- x³ + x² + 2x - 1 - 1
Evaluate the like terms
- x³ + x² + 2x - 2
Hence, the result of subtracting the expressions is - x³ + x² + 2x - 2
The largest multiplicity of the polynomialThe polynomial is given as:
y = (x² - 1)(x + 2)(x + 4)
Express x² - 1 as a difference of two squares
y = (x - 1)(x + 1)(x + 2)(x + 4)
The power of each factor in the above expression is 1.
This means that the largest multiplicity is 1
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What kind of relationship is expressed below?
5x+3=7
a. equation
b. function
c. inequality
Answer:
a. equation
Step-by-step explanation:
The LHS is equal to the RHS
Two or more expressions with an Equal sign is called as Equation. Hence Equation is the relationship of 5x+3=7.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given is 5x+3=7
It is a equation because the left hand side is equal to the RHS side
It has a equal sign.
Where as in expressions there will be no equal sign.
Expression has only numbers, operators and variables.
5x+3=7 is not a function as it has no y variable or other variable.
Hence equation is the relationship of 5x+3=7.
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Write 0.15 as a fraction in the simplest form.
Answer:
3/20
Step-by-step explanation:
0.15 = 15/100
This is not simplified though :
15/100 ÷ 5/5 = 3/20
This is simplified
Hope this helped and brainliest please.
What is x in the figure?
im not sure I'd need to see the figure
Suppose that the water level of a river is 4 feet and is increasing at a rate of 0.15 foot per day. Write the
variable expression to represent the depth of the river in terms of d, the number of days.
Answer:
The answer would be 4+0.15d.
Step-by-step explanation:
I hope this helps! :) I am so sorry if this is not right!
what is the volume of a cube if the diagonal of one side is 5sqrt(2)
Must include diagram
The what is the volume of a cube if the diagonal of one side is 5sqrt(2) is V = 125 cubic units
What is a square?A square is a shape with 4 sides
Let the side of the square be x units. If the length of the diagonal is 5√2, the value of x can be expressed using the pythagoras theorem as shown;
x² + x² = (5√2)²
2x² = 25(2)
x² = 25
x = 5 units
Determine the volume
V = x³
V = 5³
V = 125 cubic units
Hence the what is the volume of a cube if the diagonal of one side is 5sqrt(2) is V = 125 cubic units
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How many different sequences of 3 playing cards (from a single 52-card deck) exist?
22,100
140,608
132,600
24,804
There 1,32,600 possibilities to withdrawn 3 different sequence of playing cards from 52 cards.
What is Permutations?A permutation of a set is, loosely speaking, an arrangement of its members into a sequence or linear order, or if the set is already ordered, a rearrangement of its elements.
Here, total number of cards = 52
Number of Withdrawn cards = 3
Possibilities of different sequences of 3 playing cards = 52 X 51 X 50
= 132600
Thus, there 1,32,600 possibilities to withdrawn 3 different sequence of playing cards from 52 cards.
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Answer:
132,600
Step-by-step explanation:
To determine the number of different sequences of 3 playing cards from a 52-card deck, we can use the formula for permutations, which is given by:
P(n, k) = n! / (n-k)!
Where n is the total number of items (in this case, the number of cards in the deck) and k is the number of items chosen (in this case, 3 cards).
Plugging in the values:
n = 52 (total number of cards in the deck)
k = 3 (number of cards chosen)
P(52, 3) = 52! / (52-3)!
Calculating the factorial terms:
52! = 52 x 51 x 50 x ... x 3 x 2 x 1
(52-3)! = 49! = 49 x 48 x ... x 3 x 2 x 1
Simplifying the equation:
P(52, 3) = 52 x 51 x 50
P(52, 3) = 132,600
Therefore, there are 132,600 different sequences of 3 playing cards that can be formed from a single 52-card deck.
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Consider the graph of the function . f(x) = ln x
Answer:
Behold! Try using Desmos or something
#PlatoAccuracyMatters
#WhaddyaMeanPlatoLives?
Step-by-step explanation:
The functions and their matching properties are:
[tex]h(x) = f(x - \frac{1}{2}) \to[/tex] x-intercept at (1.5,0)[tex]j(x) = f(x) - \frac{1}{2} \to[/tex] vertical asymptote x = 0[tex]g(x) = -\frac 12f(x - 2) \to[/tex] function decreases as x increasesHow to match the functions with their properties?To do this, we start by plotting the graphs of the functions h(x), j(x) and g(x)
Next, we list out the properties from the graphs
From the graphs of the functions (see attachment), we have the following highlights:
[tex]h(x) = f(x - \frac{1}{2})[/tex] has an x-intercept of (1.5,0)[tex]j(x) = f(x) - \frac{1}{2}[/tex] has a vertical asymptote of x = 0The function [tex]g(x) = -\frac 12f(x - 2)[/tex] decreases as x increasesRead more about functions at:
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The simplified ratio of 32/12 is:
Answer:
8/3
Divide both sides by the GCF, 4.
32 ÷ 4 = 8
12 ÷ 4 = 3
James surveyed 120 voters at random out of 12,600
registered voters in his town. based on the results of the
survey, what is the total number of registered voters
expected to vote for miss frizzle in the upcoming election
The expected number of votes for Miss Frizzle in the election is 4725
How to determine the expected number of votes for Miss Frizzle?The data that completes the question is as follows:
Miss Frizzle = 45
Miss Reynolds = 75
The expected number of votes for Frizzle is:
Frizzle = 45/120 * 12600
Evaluate
Frizzle = 4725
Hence, the expected number of votes for Miss Frizzle in the election is 4725
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Which equation represents a line that is parallel to the line that passes through the points (-6,9) and (7,-17)?
Answer:
y = -2x-3
Step-by-step explanation:
Slope = - 2 C = - 3y =-2x-3Working alone, steve can complete a task in 6 hours. working simultaneously at their respective constant rates, he and mike can complete the same task in 4 hours. how long will it take mike working alone to complete the task
Answer:
It would take him 4 hrs.
Step-by-step explanation:
Hope this helps!
Time taken by mike alone to finish the Task is 12 hours.
steve can complete a task in 6 hours.
he and mike can complete the same task in 4 hours.
What is rate of change?
Rate of change is defined as the change in value with rest to the time is called rate of change.
Here,
Rate of steve finishing task per hour = 1/6
Rate at which both finishes the task per hour = 1/4
Rate at which mike finishes the task per hour = M
now
M = 1/4-1/6
M = 3-2/12
M = 1/12
here, mike finishes his task at 12 hours
Thus, Time taken by mike alone to finish the Task is 12 hours.
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Which statement best describes the function? Help. Please
The correct answer is option c. Which is the function is increasing when x is greater than zero.
What is a function?A function in mathematics set up a relationship between the dependent variable and independent variable. on changing the value of the independent variable the value of the dependent variable also changes.
In the graph, we can see that at the origin the graph becomes zero. When the graph proceeds rightwards the value of the function is increasing as the value of x is increasing.
Therefore the correct answer is option c. Which is the function is increasing when x is greater than zero.
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What is the probability of a flowering plant bearing flowers in january if it is a tulip? a. 68% b. 72% c. 76% d. insufficient data
The probability of a flowering plant bearing flowers in January if it is a tulip is 68%.
How to find the Probability?
From the attached table, we see the respective probabilities of each flower bearing flowers in January as;
Tulip = 68%
Anemon = 81%
Manzanita = 77%
Peony = 70%
Fuschia Flowering currant = 74%
Total = 76%
Thus, it is clear that the probability of a flowering plant bearing flowers in January if it is a tulip is 68%.
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Answer: insufficient data
Step-by-step explanation: Plato 100% right
evaluate the expression and enter your answer in the box below |98|
Hi student, let me help you out! :)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
We are asked to evaluate [tex]\pmb{|98|}[/tex].
[tex]\triangle~\fbox{\bf{KEY:}}[/tex]
The notation |x| denotes absolute value.The absolute value of a number is its distance from zero.
Absolute value is always positive; distances can't be negative, right?
So we need to find the absolute value of 98, which is:
[tex]\star~\star\mathrm{98}~\star~\star[/tex]
[tex]\ddot\bigstar[/tex] Remember this...
[tex]\fbox{The\;absolute\;value\;is\;a\;number's\;distance\;from\;zero}[/tex]
Hope it helps you out! :D
Ask in comments if any queries arise.
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~Just a smiley person helping fellow students :)
Estimate the amount of time she spent at ballet to the nearest hour
The amount of time that Lila spent at Yoga and Ballet are approximately equal to 26 hours and 13 hours respectively.
How to calculate the time spent?First of all, we would calculate the amount of time that Lila spent at Yoga by multiplying the total time spent by the percentage of time spent on Yoga as follows:
Yoga time = 92 × 28/100
Yoga time = 92 × 0.28
Yoga time = 25.76 ≈ 26 hours.
Part B.Next, we would calculate the amount of time that Lila spent at Ballet by multiplying the total time spent by the percentage of time spent on Ballet as follows:
Ballet time = 92 × 14/100
Ballet time = 92 × 0.14
Ballet time = 12.88 ≈ 13 hours.
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Complete Question:
The circle graph shows how Lila spent her after-school time during the month of October. Lila’s Activities Part A If Lila spent a total of 92 hours on these activities in the month of October, estimate the amount of time she spent at Yoga, to the nearest hour.
Part B. Estimate the amount of time she spent at Ballet, to the nearest hour.
The graph below shows the relationship between the number of months different students practiced tennis and the number of matches they won:
Part A: What is the approximate y-intercept of the line of best fit and what does it represent?
Part B: Write the equation for the line of best fit in the slope-intercept form and use it to predict the number of matches that could be won after 13 months of practice. Show your work and include the points used to calculate the slope.
Answer:
(a) (i) y-intercept = 3
(ii) Represents that the team won 3 matches without any practice.
(b) (i) Equation: y = 1.8x + 3,
(ii) 26 matches won
The approximate y-intercept can be determined by seeing when the best fit line crosses the y axis.
Part AHere the best line crosses the y-axis when y = 3. So coordinates: (0, 3)
Part BTake two best points touching the line: (0,3), (5, 12)
[tex]\sf slope \ (m) = \dfrac{y_2 - y_1}{x_2 - x_1} = \dfrac{12-3}{5-0} = 1.8[/tex]
Equation:
y - y₁ = m(x - x₁)
y - 3 = 1.8(x - 0)
y = 1.8x + 3
So, after 13 months of practice: y = 1.8(13) + 3 = 26.4 ≈ 26 matches won.
#1
The y intercept should represent how much matches the team won without practice
Here its 3
(0,3)#2
(0,3)(5,12)Slope
m=12-3/5m=9/5Equation in point slope form
y-3=9/5xy=9/5x+3After 13 months
y=9/5(13)+3=117/5+3Approximately 26matches
Solve the system of equations using subtraction.
4x - 2y = 10
4x + y = 19
Answer:
y=3 x=4
Step-by-step explanation:
4x - 2y = 10
4x + y = 19
-3y=-9
the 4x canceled out.
y=3
plug in y into one of the equations
4x + 3 = 19
4x=16
x=4
Hope this helps!
If not, I am sorry.
Answer:
(4, 3 )
Step-by-step explanation:
4x - 2y = 10 → (1)
4x + y = 19 → (2)
subtract (1) from (2) term by term
(4x - 4x) +y - (- 2y) = 19 - 10
0 + y + 2y = 9
3y = 9 ( divide both sides by 3 )
y = 3
substitute y = 3 into either of the 2 equations and solve for x
substituting into (2)
4x + 3 = 19 ( subtract 3 from both sides )
4x = 16 ( divide both sides by 4 )
x = 4
solution is (4, 3 )
Which equation can be used to solve for x in the following diagram?
The equation we can use to find the value of x in the diagram given is: B. (5x + 30) + 5x = 90.
What are Complementary Angles?Angles that give a sum of 90 degrees when added are referred to as complementary angles.
The angles, (5x + 30) and 5x are complementary angles, since the sum of both gives a right angle (90 degrees).
Therefore, the equation that we can use to find x in the diagram is: B. (5x + 30) + 5x = 90.
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B. Solve the following inequalities and graph their solution sets. Use red or blue marker and ruler for the graph. 1. 3x-7 ≤ 5 Solution:
Answer:
[tex]3x \leqslant 5 + 7 \\ 3x \leqslant 12 \\ x \leqslant 4[/tex]
Step-by-step explanation:
hope it helps
Question 9 of 10
If you vertically compress the absolute value parent function, F(x) = |x|, by
multiplying by 3/4 what is the equation of the new function?
A: G(x)= |x+3/4|
B: G(x)= 3/4 |x|
C: G(x)= |x|-3/4
D: G(x)= |3/4 x|
Answer:
B. g(x) = 3/4|x|
Step-by-step explanation:
Multiplying the function by a number in front will stretch, compress, and/or reflect the function over the x-axis.
So if the number in front is negative that will flip it upside down, over the x-axis.
If the number is greater than 1, the function will be vertically stretched, narrower, slimmer, skinnier, taller.
In this case, the graph is vertically compressed, making it flatter, fatter, wider smashed. In this case is where the number multiplied in front of the parent function is LESS than one.
g(x) = 3/4 |x|
Can someone help me with this please
Answer:
D
Step-by-step explanation:
A function input can only have ONE output value
so the number 5 can't output two different numbers
Five people, each working 8 hours a day, can assemble 400 toys in a 5-day work week. What is the average number of toys
assembled per hour, per person?
A 2
B 4
C 8
D 16
Answer:
A. 2
Step-by-step explanation:
First divide the 400 toys by the 5 people to see how many each did:
400 toys/5 people = 80 toys/person
Next let's see how many hours were worked by multiplying the hours per day by the number of days worked:
5 days x 8 hours/day
40 hours
Now to find how many toys were assembled per hour per person, let's divide the toys/person by the number of hours they each worked:
[tex]\frac{80 toys/person}{40 hours}[/tex]=2 toys/person/hour
The average number of toys per person per hour is 2.
What is Ratio?Ratio is defined as a relationship between two quantities, it is expressed one divided by the other.
Total number of toys assembled = 400
Total days of work = 5
Each person work daily for = 8 hrs
Total number of people = 5
Then, the total toys assembled per day
400/5= 80
The number of hours worked by the 5 workers per day = 8 × 5= 40
So, the number of toys assembled per person per hour = 80 / 40= 2
Hence, the average number of toys per person per hour is 2.
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Describe a situation that can be represented by an equation and a situation that can be represented by an inequality. What features determine how the situation should be represented?
The inequality sign can be used when referring to two quantities that are not the same size.
What is an inequality?An inequality is used to express a condition whereby the two quantities are not the same.
For instance, if we have the same number of students inside and outside a classroom, we can use the equality sign. In a case where we do not have the same number of students inside and outside the classroom, we can use the inequality sign.
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10 1. Use the image below to answer the following questions: Solve for the measurement of A. b. Solve for y. a. C. Solve for x. X 48 Y A
Answer:
see explanation
Step-by-step explanation:
(a)
the sum of the 3 angles in the triangle = 180° , then
∠ A = 180° - 90° - 48° = 180° - 138° = 42°
(b)
using the tangent ratio in the right triangle
tan48° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{y}{10}[/tex] ( multiply both sides by 10 )
10 × tan48° = y , then
y ≈ 11.1 units ( to the nearest tenth )
(c)
using the cosine ratio in the right triangle
cos48° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{10}{x}[/tex] ( multiply both sides by x )
x × cos48° = 10 ( divide both sides by cos48° )
x = [tex]\frac{10}{cos48}[/tex] ≈ 14.9 units ( to the nearest tenth )
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Find the value of x
Answer:
12.04
Step-by-step explanation:
add 8 and 9 by the power of two: 8^2+9^2
that equals to 145
find the square root of 145 and that equals to 12.04
Simplify the expression to yield a quadratic trinomial in standard form.
6x(x-4)-(3x− 2)
Step-by-step explanation:
6x² - 24x - 3x + 2
6x² - 27x + 2
Solve the compound inequality y + 7 ≥ –1 and y∕4 + 3 ≤ 5
A)
6 < y ≤ 32
B)
–8 < y ≤ 8
C)
–8 ≤ y ≤ 8
D)
6 ≤ y ≤ 32
What is the value of a?
A. 12
B. 15
C. 17.25
D. 21.25
Answer:
C 17.25
Step-by-step explanation:
i think aanswer its c
Step 5: to isolate x, multiply both sides by:
To isolate x , multiply both the sides by ( 5/23 )
What is an Equation ?An equation is formed when two algebraic expressions are equated using an equal sign.
The given equation is
(3/5)(x-10) = 18-4x-1
(3/5)x - 6 = 18-4x-1
(3/5)x - 6 = 17-4x
(3/5)x = 23 -4x
(23/5)x = 23
Step 5 says To isolate x , multiply both the sides by (5/23)
x = 5
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Evaluate the expression below when x = 3 54 ÷ 2•3-x²
Answer:
72
Step-by-step explanation:
54/2(3)−3^2
= 54/2(3)−3^2
=72