We want to divide 4x³ + 2x - 3 by x - 3 with the long division method
First, we rewrite the polynomial as:
4x³ + 0x² + 2x - 3
Them we divide the first term of the dividend by the highest term of the divisor:
4x²
x - 3 |4x³ + 0x² + 2x - 3
Then we multiply the divisor by this result:
| 4x²
x - 3 |4x³ + 0x² + 2x - 3
4x³ - 12x²
Now we subtract this result from the dividend:
| 4x²
x - 3 |4x³ + 0x² + 2x - 3
4x³ - 12x²
|12x² + 2x - 3
Now we can repeat all the previous steps using the last result as dividend:
| 4x² + 12x
x - 3 | 12x² + 2x - 3
12x² - 36x
|38x - 3
And we repeat these steps once more:
4x² + 12x + 38
x - 3 | 38x - 3
34x - 102
|99
The final term is the remainder
Then, we have:
4x³ + 2x - 3 = (x - 3)*(4x² + 12x + 34) + 99
A biologist wants to determine the effect of a new fertilizer on tomato plants. What would be the control?All PlantsPlants not treated with the Fertilizer.The FertilizerPlants treated with the Fertilizer.
Remember that the control variable does not change in the experiment or in any study.
So the control here will be all the plants because you can not control the type of the plant.
Answer:b
Step-by-step explanation:
You flip a coin 3 times. Let's fill out a tree diagram to see allof the possible outcomes.What is the probabilitythat you will flip a headsall 3 times?
Answer
Explanation
Given:
You flip a coin 3 times.
To determine the tree diagram to see all of the possible outcomes when you flip a coin 3 times, we first note that we can get either Heads or Tails. So the tree diagrams is shown below:
The possible outcomes would be:
HHH, HHT,HTH,HTT,THH,THT,TTH,TTT
We can notice that there are 8 possible outcomes. But, the number of cases to get exactly 3 heads is just 1.
Hence, the probability of getting 3 heads is:
Probability = 1/8 =0.125
Therefore, the probability that you flip a heads all 3 times is 0.125.
Find the a) domain, b) x-intercept and c) y - intercept: 1) f(x) = 3x-12 2x+4 2x+9 2) f(x) = x²-16 3) f(x) = x2-9
Answer
Check Explanation
Explanation
Before we start answering, we should first explain what these terms stand for
- Domain
The domain of a function refers to the values of the independent variable (x), where the dependent variable [y or f(x)] or the function has a corresponding real value. The domain is simply the values of x for which the output also exists. It is the region around the x-axis that the graph of the function spans.
- x-intercept
The x-intercept refers to the value of x when the value of y or f(x) = 0, that is, the value of x at which the graph of the function crosses the x-axis. To obtain this, we just solve for x when y or f(x) = 0
- y-intercept
The y-intercept refers to the value of y or f(x) when the value of x = 0, that is, the value of y when it crosses the y-axis. To obtain this, we just substitute 0 for x and solve for f(x)
We can now solve
[tex]f(x)=\frac{3x-12}{2x+4}[/tex]- For the domain, we can tell that x can take on any real number value and provide an answer for f(x) except the point where the denominator of this is equal to 0. At the point where the denominator is 0, f(x) will tend to infinity.
2x + 4 = 0
2x = -4
Divide both sides by 2
(2x/2) = (-4/2)
x = -2
So, the domain of this function is all real number values for x except x = -2
- For the x-intercept, we just solve for x when f(x) = 0
[tex]\begin{gathered} f(x)=\frac{3x-12}{2x+4} \\ \text{when f(x) = 0} \\ 0=\frac{3x-12}{2x+4} \\ \text{Cross multiply} \\ 3x-12=0\times(2x+4) \\ 3x-12=0 \\ 3x=12 \\ \text{Divide both sides by 3} \\ \frac{3x}{3}=\frac{12}{3} \\ x=4 \end{gathered}[/tex]The x-intercept = 4.
In coordinate form, the x-intercept is (4, 0)
- For the y-intercept, we just solve for f(x) when x = 0
[tex]\begin{gathered} f(x)=\frac{3x-12}{2x+4} \\ \text{when x = 0} \\ f(x=0)=\frac{3(0)-12}{2(0)+4} \\ f(x)=\frac{0-12}{0+4}=\frac{-12}{4}=-3 \end{gathered}[/tex]The y-intercept = -3
In coordinate form, the y-intercept is (0, -3)
For the second question
[tex]f(x)=\frac{2x+9}{x-3}[/tex]- The domain will be all real number values of x except when (x - 3) = 0
x - 3 = 0
x = 3
The domain will be all real number values of x except when x = 3.
- For the x-intercept, we just solve for x when f(x) = 0
[tex]\begin{gathered} f(x)=\frac{2x+9}{x-3} \\ when\text{ f(x) = 0} \\ 0=\frac{2x+9}{x-3} \\ \text{Cross multiply} \\ 2x+9=0 \\ 2x=-9 \\ x=-4.5 \end{gathered}[/tex]The x-intercept = -4.5
In coordinate form, the x-intercept = (-4.5, 0)
- For the y-intercept, we solve for f(x) when x = 0
[tex]\begin{gathered} f(x)=\frac{2x+9}{x-3} \\ \text{when x = 0} \\ f(x=0)=\frac{0+9}{0-3}=\frac{9}{-3}=-3 \end{gathered}[/tex]The y-intercept = -3
In coordinate form, the y-intercept is (0, -3)
For the third question
[tex]f(x)=\frac{x^2-16}{x^2-9}[/tex]- For the domain, we first solve for when x² - 9 = 0
x² - 9 = 0
x² = 9
x = ±√9
x = ±3
x = +3 or -3
The domain of this function is all real number values of x except when x = +3 and x = -3
- For the x-intercept, we solve for x when f(x) = 0
[tex]\begin{gathered} f(x)=\frac{x^2-16}{x^2-9} \\ \text{when f(x) = 0} \\ 0=\frac{x^2-16}{x^2-9} \\ \text{Cross multiply} \\ x^2-16=0 \\ x^2=16 \\ x=\pm\sqrt[]{16} \\ x=\pm4 \\ x=+4_{} \\ or\text{ x = -4} \end{gathered}[/tex]The x-intercepts are at -4 and +4.
In coordinate form, the x-intercept are (-4, 0) and (4, 0)
- For the y-intercept, we solve for f(x) when x = 0
[tex]\begin{gathered} f(x)=\frac{x^2-16}{x^2-9} \\ \text{when x = 0} \\ f(x)=\frac{0-16}{0^{}-9}=\frac{-16}{-9}=1.7778 \end{gathered}[/tex]The y-intercept = (16/9) = 1.7778
In coordinate form, the y-intercept is (0, 1.7778)
Hope this Helps!!!
If g(x)=f(x)−1, then g(x) translates the function f(x) 1 unit _[blank]_.Which word correctly fills in the blank in the previous sentence?A. upB. leftC. downD. right
To answer this question, we need to remember the rules of transformations of functions, the rules are shown below:
From the table, we notice that if we subtract a number we are performing a vertical translation down.
Therefore, the correct word to fill the blank is down and the correct option is C.
i need help with this question parts 3 - 7
Answer:
i also don't know
Step-by-step explanation:
i also don't know..,......
The equation y + 2 = 5(x – 4) represents a linear function. What is the y-intercept of the equation?
Answer:
-22
Step-by-step explanation:
Hello!
We can convert it into Slope-Intercept form: [tex]y = mx + b[/tex]
m = slopeb = y-interceptConverty + 2 = 5(x - 4)y + 2 = 5x - 20y = 5x - 22The y-intercept is -22.
Question 2.Draw diagrams to represent the following situations.a. The amount of flour that the bakery used this month was a 50% increase relative to last month.b. The amount of milk that the bakery used this month was a 75% decrease relative to last month.
Given:
a. The amount of flour that the bakery used this month was a 50% increase relative to last month.
So, we will draw a diagram that represents the situation
As shown, for last month, we have drawn a rectangle divided into two equal areas, each one represents 50%
this month was a 50% increase, so, we have drawn 3 areas which represent 50% increase
b. The amount of milk that the bakery used this month was a 75% decrease relative to last month.
As shown, for last month, we have drawn a rectangle with four equal areas
75% decrease, so, we have to remove 3 areas to make the remaining = 25%
So, the difference will give a 75% decrease
8. Three consecutive even numbers have a sum where one half of that sum is between 90 and 105. a. Write an inequality to find the three numbers. Let n represent the smallest even number. b. Solve the inequality. a. (n+(n+2)+(n+4) < −90 or −(n+(n+2)+(n+4)) > 105 b. n-62 or n > 68 a. 90 < 2(n + (n + 2) + (n + 4)) < 105 b. 13 ≤ n ≤ 15.5 a. 90 < ¹² (n + (n +2)+(n+ 4))
Given:
Three consecutive even numbers have a sum where one half of that sum is between 90 and 105.
Required:
To write an inequality to find the three numbers and to solve the inequality.
Explanation:
(a)
Three consecutive even numbers have a sum where one half of that sum is between 90 and 105.
[tex]90<\frac{1}{2}(n+(n+2)+(n+4))<105[/tex](b)
[tex]undefined[/tex]What’s 1/5 + 1/2 ? Pls help me
We need to calculate 1/5 + 1/2:
H = 1/5 + 1/2
Then: H = 7/10
Yes or no to tell wether the fact the fraction is equivalent to this decimal __(4.05)_____________________________________Is the following fractions equal to the one decimal listed? 405/99401/9981/33802/198
802/198 is equal to 4.0505
a loaf of sandwich bread contains 24 slices. which of these tables correctly shows the ratios of different of loaves of bread to the number of total slices they contain
We have that a loaf of sandwich bread contains 24 slices, then we have that the ratio must be constant between the loaves and the slices. If we have 1 loaf: 24 slices, this ratio must be equal in the table.
Therefore, we have that the only table that follows this is the table that has:
If we have:
2/48 = 1/24
3/72 = 1/24
4/96 = 1/24
The ratio of loaves to slices is the same, that is, 1 / 24.
What is the solution to the equation below? √x+9 = 11 O A. x= 2 O B. X= √ O C. x = 42 D. x = 4
answer: D. x = 4
URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
Answer:
√52
Step-by-step explanation:
[tex] \sqrt{ {(4 - ( - 2))}^{2} + {(1 - ( - 3))}^{2} } [/tex]
[tex] \sqrt{ {6}^{2} + {4}^{2} } = \sqrt{36 + 16} = \sqrt{52} [/tex]
What is the value of the expression below when w = 3?3w² - 6w - 4
ANSWER:
5
STEP-BY-STEP EXPLANATION:
We have the following expression:
[tex]3w^2-6w-4\:[/tex]We substitute the value of w, when it is equal to 3, just like this:
[tex]\begin{gathered} 3\left(3\right)^2-6\left(3\right)-4\: \\ \\ 3\cdot \:9-6\left(3\right)-4 \\ \\ 27-18-4 \\ \\ 5 \end{gathered}[/tex]The value of the expression is equal to 5
Mai is filling her fish tank water flows into the tank at a constant rate. 2.&- 0.5 1.6 time (minutes) water (gallons) 0.5 0.8 1 x1.6 1.6 x1.6 4.8 25 G 3 40 1) How many gallons of water will be in the fish tank after 3 minutes? Explain or show your reasoning. 2) How long will it take to fill the tank with 40 gallons of water? Explain or show your reasoning. 3) What is the constant of proportionality? What does it tell us about this situation?
Given
x = 0.5; y = 0.8
The constant of proportionality has to be calculated to estimate the other values.
The constant of proportionality "k" determines the relation of x and y, which can be represented as: y = kx.
So, in this exercise,
[tex]\begin{gathered} 0.8=k\cdot0.5 \\ \frac{0.8}{0.5}=k \\ k=1.6 \end{gathered}[/tex]y = 1.6y
(1) From this, we can estimate the value of y when x = 3.
[tex]\begin{gathered} y=1.6\cdot3 \\ y=4.8\text{gallons} \end{gathered}[/tex](2) If we want how long it will take to fill the tank with 40 gallons:
[tex]\begin{gathered} 40=1.6\cdot x \\ \frac{40}{1.6}=x \\ 25=x \end{gathered}[/tex]It will take 25 minutes.
(3) Finally, the constant of proportionality is 1.6 (as calculated above).
It tells us that the ratio between the gallons water of water and time. In other words, it tells us that for each 1 minute, 1.6 gallons are filled.
Use the sequence below to complete each task. 34, 25, 16, 7, ... a. Identify the common difference (a). b. Write an equation to represent the sequence. c. Find the 20th term (azo)
Problem
Solution
We have the following sequence of terms 34,25,16,7,....
Part a
The common difference for this case would be:
25-34= -9
16-25=-9
7-16= -9
Then the answer for part a would be -9
Part b
We want to write the following form:
an = a1 + (n-1) d
For this case d=-9, a1= 34
And then we can write the genral expression like this:
an = 34 + (n-1 ) (-9)
With n = 1,2,3,4....
Part c
In order to find the 20 th term we can replace n =20 and we got:
a20= 34 + (20-1) (-9) = 34-171= -137
i need help please and thank youthere are 2 pictures bc i couldn’t get it all in 1!
we have the system
y < -2x^2+4x-2
The solution for this inequality is the shaded area below the vertical dashed parabola
and
[tex]y\ge\frac{2}{3}x-3[/tex]the solution for this inequality is the shaded area above the solid line y=(2/3)x-3
therefore
the solution for this system of inequalities
Is the shaded area below the vertical dashed parabola y=-2x^2+4x-2 and above the solid line y=(2/3)x-3
see the attached figure to better understand the problem
For each value of y, determine whether it is a solution to y÷2 = 6.
y
6
16
10
14
Is it a solution?
Answer:
None are solutions.
Step-by-step explanation:
Divide each value of y by 2 and see if it equals 6. If it does, then it is a solution. If it doesn't then it isn't a solution.
6 ÷ 2 = 6
3 ≠ 6
not a solution
16 ÷ 2 = 6
8 ≠ 6
not a solution
10 ÷ 2 = 6
5 ≠ 6
not a solution
14 ÷ 2 = 6
7 ≠ 6
not a solution
Solve the equation 3x - 4y = 16 for x.16 4OA. X-B. x1643C. X= 4y + 16O D. x= 3(16+47)
To solve for x, first, we add 4y to the equation:
[tex]\begin{gathered} 3x-4y+4y=16+4y, \\ 3x=16+4y\text{.} \end{gathered}[/tex]Now, we divide by 3:
[tex]\begin{gathered} \frac{3x}{3}=\frac{16+4y}{3}, \\ x=\frac{16+4y}{3}\text{.} \end{gathered}[/tex]Answer:
[tex]x=\frac{16+4y}{3}\text{.}[/tex]35+3(8-4)
(please explain how you did it)
Answer:47
Step-by-step explanation: First multiply 3x8=24 then subtract 3x4=12 from it. Which will get you 12 then add 35 to 12 which will get you 47.
35 + 3(8-4) = ?
Do the parentheses first : 8 - 4 = 4
= 35 + 3(4)
Then multiply- that's the one that is in parentheses : 3 x 4 = 12
= 35 + 12
Then just straight up add : 35 + 12 = 47
35 + 3(8-4) = 47
So ? = 47
Susan is putting 11 colored lightbulbs into the string of lights that are three blue light bulbs to yellow light bulbs and six orange light bulb how many distinct orders of lightbulbs are there is two lightbulbs of the same color are considered identical(not distinct)
Using combinations, the number of ways is 36,036.
How to find a number of ways?Combinations are a method of calculating the total outcomes of an event where the order of the outcomes is irrelevant. We will use the formula nCr = n! / r! * (n - r)! to calculate combinations, where n represents the total number of items and r represents the number of items chosen at a time.How many distinct orders of light bulbs are there?
Since we have given thatNumber of white light bulbs = 5Number of orange light bulbs = 6Number of blue light bulbs = 2Total number of light bulbs = 13So, the number of distinct orders of light bulbs if two bulbs of the same color are considered identical.
Therefore, using combinations, the number of ways is 36,036.
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A person standing close to the edge on top of a 72-foot building throws a ball vertically upward. The
quadratic function h(t) = − 16t² + 84t+ 72 models the ball's height about the ground, h(t), in feet, t
seconds after it was thrown. Please help me identify the height of the ball in feet and how many seconds it takes to hit the ground
The height of the ball was 182.25 feet and it took 6 seconds for the ball to hot the ground.
Given that:-
Quadratic equation:-
[tex]h(t)=-16t^2+84t+72[/tex]
We have to find the ball's height, in feet and how many seconds it takes to hit the ground.
Differentiating the given equation, we get
dh/dt=-32t + 84
Putting dh/dt = 0, we get,
-32t + 84 = 0
t = 84/32 = 21/8 seconds
Putting t = 21/8, we will get the maximum height that the ball will reach.
Hence,
[tex]h(21/8)=-16(21/8)^2+84(21/8)+72[/tex]
h(21/8) = -16(441/64)+84(21/8)+72 = -110.25 + 220.50 +72 = 182.25 feet
At h = 0, the ball will have hit the ground.
Hence, we can write,
[tex]h(t) = 0 = -16t^2+84t+72[/tex]
Dividing -4 from the equation, we get,
[tex]4t^2-21t-18=0[/tex]
Using middle term split theorem, we can write,
[tex]4t^2-24t+3t-18=0\\[/tex]
4t(t-6)+3(t-6) = 0
(t-6)(4t+3) = 0
Hence, the values of t can be:-
t = 6, -3/4
As the time cannot be negative, hence the ball will hit the ground after 6 seconds.
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A COMPUTER OPERATOR MUST SELECT FOUR JOBS AMOUNG 10 AVAILABLE JOB WAITING TO BE COMPLETED. HOW MANY DIFFERENT ARRANGMENTS CAN BE MADE?
This is a problem based on permutations. We must select four jobs among ten jobs and see how many arrangments can be made.
The formula for the number of permutations is:
[tex]P(n,r)=\frac{n!}{(n-r)!}.[/tex]Where:
• n = total number of jobs = 10,
,• r = number of jobs to be selected = 4.
Replacing these data in the formula above, we get:
[tex]P(10,4)=\frac{10!}{(10-4)!}=\frac{10!}{6!}=\frac{10\cdot9\cdot8\cdot7\cdot6!}{6!}=10\cdot9\cdot8\cdot7=5040.[/tex]Answer5040
A triangle can have sides 2,3 and 5. True or false
First, remember that:
The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
In this problem, notice that:
2 + 3 is not greater than 5.
3 + 5 is not greater than 2.
2 + 5 is not greater than 3.
So, the statement is false. A triangle can't have sides 2
Someone please help me with this
Polynomial equations are those created using exponents, coefficients, and variables. It may have several exponents, with the higher one being referred to as the equation's degree.
How are polynomial equations solved?Polynomial equation illustration
Write a polynomial equation in standard form before attempting to solve it. Factor it, then set each variable factor to zero after it has reached zero. The original equations' answers are the solutions to the derived equations. Factoring cannot always be used to solve polynomial equations.
6h²(5 + 9h)(5 - 9h)
6h²(9h + 5)(5 - 9h)
6h²(9h + 5)(-9h + 5)
Distribute6h²(9h + 5)(-9h + 5)
54(-9h +5)h³ + 30(-9h + 5)h²
(-486h)4 + 270h³+30(-9h+5)h²
(-486h)4 + 270h³-270h³+150h²
(-486h)4 + 150h²
Solution(-486h)4 + 150h²
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#3b. Two bicyclists ride in the same direction. The first bicyclist rides at a speed of 8 mph.One hour later, the second bicyclist leaves and rides at a speed of 12 mph. How long will thesecond bicyclist have traveled when they catch up to the first bicyclist?I’m
Answer:
2 hours
Explanation:
[tex]\text{Speed}=\frac{Dis\tan ce}{Time}[/tex]The first bicyclist rides at a speed of 8 mph. Therefore:
[tex]\begin{gathered} 8=\frac{d}{t} \\ \implies d=8t \end{gathered}[/tex]One hour later, the second bicyclist leaves and rides at a speed of 12 mph.
Therefore, the time of the second bicyclist = (t-1) hours.
Therefore:
[tex]\begin{gathered} 12=\frac{d}{t-1} \\ \implies d=12(t-1) \end{gathered}[/tex]Since the second bicyclist will catch up to the first bicyclist, the distance traveled will be the same.
So:
[tex]\begin{gathered} 8t=12(t-1) \\ 8t=12t-12 \\ 8t-12t=-12 \\ -4t=-12 \\ \frac{-4t}{-4}=\frac{-12}{-4} \\ t=3\text{ hours} \end{gathered}[/tex]Therefore, the second bicyclist will have traveled for:
(t-1) = (3-1) =2 hours.
How do you solve the system of equations by graphing? y=-3x/2 + 6y=5x - 7
The given system of equations are
y=-3x/2 + 6
y=5x - 7
We would substitute values for x into the equations and find the corresponding y values. These values would be plotted on a graph. Where the lines of both equations meet would represent the solution of the system of equations.
For the first equation,
y = - 3x/2 + 6
if x = 0, y = 3 * 0/2 + 6 = 6
If x = 1, y = - 3 * 1/2 + 6 = 4.5
if x = 2, y = - 3 * 2/2 + 6 = 3
We would plot these values on the graph
For the second equation,
y = 5x - 7
if x = 0, y = 5 * 0 - 7 = - 7
If x = 1, y = 5 * 1 - 7 = - 2
if x = 2, y = 5 * 2 - 7 = 3
We would plot these values on the graph
The diagram of the graph is shown below
Looking at the graph, at the point where both lines meet,
x = 2, y = 3
Thus, the solution is (2,3)
Answer the following question by creating an exponential equation? 1. On the day a rumor was started, 4 people knew about the rumor. The next day, and onward, the number of people who knew about the rumor doubled. On what day did 800 people know about the rumor?
Given
Series of numbers
first day = 4
second day = 8
Third day = 16
4, 8, 16, ...
From the exponential sequence
First term a = 4
common ratio r = second term/first term
= 8/4 = 2
r = 2
[tex]undefined[/tex]n is equal to 30% of 600
Given:
[tex]n=\frac{30}{100}\times600[/tex]Solve the expression,
[tex]\begin{gathered} n=\frac{30}{100}\times600 \\ n=30\times6 \\ n=180 \end{gathered}[/tex]Answer: n = 180
You begin at the origin and travel 5 units to the right and then vertically 3 units. You will be at what ordered pair?
In a x-y coordinate plane of you moves to the right it increase the value of x and if you moves vertically it increases the value of y.
The ordered pair is (x,y)
For the given moves: (5,3)