Factor the expression completely:
x³ - 3x² - 4x + 12
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Related Questions
What is the value of m?
1/3m+3−5/6m=−15
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The value of m is 36
What is equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" symbol and terms on both sides must always be present when writing an equation. Equal treatment should be given to each party. Multiple terms, operators, and variables are not required on each side of an equation.
Given:
1/3m+3−5/6m=−15
Subtract 3 from both sides
1/3m +3 -5m/6 -3= -15-3
Simplify
1/3 m -5m /6 = -18
Now, multiply the LCM
-3m = -108
Divide both side by (-3)
-3m/(-3)= -108/ (-3)
m= 36.
Hence, the value of m is 36.
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What is 3a squared add 7 a
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_________________________________
Note: (3a)² + 7a = (3a)*(3a) + 7a = 9a² + 7a .
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A new shirt costs $14.99. If the shirt is on sale for 1/5 off its price, about how much would you save?
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Work: 14.99 / 5 = 2.99
Justin is redoing his bathroom floor with tiles measuring 6in by 13 in. the floor has an area of 8,500 in². what is the least number of tiles he will need?
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the entire floor has an area of 8500 in^2
so the least number of tiles needed is : 8500/78 = 108.97.....109 tiles are needed
What is the range of the function y=4e^x
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A is your answer
the answer (B) thank me later ;)
What are the necessary criteria for a line to be perpendicular to the given line and have the same y-intercept? The slope is and contains the point (0, 2). The slope is and contains the point (0, −2). The slope is and contains the point (0, 2). The slope is and contains the point (0, −2).
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slope = (0 +4) / (3 + 3) = 4/6 = 2/3
perpendicular so slope = -3/2
line on graph
y = mx + b
0 = 2/3 (3) + b
0 = 2+ b
b = -2
y intercept (0,-2)
answer
The slope is -3/2 and contains the point (0, −2).
Answer: D.)The slope is Negative three-halves and contains the point (0, −2).
Step-by-step explanation:
i got it correct obviously oncrip
Evaluate the numerical expression 36÷14-5-10-7
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the answer to your equation is:
-19.4285714286
Hope this helps :)
what expressions have a value of 32?
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16 x 2 has a value of 32
4² x 2 has a value of 32
hope this helps
Need answer to number six in this photo
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a(t) = -600 + 225tb(t) = 200t
If you equate them, you get -600 + 225t = 200t, which you can simplify to t=24. This means that
a(24)=b(24)=4800
So ana wins; she catches up at 4800m after 24 minutes, which is well before the end of the part.
What number has the same value as 32 tens
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Because 32x10=320
will give BRAINEST
A function has a constant halving time. What type of function does this represent?
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Answer:
Exponential decay
Step-by-step explanation:
The function which has a constant halving time represents the exponential decay or negative growth curve type of function.
What is exponential decay?When the value of one variable of the function is decreased with increase in the number of other variable, then it is called the exponential decay function with constant exponential coefficient.'
It can be given as,
[tex]f(x)=ab^x[/tex]
Here, a is the exponential coefficient.
A function which has a constant halving time is,
[tex]A(t)=A_o\left(\dfrac{1}{2}\right)^{t/h}[/tex]
Here, Ao is the initial time, t is time and h is halving time. This is an exponential decay function.
The function which has a constant halving time represents the exponential decay or negative growth curve type of function.
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What is a degree plolynomial?
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The degree of a polynomial is a very straightforward concept that is really not hard to understand
Definition: The degree is the term with the greatest exponent
Need help finding the limit as x approaches 0 of (x^2-3sin(x)/x)
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[tex] \lim_{x \to 0}\ \dfrac{x^2-3*sin(x)}{x}\\\\ = \lim_{x \to 0}\ \dfrac{x^2}{x}-3* \lim_{x \to 0}\ \dfrac{sin(x)}{x}\\\\ =0-3*1=-3\\\\ [/tex]
The sum of John’s and Matt’s ages is 42. The difference of their ages is 6. If Matt is older than John, what are their ages? Matt is 16 and John is 20. Matt is 30 and John is 14. Matt is 24 and John is 18.
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Now we divide this by two to make it equal
36÷2=18
Since John is younger, he is 18 years old
and Matt is 18+6=24 years old..
There you are all done.. ask me if you need any help understanding this!!
Find the linear function such that f(1)=8 and f(5)=-4
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f(5) = -4, is another way to say, x = 5, y = -4
so, what's the equation of a line that passes through (1, 8) and (5, -4)
[tex]\bf \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ 1}}\quad ,&{{ 8}})\quad % (c,d) &({{ 5}}\quad ,&{{ -4}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{-4-8}{5-1}\implies \cfrac{-12}{4}\implies -3[/tex]
[tex]\bf \stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-8=-3(x-1) \\\\\\ y-8=-3x+3\implies y=-3x+3+8\implies y=-3x+11[/tex]
What is 965,000,000,000,000 in scientific notation?
9.65×10−14
9.65×10−12
9.65×1012
9.65×1014
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Answer:
9.65×10¹⁴
Step-by-step explanation:
The 9 of 9.65 has been moved 14 places to the left to get to its position in 965,000,000,000,000. That is, its value has been multiplied by 10¹⁴.
_____
If you were to write 965,000,000,000,000 in expanded form, you would write it as ...
... 9×10¹⁴ +6×10¹³ +5×10¹² +0×10¹¹ +... +0×10⁰ = 9.65×10¹⁴
The first term of this sum is a clue as to how the number is written in scientific notation,
the answer is 9.65×10¹⁴
x + 4(x + 5) = 40 answer this
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x+4x+20=40
add like terms
5x+20=40
minus 20 both sides
5x=20
divide both sides by 5
x=4
angle LMP and angle PMN are complementary. Find the value of x.
Answers
Complementary means they add to make 90 degrees.
This means 2x+4x=90
2x+4x=90
combine like terms
6x=90
divide 6 from both sides
x=15
Find a quadratic equation with integer coefficients that has the following solution set of {4,4/5}
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Hope this helped!
find two consecutive odd integers if twice the larger, increased by the smaller, equals 85
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3b-12=5b-2 please answer I need for homework!!!!
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-3b -3b
-12=2b-2
+2 +2
-10=2b
/2 /2
b=-5
A play was attended by 173 people. Adult tickets were $5 each and children paid $3 for each ticket the total revenue was $703. How many of each kind of ticket were sold?
Answers
Answer: 81 children and 92 adults
Step-by-step explanation:
To solve the exercise, check the data we have from the question:
Total people: 173
Adult tickets price: $5
Children tickets price: $3
Total revenue: $703
We need to know how many of each kind of ticket were sold. To do so, we can show the data as two equations:
Equation 1:
[tex]TotalRevenue = Adults*5 + Children*3[/tex]
[tex]703=5a+3c[/tex]
Equation 2:
[tex]a+c=173[/tex]
Where a represents adults who attended the event and c represents children who attended the event. We can replace one of the unknown quantities following:
[tex]a=173-c[/tex]
[tex]703=5(173-c)+3c[/tex]
Solving:
[tex]703=865-5c+3c[/tex]
[tex]5c-3c=865-703[/tex]
[tex]2c=162[/tex]
[tex]c=81[/tex]
Then, we replace c on equation 2:
[tex]a=173-81[/tex]
[tex]a=92[/tex]
27x to second power-42x+12 if x=2
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If x = 2:
27(2)^2 - 42(2) + 12
= 27(4) - 84 + 12
= 108 - 72
= 36
will give BRAINEST
Which of these statements is true for
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5 · (6)^x
5 ·(6)^0
5 · 1
5
(0,5)
Hope this helped!
Omar recorded the number of hours he worked each week for a year. Below is a random sample that he took from his data. 13, 17, 9, 21 What is the standard deviation for the data?
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Answer:
standard deviation=4.47
Step-by-step explanation:
We have to find the standard deviation of the data set:
13 17 9 21
Now we calculate the mean of the data .
We know that mean is the average of the data values and is calculated as:
[tex]Mean=\dfrac{13+17+9+21}{4}\\ \\Mean=\dfrac{60}{4}\\\\Mean=15[/tex]
Now we find the difference of each data point from the mean as:
Deviation:
13-15=-2
17-15=2
9-15=-6
21-15=6
Now we have to square the above deviations we obtain:
4 4 36 36
now we calculate the mean of the above sets:
[tex]variance=\dfrac{4+4+36+36}{4}\\ \\Variance=\dfrac{80}{4}\\\\Variance=20[/tex]
now standard deviation is the positive square root of variance
so, standard deviation=√(20)=4.47
Final answer:
To find the standard deviation for Omar's work hours, we first calculate the mean of the data, then compute the squared differences from the mean, sum these, divide by the sample size minus one, and take the square root of this result, which is approximately 5.16 hours.
Explanation:
To calculate the standard deviation for Omar's recorded work hours: 13, 17, 9, 21, we follow these steps:
First find the mean (average) of the sample. Mean = (13 + 17 + 9 + 21) / 4 = 60 / 4 = 15 hours.
Next, subtract the mean from each data point and square the result:[tex](13-15)^2[/tex] = 4,[tex](17-15)^2[/tex] = 4, [tex](9-15)^2[/tex]= 36,[tex](21-15)^2[/tex] = 36.
Now, find the sum of these squared differences: 4 + 4 + 36 + 36 = 80.
Since this is a sample (not the full population), we divide by the sample size minus 1, which is 3: 80 / 3 ≈ 26.67.
Finally, take the square root of this quotient to find the standard deviation: √26.67 ≈ 5.16 hours.
Therefore, the standard deviation for the data is roughly 5.16 hours.
Find the parabola with equation y = ax^2 + bx whose tangent line at (2, 4) has equation y = 8x − 12.
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now, we know the tangent line at (2,4) is y = 8x - 12, now, that's already in slope-intercept form, so, the slope of that tangent at (2,4) is "8" then.
now, that means when x = 2, the slope is 8, so let's use that.
[tex]\bf \left. \cfrac{dy}{dx} \right|_{x=2}\implies 2a(2)+b=\stackrel{\textit{from tangent equation}}{8}\implies 4a+b=8 \\\\\\ 4a=8-b\implies a=\cfrac{8-b}{4}\implies \boxed{a=2-\cfrac{b}{4}}\\\\ -------------------------------\\\\ \begin{cases} x=2\\ y=4\\\\ a=2-\cfrac{b}{4} \end{cases}\implies \stackrel{y = ax^2+bx}{4=\left( \boxed{2-\frac{b}{4}} \right)(2)^2+b(2)}\implies 4=8-b+2b \\\\\\ \boxed{-4=b}\qquad thus\qquad a=2-\cfrac{-4}{4}\implies \boxed{a=3}\\\\ -------------------------------\\\\ y=3x^2-4x[/tex]
We want to get a quadratic equation by knowing its tangent line at a point. Remember that the tangent line is given by the derivative of the equation.
We will find that the parabola is:
y = 3*x^2 - 4*x
We start with the tangent line:
y₂ = 8*x - 12
The slope of this tangent line is equal to the derivative of our parabola evaluated in x = 2.
Our parabola is y = a*x^2 + b*x
Derivating we get:
y' = 2*a*x + b
Then we have:
2*a*2 + b = 8
And we also know that our parabola passes through the point (2, 4), then we must have:
4 = a*2^2 + b*2
Then we have a system of equations:
2*a*2 + b = 8
4 = a*2^2 + b*2
First we can simplify the equations:
4*a + b = 8
4 = 4*a + 2*b
We can isolate 4*a in the first equation to get:
4*a = 8 - b
Now we can replace it in the second equation:
4 = (8 - b) + 2*b
4 = 8 + b
4 - 8 = b
-4 = b
Now that we know the value of b, we can use
4*a = 8 - b
4*a = 8 + 4 = 12
a = 12/4 = 3
Then the equation of the parabola is:
y = 3*x^2 - 4*x
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A deck of cards is shuffled. what is the chance that the top card is the king of spades and the bottom card
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The probability of getting the king of spades as the top card and the bottom card of a shuffled deck depends on whether the cards are picked with or without replacement.
Explanation:The probability of getting the king of spades as the top card and the bottom card of a shuffled deck depends on whether the cards are picked with or without replacement. If the cards are picked without replacement, the probability will be different than if they are picked with replacement.
If the cards are picked without replacement, the probability of getting the king of spades as the top card is 1/52. This is because there is only one king of spades in a deck of 52 cards. After the king of spades is picked as the top card, there are 51 cards left in the deck. The probability of getting the king of spades as the bottom card is also 1/51 because there is only one king of spades left in the deck.
If the cards are picked with replacement, the probability of getting the king of spades as the top card is still 1/52, but the probability of getting the king of spades as the bottom card is also 1/52. This is because each card is put back into the deck and reshuffled before the next card is picked, so the probabilities for each card remain the same.
In this problem, y = c1ex + c2e−x is a two-parameter family of solutions of the second-order de y'' − y = 0. find a solution of the second-order ivp consisting of this differential equation and the given initial conditions. y(0) = 1, y'(0)= 8
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Use the change of base formula to compute
log46
.
Round your answer to the nearest thousandth.
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A brownie recipe asks for one and one quarter times as much sugar as chocolate chips. If one and two thirds cups of sugar is used, what quantity of chocolate chips would then be needed, according to the recipe?
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or 1,3*
is the amount of choclate chips that is needed.
Final answer:
To determine the quantity of chocolate chips needed for a recipe that calls for one and one quarter times as much sugar as chocolate chips, set up a proportion using the given sugar amount. Multiply the sugar quantity (1⅓ cups) by the reciprocal of the ratio (4/5), which results in 1⅓ cups of chocolate chips needed.
Explanation:
To determine the quantity of chocolate chips needed when the recipe asks for one and one quarter times as much sugar as chocolate chips, we can use a simple proportion based on the quantity of sugar used. The recipe specifies that 1⅔ cups of sugar are used, which is equivalent to ⅓ cups of sugar when converted to an improper fraction.
The proportion would look like this: Chocolate Chips (C) is to 1 as 1⅓ cups of sugar is to 1⅔, which can be set up as a ratio: C/1 = (1⅓)/(1⅔). To solve for C, we multiply both sides by 1 to get rid of the denominator for C, giving us:
C = (1⅓)/(1⅔)
Now, let's solve the equation:
Convert 1⅓ to an improper fraction: 5/3.
Convert 1⅔ to an improper fraction: 5/4.
Divide 5/3 by 5/4 to find the quantity of chocolate chips: (5/3) × (4/5) = 20/15 = 4/3, which simplifies to 1⅓ cups.
Therefore, you would need 1⅓ cups of chocolate chips for the recipe.