Answer:
Ok, we have that f(x) is defined for all real values of x, except for x = x0.
[tex]\lim_{x \to \ x0} f(x)[/tex]
Does it exist? why?
Remember that when we are taking the limit we are not evaluating the function in x0, instead, we are evaluating the function in values really close to x0 (values defined as x0⁺ and x0⁻, where the sign defines if we approach from above or bellow).
And because f(x) is defined in the values of x near x0, we can conclude that the limit does exist if:
[tex]\lim_{x \to \x0+} f(x) = \lim_{x \to \x0-} f(x)[/tex]
if that does not happen, like in f(x) = 1/x where x0 = 0
where the lower limit is negative and the upper limit is positive, we have that the limit does not converge.
A copy machine makes 104 copies in 3 minutes and 15 seconds. how many copies does it make per minute
Answer:
32 copiesStep-by-step explanation:
First convert 3 minutes and 15 seconds into minutes by converting 15 sec to min and add it to 3min
60 sec = 1min
15 sec = 15 / 60 × 1 min
= 0.25min
Add it to 3min
3min + 0.25min = 3.25 min
We use ratio and proportion
3.25min = 104 copies
1 min = 104× 1/ 3.25
= 104 / 3.25
= 32
The final answer is 32 copies
Hope this helps you.
Answer:
Step-by-step explanation:
3 min 15 sec = 3*60 + 15 = 180 + 15 = 195 seconds
In 195 seconds 104 copies are made
In one second, the number of copies made = [tex]\frac{104}{195}\\[/tex]
In 60 seconds, the number of copies made = [tex]\frac{104}{195}*60[/tex]
= 32 copies
Ronnie goes to the racetrack with his buddies on a weekly basis. One week he tripled his money, but then lost $12. He took his money back the next week, doubled it, but then lost $40. The following week he tried again, taking his money back with him. He quadrupled it, and then played well enough to take that much home, a total of $224. How much did he start with the first week?
Answer:
20
Step-by-step explanation:
224÷4 = 56+40 = 96÷2 = 48+12 = 60÷3 = 20
If Ronnie goes to the racetrack with his buddies on a weekly basis. How much did he start with the first week is $20.
How much did he start with?Hence:
4 [2 (3x - 12) -40] = 224
4 [6x - 24 - 40] = 224
Collect like term
24x - 256= 224
24x/24 = 480/24
Divide both side by 24
x=480/24
x=$20
Therefore How much did he start with the first week is $20.
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toilet rolls come in packs of 4 and 9
the 4 packed price $2.04
and the 9 packed is priced at $4.68
Answer: 2.04÷ 4= 0.51
4.68÷9= 0.52
4 pack is better value by 0.01
Rafael is saving money to buy a game. So far he has saved $30, which is five-sixths of the total cost of the game. How much does the game cost?
Answer:
$36
Step-by-step explanation:
30 is 5/6 of the game, so we can think that 1/6 is equal to 6, since 5(6) is 30.
If we add another sixth, we get 36, which will be the total cost of the game.
The first two steps in determining the solution set of the system of equations, y = -x2 + 4x + 12 and y=-3x + 24,
algebraically are shown in the table.
Answer:
C
Step-by-step explanation:
(3,15) and (4,12)
Answer:
C or (3, 15) and (4, 12)
Step-by-step explanation:
I just took the test on Edge 2020
Identify the vertex of the function. PLEASE HELP!!!
Answer:
Step-by-step explanation:
y-|x|+3
y=|x|+3
vertex=(0,3)
y=|x-4|-7
vertex(4,-7)
plz answer question in screen shot
Answer:
200√3
Step-by-step explanation:
The triangle given here is a special right triangle, one with angles measuring 30-60-90 degrees. The rule for triangles like these are that the side opposite the 30° angle can be considered x, and the side opposite the 60° angle is x√3, while the hypotenuse, or side opposite the right angle, is 2x. All we need to know here are the two legs to find the area.
Since b is opposite the 30° angle, it is x, while side RS is opposite the 60° angle, meaning it is equal to x√3, meaning that the area of the triangle is 1/2*x*x√3. We can substitute in 20 for x, making our area 1/2*20*20√3. Multiplying we get 10*20√3, or 200√3.
add the following - 4/9,7/12and - 3/8
Answer:
[tex] - \frac{17}{72} [/tex]Step-by-step explanation:
[tex] - \frac{4}{9} + \frac{7}{12} + ( - \frac{ 3}{8} )[/tex]
When there is a (+) in front of an expression in parentheses, the expression remains the same:
[tex] - \frac{4}{9} + \frac{7}{12} - \frac{3}{8} [/tex]
[tex] \frac{ - 4 \times 8 + 7 \times 6 - 3 \times 9}{72} [/tex]
Calculate the sum of difference
[tex] \frac{ - 32 + 42 - 27}{72} [/tex]
[tex] \frac{10 - 27}{72} [/tex]
[tex] - \frac{17}{72} [/tex]
Hope this helps..
Good luck on your assignment...
Apply the product rules to determine the sign of each expression
Answer:
Step-by-step explanation:
1). [tex](\frac{-4}{9})\times (\frac{7}{4})=(-1)(\frac{4}{9})(\frac{7}{4} )[/tex]
[tex]=-\frac{7}{9}[/tex] [Negative]
2). [tex](-2\frac{3}{4})(-1\frac{1}{5})=(-1)(2\frac{3}{4})(-1)(1\frac{1}{5})[/tex]
[tex]=(-1)^2(2\frac{3}{4})(1\frac{1}{5})[/tex]
[tex]=(2\frac{3}{4})(1\frac{1}{5})[/tex] [Positive]
3). (3)(-3)(-3)(-3)(-3) = 3.(-1).3.(-1).3.(-1).3(-1).(3)
= (-1)⁴(3)⁵
= (3)⁵ [Positive]
4). [tex](-\frac{1}{6})(-2)(-\frac{3}{5})(-9)[/tex] = [tex](-1)(\frac{1}{6})(-1)(2)(-1)(\frac{3}{5})(-1)(9)[/tex]
= [tex](-1)^4(\frac{1}{6})(2)(\frac{3}{5})(9)[/tex]
= [tex](\frac{1}{6})(2)(\frac{3}{5})(9)[/tex] [Positive]
5). [tex](-\frac{4}{7})(-\frac{3}{5})(-9)=(-1)(\frac{4}{7})(-1)(\frac{3}{5})(-1)(9)[/tex]
[tex]=(-1)^3(\frac{4}{7})(\frac{3}{5})(9)[/tex]
[tex]=-(\frac{4}{7})(\frac{3}{5})(9)[/tex] [Negative]
6). [tex](-\frac{10}{7})(\frac{8}{3})=(-1)(\frac{10}{7})(\frac{8}{3})[/tex]
[tex]=-(\frac{10}{7})(\frac{8}{3})[/tex] [Negative]
he data show the bug chirps per minute at different temperatures. Find the regression equation, letting the first variable be the independent (x) variable. Find the best predicted temperature for a time when a bug is chirping at the rate of 3000 chirps per minute. Use a significance level of 0.05. What is wrong with this predicted value?
Answer:
^Y= 26.72 + 0.0547Xi
^Y/[tex]_{X=3000}[/tex]= 190.82ºF
B. It is unrealistically high.
Step-by-step explanation:
Hello!
*Full text*
The data show the bug chirps per minute at different temperatures. Find the regression equation, letting the first variable be the independent (x) variable. Find the best predicted temperature for a time when a bug is chirping at the rate of 3000 chirps per minute. Use a significance level of .05. What is wrong with this predicted value?
Chirps in 1 min. 929 854 771 1004 1201 1027
Temperature (F) 81.3 77.3 64.8 80.3 92.2 80.9
What is the regression equation?
^y= _____ + _____
(Round the x-coefficient to four decimal places as needed. Round the constant to two decimals as needed)
What is the predicted value? ^y= _____ (Round to one decimal places as needed)
What is wrong with this predicted value?
A. The first variable should have been the dependent variable
B. It is unrealistically high.
C. It is only an approximation
D. Nothing is wrong with this value
To calculate the regression equation you have to estimate the slope and the y-intercept.
^Y= a + bX
Estimate of the slope:
[tex]b= \frac{sumXY-\frac{(sumX)(sumY)}{n} }{sumX^2-\frac{(sumX)^2}{n} }[/tex]
n= 6
∑X= 5786 ∑X²= 5691944 [tex]\frac{}{X}[/tex]= 964.33
∑Y= 476.80 ∑Y²= 38277.76 [tex]\frac{}{Y}[/tex]= 79.47
∑XY= 465940.4
[tex]b= \frac{465940.4-\frac{5786*476.80}{6} }{5691944-\frac{(5786)^2}{6} }= 0.0547[/tex]
Estimate of the Y-intercept:
[tex]a= \frac{}{Y} -b*\frac{}{X}[/tex]
[tex]a= 79.47 -0.0547*964.33= 26.696= 26.72[/tex]
The estimated regression equation is:
^Y= 26.72 + 0.0547Xi
^Y/[tex]_{X=3000}[/tex]= 26.72 + 0.0547*3000= 190.82ºF
At the rate of 3000 chirps per minute it is expected a temperature of 190.82ºF
As you can see it is unrealistic to think that the chirping rate of bugs will have any effect over the temperature. For what is known about bugs, they tend to be more active to higher temperatures.
Considering the value obtained, as it is incredible high, if this regression was correct, every time the chirping rate of bugs increases, the ambient temperature would rise to levels incompatible with life.
I hope this helps!
To determine if a particular predictor in a regression analysis is statistically significant, which statistic should one interpret
Answer:
The test statistic used to determine whether a particular predictor in a regression analysis is statistically significant is:
[tex]t=\frac{\beta_{i}}{S.E._{\beta_{i}}}[/tex]
Step-by-step explanation:
The general form of a regression equation is:
[tex]y=\alpha +\beta_{1}x_{1}+\beta_{2}x_{2}+...+\beta_{n}x_{n}[/tex]
Here,
α = y-intercept
βi = regression coefficients, (i = 1, 2, ..., n)
A regression analysis is performed to determine whether the predictor variables are statistically significant or not.
The output of the regression analysis consists of two tables.
One is the regression output and the other is the ANOVA table.
The regression output table is used to display which predictor variables are statistically significant and which are not.
The test statistic used to determine whether a particular predictor in a regression analysis is statistically significant is:
[tex]t=\frac{\beta_{i}}{S.E._{\beta_{i}}}[/tex]
And the ANOVA table displays overall regression analysis.
The F-test statistic is used to for the overall regression analysis.
Thus, the test statistic used to determine whether a particular predictor in a regression analysis is statistically significant is:
[tex]t=\frac{\beta_{i}}{S.E._{\beta_{i}}}[/tex]
A square matrix is called a permutation matrix if it contains the entry 1 exactly once in each row and in each column, with all other entries being 0. All permutation matrices are invertible. Find the inverse of the following permutation matrix.
A = [0 0 1 0, 0 0 0 1, 0 1 0 0, 1 0 0 0]
The inverse of the given permutation matrix A is
[tex]\[ A^{-1} = \begin{bmatrix}0 & 0 & 0 & 1 \\0 & 0 & 1 & 0 \\1 & 0 & 0 & 0 \\0 & 1 & 0 & 0 \\\end{bmatrix} \][/tex]
To find the inverse of the given permutation matrix A:
[tex]\[ A = \begin{bmatrix}0 & 0 & 1 & 0 \\0 & 0 & 0 & 1 \\0 & 1 & 0 & 0 \\1 & 0 & 0 & 0 \\\end{bmatrix} \][/tex]
Utilize the concept that the inverse of a permutation matrix is its transpose.
Therefore, the inverse of matrix A is:
[tex]\[ A^{-1} = A^T \][/tex]
Taking the transpose of matrix A, gives
[tex]\[ A^{-1} = \begin{bmatrix}0 & 0 & 0 & 1 \\0 & 0 & 1 & 0 \\1 & 0 & 0 & 0 \\0 & 1 & 0 & 0 \\\end{bmatrix} \][/tex]
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3. A strip of wood 78 inches long is to be cut into pieces 3 3la inches long. How many pieces can be cut?
A. 21
B. 12
C. 26
D.20
Answer:
Option D (20) is the right answer.
Step-by-step explanation:
The given values are:
Length of wood,
= 78 inches
Wood pieces,
= [tex]3\frac{3}{4} \ inches[/tex]
On converting this in proper fraction, we get
= [tex]3\frac{3}{4}[/tex]
= [tex]\frac{15}{4}[/tex]
= [tex]3.75 \ inches[/tex]
Now,
On dividing "78" from "3.78", we get
= [tex]\frac{78}{3.75}[/tex]
= [tex]20.8 \ pieces[/tex]
So we got "20 pieces".
For a segment of a radio show a disc jockey can play 10 records. If there are 12 records to select from in how many ways can the program for this segment be arranged
Answer:
66 different waysStep-by-step explanation:
This is a combination question. Combination has to do with selection. For example if r objects are to be selected from n pool of oblects, this can be done in nCr number of ways.
nCr = n!/(n-r)r!
According to the question, if a radio show can only play 10 records out of 12 records available, this can be done in 12C10 number of ways.
12C10 = 12!/(12-10)!10!
= 12!/2!10!
= 12*11*10!/2*10!
= 12*11/2
= 6*11
= 66 different ways
What is the simple interest earned on
$300 over 6 years at 4% interest?
Answer:
$72
Step-by-step explanation:
I = Prt
I = ($300)(0.04)(6)
I = $72
Which of the following illustrates the truth value of the following mathematical statements?
6 + 3 = 9, and 5.5 = 20
Answer: 6 + 3 = 9
Step-by-step explanation:
5.5 does not equal to 20
Both the P-value method and the critical value method use the same standard deviation based on the claimed proportion p, so they are equivalent to each other. Is this also true about the confidence interval method?
Answer:
Yes, it's also true about the confidence interval method.
Step-by-step explanation:
The confidence interval includes all the null hypothesis values for the population mean that would be accepted by the hypothesis test at the significance level of 5%. Now, it means this assumes a two-sided alternative.
Now, when testing claims about
population proportions, the critical method and the P-value method are equivalent due to the fact that they always produce the same result. Similarly, a conclusion based on a confidence interval estimate will be the same as a conclusion based on a hypothesis test.
So, Yes the confidence interval method and the P-value or critical methods will always lead to the same conclusion when the tested parameter is the standard deviation.
g Consider writing onto a computer disk and then sending it through a certifier that counts the number of missing pulses. Suppose this number X has a Poisson distribution with lamda = .2. a) What is the probability that a disk has exactly one missing pulse? b) What is the probability that a disk has at least two missing pulses? c) What is EX
Answer:
a) P(1) = 0.1637
b) [tex]P(x\geq 2) = 0.0176[/tex]
c) E(x) = 0.2
Step-by-step explanation:
If X follows a poisson distribution, the probability that a disk has exactly x missing pulses is:
[tex]P(x)=\frac{e^{-m}*m^x}{x!}[/tex]
Where m is the mean and it is equal to the value of lambda. So, replacing the value of m by 0.2, we get that the probability that a disk has exactly one missing pulse is equal to:
[tex]P(1)=\frac{e^{-0.2}*0.2^1}{1!}=0.1637[/tex]
Additionally, the probability that a disk has at least two missing pulses can be calculated as:
[tex]P(x\geq 2)=1-P(x<2)[/tex]
Where [tex]P(x<2)=P(0)+P(1)[/tex].
Then, [tex]P(0)[/tex] and [tex]P(x\geq 2)[/tex] are calculated as:
[tex]P(0)=\frac{e^{-0.2}*0.2^0}{0!}=0.8187\\P(x\geq 2) = 1 - (0.8187 + 0.1637)\\P(x\geq 2) = 0.0176[/tex]
Finally, In the poisson distribution, E(x) is equal to lambda. So E(x) = 0.2
EACH PAIR OF FIGURES IS SIMILAR. FIND THE MISSING SIDE!!!!
Answer:
58.1 and 17
Step-by-step explanation:
For the first triangles the similarity ratio is 1:7 so x is 8.3 × 7 = 58.1
For the second triangles the similarity ratio is 1:5 so x is 3.4 × 5 = 17
Evauluate 37/100+3/10
Answer:
67/100
Step-by-step explanation:
Find common denominators, note that what you do to the denominator, you must do to the numerator.
The common denominator is 100:
(3/10)(10/10) = (3 * 10)/(10 * 10) = 30/100
Add:
37/100 + 30/100 = 67/100
67/100 is your answer.
~
Answer:
67/100
Step-by-step explanation:
37/100+3/10
Get a common denominator
37/100 + 3/10 *10/10
37/100+30/100
67/100
On a unit circle, the vertical distance from the x-axis to a point on the perimeter of the circle is twice the horizontal
distance from the y-axis to the same point. What is sine?
Answer:
(2/5)√5 ≈ 0.894427
Step-by-step explanation:
You require the y-coordinate of the point that satisfies two equations:
x^2 +y^2 = 1
y = 2x
Substituting for x, we have ...
(y/2)^2 +y^2 = 1
y^2(5/4) = 1
y^2 = 4/5
y = (2/5)√5 ≈ 0.894427
The sine of the angle is (2/5)√5 ≈ 0.894427.
Answer:
The answer would be C.
Step-by-step explanation:
Find the first, fourth, and eighth terms of the sequence.
A(n) = -2x2^n-1
Answer:
first term = -2
fourth term = -16
eighth term = -256
Step-by-step explanation:
Given;
A sequence with function;
A(n) = -2x2^(n-1)
The first, fourth, and eighth terms of the sequence can be calculated by substituting their corresponding values of n;
First term A(1); n = 1
A(1) = -2x2^(1-1) = -2×1 = -2
Fourth term A(4); n = 4
A(4) = -2x2^(4-1) = -2×8 = -16
Eighth term A(8); n = 8
A(8) = -2x2^(8-1) = -2×128 = -256
Therefore,
first term = -2
fourth term = -16
eighth term = -256
P(x)⋅Q(x)=R(x); if P(x)=x+2 and R(x)=x3−2x2−6x+4, what is Q(x)?
Answer: Q(x) = x² - 4x + 2
Step-by-step explanation:
P(x) · Q(x) = R(x) ⇒ Q(x) = R(x)/P(x)
R(x) = x³ - 2x² - 6x + 4 ÷ P(x) = x + 2
I will use synthetic division (but you can also use long division).
-2 | 1 -2 -6 4
| ↓ -2 8 -4
1 -4 2 0 ← remainder
The reduced polynomial is: x² - 4x + 2
Find a tangent vector of unit length at the point with the given value of the parameter t. r(t) = 2 sin(t)i + 7 cos(t)j t = π/6
The tangent vector to r(t) at any t in the domain is
[tex]\mathbf T(t)=\dfrac{\mathrm d\mathbf r(t)}{\mathrm dt}=2\cos t\,\mathbf i-7\sin t\,\mathbf j[/tex]
At t = π/6, the tanget vector is
[tex]\mathbf T\left(\dfrac\pi6\right)=\sqrt3\,\mathbf i-\dfrac72\,\mathbf j[/tex]
To get the unit tangent, normalize this vector by dividing it by its magnitude:
[tex]\left\|\mathbf T\left(\dfrac\pi6\right)\right\|=\sqrt{(\sqrt3)^2+\left(-\dfrac72\right)^2}=\dfrac{\sqrt{61}}2[/tex]
So the unit tangent at the given point is
[tex]\dfrac{\mathbf T\left(\frac\pi6\right)}{\left\|\mathbf T\left(\frac\pi6\right)\right\|}=2\sqrt{\dfrac3{61}}\,\mathbf i-\dfrac7{\sqrt{61}}\,\mathbf j[/tex]
Applying derivatives, the tangent vector of unit length at the point given is:
[tex]r_{u}{\prime}(\frac{\pi}{6}) = \frac{2\sqrt{3}}{\sqrt{61}}i - \frac{7}{\sqrt{61}}j[/tex]
The vector function is:
[tex]r(t) = 2\sin{(t)}i + 7\cos{(t)}j[/tex]
The tangent vector is it's derivative, which is given by:
[tex]r^{\prime}(t) = 2\cos{(t)}i - 7\sin{(t)}j[/tex]
At point [tex]t = \frac{\pi}{6}[/tex], we have that:
[tex]r^{\prime}(\frac{\pi}{6}) = 2\cos{(\frac{\pi}{6})}i - 7\sin{(\frac{\pi}{6})}j[/tex]
[tex]r^{\prime}(\frac{\pi}{6}) = \frac{2\sqrt{3}}{2}i - \frac{7}{2}[/tex]
[tex]r^{\prime}(\frac{\pi}{6}) = \sqrt{3}i - \frac{7}{2}[/tex]
The norm of the vector is:
[tex]|r^{\prime}(\frac{\pi}{6})| = \sqrt{\sqrt{3}^2 + (-\frac{7}{2})^2}[/tex]
[tex]|r^{\prime}(\frac{\pi}{6})| = \sqrt{\frac{61}{4}}[/tex]
[tex]|r^{\prime}(\frac{\pi}{6})| = \frac{\sqrt{61}}{2}[/tex]
The unit vector is given by each component divided by the norm, thus:
[tex]r_{u}{\prime}(\frac{\pi}{6}) = \frac{\sqrt{3}}{\frac{\sqrt{61}}{2}}i - \frac{7}{2\frac{\sqrt{61}}{2}}j[/tex]
[tex]r_{u}{\prime}(\frac{\pi}{6}) = \frac{2\sqrt{3}}{\sqrt{61}}i - \frac{7}{\sqrt{61}}j[/tex]
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In a fish tank the number of orange fish is 1 1/4 times the number of blue fish. Drag the blue fish to represent the number of blue fish in the tank dor every 5 orange fish
Answer:
4 blue fish for every 5 orange fish
Step-by-step explanation:
(orange fish) = (1 1/4)·(blue fish) . . . . . the given relation
(orange fish) = (5/4)·(blue fish) . . . . . write as improper fraction
(orange fish)/(blue fish) = 5/4 . . . . . divide by "blue fish"
There are 4 blue fish for every 5 orange fish.
The sum of an irrational number and a rational number is irrational. Sometimes True Always True Never True
Answer:
Always true
Step-by-step explanation:
Trust me
Answer:
true
Step-by-step explanation:
Robert wants to arrange the books for statistics, calculus, geometry, algebra, and trigonometry on a shelf. In how many arrangements can he keep them on the shelf such that the algebra and trigonometry books are not together?
Answer: 72 arrangements
Step-by-step explanation:
The books are:
Statistics, calculus, geometry, algebra, and trigonometry.
So we have 5 books.
We want that algebra and trigonometry are not together.
Suppose that we have 5 positions:
Now, we can start with algebra in the first position.
Now, we have 3 positions for trigonometry (3rd, 4th and 5th).
Now, once those two books are in position, we have 3 other positions and 3 other books, so for the first selection we have 3 options, for the second position we have 2 options, and for the last option we have 1 option.
The number of combinations is equal to the number of options in each selection:
3*(3*2*1) = 18
Now, if Algebra is in the second place, then for trigonometry we have only 2 possible options (4th and 5th)
and for the other 3 books again we have 3*2*1 combinations:
the total number of combinations is:
2*(3*2*1) = 12
If algebra is in the 3rd position, trigonometry has 2 options (1st and 5th)
For the other 3 books, we have 3*2*1 combinations.
The total number of combinations is:
(3*2*1)*2 = 12
in the fourth position is the same as the second position, so here we have again 12 combinations.
For the fifth position is the same as for the first position, so we have 18 combinations.
The total number of combinations is:
C = 18 + 12 +12 +12 +18 = 72
If s=1/2 unit and A=12s^2, what is the value of A, in square unit?
Answer:
3 square units
Step-by-step explanation:
Put the numbers in the formula and do the arithmetic.
A = 12(1/2)² = 12(1/4) = 3 . . . square units
__
Comment on the working
It might be helpful to you to see how this works when the units of the number are attached to the number.
A = 12(1/2 unit)² = 12(1/2 unit)(1/2 unit) = 12(1/2)(1/2)(unit)(unit) = 3 unit²
I often choose to keep the units with the numbers, just to make sure that the numbers and units are correct. For example, you can multiply inches by feet, but you get in·ft, which is not square inches and not square feet. You have to do a conversion to get the result in square units.
the sum of the first 20 terms of an A.P is identical to the sum of the first 22 term.If the common difference is -2; find the first terms
Answer:
First term a = 41
Step-by-step explanation:
Arithmetic Progression:
Common differences d = -2
[tex]S_{n}=\frac{n}{2}(2a+[n-1]d)\\\\S_{20}=\frac{20}{2}(2a+19*[-2])\\\\[/tex]
= 10*(2a - 38)
= 10*2a - 10*38
=20a - 380
[tex]S_{22}=\frac{22}{2}(2a+21*[-2])\\\\[/tex]
= 11 (2a -42)
=11*2a - 11*42
= 22a - 462
[tex]S_{22}=S_{20}\\\\[/tex]
22a - 462 = 20a - 380
22a = 20a - 380 + 462
22a = 20a + 82
22a - 20a = 82
2a = 82
a = 82/2
a = 41
First term a = 41
The polynomial 24x3 − 54x2 + 44x − 99 is factored by grouping. 24x3 − 54x2 + 44x − 99 24x3 + 44x − 54x2 − 99 4x(____) − 9(____) What is the common factor that is missing from both sets of parentheses? 6x + 11 6x − 11 6x2 + 11 6x2 − 11
Answer: 6x² + 11
Step-by-step explanation:
24x³ - 54x² + 44x - 99
= 6x²(4x - 9) + 11(4x - 9)
= (6x² + 11) (4x - 9)
This can be rewritten as: 4x(6x² + 11) - 9(6x² + 11)
This is the answer to your problem.