Combine like terms: [tex]6x^{3}[/tex] and [tex]4x^{3}[/tex] make [tex]10x^{3}[/tex]. At that point, disentangle constants: -8 + 6 rise to -2. Result:[tex]10x^{3} - 2x^{2} + 9x - 2[/tex].
How to simplify the expressionTo simplify the given expression, take after the arrangement of operations (PEMDAS/BODMAS):
Perform operations inside parentheses/brackets.Assess examples (powers).Perform increase and division from cleared out to right.Perform expansion and subtraction from cleared out to right.Given expression: [tex]6x^{3} - 2x^{2} + 9x - 8 + 4x^{3} - 2x + 6[/tex]
Step 1: Combine like terms (terms with the same variable and example):
[tex]6x^{3} + 4x^{3} = 10x^{3}[/tex]
Step 2: Combine the steady terms:
-8 + 6 = -2
The expression presently gets to be:
[tex]10x^{3} - 2x^{2} + 9x - 2[/tex]
So, the disentangled expression is [tex]10x^{3} - 2x^[2} + 9x - 2.[/tex]
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The complete question:
Simplify the expression:
6 x 3-2x2+9x-8+4x3-2x+6
Identify the missing justifications.
(a) =
(b) =
A 2-column table has 7 rows. The first column is labeled Step with entries 2 x minus 7 = 15, 2 x minus 7 + 7 = 15 + 7, 2 x + 0 = 22, 2 x = 22, (one-half) 2 x = (one half) 22, 1 x = 11, and x = 11. The second column is labeled Justification with entries Given, Addition property of equality, (a), Additive identity, (b), Multiplicative inverse, and Multiplicative identity
The missing algebra property justification for the equation solution is; Multiplicative Inverse
How to use algebraic properties?
We are given the equation;
2x - 7 = 15
Step 1; Add 7 to both sides to get; 2x - 7 + 7 = 15 + 7
2x = 22
Reason; Addition property of equality
Step 2; Multiply both sides by 1/2(one half) to get;
(1/2) * 2x = (1/2) * 22
x = 11
Reason; Multiplicative Inverse
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What is the range of the function in the graph?
y
70
60
50
40
30
20
10
012
1 2 3 4 5 6 7 X
Answer:
[tex]1234567x = [/tex]
Find the absolute extreme of the function on the closed interval. y=9e^xsinx , [0,pi]
For convenience sake, I will let [tex]y=f(x)=9e^{x}\sin x[/tex]
First, we evaluate the function at the endpoints of the interval.
[tex]f(0)=9e^{0}\sin(0)=0\\\\f(\pi)=9e^{\pi}\sin(\pi)=0[/tex]
Then, we need to find the critical points.
We can start by taking the derivative using the power rule.
[tex]f'(x)=9e^{x} \frac{d}{dx} \sin x+9\sin x \frac{d}{dx} e^{x}=9e^{x}(\cos x+\sin x)[/tex]
Setting this equal to 0,
[tex]9e^x (\cos x+\sin x)=0[/tex]
Since [tex]9e^x > 0[/tex], we can divide both sides by [tex]9e^x[/tex].
[tex]\cos x+\sin x=0\\\\\sin x=-\cos x\\\\\tan x=-1\\\\x=\frac{3\pi}{4}[/tex]
[tex]f\left(\frac{3\pi}{4} \right)=9e^{3\pi/4}\sin \left(\frac{3\pi}{4} \right)=\frac{9\sqrt{2}e^{3\pi/4}}{2}[/tex]
So, the absolute minimum is [tex]\boxed{\left(\frac{3\pi}{4}, \frac{9\sqrt{2}e^{3\pi/4}}{\sqrt{2}} \right)}[/tex] and the absolute minima are [tex]\boxed{(0,0), (\pi, 0)}[/tex]
Giving brainliest :)
Answer:
[tex]f^{-1}(x)=x^2+1[/tex]
Step-by-step explanation:
The inverse of a function is when the x and y are swapped. So the first step is to write f(x) as y and then swap the x and y
Original Equation:
[tex]f(x)=\sqrt{x-1}\\[/tex]
write f(x) as y (since that's what it represents)
[tex]y=\sqrt{x-1}[/tex]
Swap x and y
[tex]x=\sqrt{y-1}[/tex]
Square both sides
[tex]x^2=y-1[/tex]
Add 1 to both sides
[tex]x^2+1=y[/tex]
So this gives you the equation:
[tex]f^{-1}(x)=x^2+1[/tex]
What is the transformation of f(x)= x^3:
NO LINKS!!! THIS IS NOT MULTIPLE CHOICE!!!!!!
Part 3:
7. f(x)= x^3 - 5
8. f(x)= -x^3
9. f(x)= 5x^3
Answer:
7. Down 5
8. Horizontal reflection
9. Vertical stretch by a factor of 5
Step-by-step explanation:
Transformations of Graphs (functions) is the process by which a function is moved or resized to produce a variation of the original (parent) function.
Transformations
For a > 0
[tex]f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}[/tex]
[tex]f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}[/tex]
[tex]f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}[/tex]
[tex]f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}[/tex]
[tex]y=a\:f(x) \implies f(x) \: \textsf{stretched parallel to the y-axis (vertically) by a factor of}\:a[/tex]
[tex]y=f(ax) \implies f(x) \: \textsf{stretched parallel to the x-axis (horizontally) by a factor of} \: \dfrac{1}{a}[/tex]
[tex]y=-f(x) \implies f(x) \: \textsf{reflected in the} \: x \textsf{-axis}[/tex]
[tex]y=f(-x) \implies f(x) \: \textsf{reflected in the} \: y \textsf{-axis}[/tex]
Identify the transformations that take the parent function to the given function.
Question 7
[tex]\textsf{Parent function}: \quad f(x)=x^3[/tex]
[tex]\textsf{Given function}: \quad f(x)=x^3-5[/tex]
Comparing the parent function with the given function, we can see that 5 has been subtracted from the parent function.
Therefore, the transformation is:
[tex]f(x)-5 \implies f(x) \: \textsf{translated}\:5\:\textsf{units down}[/tex]
Question 8
[tex]\textsf{Parent function}: \quad f(x)=x^3[/tex]
[tex]\textsf{Given function}: \quad f(x)=-x^3[/tex]
Comparing the parent function with the given function, we can see that the parent function has been multiplied by -1.
Therefore, the transformation is:
[tex]y=-f(x) \implies f(x) \: \textsf{reflected in the} \: x \textsf{-axis}[/tex]
Question 9
[tex]\textsf{Parent function}: \quad f(x)=x^3[/tex]
[tex]\textsf{Given function}: \quad f(x)=5x^3[/tex]
Comparing the parent function with the given function, we can see that the parent function has been multiplied by 5.
Therefore, the transformation is:
[tex]y=5\:f(x) \implies f(x) \: \textsf{stretched parallel to the y-axis (vertically) by a factor of}\:5[/tex]
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Answer:
7. Down 5
8. Horizontal Reflection.
9. Vertical Stretch by a factor of 5.
Explanation:
Parent function: f(x) = x^3
7. f(x)= x^3 - 5
Comparing it with f(x) - d which gives function shifted d units down.
Here the function has shifted 5 units down.
8. f(x)= -x^3
Comparing with -f(x) gives reflection over x-axis (horizontal reflection).
Here the function f(x) = (-1x^3) has been reflected horizontally.
9. f(x)= 5x^3
Comparing with a(f(x)) gives vertical stretch when |a| > 1 or compression when 0 < |a| < 1 by a factor of a.
Here the function f(x) = 5x^3 has been vertically stretched by a factor of 5.
A carpenter constructed a rectangular sandbox with a capacity of 10 cubic feet. If the carpenter were to make a similar sandbox twice as long, twice as wide, and twice as high as the first sandbox, what would be the capacity, in cubic feet, of the second sandbox?
Considering the volume of a rectangular prism, the capacity of the second sandbox would be of 80 cubic feet.
What is the volume of a rectangular prism?The volume of a rectangular prism with length l, width w and height h is given by the multiplication of the measures, that is:
V = lwh.
In this problem, the capacity is of 10 cubic feet, that is:
V = lwh = 10.
When each measure is doubled, the volume will be given as follows:
V= 2l x 2w x 2h = (2 x 2 x 2)lwh = 8lwh = 8V = 80 cubic feet.
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In a 24 marathon, solve the 24 puzzle given by the poster above you, and post a new 24 puzzle of your own!
Answer:
At Less In Number 20
Step-by-step explanation:
1234567891011121314151617181920
Clear my choice
Wind Song is paid $14.70 per hour, with overtime pay of time-and-a-half for Saturday work and double time for Sunday. Calculate her
gross pay if she worked 33 hours during the week (Monday through Friday) and 10 hours Sunday. (Round your answer to the nearest
cent)
a. $879.10
b. $532.21
c. $632.21
d. $779.10
Using proportions, her gross pay is given as follows:
d. $779.10.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
Her gross pay is divided as follows:
$14.70 for 33 hours.2 x $14.70 for 10 hours.Hence the total pay is:
33 x 14.70 + 2 x 10 x 14.70 = $779.10.
Which means that option d is correct.
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a recent study by a researcher found that 82% of teenagers have used cellphones while driving a vehicle.suppose a random sample of 100 teen drivers is taken.calculate the probability that the sample proportion is less than 0.80
The probability that the sample proportion is less than 0.80 is mathematically given as P(z<-0.52)
What is the probability that the sample proportion is less than 0.80?Generally, the equation for probability is mathematically given as
p=82/100
Therefore
p=0.82
q=1-p
q=1-0.82
q=0.18
[tex]SE=\sqrt{\frac{p(1-p)}{n}}\\\\SE=\sqrt{\frac{0.8(1-0.8)}{100}}\\\\SE=0.03841[/tex]
b)
[tex]P(p < 0.80)=p(\frac{p-0.82}{0.0384} < \frac{0.8-0.82}{0.0384})\\\\P(z < -0.52)[/tex]
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What is the perimeter of A ABC?
Round each step to the nearest tenth.
Enter your answer in the box.
Answer: 11.4
Step-by-step explanation:
Using the distance formula,
[tex]AC=\sqrt{(-3-1)^2 + (-1-2)^2}}=5\\\\AB=\sqrt{(-3-0)^2 +(-1-3)^2}=5\\\\BC=\sqrt{(1-0)^2 + (2-3)^2}=\sqrt{2} \approx 1.4\\\\\implies P \approx 5+5+1.4=\boxed{11.4}[/tex]
Kevin makes bracelets and keychains to sell in his online store for $12 each. On Monday, Kevin made $180. If he sold 12 keychains, how many bracelets did he sell?
how many natural numbers between 97 and 256
Answer:
159
Step-by-step explanation:
all natural numbers are numbers that go above 0 and etc…
Therefor, 256 - 97
= 159
Answer:
158
Step-by-step explanation:
Between means 97 and 256 are not included
Therefore its should be:
=(256-97)-1
=158
Shelly completed 10 problems. She has 2/7 to complete. How many problems are left?
The number of problems Shelly has to complete is 25 problems
Fraction:Total problems = xNumber of problems completed = 10Number of problems to complete = 2/7xx = 10 + 2/7x
x - 2/7x = 10
(7x-2x)/7 = 10
5/7x = 10
x = 10 ÷ 5/7
= 10 × 7/5
= 70/5
x = 35 problems
So,
Number of problems to complete = Total problems - completed problem
= 35 - 10
= 25 problems
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In a psychology class, 44 students have a mean score of 96.6 on a test. Then 13 more students take the test and their mean score is 66.3.
What is the mean score of all of these students together? Round to one decimal place.
mean of the scores of all the students
Answer: 89.7
Step-by-step explanation:
The mean of a data set is the average of all the information given. Therefore, the total combined score is the number of students multiplied by the mean
The total score of the first 44 students: 96.6*44 = 4250.4
The total score of the later 13 students: 66.3*13 = 861.9
(4250.4 + 861.9)/(44 + 13) = 89.7
Hope this helped
Find the value of 7.1a when a=1.5.
Final answer:
The answer is 10.65.
Step-by-step explanation:
Step 1
Substitute a=1,5 into expression
7.1a, a=1.5
7.1 x 1.5
Step 2
Multiply the numbers
7.1 x 1.5 = 10.65
Answer:
10.65
Step-by-step explanation:
Plug a into the expression
[tex]7.1\times1.5=10.65[/tex]
Hope I helped you in some way!
A local school is considering requiring students to pass a state administered math reasoning and reading comprehension test in order to graduate high school. The local school board believes that passing the state math and reading tests will be a predictor of a student’s success in college.
I do not agree that passing the state math and reading tests will be a predictor of a student's success in college.
What are the factors that determine a student's success in college?The factors that determine a student's success in college include the following:
Students' attitudes to learningTeachers' attitudes to sharing knowledgeTeaching methods for imparting knowledgeClassroom learning environmentStudent's belief in gender stereotypesParental factors.Question Completion:Do you agree with the board? Mention the factors that determine a student's success in college.
Thus, it is not necessarily true that passing the state math and reading tests will be a predictor of a student's success in college.
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Elizabeth company has 10,000 units of their new product in warehouse. They sold 10,000 in pre-order that will need to be shipped immediately. They are producing 1,000 units per week and they are receiving 700 order per week. How long will it take to fill the warehouse to maximum capacity at the current production rate?
Answer:
m = 300w OR w = m/300
Step-by-step explanation:
They start with 10k, but that's immediately sold, so they're back at a flat 0. Every week they gain 1000 but lose 700 for a net profit of positive 300.
Therefore, the maximum capacity would be 300 multiplied by the number of weeks. If we know the maximum, then the answer would be m (maximum) divided by 300.
Adam's favorite online retail store is having a sale: jeans are $17 each and sweaters are $9 each, sales tax included. If Adam purchases at least $75 worth of jeans and sweaters, he will receive free shipping and handling. Let x represent the number of jeans purchased and let y represent the number of sweaters purchased. Which of the following inequalities represents the number of jeans and sweaters Adam must purchase in order to receive free shipping and handling?
The inequality which represents the number of jeans and sweater which he must purchase is; $17x + $9y >= $75.
Which inequality represents his purchase to receive free shipping?It follows from the task content that, to receive free shipping, $75 or more must be spent on the pieces of clothing to receive free shipping.
On this note, it follows that the required inequality is; $17x + $9y >= $75.
This follows from the fact that jeans are $17 each and sweaters are $9 each.
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What is the solution to the inequality?
15<4+x
Answer:
Step-by-step explanation:
Hello!
15 < x + 4
We can subtract 4 from both sides, to cancel it out.
15 - 4 is 11.
11 < x
x = {12,13,14,15,16,..........................................................................Infinity}
Hope I Helped!
How many times can 0.1 fit into 100?
Answer:
1000 times
Step-by-step explanation:
To find out how many times 0.1 can fit into 100, we can just divide 100 by 0.1.
But, we first find out how many times can 1 fit into 100.
No. of times 1 fit into 100 = 100 / 1 = 100 times
Now we know 1 is 10 times of 0.1, so we multiply the above by 10,
so 100 * 10 = 1000 times.
Therefore 0.1 can fit into 100 a 1000 times.
Answer:
1000
Step-by-step explanation:
100 divide by 0.1 the answer is 1000
Use the properties of exponents to simplify the expression (27 1/2) 2/3
Answer:
3
Step-by-step explanation:
using the power we multiply the exponents (27^1/2)^2/3 to get 27^1/3=3
solve for X in the figure
Answer:
35
Step-by-step explanation:
This shape has 6 sides.
Sum of interior angles of a 6 sided shape is 720.
117 + 4x - 5 + 4x - 3 + 118
+ 3x + 6 + 3x - 3 = 720
4x + 4x + 3x + 3x
+ 117 + 118 + 6 - 5 - 3 - 3 = 720
14x + 241 - 11 = 720
14x + 230 = 720
14x = 720 - 230
14x = 490
x = 490/14
x = 35
Let
X
be a random variable such that
E
(
X
2
)
=
81
and
V
(
X
)
=
58
. Compute V
(
2
X
+
10
)
E
(
2
X
+
10
)
What I gather from the question is that [tex]X[/tex] has second moment [tex]E(X^2)=81[/tex] and variance [tex]V(X) = 58[/tex], and you're asked to find the expectation and variance of the random variable [tex]Y=2X+10[/tex].
From the given second moment and variance, we find the expectation of [tex]X[/tex] :
[tex]V(X) = E(X^2) - E(X)^2 \implies E(X) = \sqrt{E(X^2) - V(X)} = \sqrt{23}[/tex]
Expectation is linear, so
[tex]E(Y) = E(2X+10) = 2 E(X) + 10 = \boxed{2\sqrt{23} + 10}[/tex]
Using the same variance identity, we have
[tex]V(Y) = V(2X+10) = E((2X+10)^2) - E(2X+10)^2[/tex]
and
[tex]E((2X+10)^2) = E(4X^2 + 40X + 100) = 4E(X^2) + 40E(X) + 100 = 424 + 40\sqrt{23}[/tex]
so that
[tex]V(Y) = V(2X+10) = (424 + 40\sqrt{23}) - (2\sqrt{23} + 10)^2 = \boxed{232}[/tex]
Alternatively, we can use the identity
[tex]V(aX+b) = a^2 V(X) \implies V(2X+10) = 4V(X) = 232[/tex]
Calculate the amount of air in a room 6m long, 5m wide and 3mm high.
Answer:
90.000 m³
Step-by-step explanation:
L = 6 mW = 5 mH = 3 mm = 3.000 mV = L × W × H
V = 6 × 5 × 3.000
V = 30 × 3.000
V = 90.000 m³
Hello !
[tex]6 \times 5 \times 3 = 90 {m}^{3} [/tex]
The amount of air is 90m³.
Have a nice day ;)
it is 1.8 km from Rachel's house to the nearest mailbox Use the facts to find how far this is in meters.
Answer:
1800 m
Step-by-step explanation:
1 km = 1000 m
1.8 km = 1.8 × 1 km = 1.8 × 1000 m = 1800 m
The circumference of a circle is 8 pi
kilometers. What is the diameter?
Answer:
Using the formulas
C=2πr
d=2r
Solving for d
d=C
π=8
π≈2.54648
d≈2.55
PLEASE ANSWER THIS QUESTION! I BEG OF YOU
Two function are represent below.
FUNCTION A FUNCTION B
y=35x. (image below)
What is the difference in the rate of change between Function A and Function B? Be sure to include the rate of change of each function in your answer.
EXPLAIN THE ANSWER!
The difference between the rate of change of B and the rate of change of A is 15.
How to get the difference in the rates of change?
First, we need to get the two rates of change.
We have two linear functions.
A: y = 35*x
For function A the rate of change is the slope, wich is 35.
Function B is graphed.
Remember that if a line passes through two points (x₁, y₁) and (x₂,y₂) then the slope is:
[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
In the graph, we can see that line B passes through (0, 0) and (1, 50), then the slope is:
[tex]a = \frac{50 - 0}{1 - 0} = 50[/tex]
Then the rate of change of B is 50.
The difference between the rates of change is:
diff = 50 - 35 = 15
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What are the horizontal shift and vertical shift for y=srx+2-3
Answer:
vertical shift is 3 units down
horizontal shift is 2 units left
Step-by-step explanation:
y=srx+2-3
vertical shift is 3 units down
horizontal shift is 2 units left
A TV studio has brought in 6 boy kittens and 8 girl kittens for a cat food commercial.
The director is going to choose 7 of these kittens at random to be in the commercial.
What is the probability that the director chooses 4 boy kittens and 3 girl kittens? Round your answer to three decimal places.
The required probability is given by 0.012 for the director chooses 4 boy kittens and 3 girl kittens
A TV studio has brought in 6 boy kittens and 8 girl kittens for a cat food commercial.
Probability, can be define as the ratio of favorable events to the n number of total events
The director is going to choose 7 of these kittens at random to be in the commercial. the director chooses 4 boy kittens and 3 girl kittens.
Here, probability of to choose 7 of these kittens at random
= c(14,7)
probability to chooses 4 boy kittens and 3 girl kittens
= c(6,4) x c(8,3)
Required probability = [tex]\frac{c(6, 4) * c(8, 3)}{c(14, 7)}[/tex] = 0.012
Thus, The required required probability is given by 0.012 for the director chooses 4 boy kittens and 3 girl kittens.
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-(8/24)^{2} ÷ -(8/24)^{0}
Answer: 1/9
Step-by-step explanation:
-(8/24)^2 / -(8/24)^0
cancel the negatives and simplify 8/24 to 1/3
(1/3)^2 / (1/3)^0
(1/3)^0 = 1
so,
(1/3)^2 = 1/9