Step-by-step explanation:
x^3 is a perfect cube, 8 is a perfect cube, so we use difference of cubes.
[tex] {a}^{3} - {b}^{3} = (a - b)( {a}^{2} + ab + {b}^{2} )[/tex]
Cube root of x^3 is x.
Cube root of 8 is 2
So
a=x
b= 2.
[tex](x - 2)( {x}^{2} - 2x + 4)[/tex]
Set these equations equal to zero
[tex]x - 2 = 0[/tex]
[tex]x = 2[/tex]
[tex] {x}^{2} - 2x + 4 = 0[/tex]
If we do the discriminant, we get a negative answer so we would have two imaginary solutions,
Thus the only real root is 2.
If you want imaginary solutions, apply the quadratic formula.
[tex]1 + i \sqrt{ 3 } [/tex]
and
[tex]1 - i \sqrt{3} [/tex]
Which of the following expressions are equal to -8/11 - 3/4 - 1/4
In the expressions that we are given, we can note that there is a negative in all of them. This means that we can factor out the negative.
With the negative factored out, it will look like this: [tex]-(\frac{8}{11} + \frac{3}{4} + \frac{1}{4} )[/tex]
The reasoning for this is because you distribute the negative to each term. For example 8/11 is a term, and so is 3/4, and 1/4. So our first answer is D.
Another way we can do this is by combining like terms. We see that in the denominator for -3/4 and -1/4 they both share 4. We can combine it so it becomes -4/4 or -1. It would be E.
The third way we can do this is by rewriting it. Answer A rewrites it so that it is + -, effectively just -. This allows us to treat the equation as if it were the original one.
Hopefully this helps you out, brainliest would help me out.
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n
Sigma 2k+4
k=1
4th term in sequence?
Answer:
12
Step-by-step explanation:
2k+4= 2*4 +4=8+4=12
hope it will help
Answer:
12
Step-by-step explanation:
Given:
[tex]\displaystyle \sum^n_{k=1}2k+4[/tex]
The 4th term in the sequence is when k = 4.
Therefore, substitute k = 4 into 2k + 4:
⇒ 2k+ 4 = 2(4) + 4
= 8 + 4
= 12
Therefore, the 4th term in the sequence is 12
Name the property that justifies the statment If AB - BC = 12, then AB = 12 + BC.
The property that justifies the statement is the commutative law of addition
Commutative law of additionThis law occurs if the same number or constant is added to both sides of an equation.
Given the equation
AB - BC = 12
Add BC to both sides
AB - BC + BC = 12 + Bc
AB = 12 + BC
Hence the property that justifies the statement is the commutative law of addition
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Homework:Section 5.3 Homework
Question 5, 5.3.21
Part 1 of 2
HW Score: 50%, 4 of 8 points
Points: 0 of 1
Question content area top
Part 1
In airline applications, failure of a component can result in catastrophe. As a result, many airline components utilize something called triple modular redundancy. This means that a critical component has two backup components that may be utilized should the initial component fail. Suppose a certain critical airline component has a probability of failure of 0.0056 and the system that utilizes the component is part of a triple modular redundancy.
(a) Assuming each component's failure/success is independent of the others, what is the probability all three components fail, resulting in disaster for the flight?
(b) What is the probability at least one of the components does not fail?
The probability that all three components fail is 1.756 × 10⁻⁷. The probability of at least one of the components does not fail 0.9999998244.
What is a Probability?Probability is the likelihood for an event to occur. In a given statistical distribution, the probability explains the range of values and probabilities that a randomized variable could have.
From the given information;
Assuming each component's failure/success is independent of the others: the probability that all three components fail is:
P(three components fail) = (0.0056)^3
P(three components fail) = 1.756 × 10⁻⁷
The probability that at least one does not fail is:
P(at least one does not fail) = 1 - P(all three components fail)
P(at least one does not fail) = 1 - 1.756 × 10⁻⁷
P(at least one does not fail) = 0.9999998244
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Can someone check whether its correct or no? this is supposed to be the steps in integration by parts
Answer:
[tex]\displaystyle - \int \dfrac{\sin(2x)}{e^{2x}}\: \text{d}x=\dfrac{\sin(2x)}{4e^{2x}}+\dfrac{\cos(2x)}{4e^{2x}}+\text{C}[/tex]
Step-by-step explanation:
Fundamental Theorem of Calculus
[tex]\displaystyle \int \text{f}(x)\:\text{d}x=\text{F}(x)+\text{C} \iff \text{f}(x)=\dfrac{\text{d}}{\text{d}x}(\text{F}(x))[/tex]
If differentiating takes you from one function to another, then integrating the second function will take you back to the first with a constant of integration.
Given integral:
[tex]\displaystyle -\int \dfrac{\sin(2x)}{e^{2x}}\:\text{d}x[/tex]
[tex]\textsf{Rewrite }\dfrac{1}{e^{2x}} \textsf{ as }e^{-2x} \textsf{ and bring the negative inside the integral}:[/tex]
[tex]\implies \displaystyle \int -e^{-2x}\sin(2x)\:\text{d}x[/tex]
Use integration by parts.
[tex]\boxed{\begin{minipage}{5 cm}\underline{Integration by parts} \\\\$\displaystyle \int u \dfrac{\text{d}v}{\text{d}x}\:\text{d}x=uv-\int v\: \dfrac{\text{d}u}{\text{d}x}\:\text{d}x$ \\ \end{minipage}}[/tex]
[tex]\textsf{Let }\:u=\sin (2x) \implies \dfrac{\text{d}u}{\text{d}x}=2 \cos (2x)[/tex]
[tex]\textsf{Let }\:\dfrac{\text{d}v}{\text{d}x}=-e^{-2x} \implies v=\dfrac{1}{2}e^{-2x}[/tex]
Substituting the defined parts into the formula:
[tex]\begin{aligned}\implies \displaystyle -\int e^{-2x}\sin(2x)\:\text{d}x & =\dfrac{1}{2}e^{-2x}\sin (2x)- \int \dfrac{1}{2}e^{-2x} \cdot 2 \cos (2x)\:\text{d}x\\\\& =\dfrac{1}{2}e^{-2x}\sin (2x)- \int e^{-2x} \cos (2x)\:\text{d}x\end{aligned}[/tex]
[tex]\displaystyle \textsf{For }\:-\int e^{-2x} \cos (2x)\:\text{d}x \quad \textsf{integrate by parts}:[/tex]
[tex]\textsf{Let }\:u=\cos(2x) \implies \dfrac{\text{d}u}{\text{d}x}=-2 \sin(2x)[/tex]
[tex]\textsf{Let }\:\dfrac{\text{d}v}{\text{d}x}=-e^{-2x} \implies v=\dfrac{1}{2}e^{-2x}[/tex]
[tex]\begin{aligned}\implies \displaystyle -\int e^{-2x}\cos(2x)\:\text{d}x & =\dfrac{1}{2}e^{-2x}\cos(2x)- \int \dfrac{1}{2}e^{-2x} \cdot -2 \sin(2x)\:\text{d}x\\\\& =\dfrac{1}{2}e^{-2x}\cos(2x)+ \int e^{-2x} \sin(2x)\:\text{d}x\end{aligned}[/tex]
Therefore:
[tex]\implies \displaystyle -\int e^{-2x}\sin(2x)\:\text{d}x =\dfrac{1}{2}e^{-2x}\sin (2x) +\dfrac{1}{2}e^{-2x}\cos(2x)+ \int e^{-2x} \sin(2x)\:\text{d}x[/tex]
[tex]\textsf{Subtract }\: \displaystyle \int e^{-2x}\sin(2x)\:\text{d}x \quad \textsf{from both sides and add the constant C}:[/tex]
[tex]\implies \displaystyle -2\int e^{-2x}\sin(2x)\:\text{d}x =\dfrac{1}{2}e^{-2x}\sin (2x) +\dfrac{1}{2}e^{-2x}\cos(2x)+\text{C}[/tex]
Divide both sides by 2:
[tex]\implies \displaystyle -\int e^{-2x}\sin(2x)\:\text{d}x =\dfrac{1}{4}e^{-2x}\sin (2x) +\dfrac{1}{4}e^{-2x}\cos(2x)+\text{C}[/tex]
Rewrite in the same format as the given integral:
[tex]\displaystyle \implies - \int \dfrac{\sin(2x)}{e^{2x}}\: \text{d}x=\dfrac{\sin(2x)}{4e^{2x}}+\dfrac{\cos(2x)}{4e^{2x}}+\text{C}[/tex]
Differentiation Rules used:
[tex]\boxed{\begin{minipage}{5.7 cm}\underline{Differentiating $\sin(k)$}\\\\If $y=\sin(kx)$, then $\dfrac{\text{d}y}{\text{d}x}=k\cos(kx)$\\\end{minipage}}[/tex]
[tex]\boxed{\begin{minipage}{5.7 cm}\underline{Differentiating $\cos(k)$}\\\\If $y=\cos(kx)$, then $\dfrac{\text{d}y}{\text{d}x}=-k\sin(kx)$\\\end{minipage}}[/tex]
Integration Rules used:
[tex]\boxed{\begin{minipage}{4 cm}\underline{Integrating $e^{kx}$}\\\\$\displaystyle \int e^{kx}\:\text{d}x=\dfrac{1}{k}e^{kx}+\text{C}$\end{minipage}}[/tex]
The changes in account balances for Elder Company for 2021 are as follows:
Assets $ 480,000 debit
Common stock 250,000 credit
Liabilities 160,000 credit
Paid-in capital—excess of par 30,000 credit
Assuming the only changes in retained earnings in 2021 were for net income and a $50,000 dividend, what was net income for 2021?
The changes in account balances for Elder Company for 2021 are net income will be $160000
We have given debt common stock = $680000
Credit liabilities = 350000
Credit paid in capital = 190000
And an excess of par 30,000 credit Assuming the only changes in retained earnings
So 680000 = 350000+190000+30000+ retained earning
What is the net income?Net income is an entity's income minus the cost of goods sold, expenses, depreciation and amortization, interest, and taxes for an accounting period.
So retained earning = $110000
Dividend paid = $50000
So Net income = dividend paid + retained earning
Net income = $110000+$50000
Net income = $160000
So option (c) will be the correct answer.
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A movie theater sells up to 10 tickets at a time online.what is the domain of this graph.
The domain of the function is whole numbers from 0 to 10.
How to explain the domain?Given the graph of function represents the tickets sold vs cost. A movie theater sells up to 10 tickets at a time online. we have to find the domain of the graph.
As shown in the graph the number of tickets sold is 0 to 10 and also the number of tickets are always positive and a whole number. It can never be negative or in fraction form.
Hence, the value of x is a positive whole number. The domain of the function is the complete set of possible values of x. The domain of the function is whole numbers from 0 to 10.
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Michael went to the game store there was so much games he wanted and if one of them was $42.29 and the other one was $87.99 and he had $142 how much would he have left
Answer:
$11.72
Step-by-step explanation:
Add: $42.29 + $87.99 = $130.28
Subtract: $142 - $130.28 = $11.72
Answer:
he would have spent 131.08 dollars meaning he has 11.72 dollars left.
Step-by-step explanation:
How do I do this? The question is in the picture.
Answer:
Step-by-step explanation:
Which of the following options is a 3rd degree polynomial with exactly 1 real
root?
A. F(x)=x²-9x² +27x-27
B. F(x)=x+3x² +9x+27
C. F(x)= x +9x² +27x+27
D. F(x)=x+3x² -9x-27
Write this fraction as a mixed number.
Answer:
7/6=2/7/6
7/6=2
7/6=27/6
7/6=2
7/6
Which functions have a vertex with a x-value of 0? Select three options.
f(x) = |x|
f(x) = |x| + 3
f(x) = |x + 3|
f(x) = |x| − 6
f(x) = |x + 3| – 6
Answer:
f(x) = |x|f(x) = |x| + 3f(x) = |x| − 6Answer:
A,B,D
Step-by-step explanation:
Solve each inequality and graph the solution set and a number lined, express the Solution set in interval notation. 6 < x + 3 < 8 Solve each inequality and graph the solution set and a number lined , express the Solution set in interval notation . 6 < x + 3 < 8
The solution set for the given inequality is 3<x<5.
The given inequality is 6<x+3<8.
What is the solution set?In mathematics, a solution set is the set of values that satisfy a given set of equations or inequalities.
Now, solve the given inequality:
6<x+3<8⇒6<x+3 and x+3<8
6-3<x ⇒3<x
x+3<8⇒x<5
Thus, 3<x<5.
Therefore, the solution set is 3<x<5.
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Inequality and graph the solution set and a number line, express the Solution set in interval notation is 3 < x < 5
6<x+3<8
[tex]6 < x+3\quad \mathrm{and}\quad \:x+3 < 8[/tex]
What is the rule of inequality?[tex]\mathrm{If}\:a < u < b\:\mathrm{then}\:a < u\quad \mathrm{and}\quad \:u < b[/tex]
[tex]\mathrm{Combine\:the\:intervals}[/tex]
[tex]x > 3\quad \mathrm{and}\quad \:x < 5[/tex]
[tex]3 < x < 5[/tex]
Therefore the Inequality and graph of the solution set and a number line, express the Solution set in interval notation as 3 < x < 5.
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if f(x)=5^2x-2 and g(x)=x+1, find (f-g) (x)
The function (f-g) (x) is represented as 5^2x - 3 - x .
What is a function?The function is a type of relation, or rule, that maps one input to specific single output.
Given;
f(x)=5^2x-2
g(x)=x+1
Then, the function
(f-g) (x) = 5^2x-2 - (x+1)
Distribute the negative;
(f-g) (x) = 5^2x-2 - x - 1
(f-g) (x) = 5^2x - 3 - x
Hence, the function (f-g) (x) is represented as 5^2x - 3 - x .
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Olympic Enterprises has the following inventory data: Assuming average cost, what is the cost of goods sold for the June 14 sale?
Assuming average cost of $55.5, the cost of goods sold by Olympic Enterprises for the June 14 sale is equal to $444.
How to calculate cost of goods?In Financial accounting, the cost of goods sold for a business firm can be calculated by multiplying the total quantity of goods by an average cost. Mathematically, this is given by:
Cost of goods = quantity × average cost
Note: We would assume an average cost of $55.5.
Substituting the parameters into the formula, we have:
Cost of goods sold = 8 × 55.5
Cost of goods sold = $444.
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Curved surface area of a right circular cylinder is 4.4 m². If the radius of the base of the cylinder is 0.7 m, find its height. [Assume π = 22/7]
[tex]{\large{\textsf{\textbf{\underline{\underline{Given :}}}}}}[/tex]
★ Curved surface area of right circular cylinder is 4.4 m².
★ Radius of base of the cylinder is 0.7 m.
★ [tex]\tt \pi = \dfrac{22}{7}[/tex]
[tex]{\large{\textsf{\textbf{\underline{\underline{To \: Find :}}}}}}[/tex]
★ The height of cylinder.
[tex] {\large{\textsf{\textbf{\underline{\underline{Using \: Formula :}}}}}}[/tex]
[tex] \star \: \tt C.S.A \: of \: cylinder = \boxed{ \tt \pink{{ 2πrh}}}[/tex]
[tex] {\large{\textsf{\textbf{\underline{\underline{Solution :}}}}}}[/tex]
Let,
❍ The height of circular cylinder be [tex]h[/tex]
❍ Radius [r] of base of cylinder be 0.7 m
We know,
[tex] \star \: \tt C.S.A \: of \: cylinder = 2πrh[/tex]
Putting,
☆ [tex]\tt \pi = \dfrac{22}{7}[/tex]
☆ r as 0.7
[tex] \longrightarrow \tt 4.4 {m}^{2} = 2πrh[/tex]
[tex] \longrightarrow \tt 4.4 {m}^{2} = \bigg( 2 \times \dfrac{22}{7} \times 0.07 \times h \bigg)m[/tex]
[tex] \longrightarrow \tt \dfrac{44}{10} {m}^{2} = \bigg( {2 }\times \dfrac{22}{ \cancel{7}} \times \dfrac{ \cancel{7}}{10} \times h \bigg)m[/tex]
[tex] \longrightarrow \tt \dfrac{44}{10} {m}^{2} = \bigg( 44 \times \dfrac{ {1}}{10} \times h \bigg)m[/tex]
[tex] \longrightarrow \tt \dfrac{44}{ \cancel{10}} \times \cancel{10} \: m = \bigg( 44 \times 1 \times h \bigg)[/tex]
[tex] \longrightarrow \tt 44 m = 44h[/tex]
[tex]\longrightarrow \tt \dfrac{44}{44} m = h[/tex]
[tex]\longrightarrow \tt \red{ 1 m } = h[/tex]
Therefore, the height of cylinder = 1 m.
[tex]\begin{gathered} {\underline{\rule{290pt}{2pt}}} \end{gathered}[/tex]
*
Which of the following are situations that can be modeled with a quadratic function? Select all that apply.
O
0
A tree decays 10% every six weeks.
The height of a diver after jumping from a high dive into the water.
The height of a ball rolled down a hill.
A gym charges $15 perfitness class.
An ant bocid eliminates 50% of bacteria every 24 hours
The height of a rocket after it is Bunched
Answer:
Option 2 and 5 are correct. Look down for my explanation↓:
Step-by-step explanation:
So We need to tell which one of them is quadratic function.
Option 1 is exponential decay so, it is not quadratic.
Option 2 is quadratic because the diver will take the parabolic shape when jumps.
Option 3 is not quadratic. Option 4 is not quadratic it is linear.
Option 4 is again exponential not quadratic.
Option 5 is quadratic because it takes the parabolic shape again.
Which is not a solution of sin 20 = 1?
A = 90
B = 45
C = 225
D = - 135
Which is the graph of f,(x) = 0.5(4)*
I assume you meant [tex]f(x)=0.5(4)^{x}[/tex]. The graph is shown below.
One person ran 4 miles in 24 minutes. At this rate, how long would it take to run 26 miles?
Which of the following rational functions is graphed below?
10-
10
-10
-10-
O A. F(x) =
X-2
x(x + 5)
OB. F(x)=
1
(x+5)(x-2)
O C. F(x) = (x+5)(x - 2)
X
O D. F(x) = (x+5)(x-2)
X
The graph of the function f(x) = x(x + 5)(x - 2) have x intercepts at x = 0, -5 and 2
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given the equation:
f(x) = x(x + 5)(x - 2)
x(x + 5)(x - 2) = 0
x = 0, x + 5 = 0, x - 2 = 0
x = 0, -5 and 2
The graph of the function f(x) = x(x + 5)(x - 2) have x intercepts at x = 0, -5 and 2
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help! asap! algebra 2
We can subtract the function that represents the cost in 2000 from the function that represents the cost in 1990.
Doing this gives us [tex](-20t^{2}+1000)-(-10t^{2}+1500)=\boxed{-10t^{2}-500}[/tex]
Lines b and care parallel.
1/2
(7x+1)/(18x+4)
5/6
7/8
b
What is the measure of 22?
O m2 = 31°
Om42 = 50°
Om42 = 120°
Om22 130°
Answer:
Option 2angle 2 = 7x + 1 ( vertically opposite angles)
7x + 1 + 18x + 4 = 180° ( forming linear pair).
7x + 18x + 4 +1 = 180°
25x + 5 = 180°
25x = 180 - 5
25x = 175
x = 7°
angle 2 = 7(7)+ 1
= 50°
The measure of angle ∠2 of the parallel lines is ∠2 = 50°
What are angles in parallel lines?Angles in parallel lines are angles that are created when two parallel lines are intersected by another line. The intersecting line is known as transversal line.
We can conclude three factors determining parallel lines ,
Alternate angles are equal
Corresponding angles are equal
Co-interior angles add up to 180°
Given data ,
Let the parallel lines be b and c
Now , the measure of ∠1 + ∠2 = 180° ( angles on the same line )
And , the measure of ∠2 = ( 7x + 1 )° ( alternate angles are equal )
So , ( 7x + 1 ) + ( 18x + 4 ) = 180° ( angles on the same line )
On simplifying , we get
25x + 5 = 180
25x = 175
x = 7
So , the measure of angle ∠2 = ( 7 ( 7 ) + 1 )
The measure of angle ∠2 = 50°
Hence , the angle is ∠2 = 50°
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Divide.
74.48 ÷ 7.6
Enter your answer as a decimal in the box.
Math: Evaluating a piece wise function...help!
The values of the functions are g(-0.5) = -1, g(0.3) = 0 and g(0.5) = 1
How to evaluate the piece wise function?The function is given as:
[tex]g(x) = \left[\begin{array}{cc}-2&-2.5 < x \le -1.5\\-1&-1.5 < x \le -0.5\\0&-0.5 < x < 0.5&1&0.5 \le x < 1.5\end{array}\right[/tex]
To calculate g(-0.5), we make use of the domain -1.5 < x ≤ -0.5
At this domain;
g(x) = -1
So, the value of g(-0.5) is
g(-0.5) = -1
To calculate g(0.3), we make use of the domain -0.5 < x 0.5
At this domain;
g(x) = 0
So, the value of g(0.3) is
g(0.3) = 0
To calculate g(0.5), we make use of the domain 0.5 ≤ x 1.5
At this domain;
g(x) = 1
So, the value of g(0.5) is
g(0.5) = 1
Hence, the values of the functions are g(-0.5) = -1, g(0.3) = 0 and g(0.5) = 1
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Solve the system of equations : y = x/2 , y = -x - 3 . You can use any method you wish for solving systems of equations. Check your answer.
Answer:
x=−2 and y=−1
Step-by-step explanation:
Problem:
Solve y=x2;y=−x−3
Steps:
I will solve your system by substitution.
y=1/2x;y=−x−3
Step: Solve y= 1/2x for y:
Step: Substitute 1/2 x for y in y=−x−3:
y=−x−3
1/2x= =−x−3
1/2x+x=−x−3+x(Add x to both sides)
3/2x = -3
3/2x/3/2 = -3/3/2 (Divide both sides by 3/2)
x=−2
Step: Substitute −2 for x in y=1/2x:
y=1/2x
y=1/2(-2)
y=−1(Simplify both sides of the equation)
Answer:
x=−2 and y=−1
Your load is a container full of water. The container measures
1.0m x 1.25m x 1.1m and weighs 50kg when empty. Since 1 cubic
metre of water weighs 1 tonne, find the weight of the load
Answer:
1282kg
Step-by-step explanation:
1.0*1.12*1.1=1.232 tonnes
50kg + 1232kg = 1282kg
Hope this helps :)
Helppp needed plx as fast as u can
Answer:
The answer is either 30 degrees or 36 degrees.
You need a protractor to measure it.
Most probably, the answer is 30 degrees.
BUT PLEASE MEASURE THE ANGLE WITH A PROTRACTOR!
Answer:
d. 60°
Step-by-step explanation:
Since the clock is a full circle, it has a degree span of 360°.
∴ every 5-min interval on the clock
= 360° ÷ 12 five min intervals
= 30°
∴ acute angle formed by clock in figure
= two 5-min intervals
= 60°
Select the correct answer.
x
f(x)
2.0 2.8
2.5 1.1
3.0 –0.8
3.5 –1.2
4.0 –0.3
4.5 0.7
For the given table of values for a polynomial function, where must the zeros of the function lie?
A.
between 2.0 and 2.5 and between 4.0 and 4.5
B.
between 2.5 and 3.0 and between 4.0 and 4.5
C.
between 2.0 and 2.5 and between 3.5 and 4.0
D.
between 2.5 and 3.0 and between 3.5 and 4.0
Polynomials are mathematical expressions involving variables raised with non-negative integers and coefficients. The correct option is B.
What is a polynomial?Polynomials are mathematical expressions involving variables raised with non-negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication, and non-negative exponentiation of variables involved.
Example:
x² + 3x + 5
In order to find the values at which the given polynomial will have zeros of the function, we need to find the values at which f(x) changes from positive to negative or vice versa. Since this is the range at which the function must have crossed the x-axis on the graph.
As per the given table, the value of f(x) is changing from negative to positive and positive to negative are between 2.5 and 3.0 and between 4.0 and 4.5.
Hence, the correct option is B.
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-0.38 written as a fraction is
