The asymptote of the function given in the task content is the line; x = 25.
What is the asymptote of the function?It follows from the task content that the function given is a rational function and hence, the asymptote of the function is the X-value which renders the function undefined in which case, the denominator is equal to 0.
x - 25 = 0.
x = 25.
The end behaviour of the functions graph is that it approaches the line x = 25 but never touches the line.
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Find the coefficient of x^7y^3 in the expansion of (x - 2y)^10
Answer:
-960
Step-by-step explanation:
1) Expand [tex](x - 2y)^{10}[/tex] using the binomial theorem.
Binomial Theorem: [tex]\left(a+b\right)^n=\sum _{i=0}^n\binom{n}{i}a^{\left(n-i\right)}b^i[/tex]
1.1) Substitute the values into the theorem.
[tex]\sum _{i=0}^{10}\binom{10}{i}x^{\left(10-i\right)}\left(-2y\right)^i[/tex]
1.2) Expand summation.
[tex]=\frac{10!}{0!\left(10-0\right)!}x^{10}\left(-2y\right)^0+\frac{10!}{1!\left(10-1\right)!}x^9\left(-2y\right)^1+\frac{10!}{2!\left(10-2\right)!}x^8\left(-2y\right)^2+\frac{10!}{3!\left(10-3\right)!}[/tex]
[tex]x^7\left(-2y\right)^3+\frac{10!}{4!\left(10-4\right)!}x^6\left(-2y\right)^4+\frac{10!}{5!\left(10-5\right)!}x^5\left(-2y\right)^5+\frac{10!}{6!\left(10-6\right)!}x^4\left(-2y\right)^6+\frac{10!}{7!\left(10-7\right)!}x^3\left(-2y\right)^7+\frac{10!}{8!\left(10-8\right)!}x^2\left(-2y\right)^8+\frac{10!}{9!\left(10-9\right)!}x^1\left(-2y\right)^9+\frac{10!}{10!\left(10-10\right)!}x^0\left(-2y\right)^{10}[/tex]
1.3) Simplify them.
1.4) You will get:
[tex]=x^{10}-20x^9y+180x^8y^2-960x^7y^3+3360x^6y^4-8064x^5y^5+13440x^4y^6-15360x^3y^7+11520x^2y^8-5120xy^9+1024y^{10}[/tex]
2) We are told to find the coefficient of [tex]x^{7} y^{3}[/tex]. Find it from the simplified expansion. The coefficient is -960.
If P = (-2,7), Find:
Rx-1(P)
([?], [])
Answer is (4,7)
Step-by-step explanation:
A cuboid measures X cm by 3X cm by 5X cm. Calculate the volume of the cuboid in terms of X.
How many solutions exist for the system of equations in the graph?
Answer:
Two solutions exist for the system of equations in the graph.
Step-by-step explanation:
Solutions are when the two graphs intersect.
The table above shows cell phone sales by color. What percent of the cell phones sold were blue?
Answer:
20percent
Step-by-step explanation:
First we will find the value of k.
Given
White + Black + Blue + Red = Total
8k+30+(30-2k)+k+5 = 100
8k+30+30-2k+k+5=100
7k+65=100
7k+65-65=100-65
7k=35
k = 35/7 = 5
Now given number of blue cell phone sold is 30-2k = 30 - 2(5) = 30 - 10 = 20,
Percentage of Blue cell phones = [tex]\frac{Blue}{Total} *100\\=\frac{20}{100} *100\\=20%[/tex]percent
estimate 789×215 can any one answer
"Bobby, you should know that the minimum legal speed for this highway is 45 MPH, and the maximum legal speed is 65 MPH."
Inequalities help us to compare two unequal expressions. The inequality that represents the given statement is 45≤x≤ 65.
What are inequalities?Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed.
It is mostly denoted by the symbol <, >, ≤, and ≥.
Given the maximum legal speed on the highway is 65 MPH, therefore, the value of x must not exceed 65 MPH.
x ≤ 65
Also, the minimum legal speed on the highway is 45 MPH, therefore, the value of x must not be less than 45 MPH.
45≤x
By combining the two inequalities, we will get,
45≤x≤ 65
Hence, the inequality that represents the given statement is 45≤x≤ 65.
The complete question is:
Write an inequality that accurately represents the following statement: "Bobby, you should know that the minimum legal speed for this highway is 45 MPH, and the maximum legal speed is 65 MPH."
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Please answer all parts as I know the answers but need the work to go with them. Thus, I believe that some answers are correct. Thank you!
The number of the sample that is necessary is 171. The number of employees that would be selected if E is 30 = 476
How to solve for the number of the sampleThe standard deviation = 398
error E = 50
Alpha is = 1-0.90 = 0.10
a. We are to find the value of the size of the sample
Z∝/2 = Z0.05
= 1.645
sample size,n >= [Za/2 *(sigma/E)]^2
n >= [1.645 * (398/50)] ^2
n >= 171.46
n = 171
b.
error,E = 30
n >= [1.645 * (398/30)] ^2
n >= 476.27
n = 476
Complete questionA survey is planned to determine the mean annual family medical expenses of employees of a large company. The management of the company wishes to be 90% confident that the sample mean is correct to within ±$50 of the population mean annual family medical expenses. A previous study indicates that the standard deviation is approximately $398. a. How large a sample is necessary?
b. If management wants to be correct to within ±$30, how many employees need to be selected?
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Tony is installing a window that is shaped like a parallelogram. He has 6 square meters of glass and knows that the base of the window needs to be 2 and 1 half meters. What must the height of the window be if he uses all the glass? Write your answer as a mixed number.
The required height of window of the glass 2.4 meters.
Tony is installing a window that is shaped like a parallelogram. He has 6 square meters of glass and knows that the base of the window needs to be 2 and 1 half meters.
What is parallelogram?parallelogram is a quadrilateral consist of pairs of parallel side.
Area of parallelogram = base x height
6 = 2.5 x height
height = 2.4 m
Thus the required height of window is given by 2.4 meters.
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what should be added to 4x²-3x²+1 to make it a perfect square
[tex]im \: guessing \: its \: 4x {}^{2} - 3x + 1 \\ (correct \: me \: if \: im \: wrong)[/tex]
[tex](a - b) {}^{2} = a {}^{2} - 2ab + {b}^{2} [/tex]
[tex]4x {}^{2} = a {}^{2} \: \: \: \: \: \: \: \: \: \: \: b {}^{2} = 1 \\ a = 2x \: \: \: \: \: \: \: \: \: \: \: \: \: \: b = 1[/tex]
[tex](2x - 1) {}^{2} = 4x {}^{2} -4x + 1[/tex]
[tex]we \: need \: to \: add \: a \: - x \\ \: to \: the \: original \: equation[/tex]
Note that this problem can be approached in many ways. For instance, we can add to the b² term instead of changing the middle term...Mr. Chan’s lawn grows 2 1/8 inches every 2 week. He mows his lawn every 2 weeks and cuts off the top 1 3/4 inches of lawn. If Mr. Chan’s lawn was 4 inches tall at the beginning of the season, how many inches tall, in decimal form, is Mr. Chan’s lawn after 8 weeks.
Answer:
5.5 in
Step-by-step explanation:
First we will calculate the total lawn grown after 8 weeks.
Grow Rate = [tex]2\frac{1}{8} in/2 weeks[/tex]
Total lawn grown after 8 weeks = [tex]2\frac{1}{8} *4\\=8.5 in[/tex]
Next we will calculate the total lawn mown after 8 weeks.
Mowing Rate = [tex]1\frac{3}{4} in/2weeks[/tex]
Total lawn mown after 8 weeks = [tex]1\frac{3}{4} *4\\=7 in[/tex]
Lawn Height after 8 weeks = Initial Lawn Height + Total lawn grown - Total lawn mown
= 4 in + 8.5 in - 7 in
= 5.5 in
(2a+b) (a-b) + (2a-b) (a+b)
Answer: 4a^2-2b^2 (I think this is right)
Step-by-step explanation:
Using the order of operations I started by multiplying both of the sides separately. The left side of the equation becomes 2a^2-b^2-ab while the right becomes 2a^2-b^2+ab. Then I put the sides together to add them and after combining like terms it becomes 4a^2-2b^2.
A company has the following account balances at the end of the year.
Accounts Balances
Equipment $ 22,000
Accounts payable 2,200
Salaries expense 29,000
Common stock 12,000
Land 14,000
Notes payable 16,000
Service revenue 35,000
Cash 5,200
Retained earnings ?
Based on the account balances at the end of year, the retained earnings are $5,000.
What are the retained earnings?First, find the net income:
= Service revenue - Salaries
= 35,000 - 29,000
= $6,000
Then find the assets:
= 22,000 + 14,000 + 5,200
= $41,200
Then the liabilities:
= 2,200 + 16,000
= $18,200
Retained earnings:
= Assets - Liabilities - Net income - Common stock
= 41,200 - 18,200 - 6,000 - 12,000
= $5,000
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Am I correct with my answers?
Answer:
w = 70° . . . . alternate interior anglesx = 70° . . . . alternate interior anglesy = 40° . . . . angle sum in a trianglez = ?? . . . . not enough informationStep-by-step explanation:
The alternate interior angles theorem, and the angle sum theorem can be used here.
Alternate interior anglesAlternate interior angles are found on either side of a transversal where it crosses a pair of parallel lines. They are between the parallel lines. Their vertices are at the junction of the transversal and the parallel lines. Alternate interior angles are congruent.
In this diagram, there are two pairs of alternate interior angles where the two transversals AD and BD cross parallel lines AB and CD.
At points A and D, the alternate interior angles are 70° and x, respectively. This tells you ...
x = 70° . . . . alternate interior angles theorem
At points B and D, the alternate interior angles are w and 70°, respectively. This tells you ...
w = 70° . . . . alternate interior angles theorem
Angle sumThe angle sum theorem tells you the sum of angles in a triangle is 180°. This fact can be used to find the measure of angle y.
70° +w +y = 180°
y = 180° -70° -w = 110° -70°
y = 40° . . . . angle sum theorem
There is not enough information to determine the measure of angle z.
z = indeterminate
At the end of January 2003, the population of my town was 11,212. The population of my town increases by 322 every month. In what month does the population of my town first exceed 15,000?
In 11.76 months, the value of the population will be 15000.
We have given that,
At the end of January 2003, the population of my town was 11,212.
the population is increased by 322 every month
So at the end of the second-month population will be 11534.
suppose x represents the year and y represent the population
The population increased by 322 every month
Therefore the value of m =322
[tex](x_1,y_1)=(0,11212)[/tex]
We have m=332
[tex](x_2,y_2)=(x_2,15000)[/tex]
We have to determine the value of the x_2
What is the slope point form of the line?[tex](y_2-y_1)=m(x_2-x_1)[/tex]
[tex]322\left(x_2-0\right)=15000-11212[/tex]
[tex]322\left(x_2-0\right)=3788[/tex]
[tex]\frac{322\left(x_2-0\right)}{322}=\frac{3788}{322}[/tex]
[tex]x_2=\frac{1894}{161}[/tex]
[tex]x_2=11.76[/tex]
Therefore in 11.76 months, the value of the population will be 15000.
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Solve the system using substitution. -x+y=9 and x-y=-9
Answer:
Infinite Number of Solutions
Step-by-step explanation:
Hello!
We can solve for y in the first equation, and plug that value in for y in the second equation.
Find the Equation for Y-x + y = 9y = 9 + xNow that we know the equation for y, we can plug that in for y into the second equation to solve for x.
Solve for Xx - y = -9x - (9 + x) = -9x - 9 - x = -9-9 = -9Since the equations match, there are an infinite number of solutions.
If we take a close look at the equations, we can also see that they are the same equation, but with flipped signs.
What’s the error in these equations with steps will give Brainily
Answer:
2. (3+4) should be (3*4)
3. x is also x^1, so it should be x^(6+3+1)
4. you have to do 3^4 and 2^3 before timing them together
Part E
Christopher Columbus set sail from Spain in 1492. In what year did the Civil War end?
I know he died 1865 but you explain the answer
Question A librarian weighs each book that was returned to the library (to the nearest pound). Below is the data. 245 55 Make a dot plot that represents the library book data. 3 4 3 4 4 2 199 CO 8 5 2 CO 8 3 3 Question A librarian weighs each book that was returned to the library ( to the nearest pound ) . Below is the data . 245 55 Make a dot plot that represents the library book data . 3 4 3 4 4 2 199 CO 8 5 2 CO 8 3 3
The dot plot that represents the library book data is shown in the image below.
How to Construct a Dot Plot?To construct a dot plot, each data point is represented as a dot. The number of dots one data point has represents the frequency at which that data point occurs in the data set.
The data set given in the table will have the following data points and frequencies:
1: 1
2: 3
3: 4
4: 4
5: 4
6: 0
7: 2
8: 2
The dot plot for the data is shown in the image below.
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What is the equation of a parabola that has intercepts of x=-2 and x=6 and passes through point (8,6).....
The equation of a parabola that has intercepts of x=-2 and x=6 and passes through point (8,6) is f(x) = 3/10(x+2)(x-6)
Equation of a parabolaThe standard equation of a parabola is in the form f(x) = (x-a)(x-b)
where a and b are the intercepts of the graph. Given the parabola that has intercepts of x=-2 and x=6, the resulting equation will be:
f(x) = a(x-(-2))(x-6)
f(x) = a(x+2)(x-6)
If the parabola passes through (8, 6), then;
6 = a(8+2)(8-6)
6 = a(20)
a = 6/20
a = 3/10
Substitute
f(x) = 3/10(x+2)(x-6)
Hence the equation of a parabola that has intercepts of x=-2 and x=6 and passes through point (8,6) is f(x) = 3/10(x+2)(x-6)
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Can a function ever have 2 y-
intercepts?
Answer:
yes I think I'm new to this but I think that's a yes
Use the ray tool to graph the function. f(x)=−|x+2|+1
The graph of the function. f(x)=−|x+2|+1 is illustrated.
How to illustrate the function?The given function is f(x)=−|x+2|+1.
We will have to draw the graph of the function.
When x = 1, f(1) will be -2. When x = 2, f(2,) will be -3
The points are illustrated based on the information given and the appropriate graph is illustrated and attached.
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What is the value of g(f(x)) when x = -2 if f(x) = x³
and g(x) =
2x+1
when x < 0
x²-1
when x>0
Answer:
g(f(-2)) = -15
Step-by-step explanation:
• f(x) = x³
Then
f(-2) = (-2)³ = -8
• When x = -2 → g(f(x)) = g(f(-2)) = g(-8)
Since -8 ≤ 0 then g(-8) = 2×(-8) + 1 = -16 + 1 = -15
Conclusion:
g(f(-2)) = -15
The length of a rectangle is 2x-3 feet, and the width is 5 feet. What is the area of the rectangle in square
A. 7x-15
B. 10x-15
C. 10x-8
D. 7x-8
Answer:
The answer is D. 7x-8
Step-by-step explanation:
We can solve this problem by finding the area of the rectangle, which is equal to the length times the width. In this case, the length is 2x-3 feet and the width is 5 feet. Therefore, the area of the rectangle is (2x-3)(5), or 7x-8.
In the diagram below of AACT, BE | AT.
C
F
If CB = 3, CA = 10, and CE = 6, what is the length
of ET?
1)
5
2)
14
3)
20
4)
26
Answer:
14
Step-by-step explanation:
CB/AB = CE/ET
3/7 = 6/ET
ET = 14
Which inequality will have a shaded area below the boundary line?
A.
y – x > 5
B.
2x - 3y ≤ 3
C.
2x – 3y
D.
7x + 2y ≤ 2
E.
3x + 4y > 12
Option c) 2x-3y ≥ 3 is correct inequality which has a shaded area below the boundary line.
Attempting all the equation on the graph to get the solutions
Inequality can be define as the relation of equation contains the symbol of ( ≤, ≥, <, >) instead of equal sign in an equation.
Since, while attempting all the option on graph. The one equation that satisfies the condition is 2x-3y ≥ 3 of having shaded area below the boundary line.
Thus, the option c) 2x-3y ≥ 3 is correct implification on graph which shows the shaded area below the boundary line.
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Find the perimeter of the triangle whose vertices are (−7,−1), (5,−1), and (5,4). Write the exact answer. Do not round.
The perimeter of the triangle is 30 units
How to determine the perimeter?The vertices are (−7,−1), (5,−1), and (5,4).
Start by calculating the distance between the vertices using:
[tex]d = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2[/tex]
So, we have:
[tex]d1 = \sqrt{(-1 + 1)^2 + (5 + 7)^2[/tex]
d1 = 12
[tex]d2 = \sqrt{(-1 - 4)^2 + (5 - 5)^2[/tex]
d2 =5
[tex]d3 = \sqrt{(-1 - 4)^2 + (-7 - 5)^2[/tex]
d3 = 13
The perimeter is then calculated as:
P = d1 + d2 + d3
This gives
P = 12 + 5 + 13
Evaluate
P = 30
Hence, the perimeter of the triangle is 30 units
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12:00,10:00,6:00,4:00. What is the missing time?
in rhombus PQRS below ,PT=11 m and QT =9m.Find the area of the rhombus .
Answer:
198 [m²].
Step-by-step explanation:
1) required area can be calculated as four area of the triangle PQT:
A=4*A(ΔPQT);
2) A(ΔPQT)=0.5*PT*QT, then
3) A=4*0.5*PT*QT; ⇔
A=2*PT*QT; ⇒
4) finally,
A=2*11*9=198 [m²].
The area of the rhombus PQRS is 198 m².
What is Rhombus?A rhombus is a quadrilateral with four vertices, four sides and four angles with all four sides are equal. It has basically a diamond shape. Rhombus will become square if all the angles of the rhombus equals 90°.
Given that, PT = 11 m and QT = 9 m.
We know that diagonals of a rhombus are perpendicular bisectors.
Therefore, RT = 11 m and ST = 9 m.
Area of a rhombus can be found using diagonals as,
Area = [tex]\frac{1}{2}[/tex] × D₁ × D₂
where D₁ and D₂ are the length of two diagonals of the rhombus.
D₁ = PT + RT = 11 + 11 = 22 m
D₂ = QT + ST = 9 + 9 = 18 m
Area = [tex]\frac{1}{2}[/tex] × 22 × 18
= 22 × 9
= 198 m²
Hence the area of the rhombus given is 198 m².
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The question is down below
also I home school and have permission to post this question
Answer:
960
Step-by-step explanation:
(if i made any typos, sorry it is kind of hard to type on computer over writing on paper.)
A=2AB+(a+b+c)h
AB=s(s﹣a)(s﹣b)(s﹣c)
s=(a+b+c)/2
Solving forA
A=ah+bh+ch+1/2 sqrt(﹣a^4+2(ab)^2+2(ac)^2﹣b4+2(bc)^2﹣c^4)=10·12+24·12+26·12+1
2·﹣104+2·(10·24)2+2·(10·26)2﹣244+2·(24·26)2﹣264=960