The area of one wall of the room is 72 square feet.
What is the area of a square?The area of a square is given by -
A{S} = a²
where -
{a} is side of square.
Given is a square room has a floor area of 144 square feet. The height of the room is 6 feet.
It is given that -
floor area = 144
a² = 144
a = √(144)
a = √(12 x 12)
a = 12
The area of the wall will be equivalent to -
A{W} = h x a
A{W} = 6 x 12
A{W} = 72 square feet.
Therefore, the area of one wall of the room is 72 square feet.
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The profits shown in retained earrings can be used for_
A. Predicting future income.
B.re-investment into the company
C. Buying a house.
D. Investing into other companies.
The profit shows in retained earning can be used for reinvestment into the company
There are many measures and uses of earnings. Some analysts like to calculate earnings before taxes (EBT), also known as pre-tax income. Some analysts prefer to see earnings before interest and taxes (EBIT). Still, other analysts, mainly in industries with a high level of fixed assets, prefer to see earnings before interest, taxes, depreciation, and amortization, also known as EBITDA.
Earnings that deviate from the expectations of the analysts that follow that stock can have a great impact on the stock's price, at least in the short term. For instance, if analysts on average estimate that earnings will be $1 per share and they come in at $0.80 per share, the price of the stock is likely to fall on that "earnings miss."
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Pigeonhole suppose that every student in a discrete mathematics class of 25 students is a sophomore, a junior, or a senior. is the following statement true or false:
Suppose that every student in a discrete mathematics class of 25 students is a sophomore, a junior, or a senior: FALSE
What is a sophomore?A sophomore in the United States is a student in their second year at an educational institution, usually a secondary school or a college or university, but also other types of post-secondary educational institutions. A sophomore in high school is equivalent to a tenth-grade or Class-10 student.In sports, a sophomore is a professional athlete in their second season.As in the description, it is given that a sophomore in high school is equivalent to a tenth-grade or Class-10 student.
So, the above-given statement becomes false as it says that every student is a sophomore but the class has juniors and seniors.
Therefore, the statement "suppose that every student in a discrete mathematics class of 25 students is a sophomore, a junior, or a senior" is FALSE.
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The complete question is given below:
Suppose that every student in a discrete mathematics class of 25 students is a sophomore, a junior, or a senior. Is the following statement true or false:
"The course must have at least five sophomores, or at least 20 juniors, or at least 10 seniors."
A board is 17 5/8 in. long. If it must be divided into seven pieces of equal length, how long must each piece be?
a) x³y²if x = 2 and y = 4
Answer:
128
Step-by-step explanation:
x³y²if x = 2 and y = 4
x³*y²
[tex](2)^{3} * (4)^{2}[/tex]
(2*2*2)*(4*4)
(8)*(16)
128
A magnetic levitation train travels between the city center of shanghai china and pudong international airport. the trip covers 30 kilometers i'm just 8 minutes. what is the average speed of the train in miles per hour
Average speed of the train as it covered 30 kilometers in 8 minutes is equal to 139.8 miles per hour.
As given,
Total distance= 30 kilometers
Total time taken = 8 minutes
1 kilometer = 0.62137 miles
30 kilometers = 30 × 0.62137
= 18.641 miles
8 minutes = ( 8 / 60) hour
Average speed= total distance / total time taken
= 18.641 / (8/60)
= 139.8 miles/ hour
Therefore, average speed of the train as it covered 30 kilometers in 8 minutes is equal to 139.8 miles per hour.
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∠A and angle B∠B are complementary angles. If m angle A=(x+13)m∠A=(x+13)
and m angle B=(7x+13)^∠B=(7x+13) then find the measure of angle B∠B
The value of angle B is 69°.
How to calculate the angle?It should be noted that the sum of a complementary angle is 90°.
Therefore, the value will be:
x + 13 + 7x + 13 = 90
8x + 26 = 90
Collect like terms
6
8x = 90 - 26
8x = 64
Divide
x = 64/8
x = 8
Angle B = 7x + 13
= 7(8) + 13
= 56 + 13
= 69
Angle B is 69°.
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Show ([tex]\frac{\sqrt{11} }{6} ,[/tex][tex]\frac{5}{6}[/tex]) is or is not on the unit circle. State the unit circle definitions and definitions in terms of other trig functions.
By using coordinates in rectangular form and Pythagorean theorem, we conclude that the point (x, y) = (√11 / 6, 5 / 6) is on the unit circle as its norm is equal to 1.
Is a given point on Cartesian plane lying on the unit circle?
We find a point in rectangular form, that is, a point of the form (x, y). Unit circles are circles with a radius 1 that are commonly used to represent graphically angles. The given point is in the units if and only if its norm is equal to 1. The norm of the point is determined by using the Pythagorean theorem:
r = √[(√11 / 6)² + (5 / 6)²]
r = √[(11 / 36) + (25 / 36)]
r = √(36 / 36)
r = √1
r = 1
By using coordinates in rectangular form and Pythagorean theorem, we conclude that the point (x, y) = (√11 / 6, 5 / 6) is on the unit circle as its norm is equal to 1.
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Find the equation of the line shown.
Answer: y=0.5x+0.5
Step-by-step explanation:
[tex]\displaystyle\\(1,1)\ \ \ \ (-3,-1)\\\\\boxed {\frac{x-x_1}{x_2-x_1}=\frac{y-y_1}{y_2-y_1} }\\\\x_1=1\ \ \ \ x_2=-3\ \ \ \ y_1=1\ \ \ \ y_2=-1\\\\\frac{x-1}{-3-1}=\frac{y-1}{-1-1} \\\\\frac{x-1}{-4}=\frac{y-1}{-2} \\[/tex]
Multiply both parts of the equation by -2:
[tex]\displaystyle\\\frac{x-1}{2} =y-1\\\\\frac{x}{2}-\frac{1}{2} =y-1\\\\\frac{x}{2}-\frac{1}{2}+1 =y-1+1\\\\\frac{x}{2}+\frac{1}{2} =y \\[/tex]
Thus,
y=0.5x+0.5
Randalstown Rugby Club play 20 matches and win 17 of the matches.
What percentage of the matches did Randalstown win?
Answer:
85%
Step-by-step explanation:
Total no. of matches played,
→ x = 20 matches
No. of matches they won,
→ y = 17 matches
Now the win percentage will be,
→ (y/x) × 100
→ (17/20) × 100
→ 0.85 × 100
→ 85%
Hence, the percentage is 85%.
Find x and y. Please
Answer:
x = 4 y = 21
Step-by-step explanation:
16x - 23 = 10x + 1
16x - 10x = 23 + 1
6x = 24
24/6 = x
x = 4
16(4) - 23 = 41
41 + (180 - 62) + y = 180
41 + 118 + y = 180
y = 21
Find the complement of the set given that u = {0, 1, 2, 3, 4, 5, 6, 7, 8}. (enter your answers as a comma-separated list.) the set of odd natural numbers less than 8
{ 0,2,4,6,8} is the complement of the set.
What is natural number in math?
Normative Numbers The numbers we use to count or place things in order are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, and 11. Complete numbers the range of numbers that includes zero and natural numbers.Is zero a natural number?
0 is not a natural number, so no. As we all know, natural numbers are positive integers with a range of 1 to infinity. However, we get a number when we combine 0 with a positive integer like 10, 20, or another number.u = {0, 1, 2, 3, 4, 5, 6, 7, 8}
Odd number less than 8 = { 1,3,5,7 }
complement = {0, 1, 2, 3, 4, 5, 6, 7, 8} - { 1,3,5,7 }
= { 0,2,4,6,8}
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The expression
³√x²y³ = x²y³
where x and y are non-negative real numbers.
r, the exponent of X, is:
s, the exponent of y, is:
Using exponent power property, ³√x²y³ = x^r y^s, where x and y are non-negative real numbers.
r, the exponent of x, is: 2/3
s, the exponent of y, is: 1
What is Exponent power property?According to the Power of a Power Property, you can multiply the exponents if one exponent is increased to a higher exponent. This characteristic may be used to resolve the equation (3 x 2) 3.
³√x²y³ = x^r y^s
Cubing on both sides,
x²y³ = x^3r y^3s
As base is same, equating the powers
⇒ 2 = 3r; r = 2/3
⇒ 3 = 3s; s = 1
The correct question is -The expression
³√x²y³ = x^ry^s
where x and y are non-negative real numbers.
r, the exponent of X, is:
s, the exponent of y, is:
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Did Paul or pippa do it correctly
Triangle A'B'C' is the result of dilation about the origin with a scale factor of 2 / 3 on triangle ABC. (Translation: Pippa was right)
How to determine the scale factor to modify a right triangle
Herein we find a picture a graph with two proportional right triangles, which means that the small triangle is the consequence of a rigid transformation. The kind of rigid transformation used is a dilation around the origin, whose formula is shown below:
P'(x, y) = k · P(x, y)
Where k is the scale factor.
There is a dilation if and only if each point is scaled by the same factor. If we know that A(x, y) = (3, 9), A'(x, y) = (2, 6), B(x, y) = (9, 9), B'(x, y) = (6, 6), C(x, y) = (3, 3) and C'(x, y) = (2, 2), then the scale factor for each point is:
Point A
(2, 2) = k · (3, 3)
k = 2 / 3
Point B
(6, 6) = k · (9, 9)
k = 2 / 3
Point C
(2, 2) = k · (3, 3)
k = 2 / 3
Then, triangle A'B'C' is the result of dilation about the origin with a scale factor of 2 / 3 on triangle ABC.
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Is it possible to have a function f defined on [ 4 , 5 ] and meets the given conditions? f is continuous on [ 4 , 5 ], is non-constant, and takes on only integer values.
No, It is not possible that f is continuous on [ 4 , 5 ] is non-constant, and takes on only integer values.
Here,
A function f defined on [ 4 , 5 ].
We have to find, is it possible to f is continuous on [ 4 , 5 ], is non-constant, and takes on only integer values.
What is Intermediate value theorem?
Intermediate value theorem states that if “f” be a continuous function over a closed interval [a, b] with its domain having values f(a) and f(b) at the endpoints of the interval, then the function takes any value between the values f(a) and f(b) at a point inside the interval.
Now,
A function f defined on [ 4 , 5 ].
Assume that the function,
f : [ 4 , 5 ] → Z is a non constant continuous function.
Then, f(4) and f(5) both are integers and not equal to each other.
By, Intermediate value theorem;
Function f takes all real numbers between f(4) and f(5) at least once.
These would contain all non integers rational and irrational number between f(4) and f(5), contradicting the assumption that function takes only integer values.
Hence, It is not possible that f is continuous on [ 4 , 5 ] is non-constant, and takes on only integer values.
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2×3÷2+1+2×33 what's the answer
Answer: 70
Step-by-step explanation:
2×3÷2+1+2×33
PEMDAS, do all the multiplication first.
2×3 = 6, 2×33=66
Do division next.
6÷2=3
3+1+66=70
What is the converse of the following statement?
"If cows make milk, then chickens make eggs. "
Answer:
"If chickens make eggs, then cows make milk."
Step-by-step explanation:
Answer: A: If chickens make eggs, then cows make milk.
Step-by-step explanation: Hope that helped
Write the equation of the line passing through the points (−3,9) and (−9,3).
Question content area bottom
Part 1
The equation of the line is enter your response here.
The equation of the line is y=x+12.
What is line?A line is a straight one-dimensional figure having no thickness and extending infinitely in both directions. A line is made of a set of points which is extended in opposite directions infinitely. It is determined by two points in a two-dimensional plane. The two points which lie on the same line are said to be collinear points.
Given:
The points are
(-3,9)=[tex](x_{1} ,y_{1} )[/tex] and (-9,3)=[tex](x_{2} ,y_{2} )[/tex]
The equation y = mx + c is the general equation of any straight line where m is the gradient of the line (how steep the line is) and c is the y -intercept (the point in which the line crosses the y -axis).
We have to Write the equation of the line.
According to given question we have,
Equation of line passing through the point (-3,9) and (-9,3).
Slope of the line=
[tex]\frac{y_{2}-y_{1} }{x_{2} -x_{1} } \\\\=\frac{3-9}{-9+3} \\\\=\frac{-6}{-6} \\\\=1[/tex]
⇒y−9=1(x+3)
⇒y-9=x+3
Add 9 on both sides we get,
y=x+12
∴ y=x+12 which is in the form y=mx +c is the required equation.
Therefore, the equation of the line is y=x+12.
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y = x + 12
What is equation of a line?
The standard form of equation of a line is ax + by + c = 0. Here a, b, are the coefficients, x, y are the variables, and c is the constant term. It is an equation of degree one, with variables x and y. The values of x and y represent the coordinates of the point on the line represented in the coordinate plane.
y-y₁=m(x-x₁)
mm₁=-1
Points (-3,9) and (−9,3).
Slope of the line m = (y₂ - y₁)/(x₂ - x₁)
m = (3-9)/(-9+3)
m = 1
Now equation of line passing through two points
(y - y₁)/(y₂ - y₁) = m*(x - x₁)/(x₂ - x₁)
(y - 9)/(3-9) = 1*(x - 3)/(-9+3)
y - 9 = x + 3
y = x + 12
Therefore, the equation of line is y = x + 12
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6. CalC1c02a 10 pts possible
Find the function g that is finally graphed
after the following transformations are ap-
plied in the order given to the graph of a
function f:
(1) reflect about the x-axis;
(2) shift down 2 units;
(3) stretch vertically by a factor 5;
(4) reflect about the y-axis.
1. g(x) = -10-5f(-x)
2. g(x) = 10-5f(x)
x 3. g(x) = 10 +5f(-x)
× 4. g(x) =
10 - 2ƒ(−x)
5. g(x) = 5f(x) - 10
help!!
The function g that is finally graphed after the transformations are applied is g(x) = -5f(-x) - 10
How to find the function g that is finally graphed after the following transformations are applied?The function is given as:
f(x)
Next, we apply the transformations
So, we have:
(1) reflect about the x-axis;
This is represented as
(x, y) = (x, -y)
So, we have
g(x) = -f(x)
(2) shift down 2 units;
This is represented as
(x, y) = (x, y - 2)
So, we have
g(x) = -f(x) - 2
(3) stretch vertically by a factor 5;
This is represented as
(x, y) = (x, 5y)
So, we have
g(x) = 5(-f(x) - 2)
Evaluate
g(x) = -5f(x) - 10
(4) reflect about the y-axis.
This is represented as
(x, y) = (-x, y)
So, we have
g(x) = -5f(-x) - 10
Hence, the function g that is finally graphed after the following transformations are applied is g(x) = -5f(-x) - 10
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Suppose that for a function g (x), g (4) = 7. Select all of the statements that are true.
A.
B.
C.
D.
E.
4 is in the range of g.
For a value a, it is possible that g (a) = 4.
For a value y, it is possible that g (4) = y.
The point (4,7) is on the graph of y = g(x).
The point (7,4) is on the graph of y = g(x).
7 gifts are to be distributed among 10 children. how many distinct results are possible if no child is to receive more than 1 gift?
1.00 *10³ + 4.235 *10*
either 1042.35 or 1.04235*10^3
Find the weighted average of a data set where 20 has a weight of 3, 40 has a weight of 5, and 50 has a weight of 2.
The weighted average of a data set is 36.
Here,
Given data set;
20 has a weight of 3, 40 has a weight of 5, and 50 has a weight of 2.
We have to find the weighted average of a data set.
What is Weighted Average?
Weighted average is a calculation that takes into account the varying degrees of importance of the numbers in a data set.
Now,
Given data set;
20 has a weight of 3, 40 has a weight of 5, and 50 has a weight of 2.
The weighted average is given by the formula;
[tex]x = \frac{f_{1} x_{1} + f_{2} x_{2}+ f_{3} x_{3}+ ...... f_{n} x_{n}}{f_{1} +f_{2} + f_{2}}[/tex]
Hence,
The weighted average of a data set;
x = 20 x 3 + 40 x 5 + 50 x 2 / 3+5+2
x = 360/10 = 36
Hence, The weighted average of a data set is 36.
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el ortocentro y varicentro de un triángulo equilátero son el mismo punto
Answer: The orthocenter and varicenter of an equilateral triangle are the same point?
Step-by-step explanation
Answer: De nuevo, puedes ver que el baricentro, el ortocentro y el circuncentro son todos el mismo punto para un triángulo equilátero. Tenemos un centro más para comparar, el incentro. Como habrás sospechado, el incentro es el mismo punto que los otros tres para un triángulo equilátero.
Step-by-step explanation:
Simplify the expression.
12e +6-2e + 5
Answer:
10e + 11
Step-by-step explanation:
12e + 6 - 2e + 5 ← collect like terms
= (12e - 2e) + (6 + 5)
= 10e + 11
Three friends go to a store to rent games and movies.
Calvin rents 3 movies and 2 video games and spends a
total of $25. Samantha rents 2 movies and 1 video game
and spends a total of $14.75.
Answer:
Let x = the cost of a movie
Let y = the cost of a game
Using these variables, we can set up equations.
3x + 5y = 42 eq1
9x + 7y = 72 eq2
We have here a system of equations, where we have two or more equations with two or more different variables. We use the elimination method to solve for the variables.
Multiply eq1 by 3. Keep eq2.
9x + 15y = 126 eq1
9x + 7y = 72 eq2
Subtract eq2 from eq1 to eliminate the x terms.
8y = 54
y = 6.75
This rental cost of one video game is $6.7
Substitute the value of y into eq1 to solve for x. This will give you the rental cost of one movie.
Step-by-step explanation:
pa brainly po
The cost of movie is $4.5 and cost of video game is $5.75.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Let x be the cost of movie and y be the cost of video game
Calvin rents 3 movies and 2 video games and spends a total of $25.
3x+2y=25...(1)
Samantha rents 2 movies and 1 video game and spends a total of $14.75.
2x+y=14.75
y=14.75-2x..(2)
Substitute (2) in equation (1)
3x+2(14.75-2x)=25
3x+29.5 -4x=25
-x+29.5 = 25
Subtract 29.5 from both sides
-x=25-29.5
x=4.5
Now let us plug in x value in equation (2)
y=14.75-2(4.5)
y=5.75
Hence, the cost of movie is $4.5 and cost of video game is $5.75.
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question is attached to image
question 9a
pls help
Answer:
(x-2y){5-(x-2y)}
=(x-2y)(5-x+2y)
AD = 6x - 4 and AC = 4x - 3
Answer:
CD= 2x-1
Step-by-step explanation:
AD = 6x-4
AC = 4x - 3
CD= AD- AC
CD= 6x-4 - (4x - 3)
CD= 6x - 4 - 4x +3
CD= 2x -1
Therefore, the value of CD= 2x-1
Martin wants to clean his swimming pool.
He hired a cleaning machine to do this job.
The cost of hiring the cleaning machine was
£35.54 for the first day,
then £18.25 for each extra day.
Estimate how much it would cost to rent the machine for 4 days.
Help plssss
Answer:
90.29
Step-by-step explanation:
I did math
Solve the given differential equation by using an appropriate substitution. the de is a bernoulli equation. xdy/dx-(1 x)y=xy^2
-ln ( 1 - x/y - x) = c is a bernoulli equation. xdy/dx-(1 x)y=xy^2.
What is a differential equations explain?
Any equation with one or more terms and one or more derivatives of the dependent variable with respect to the independent variable is referred to as a differential equation (i.e., independent variable) dy/dx = f(x) (x)
[tex]\frac{-1}{y} = u[/tex]
[tex]\frac{y'}{y^{2} } = u'[/tex]
[tex]xy' - ( 1 + x )y = xy^{2}[/tex]
[tex]x\frac{y'}{y^{2} } - ( 1 + x ) \frac{1}{y} = x[/tex]
xu' + ( 1 + x )u = x
xu' + u + ux = x
xu = s
u + xu' = s'
s' + s = x
s - x =t
s' - 1 = t'
t' + 1 + t = 0
dt/dx = - ( 1 + t)
-∫ [tex]\frac{dt}{1 + t} =[/tex] ∫dx
-ln ( 1+ t ) = x + c
-in ( 1 + s - x ) = x + c
-ln ( 1 + xu - x ) = x + c
-ln ( 1 - x/y - x) = c
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Fritz can build a bookcase in 8 hours and Holly can build the same bookcase in 10 hours. After working together for 3 hours, Fritz leaves how long will it take holly to finish the bookcase by herself?
Holy will take 13/5 or 2.6 hours to finish the bookcase.
What is relation between time and work?The relation between time and work is
Work Done = Time Taken × Rate of Work ·
or, Rate of Work = 1 / Time Taken ·
or, Time Taken = 1 / Rate of Work ·
Now it is given that,
Time taken by Fritz to build a bookcase = 8 hours
So, Bookcase build by Fritz in 1 hour = 1/8
Similarly,
Time taken by Holly to build a bookcase = 10 hours
So, Bookcase build by Holly in 1 hour = 1/10
So, bookcase build in 3 hours
Fritz = 3/8
Holly = 3/10
Total bookcase build in 3 hours = 3/8 + 3/10 = 27/40
So. remaining work = 1 - 27/40 = 13/40
Thus, Time taken by Fritz to complete the bookcase = 8 * (13/40) hours
= 13/5 or 2.6 hours
Thus, Holy will take 13/5 or 2.6 hours to finish the bookcase.
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