The shape of Tina's kitchen is a rectangle 925 cm long by 485 cm wide.
a) Work out the area of Tina's kitchen in square meters.
Show how to use estimation to check your answers.
Flooring costs $56 per square meter.
It is only sold in whole numbers of square meters.
B) How much does Tina pay to buy flooring for her kitchen floor?
Show how to use inverse operations to check your answer
Answers
a) The area of Tina's kitchen is 44.8625 square meters. b) Tina cost $2520 to buy flooring for her kitchen floor.
a) To work out the area of Tina's kitchen in square meters, we need to divide the area in square centimeters by 10,000, which is the number of square centimeters in a square meter:
Area = length x width = 925 cm x 485 cm = \(448,625 cm^2\)
Area in square meters =\(448,625 cm^2 / 10,000 cm^2/m^2 = 44.8625 m^2\)
b) To find how many whole square meters of flooring Tina needs, we round the area of the kitchen up to the nearest whole number:
Area in square meters rounded up = ceil(44.8625) = \(45 m^2\)
The cost of the flooring is $56 per square meter, so Tina pays:
Total cost = \(45 m^2 * $56/m^2 = $2520\)
To use inverse operations to check this answer, we can divide the total cost by the cost per square meter to get the number of square meters, and then multiply by the cost per square meter to check that we get back to the total cost:
Number of square meters =\($2520 / $56/m^2 = 45 m^2\)
Total cost = \(45 m^2 x $56/m^2 = $2520\) (same as the original answer)
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Related Questions
3. Given the following open-loop single-input, single-output four-dimensional linear time-invariant state equations, namely, ⎣
⎡
x
˙
1
(t)
x
˙
2
(t)
x
˙
3
(t)
x
˙
4
(t)
⎦
⎤
= ⎣
⎡
0
0
0
−680
1
0
0
−176
0
1
0
−86
0
0
1
−6
⎦
⎤
⎣
⎡
x 1
(t)
x 2
(t)
x 3
(t)
x 4
(t)
⎦
⎤
+ ⎣
⎡
0
0
0
1
⎦
⎤
u(t)
y(t)=[ 100
20
10
0
] ⎣
⎡
x 1
(t)
x 2
(t)
x 3
(t)
x 4
(t)
⎦
⎤
+[0]u(t)
find the associated open-loop transfer function H(s).
Answers
The transfer function H(s) is given by the ratio of the output Y(s) to the input U(s):
H(s) = Y(s)/U(s) = C(sI - A)^(-1)B + D
To find the open-loop transfer function H(s) associated with the given state equations, we need to perform a Laplace transform on the state equations.
The state equations can be written in matrix form as:
ẋ(t) = A*x(t) + B*u(t)
y(t) = C*x(t) + D*u(t)
Where:
ẋ(t) is the vector of state derivatives,
x(t) is the vector of state variables,
u(t) is the input,
y(t) is the output,
A is the system matrix,
B is the input matrix,
C is the output matrix,
D is the feedforward matrix.
Given the system matrices:
A = ⎣
⎡
0
0
0
−680
1
0
0
−176
0
1
0
−86
0
0
1
−6
⎦
⎤
, B = ⎣
⎡
0
0
0
1
⎦
⎤
, C = [100 20 10 0], and D = [0]
We can write the state equations in Laplace domain as:
sX(s) = AX(s) + BU(s)
Y(s) = CX(s) + DU(s)
Where:
X(s) is the Laplace transform of the state variables x(t),
U(s) is the Laplace transform of the input u(t),
Y(s) is the Laplace transform of the output y(t),
s is the complex frequency variable.
Rearranging the equations, we have:
(sI - A)X(s) = BU(s)
Y(s) = CX(s) + DU(s)
Solving for X(s), we get:
X(s) = (sI - A)^(-1) * BU(s)
Substituting X(s) into the output equation, we have:
Y(s) = C(sI - A)^(-1) * BU(s) + DU(s)
Finally, the transfer function H(s) is given by the ratio of the output Y(s) to the input U(s):
H(s) = Y(s)/U(s) = C(sI - A)^(-1)B + D
Substituting the values of A, B, C, and D into the equation, we can calculate the open-loop transfer function H(s).
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Which is equivalent to the expression (2m^5n^4)^3?
A - 8m^15n^12
B - 6m^15n^12
C - 8m^8n^7
D - 5m^8n^7
Answers
Hope this helps
Have a great day/night
Factor each completely and show your work.
2n^2 + 5n + 2
Answers
One possible method is to use the factoring by grouping method:
2n^2 + 5n + 2
= 2n^2 + 4n + n + 2
= 2n(n + 2) + 1(n + 2)
= (2n + 1)(n + 2)
Therefore, the factored form of 2n^2 + 5n + 2 is (2n + 1)(n + 2).
expand the following:2(x+3)
Answers
2(x+3)
2*x=2x
2*3=6
Answer=2x+6
PLEASE GUYS HELP ME :D
Answers
What is the slope of the line on the graph?
Answers
Answer:
87
Step-by-step explanation: im genius at math
Answer:
I think the slope would be (2,4)
Step-by-step explanation:
Becuse it rises by 2 and runs by 4
What are the coordinates of Q' if PQR is translated two units right and three units down ?
Answers
EXPLANATION:
Q is currently at 0,5.
If we go 2 units right, then it is 0 + 2.
Now we have 2,5.
If we go 3 units down, then its 5 - 3.
Now we have 2,2.
Hope this helps! Gl!
Step-by-step explanation:
A hashing algorithm is a routine that converts a primary key value into a relative record number. T/F
Answers
True. A hashing algorithm is a mathematical routine used to generate a hash value from a primary key value.
A relative record number that may be used to retrieve the required record in a data structure is created using this hash value.
In order to facilitate quick access to the data, the hashing algorithm makes sure that the same hash value is generated for every primary key. How quickly the requested record can be found depends on how effective the hashing method is.
Also, it must be safe enough to prevent two main key values from producing the same hash value, as doing so might result in accessing the wrong records.
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Find the equation for the plane through (2,4,5) , (1,5,7) and(-1,6,8).
Answers
2x + 4y + 5z = 25.
The equation for the plane through the points (2,4,5), (1,5,7), and (-1,6,8) is 2x + 4y + 5z = 25.
To find this equation,
use the formula for a plane, Ax + By + Cz = D.
Plug in the coordinates for the three points and solve for the coefficients A, B, and C.
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When graphing y = x2 – 14x + 24 and y = 20 – |x + 3|, which value would be the best minimum x- and minimum y-values for the viewing window so that all intercepts, minimums, maximums, and points of intersection are able to be seen as closely as possible?
–50
–45
–25
–20
Answers
Answer: -45
It would be better if 30 were an option!
Step-by-step explanation:
At 25, all the important points will be in the graph-- barely. The vertex of the first equation is right at -25! So to be safe, it is better to go a bit larger.
If the viewing window is much larger, it is difficult to see small increments on the scale.
Answer:
-25
Step-by-step explanation:
on edge, i took the test
what is the slope intercept form of the line y-3=-5(x+1)
Answers
Answer:
y = -5x - 2
Step-by-step explanation:
y - 3 = -5(x + 1)
y - 3 = -5x - 5
y = -5x - 2
Evaluate the expression 5 - -4 + 3
Answers
Answer:
Step-by-step explanation:
5- -4=1 +3=4
In the number 78.018, how does the value of the 8 in the thousandths place compare to the value of the 8 in the ones place?
Drag and drop a fraction into the box to correctly complete the statement.
The value of the 8 in the thousandths place is Response area the value of the 8 in the ones place.
Answers
Each digit the decimal place moves can be thought of as multiplying or dividing the original value by 10 (depending on which way it is moved)
Answer:
1/1000
Step-by-step explanation:
two hundred five thousandths in decimal numbers
Answers
The required decimal form of two hundred five thousandths is 0.205.
When we write a decimal number, each digit represents a different power of 10, with the digit to the left of the decimal point representing the one place, and the digits to the right of the decimal point representing fractions of a whole.
So, to represent two hundred five thousandths in decimal form, we need to write 2 in the thousandth place, which is three digits to the right of the decimal point. This gives us the number 0.205.
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HELP PLZ!!!!
The length and width of a rectangular
garden are represented by x and x + 4
Write an expression that represents the
area of the rectangle, if a = lw.
Answers
Answer: a= x^2 + 4x
Step-by-step explanation:
length= x
width= x+4
area= length x width
area = x(x+4)
area= x^2 + 4x
hope this helps :)
On a coordinate plane, a trapezoid has points A double-prime (negative 4, negative 2), B double-prime (negative 2, negative 1), C double-prime (negative 2, negative 4), D double-prime (negative 4, negative 3).
What are the coordinates of the vertices of the pre-image given? ry= −x ◦ T1, −2(x, y)
A
B
C (3, 4)
D
Answers
Answer:
D
Step-by-step explanation:
Answer:
A: (1, 6)
B: (0, 4)
C: (3, 4)
D: (2, 6)
Step-by-step explanation:
Enter the slope intercept equation of the line shown below
Answers
Answer:
y = -x + 1
Step-by-step explanation:
you know that it must be y = mx + b form so you know that b is the y-intercept and the only time it touches is on positive one so you know it needs a positive one. then to find the slope you need to use the two points that are given. Rise/Run(rise over run) it only goes up one and over -1 so divide and you get -1 for the slope.
hope this helps!
The diagram shows a cuboid ABCDEFGH
AG= 24 cm and AB = 2BC.
CG=6cm,
(a) Calculate AB
Answers
Length of AB in the cuboid is 20.784cm.
What are basic properties of Cuboid?There are 6 faces, 12 edges, and 8 vertices on a cuboid.
All of the cuboid's faces have rectangular shapes.
The cuboid's opposing edges are parallel to one another.
The three dimensions of a cube are length, width, and height.
All of the angles created at the cuboid's vertices are 90 degree angles.
Length of Diagonal of cuboid is \(\sqrt{a^2+b^2+c^2}\), where a,b,c are side lengths of cuboid,
Calculation:Given:
AG=24cm;
AB=2BC;
CG=6m;
We know that diagonal of cuboid length is \(\sqrt{a^2+b^2+c^2}\)
Here
Let AB=a, BC=b, CG=c;
So a=2b;
Now
\(AG=\sqrt{a^2+b^2+c^2}=\sqrt{(2b)^2+b^2+6^2}=\sqrt{ 5b^2+36 }=24\\5b^2+36=576\\5b^2=540\\b=10.392cm\\AB=a=2b=20.784cm\)
Length of AB in the cuboid is 20.784cm.
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It says to list the new points of W’ X’ Y’ Z, could anyone please help?
Answers
Answer:
x -2,2
Y -4,3
z -4,6
w -2,6
Find the surface area of an open-top box with length 9cm width 8cm and height 7m = cm2
Answers
The surface area of the open-top box is 23872 cm².
In the question, we are asked to find the surface area of an open-top box with a length of 9cm, a width of 8cm, and a height of 7m.
The length is given to be, l = 9 cm.
The width is given to be, w = 8 cm.
The height s given to be, h = 7 m = 700 cm.
The box is in the shape of a cuboid.
The surface area of a cuboid is calculated using the formula, A = 2(lw + wh + hl).
But, the given box has an open top. Thus, one surface involving the length and width, that is, with an area of lw is missing.
Thus, the surface area of the open-top box can be calculated as:
A = 2(lw + wh + hl) - lw,
or, A = lw + 2h(w + l).
Substituting the values now, we get:
A = 9*8 + 2*700/(9 + 8),
or, A = 72 + 1400*17,
or, A = 72 + 23800,
or, A = 23872 cm².
Thus, the surface area of the open-top box is 23872 cm².
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Type the correct answer in each box. Use numerals instead of words.
Dane has a handful of change worth $2.65. There are 17 coins, including quarters, dimes, and nickels. If Dane has four times as many dimes as
nickels, how many of each coin does he have?
Dane has
quarters
dimes, and
nickels.
Answers
Answer:
Quarters=7
Dime=8
Nickel=2
Step-by-step explanation: 8*.10=.80, 2*.05=.10, 7*.25=1.75 If you add them up you get 2.65.
convert totalinches to yards, feet, and inches, finding the maximum number of yards, then feet, then inches. ex: if the input is 50, the output is:
Answers
By finding the maximum number of yards, then feet, then inches, if the input is 50, then the output is 1 yard, 4 feet, and 2 inches.
Conversion from inches to yard, and feetTo convert a length in inches to yards, feet, and inches
Note the followings:
There are 12 inches in a foot and 3 feet in a yard.
Divide the total length in inches by 36 (the number of inches in a yard) to find the number of yards, then take the remainder and divide it by 12 to find the number of feet, and finally take the remaining inches.
Given that, the input is 50 inches, the output will be
Maximum number of yards: 1 (since 36 inches is the largest multiple of 36 that is less than or equal to 50)
Maximum number of feet: 4 (since there are 12 inches in a foot, the remainder after dividing by 36 is 14, which is equivalent to 1 foot and 2 inches)
Remaining inches: 2 (since there are 12 inches in a foot, the remainder after dividing by 12 is 2)
Therefore, 50 inches is equivalent to 1 yard, 4 feet, and 2 inches.
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Leon has already had 4 science quizzes this semester. Going forward, he expects to have 4 quizzes per month.
Write an equation that shows how the total number of science quizzes, y, depends on the number of months that have passed, x.
Answers
The equation that shows how the total number of science quizzes, y, depends on the number of months that have passed, x is y = 4x.
An equation is a mathematical statement that shows the relationship between two or more values.
In this case, Leon has already had 4 science quizzes this semester and expects to have 4 quizzes per month going forward.
We can use an equation to show how the total number of science quizzes, y, depends on the number of months that have passed, x.
The equation for this would be y = 4x, where x is the number of months that have passed and y is the total number of science quizzes.
This equation shows that for each month that passes, the total number of science quizzes increases by 4
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in the following figure are: ΕΑ = α, ΑΒ = β, ΓΔ = γ, ΔΑ = δ. to match each element of column (A) with its equal in column (B)
Answers
Answer:
a
Step-by-step explanation:
On Monday, Florencia's hair was h centimeters long. She got a haircut on Tuesday, so her hair was only 75% percent of the length it was on Monday.
Which expressions could represent how many centimeters long Florencia's hair was after the haircut?
Answers
What is h?
maybe 25%
i hope it helped you sorry if it didn't
Answer:
25%
Step-by-step explanation:
Can anyone give me examples of this songwriting project?
Answers
Answer:
First find what to sing about. Next get your rythim. Last get the lyrics together.
Step-by-step explanation:
A quadratic function y = f(x) is plotted on a graph and the vertex of the resulting
parabola is ( 3, -3 ). What is the vertex of the function defined as g(x) = -f (x – 3)
Answers
Answer:
The vertex of g(x) is (6,3).
Step-by-step explanation:
Quadratic Function
The vertex form of the quadratic function has the following equation:
\(y=a(x-h)^2+k\)
Where (h, k) is the vertex of the parabola that results when plotting the function, and a is the leading coefficient.
We know a quadratic function y=f(x) is represented by a parabola whose vertex is at (3,-3). Substituting in the equation:
\(y=a(x-3)^2-3\)
The function g(x) is defined as:
\(g(x)=-f(x-3)\)
Substituting f(x):
\(g(x)=-[a(x-3-3)^2-3]\)
Operating:
\(g(x)=-a(x-6)^2+3\)
This function is represented by a parabola with its vertex at (6,3).
The vertex of g(x) is (6,3).
what is the distance along the unit circle between any two successive 8th roots of 1?
a. π/8
b. π/6
c. π/4
d. π/2
Answers
The distance along the unit circle between any two successive 8th roots of 1 is c) π/4.
To find the distance along the unit circle between any two successive 8th roots of 1, we can consider the concept of angular displacement.
Each 8th root of 1 represents a point on the unit circle that is evenly spaced by an angle of 2π/8 = π/4 radians.
Starting from the point corresponding to 1 on the unit circle, we can move π/4 radians to reach the first 8th root of 1. Moving π/4 radians further will bring us to the second 8th root of 1, and so on.
Since we are moving by π/4 radians for each successive 8th root of 1, the distance between any two successive 8th roots of 1 is π/4 radians.
Therefore, the correct answer is option c. π/4.
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what is a congruent polygon
Answers
A congruent polygon refers to two or more polygons that have the same shape and size. There must be an equal number of sides between two polygons for them to be congruent.
Congruent polygons have parallel sides of equal length and parallel angles of similar magnitude. When two polygons are congruent, they can be superimposed on one another using translations, rotations, and reflections without affecting their appearance or dimensions. Concluding about the matching sides, shapes, angles, and other geometric properties of congruent polygons allows us to draw conclusions about them.
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which of the following statements is true about a rational function of the form where g and h are polynomial functions?
Answers
The true statement about the function is that (c) the domain of f(x) consists of all values of x such that g(x) does not equal 0 and h(x) does not equal 0.
How to determine the true statement of the function f(x)?The complete question is added at the end of this solution
From the complete question, we have the following equation
f(x) = g(x)/h(x)
The above equation means that
The function f(x) is the quotient of the functions g(x) and h(x)
For the function f(x) to have real values, the function h(x) must not equal 0
i.e. h(x) ≠ 0
This is so because
A number or an expression divided by 0 is not a real number
Hence, the true statement is that the domain of f(x) consists of all values of x where h(x) does not equal 0.
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Complete question
which of the following statements is true about a rational function of the form where g and h are polynomial functions?
A. If the rational function has a removable discontinuity, then it cannot have a vertical asymptote. g(x)
B. The rational function f(x) h(x) will have a removable discontinuity at x = a if g(a) = 0. g(x)
C. The domain of f(x) consists of all values of x such that g(x) does not equal 0 and h(x) does not equal 0.
D. If the rational function has a removable discontinuity, then it cannot have a horizontal asymptote.