A scale drawing for an apartment is shown below. In the drawing, 2 cm represents5m. Assuming the bed room is rectangular, find the area of the real bedroom.
Answers
The drawn bedroom ookis like this
as this is drawn to scale, to find the area of the real bedroom we should find the lengths of the real bedroom first. We are told that every 2cm represent 5m. So, we will define our scaling factor as
[tex]\frac{5m}{2cm}[/tex]as every 2 cm represent 5m. Now, to calculate the real lengths, we simply take the scaled lengths and multiply it by the scaling factor. So we have s
[tex]2cm\cdot\frac{5m}{2cm}=5m[/tex][tex]4cm\cdot\frac{5m}{2cm}=2\cdot5m=10m[/tex]so the real bedroom looks like this
which is a rectangl of height 210m and base 5m. Recalling tha the area of a rectangle is the product of it s height and its base, we have that the area of this rectangle would be
[tex]A=10m\cdot5m=50m^2[/tex]
Related Questions
I need help in math can you please help me 0
Answers
Answer:
We will use the following identities:
[tex]\begin{gathered} \csc (x)=\frac{1}{\sin (x)} \\ \cot (x)=\frac{\cos (x)}{\sin (x)} \end{gathered}[/tex]So, replacing the identities on the left side, we get:
[tex]\frac{1+\csc^2(x)}{\cot^2(x)+1}=\frac{1+(\frac{1}{\sin(x)})^2}{(\frac{\cos (x)}{\sin (x)})^2+1}[/tex]Then, solving the power and adding the expressions, we get:
[tex]\frac{1+csc^2(x)}{\cot^2(x)+1}=\frac{1+\frac{1}{\sin^2(x)}}{\frac{\cos^2(x)}{\sin^2(x)}+1}[/tex][tex]\frac{1+csc^2(x)}{\cot^2(x)+1}=\frac{\frac{\sin^2(x)+1}{\sin^2(x)}}{\frac{\cos ^2(x)+\sin ^2(x)}{\sin ^2(x)}}[/tex]Dividing the expression and simplifying, we get:
[tex]\frac{1+csc^2(x)}{\cot^2(x)+1}=\frac{\sin ^2(x)+1}{\cos ^2(x)+\sin ^2(x)}[/tex]Finally, we know that cos²(x) + sin²(x) = 1, so we can rewrite the expression as:
[tex]\begin{gathered} \frac{1+\csc^2(x)}{\cot^2(x)+1}=\frac{\sin ^2(x)+1}{1} \\ \frac{1+\csc^2(x)}{\cot^2(x)+1}=\sin ^2(x)+1 \end{gathered}[/tex]a+3 divided by b =c
solve for a
Answers
The value of a in the equation given as a+3 divided by b =c is a = bc - 3.
What is an equation?A mathematical equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe a scenario
From the information, a+3 divided by b =c. We have to make a the subject of the formula. This will be:
a + 3 / b = c
Cross multiply
a + 3 = bc
Subtract 3 from both sides
a + 3 - 3 = bc - 3
a = bc - 3
Therefore, a = bc - 3.
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Lynn paid a coeal of $2,780 for 261 tickets to the heater. Student tickets cost $10 and adult tickets cost urs. how many student tickets and how many acuit tickets did Lynn buy?
Answers
Answer:
245 students and 16 adults
Step-by-step explanation:
polite
What is the area?
omor
1 ft
& in l
8
10
xx
10 in
Answers
The area of parallelogram is 0.64
What is parallelogram ?A parallelogram is a geometric object with sides that are parallel to one another in two dimensions. It is a form of polygon with four sides (sometimes known as a quadrilateral) in which each parallel pair of sides have the same length. A parallelogram has adjacent angles that add up to 180 degrees.
Given : a parallelogram of height = 8 inch = 0.64 feet [ 1 inch = 0.08 feet ]
breadth = 1 feet
The area of the parallelogram = Height X Base
= 0.64 X 1
0.64 square feet
The area of parallelogram = 0.64 square feet
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16) F(x) = (x + 1)exponetn (2) Identify the function family to which this belongs. A Absolute Value B Constant CLinear D Quadratic
Answers
D quadratic
Explanation
[tex]f(x)=(x+1)^2[/tex]
you can easily identify a function with this :
if the exponent of the variable (x) is 1 , then it is a linear function:example
[tex]\begin{gathered} y=x,\text{ linear function} \\ y=3x+8 \end{gathered}[/tex]if the exponent of the variable (x) is 2 , then it is a quadratic function
[tex]\begin{gathered} y=x^2 \\ y=(x+1)^2 \end{gathered}[/tex]the absolute value has this symbol
[tex]y=\left|x\right|[/tex]a constant function is a number, with no variable, example
[tex]\begin{gathered} y=4 \\ Y=-7 \end{gathered}[/tex]so, the answer is D quadratic
Line I is parallel to line m. If the measure of <6 is 75^ what is the measure of <3
Answers
Solution:
Given;
[tex]m\angle6=75^o[/tex]Thus;
[tex]\begin{gathered} m\operatorname{\angle}8+m\operatorname{\angle}6=180^o.............\text{ Sum of angles on a straight line} \\ \\ m\operatorname{\angle}8=180^o-75^o \\ \\ m\operatorname{\angle}8=105^o \\ \end{gathered}[/tex]Then;
[tex]m\operatorname{\angle}8=m\operatorname{\angle}3...........\text{ Corresponding angles are equal}[/tex]Thus;
[tex]m\operatorname{\angle}3=105^o[/tex]perform the operation and simplify completely show all work. properties of expoenents/ super helpful property.
Answers
The rule of multiplication of the exponents is
[tex]a^m.a^n=a^{m+n}[/tex]We will use this rule with our question
[tex]x^{\frac{5}{9}}.x^{\frac{2}{3}}[/tex]We must add the fractions 5/9 and 2/3
To add fractions they must have the same denominators
Since the lowest common factor of 9 and 3 is 9, then
[tex]\frac{5}{9}+\frac{2}{3}=\frac{5}{9}+\frac{2\times3}{3\times3}=\frac{5}{9}+\frac{6}{9}=\frac{11}{9}[/tex]Then the expression is
[tex]x^{\frac{5}{9}}.x^{\frac{2}{3}}=x^{\frac{5}{9}+\frac{2}{3}}=x^{\frac{11}{9}}[/tex]Draw an angle in standard position such that the terminal side passes through the given point. (7, 4)
Answers
we have the point (7,4)
the x-coordinate and the y-coordinate are positive numbers
that means
The point lies on the First quadrant
see the figure below to better understand the problem
the value of the angle θ is equal to
tanθ=4/7
θ=29.7 degrees
Parent Function Description: A cubic (cubing) function that is reflected over thex axis, has a vertical stretch of 3 units, is shifted right 2 units, and is shifted down4 units.
Answers
Parent function:
f(x) = x³
that is reflected over the x axis
f(x) = -x³
has a vertical stretch of 3 units:
f(x) = -3x³
is shifted right 2 units:
f(x) = -3(x - 2)³
and is shifted down 4 units:
f(x) = -3(x - 2)³ - 4
Fred has a spinner that is split into four equal sections: red, blue, green, and yellow. Fred spun the spinner 500 times. Which of the following would be a good estimate of the number of times the spinner lands on the green section? A. 142 B. 175 C. 250 D. 415
Answers
Answer
I don't know
asdnsiuuuuuuuuuuuuuuuuuuuuuuuuuuwlefnhiug4efbglvliaufngkrhbg
Sammi had a total of 25 ft of ribbon. She cut off 13 ½ feet to keep, the remaining fabric she cut into 3 inch sections to make ribbons. How many ribbons would she be able to make?
Answers
First, find the total length of the remaining fabric by substracting 13 1/2 from 25:
[tex]\begin{gathered} 25-13\frac{1}{2} \\ =25-13-\frac{1}{2} \\ =12-\frac{1}{2} \\ =11\frac{1}{2} \end{gathered}[/tex]Since one feet equals 12 inches, multiply 11 1/2 by 12 to find the total length of the remaining fabric in inches:
[tex]\begin{gathered} 11\frac{1}{2}\times12=11\times12+\frac{1}{2}\times12 \\ =132+\frac{12}{2} \\ =132+6 \\ =138 \end{gathered}[/tex]Since each ribbon takes 3 inches, divide 138 over 3 to find the total amount of ribbons that can be made:
[tex]\frac{138}{3}=46[/tex]Therefore, Sammi is able to make 46 ribbons.
Solve the system of equations for x, y, and z.
x+2y+z=13
4x+6y=16
3x-6y = -30
Answers
By solving equations, the values of x, y, and z are 10.8, 10.4, and -18.6.
What are equations?A mathematical equation is a formula that uses the equals sign to express the equality of two expressions. The meanings of the word equation and its cognates in other languages can vary slightly. For instance, in French, an equation is defined as having one or more variables, whereas, in English, an equation is any well-formed formula that consists of two expressions linked by the equals sign. Based on the degree, there are three different types of equations. Equations that are linear, quadratic, and cubic.So, the values of x, y, and z are:
Take equation (3) and solve for 'x'":
3x-6y = -303x = -30 + 6yx = (-30 + 6y)/3Now, substitute x = (-30 + 6y)/3 in equation (2):
4x+6y=164[(-30 + 6y)/3]+6y=16(-120 + 24y)/12 + 6y = 16-120 + 24y + 6y = 19230y = 192 + 1030y = 312y = 312/30y = 10.4Put y = 10.4 in equation (3) as follows:
3x-6y = -303x-6(10.4) = -303x - 62.4 = -303x = -30 + 62.43x = 32.4x = 32.4/3x = 10.8Now, put x = 10.8 and y = 10.4 in equation (1):
x+2y+z=1310.8 + 2(10.4) + z = 1310.8 + 20.8 + z = 1331.6 + z = 13z = 13 - 31.6z = -18.6Therefore, by solving equations, the values of x, y, and z are 10.8, 10.4, and -18.6.
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Classify the following lines Y = 1 X – 2 3 & – 60 + 2y = 18 Intersecting, but not perpendicular Parallel Perpendicular The same line
Answers
7) We rearrange the second equation to compare it to the first one:
[tex]\begin{gathered} -6x+2y=18 \\ 2y=6x+18 \\ y=3x+9 \end{gathered}[/tex]The slopes are m1=1/3 and m2=3. They are not equal, nor negative reciprocals, so they are not parallel nor perpendicular. As they don't have the same slope, they will intersect.
Answer: Intersecting but not perpendicular.
8)
[tex]\begin{gathered} 2x+3y=10 \\ 3y=-2x+10 \\ y=-\frac{2}{3}x+\frac{10}{3} \end{gathered}[/tex][tex]\begin{gathered} -3x+2y=11 \\ 2y=3x+11 \\ y=\frac{3}{2}x+\frac{11}{2} \end{gathered}[/tex]The slopes are negative reciprocals:
[tex]m_1=-\frac{1}{m_2}[/tex]As the slopes are negative reciprocals, both lines are perpendicular.
Answer: Perpendicular.
What are the solutions to the equation x² + 9 = 0
Answers
To determine the solution of the given equation, isolate the variable x by subtracting 9 on both sides of the equation,
[tex]x^2+9-9=0-9[/tex][tex]x^2=-9[/tex]Get the square root on both sides of the equation.
[tex]\sqrt{x^2}=\sqrt{-9}[/tex][tex]x=\pm\sqrt{-9}[/tex]As we can see, the value of x is a negative number under the radical sign. However, a negative number under a radical sign is not considered a real number.
Hence, the solution to this equation is an imaginary number +3i and -3i.
A rectangular garden has a walkway around it. The area of the garden is 4(4.5x+3.5). The combined area of the garden and the walkway is 5.5(8x+6). Find the area of the walkway around the garden as the sum of two terms.
Answers
We can express the area of the walkway around the garden as the sum of two terms as given - A[W] = 26x + 19.
What is a Rectangle?Rectangle is a plane figure with four straight sides and four right angles, especially one with unequal adjacent sides, in contrast to a square.
Given is a rectangular garden that has a walkway around it. The area of the garden is 4(4.5x + 3.5). The combined area of the garden and the walkway is 5.5(8x + 6).
The area of the walkway (A[W]) can be calculated by subtracting the area of garden (A[G]) from the combined area of the garden and the walkway (A[T]).
A[W] = A[T] - A[G]
A[W] = 5.5(8x + 6) - 4(4.5x + 3.5)
A[W] = 44x + 33 - 18x - 14
A[W] = 26x + 19
Therefore, we can express the area of the walkway around the garden as the sum of two terms as given - A[W] = 26x + 19.
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6.0 x 10^4 ÷ 4.0 x 10^8
Scientific notation
Answers
The scientific notation for 6.0 x 10^4 ÷ 4.0 x 10^8 is 1.5 × 10^-4.
Whet is scientific notation?It should be noted that scientific notation simply means the power format that is used for expressing numbers that are too large or two small.
Based on the information given, the number illustrated is given as:
6.0 x 10^4 ÷ 4.0 x 10^8
It should be noted that since we are dividing,, we'll have to subtract the powers. This will be illustrated this
= 6.0 x 10^4 ÷ 4.0 x 10^8
= (6.0 / 4.0) × 10^(4 - 8)
= 1.5 × 10^-4
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Select the new equation formed after collecting all variables on one side of the equal sign. (There is more than 1 correct answer.)
1/2(6x + 8) = x − 8
A. 4 = -2x - 8
B. 2x + 8 = 8
C. 3x = x -12
D. 8 = -2x - 8
E. 2x + 4 = -8
F. 3x + 12 = x
Answers
The equivalent equations to 1/2(6x + 8) = x − 8 include:
A. 4 = -2x - 8
E. 2x + 4 = -8
What is an equation?It should be noted that an equation shows the relationship between the variables. This usually illustrated by having and equal to sign.
In this case, 1/2(6x + 8) = x − 8 will be:
3x + 4 = x - 8
Collect like terms
3x - x = -8 - 4.
2x = -12
Divide
x = -12/2
x = -6
Therefore, 4 = -2x - 8
2x = -8 - 4
2x = -12
x = -12/2 = -6
Therefore, A is correct.
E. 2x + 4 = -8
2x = -8 - 4
2x = -12
x = -12/2
x = -6
E is also correct.
The correct options are A and E.
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Find the amplitude and period of ft=-tan0.4t
Answers
For function f(t)=-tan(0.4t) , there is no amplitude for tan function and period is equal to 5π/2.
As given in the question,
Given function:
f(t)=-tan(0.4t)
Standard equation for tan function:
f(x) =a tan(bx)
Compare both given and standard equation of a function,
a =-1
b =0.4
=4/10
=2/5
Period of a tangent function, y=a tan(bx),is the distance between any two consecutive vertical asymptotes.
Period of the given function =π/b
=π/(2/5)
=5π/2
Amplitude:
Tangent function have no amplitude as it has no maximum or minimum value.
It tends to ∞ to both the side of y -axis.
Therefore, for function f(t)=-tan(0.4t) , there is no amplitude for tan function and period is equal to 5π/2.
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what is 200000000000000000000000000000 divided 4
Answers
Answer:5e+28
Step-by-step explanation:
It's very complicated.
Need help with this please
Answers
Answer:225
Step-by-step explanation:
27 . 24
648
648-423 = 225 hope this helped
have a good day ^^
5 out of 8 students said football is their fav sport what is the decimal equivilant of students who chose football
(with explaining)
Answers
Answer:
0.625
Step-by-step explanation:
another way to write 5 out of 8 is 5/8 or 5 divided by 8
because 5 of the group of 8 chose football
so we do 5÷8=0.625
A bottle contains 10 mL of a 40 mg/2.5 mL medicine solution. How many mL of thesolution should be poured out and replaced with pure water to have 10 mL of 30mg/2.5 mL solution?
Answers
Suppose the bottle contains x units of medicine and y units is taken out and replaced with water. The expression to find the the amount of pure medicine solution after replacement by n times is given by
[tex]\begin{gathered} \text{The amount of pure medicine remaining, v=} \\ x(1-\frac{y}{x})^n \\ \end{gathered}[/tex]In the given question, v =30mg, x=40 mg.
n=1, since replacement is done only one time. We have to find y.
Substitute values in equation.
[tex]\begin{gathered} 30=40(1-\frac{y}{40})^1 \\ \frac{30}{40}=\frac{40-y}{40} \\ 30=40-y \\ y=40-30 \\ =10mg \\ \end{gathered}[/tex]So, 10 mg/2.5 ml solution is poured out and replaced with water
Please help on this if m=45 fund m3
Answers
In m=45 fund m3 then 55;<3and <4 are complementary angles so m<3=90-m<4. Two complimentary angles add up to 90 degrees, and one is referred to as the other's "complement." Therefore, an angle's complement can be calculated by deducting it from 90 degrees. 90-x° is the counterpart of x°.
What is complementary angles?complementary angles are a pair of two angles that add up to give us 90 degree.Two angles are said to be supplementary if their sums total 180 degrees.When two angles add up to 90 degrees, they are said to be complementary. By deducting an angle from 90, one can find its complement. For instance, 90° - 40° = 50° is the complement of 40°. thus angle 4 and angle 3 are complementary anglesm<ACD=90 degree m<4=35 degree thereforem<ACD=m<4+m<390 degree=35 degree + m<3substract 35 from both sides90-35=35+m<3-3555=m<3m<3=55 degreeTo learn more about complementary angles refer to:
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Multiply (6 – 5i)2.Question 20 options:A) 11 – 60iB) 36 – 25iC) 11 + 60iD) 36 + 25i
Answers
Multiply (6 – 5i)2
Apply distributive property
6(2)+(-5i)(2)
12-10i
the answer is
12-10i
Part 2
we have
(6-5i)^2
so
(6)^2-2(6)(5i)+(5i)^2
36-60i+25i^2
Remember that
i^2=-1
substitute
36-60i+25(-1)
36-60i-25
combine like terms
11-60i
the answer is option AMrs. Sullivan's 5th grade class
scooped 494 seeds out of a
pumpkin and roasted them. The
seeds were divided evenly
among the 26 students in the
class. How many seeds did each
student receive?
Answers
Answer: = 19
Step-by-step explanation:
For this worded question, you have to take out the values.. the question is essentially asking how many seeds each student received. There are 494 seeds, and 26 students. This is a division question.
494 ÷ 26 = 19.
(In tests you should be permitted to use a calculator if you bring one.. so no need to memorise how to divide large numbers, although you can always use long division to work our division related questions.)
To learn about long division learning from this link :
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the company for ocean has already cleared the Earth oceans of 125 million pounds of trash they are committed to picking up exactly 550 pounds of trash per day . write an equation to represent P pounds of trash removed as a function of number of the days passed? how many years have passed if the the company for ocean has a total of 125,602,250 pounds cleared from the ocean ?
Answers
1. pounds of trash cleared, P = 550D+125,000,000
2. 125,602,250=550D+ 125,000,000
550d=602250, therefore D= 602250/550 = 1095 days=1095/365= 3 years
2 What is the slope of a line that is parallel to the following: y= 3x -4
Answers
Parallel lines are defined by the same slope and will never intersect. They continue without touching eachother assuming them on the same plane.
Lines are represented by the following expression:
[tex]\begin{gathered} y=mx+b \\ \text{where,} \\ m=\text{slope} \\ b=y-\text{intercept} \end{gathered}[/tex]Then, for a parallel line to:
[tex]y=3x-4[/tex]The slope would be 3.
During summer vacation, you charge $12 per hour for golf lessons and a registration fee of $50. If you make$98 one day, how many hours did you spend teaching lessons? Let g represent golf lessons, write an equationfor the situation.
Answers
Solution:
The question indicates a linear equation showing the relationship between the fee charged on golf lessons and the hour spent.
The linear equation can be represented by;
[tex]\begin{gathered} y=r+g \\ \text{where y is the total f}ee\text{ charged} \\ r\text{ is the registration fe}e \\ g\text{ is the golf lesson fe}e \end{gathered}[/tex]Given:
[tex]\begin{gathered} r=\text{ \$50} \\ g=12t,\text{ where t is the number of hours for the golf lesson} \\ y=\text{ \$98} \end{gathered}[/tex]From the above,
The equation can be re-written as;
[tex]y=50+12t[/tex]Hence, substituting the total amount made for the day into the equation to get the number of hours used teaching the lessons;
[tex]\begin{gathered} 98=50+12t \\ \text{Collecting the like terms to get t,} \\ 98-50=12t \\ 48=12t \\ \text{Dividing both sides by 12;} \\ t=\frac{48}{12} \\ t=4\text{hours} \end{gathered}[/tex]Therefore, 4 hours was spent teaching the lessons for the day $98 was made.
3 feeding 54C 3. What is the constant of proportionality? What does it tell us about the situation? day 4. If we switched the columns in the table, what would be the constant of proportionality? Explain your reasoning. 5. Use d for number of days and f for amount of food in grams that a shrimp eats to write two equations that represent the relationship between d and f. 6. If a tank has 10 shrimp in it, how much food is added to the tank each day? 7. If the aquarium manager has 300 grams of shrimp food for this tank of 10 shrimp, how many days will it last? Explain or show your reasoning.
Answers
3) 0.6 grams per day
4) 1.67 grams per day
5) f = kd
k = f/d
Explanation:3) y = kx
where k = constant of proportionality
from the table, let x = number of days
y = food in grams
when x = 1, y = 0.6
we find k:
0.6 = k(1)
0.6 = k
Hence, the constant of proportionality is 0.6
It means the rate at which the shrimp is fed is 0.6grams per day
4) if columns are switched, the number of days = y
food in grams = x
let's use the same values but it will be interchanged:
when x = 0.6, y = 1
y = kx
1 = k(0.6)
1 = 0.6k
k = 1/0.6
k = 1.67 or 5/3
The rate at which the shrimp is fed is 1.67 grams per day
Here the rate is higher than the previous result. This is because the y value is greater then the x value.
5) if f = amount of food in grams
d = number of days
Since the relationship between the amount of food and number of days is proportional (it has beeen established previously), we would use the proportional equation:
y = f = amount of food in grams
x = d = number of days
f = kd (one equation)
it can also be written as:
f = kd
k = f/d (2nd equation)
Help with number one a-f is all part of number one.Part e is: P(7).
Answers
Given the spinner that goes from 1 to 8, you can identify that the total number in the spinner is:
[tex]TotalNumbers=8\text{ }[/tex]a. By definition, Odds Numbers are those numbers that are not divisible by 2.
In this case, you can identify that the Odd Numbers the spinner has are:
[tex]1,3,5,7[/tex]Knowing that there are four Odd Numbers, you can determine that:
[tex]P(odds)=\frac{4}{8}[/tex][tex]P(odds)=\frac{1}{2}[/tex]b. By definition, Even Numbers are divisible by 2.
In this case, you can identify that the Even Numbers in the spinner are:
[tex]2,4,6,8[/tex]Knowing that there are four Even Numbers, you get:
[tex]P(evens)=\frac{4}{8}[/tex][tex]P(evens)=\frac{1}{2}[/tex]c. Since there is only one number 3:
[tex]P(3)=\frac{1}{8}[/tex]d. By definition:
[tex]P(A\text{ or}B)=P(A)+P(B)[/tex]Then:
[tex]P(4\text{ or }6)=P(4)+P(6)[/tex]Since there is only one number 4 and only one number 6:
[tex]P(4)=P(6)=\frac{1}{8}[/tex]Therefore:
[tex]P(4\text{ or }6)=\frac{1}{8}+\frac{1}{8}[/tex][tex]P(4\text{ or }6)=\frac{2}{8}[/tex][tex]P(4\text{ or }6)=\frac{1}{4}[/tex]e. Since there is only one number 7:
[tex]P(7)=\frac{1}{8}[/tex]f. Knowing that there is only one number 1:
[tex]P(1)=\frac{1}{8}[/tex]Hence, the answers are:
a.
[tex]P(odds)=\frac{1}{2}[/tex]b.
[tex]P(evens)=\frac{1}{2}[/tex]c.
[tex]P(3)=\frac{1}{8}[/tex]d.
[tex]P(4\text{ or }6)=\frac{1}{4}[/tex]e.
[tex]P(7)=\frac{1}{8}[/tex]f.
[tex]P(1)=\frac{1}{8}[/tex]