The perimeter of the floor in the scale drawing is 58 inches.
Define Perimeter of the rectangle.The whole distance that the sides or limits of a rectangle cover is known as its perimeter. Since a rectangle has four sides, its perimeter will be equal to the sum of those four sides. Given that the perimeter is a linear measurement, the rectangle's perimeter will be expressed in meters, centimeters, inches, feet, etc.
The letter "p" stands for the perimeter, which is equal to twice the width plus twice the length of the rectangle.
Given, the length of rectangular classroom is 36 feet
and the width is 22 feet.
The scale drawing has a length of 18 inches.
Here we can see that two different units are used.
So, we need to convert feet to inches.
1 foot = 12 inches
Now we will convert the length in inches,
36 feet = 36*12 inches
= 432 inches
Now we will convert the width in inches,
22 feet = 22*12
= 264 inches
Now, we will calculate by how many times the length has been scaled down:
[tex]\frac{432}{18} = 24[/tex]
So, the length has been scaled down to 24 times.
Now, we will scale down the width 24 times:
[tex]\frac{264}{24} = 11[/tex]
So, the width of the scale drawing is 11 inches.
Now, we will find the perimeter of the scale drawing:
Perimeter = 2(scale down length + scale down width)
= 2(18+11)
=2*29
=58 inches
Therefore, the perimeter of the scale down drawing is 58 inches.
To know more about perimeter, visit:
https://brainly.com/question/15287805
#SPJ4
If f(x) = |x – 1] + 2 is changed to g(x) = -2f(x) + 8, how is the graph of the function transformed?
we have
f(x) = |x – 1] + 2
g(x) = -2f(x) + 8
substitute the value of f(x) in g(x)
so
g(x)=2(|x – 1] + 2) +8
g(x)=2|x – 1] + 4 +8
g(x)=2|x – 1] + 12
Using a graphing tool
see the attached image
From the diagram below, if AC is a tangent line, and if PD = 8 and DC = 9, find the length of BC.
Given,
PD = 8 and DC = 9
Required
The length of line BC.
Here, PB and PD are the ardius of the circle. By the definition of circle, the measure of all radius is equal.
So, PB = PD = 8.
The tangent is always perpendicular to the radius at the point of tanjency.
By the pythagoras theorem,
[tex]\begin{gathered} PB^2+BC^2=PC^2 \\ 8^2+BC^2=(17)^2 \\ BC^2=289-64 \\ BC^2=225 \\ BC=15 \end{gathered}[/tex]Hence, the measure of BC is 15 units.
Find the slope of the line that passes through (2, 7) and (-4, 19).
m =
The slope, m, of the line that passes through (2, 7) and (-4, 19) is -2.
According to the question,
We have the following information:
A line is passing through two points (2,7) and (-4,19).
We know that the slope of the line is denoted by m and the following formula is used to find the slope of the line passing through two points:
m = (y2-y1)/(x2-x1)
(More to know: we can also easily find the equation of the line using the slope given and the points from which the line is passing.)
In this case, we have x1 = 2, y1 = 7, x2 = -4 and y2 = 19.
m = (19-7)/(-4-2)
m = 12/(-6)
m = -2
Hence, the slope, m, of the line that passes through (2, 7) and (-4, 19) is -2.
To know more about slope here
https://brainly.com/question/16180119
#SPJ1
Please help me! It is about proofs, SSS and SAS.
The two given triangles are congruent because of SAS.
What does congruency mean?In geometry, two figures or objects are congruent if their shapes and sizes match, or if one is the mirror image of the other. Both of the bread slices have the same shape and size when stacked on top of the other. Congruent refers to having the same precise size and shape. Having the same size and shape makes two shapes congruent. The mirror image of one shape is the same as the other if the two shapes are congruent.
The given triangles are RTP and STP
P is the midpoint of RS and TP is the altitude of triangle RTS.
In the triangles RTP and STP
TP = TP (common)
∠RPT = ∠ SPT (90°)
RP = SP (median divides the side equally)
So, both triangles are congruent using SAS property.
To know more about congruency, visit:
brainly.com/question/28949682
#SPJ1
Write an equation in slope-intercept form that represents the data in the table.
The equation of the line that represents the data in the table is y = 30x + 30.
How to determine the equation of line from points?The formula for equation of line is expressed as;
y = mx + b
Where m is slope and b is y-intercept
From the data;
Point 1( 0,30 )
x₁ = 0y₁ = 30Point 2( 2,90 )
x₂ = 2y₂ = 90First, we determine the slope.
Slope m = ( y₂ - y₁ )/( x₂ - x₁ )
Slope m = ( 90 - 30 )/( 2 - 0 )
Slope m = ( 60 )/( 2 )
Slope m = 30
Next, we determine the y-intercept b by substituting the given values into the equation of line formula.
y = mx + b
30 = (30)0 + b
30 = b
b = 30
Now, plug these values into y = mx + b to determine the equation of the line.
y = mx + b
y = 30x + 30
Therefore, y = 30x + 30 is the equation of the line.
Learn more about equation of line here: brainly.com/question/2564656
#SPJ1
Alizeh invests $9,000 in an actively managed mutual fund that has an annual expense ratio of 1.1%. The investment earns a 5% rate of return. How much does she pay in fees for her actively managed fund?
As per the given interest rates, she have to pay $103.95 in fees for her actively managed fund.
Interest:
Interest means the amount to be paid on the borrowed money or the amount received on the money lent.
Given,
Alizeh invests $9,000 in an actively managed mutual fund that has an annual expense ratio of 1.1%. The investment earns a 5% rate of return.
Here we need to find the fees for her actively managed fund.
First we have to change rate of return percent to decimal form,
That is,
5% = 0.05
Now, we have to multiply the amount and decimal to get Alizeh 's profit,
=> 9000 x 0.05
=> 450
Therefore, the fund's total after 1 year, including initial investment and profit is
=>9000 + 450
=> 9450.
Now, we have to change fee percent that is the expense ratio into decimal form,
=> 1.1% = 0.011
Therefore, the fees for her fund is,
=> 9450 x 0.011
=> 103.95
Therefore, she have to pay $103.95 for her managed fund.
To know more about Interest here.
https://brainly.com/question/26457073
#SPJ1
(-5p+8)(-3p-5) pls help me solve this asappp
Step-by-step explanation:
(-5p + 8)(-3p - 5)
[tex]15p^2 +25p - 24p -40[/tex]
[tex]15p^2 +p -40[/tex]
A building security code has 2 numeric digits, 0 through 9, followed by 2 letters. What is the probability that the first digit is nine and the last letter is a?.
The probability of the event that the first digit is nine and the last letter is a is 1/260.
The building security code has 2 numeric digits in between 0-9 and 2 letters.
The choices for letters is 26 each and the choices for digits is 10 each.
So, the total possible security code can be,
Total security codes possible = 10 × 10 × 26 × 26
Total security codes possible = 67600
Now, the number of codes that starts with 9 and end with a are,
= 1 × 10 × 26 × 1
= 260
The probability that the first digit is nine and the last letter is a is,
P(E) = 260/67600
P(E) = 1/260
So, the probability that the first digit is nine and the last letter is a is 1/260.
To know more about probability, visit,
https://brainly.com/question/24756209
#SPJ4
A 2 liter bottle filled is filled with water the water leaks 80 milliliters of water every 3 minutes will the bottle be empty in 1 hour why or why not?
Answer:
the program I will get back to you on that date is approaching the
Step-by-step explanation:
the program I will get back to you on that date is approaching the
a. Complete the area model and the
equation.
23 x 62 =
Answer:
Step-by-step explanation:
2km:0.2m .....................
i 45° 1030 909 600 9. Is the pentagon a regular pentagon?
internal angles of the polygon
angle a = 180 - 45 = 135°
angle b = 180 - 90 = 90°
angle c = 180 - 60 = 120°
angle d = 540 - 135 - 90 - 120 - 77 = 118°
angle e = 180 - 103 = 77 °
angle x = 180 - 118 = 62°
the polygon is not a regular polygon because the measure of its angles are different
Please answer this question!
Answer: 1/4
Step-by-step explanation: 1/2 turned into decimal form is 0.5 but halved equals 0.25 which in fraction form is 1/4
i need help with the question where I wrote +1 and +2. to find the slope do I just do 2/1
To find out the slope we need two points
from the table
we take
(0,1) and (1,3)
so
m=(3-1)/(1-0)
m=2/1
m=2what is the value of f(-9) to the nearst hundredth
For this problem, we are given the expression for a function, f(x), and we need to determine the value of f(-9) to the nearest hundredth.
The expression is:
[tex]f(x)=2^{8+x}+7[/tex]We need to replace "x" with the value "-9", and simplify the expression.
[tex]\begin{gathered} f(-9)=2^{8-9}+7 \\ f\mleft(-9\mright)=2^{-1}+7 \\ f\mleft(-9\mright)=\frac{1}{2}+7 \\ f\mleft(-9\mright)=0.5+7=7.5 \end{gathered}[/tex]The value of f(-9) is 7.5
A number time 5 less that number has a product of -4. What are the two numbers?
Let the first number be x.
The second number is 5 times less than x => x - 5
Therefore, we can write the statement as
[tex]\begin{gathered} x\times(x-5)=-4 \\ x^2-5x=-4 \\ \therefore \\ x^2-5x+4=0 \end{gathered}[/tex]Solving the quadratic equation:
Let us replace -5x in the equation with -4x and -x to be able to factorize.
Hence,
[tex]\begin{gathered} x^2-4x-x+4=0 \\ x(x-4)-1(x-4)=0 \\ (x-4)(x-1)=0 \\ \text{Therefore} \\ x-4=0\text{ } \\ or \\ x-1=0 \end{gathered}[/tex]Hence,
[tex]\begin{gathered} x=1 \\ or \\ x=4 \end{gathered}[/tex]Therefore, the number can be 1 or 4.
The second number can be
[tex]\begin{gathered} 1-5=-4 \\ or \\ 4-5=-1 \end{gathered}[/tex]Therefore, the pair of numbers can be
[tex](1,-4)\text{ or (4, -1)}[/tex]Write the fraction 27/72 in simplest form
Therefore, 27/72 simplified to lowest terms is 3/8.
write parallel and perpendicular equation thru (-3,5) y=2/3x + 1
Answer:
Step-by-step explanation:
1 Simplify (-3,5)y(−3,5)y to -3,5y−3,5y.
-3,5y=\frac{2}{3}x+1
−3,5y=
3
2
x+1
2 Simplify \frac{2}{3}x
3
2
x to \frac{2x}{3}
3
2x
.
-3,5y=\frac{2x}{3}+1
−3,5y=
3
2x
+1
3 Switch sides.
\frac{2x}{3}+1=-3,5y
3
2x
+1=−3,5y
4 Break down the problem into these 2 equations.
\frac{2x}{3}+1=-3
3
2x
+1=−3
\frac{2x}{3}+1=5y
3
2x
+1=5y
5 Solve the 1st equation: \frac{2x}{3}+1=-3
3
2x
+1=−3.
x=-6
x=−6
6 Solve the 2nd equation: \frac{2x}{3}+1=5y
3
2x
+1=5y.
x=\frac{3(5y-1)}{2}
x=
2
3(5y−1)
7 Collect all solutions.
x=-6,\frac{3(5y-1)}{2}
x=−6,
2
3(5y−1)
Brian drove from Houston to New York, then to Chicago, then back to Houston. How far did he drive altogether?
Houston to NY= 1608
NY to Chicago=802
Chicago to Houston=1067
need help with error analysis assingment, im in high school and ive always struggled with math alot pls help
Given
A) The angles A and B are supplementary.
If,
[tex]\begin{gathered} \angle A=x+6 \\ \angle B=7x+30 \end{gathered}[/tex]B) The figure,
To find
A) The value of x.
B) The value of x.
Explanation:
A) It is given that,
Angle A and angle B are supplementary.
Then,
[tex]\angle A+\angle B=180\degree[/tex]Hence, the error is in the statement,
Since the angles are supplementary, when added together they equal 90.
As, the correct answer is when added together they equal 180.
That implies,
[tex]\begin{gathered} x+6+7x+30=180 \\ 8x+36=180 \\ 8x=180-36 \\ 8x=144 \\ x=\frac{144}{8} \\ x=18\degree \end{gathered}[/tex]Hence, the value of x is 18 degrees.
B) It is given that,
From, the figure the given angles are interior angles.
Also, the interior angles on the same side of the transversal is supplementary.
Which means when you add them they equal 180.
Hence, the error is in the statement,
Since the angles are adjacent, they are complementary angles.
Which means when you add them they equal 180.
As, the angles are interior angles on the same side of the transversal.
Also,
[tex]\begin{gathered} 64+x=180 \\ x=180-64 \\ x=116\degree \end{gathered}[/tex]Hence, the value of x is 116 degrees.
Philip drove 66km from Liverpool to Sheffield at 80km/h.
How many minutes did this take him?
Answer:
49.5 minutes
Step-by-step explanation:
Amount of time that Philip took
= [tex]\frac{distance}{speed}[/tex]
= [tex]\frac{66km}{80km/h}[/tex]
= [tex]0.825h[/tex]
= [tex]49.5 min[/tex]
Which value of y makes this equation true?
Which value of y makes this equation true?
12y - 1/2 = 9y +8/5
A. 1/6
B. 1/2
C. 2
D. 6
On solving the given equation the value of y=7/10 so this value the given equation will be true as the definition of solution of equation says ,"A solution to an equation is a number that can be plugged in for the variable to make a true number statement. "
What is solution to equation?A number that can be entered for the variable to produce a true number statement is the solution to an equation. One-step equations can be solved in four different ways: by adding, subtracting, multiplying, and dividing. In an equation, both sides will remain equal if we add the same amount to each side. Systems of equations can be solved using one of three techniques: graphing, substitution, or elimination. Simply plot the given equations on a graph and locate the point(s) where they all intersect to solve a system by graphing. You can find the values of the variables you are solving for by finding the coordinate of this point.
Here,
12y - 1/2 = 9y +8/5
3y=8/5+1/2
3y=(16+5)/10
3y=21/10
y=7/10
According to the definition of an equation's solution, "A solution to an equation is a number that can be plugged in for the variable to make a true number statement," the value of y will be 7/10 when the given equation is solved.
To know more about solution of equation,
https://brainly.com/question/10413253?referrer=searchResults
#SPJ1
Priya practiced the violin for 152% as much time as Han practiced the piano hiw long did she practiced, if Han practiced for 74 minutes
To find the time that Priya spent practicing violin, calculate what is 152% of 74 minutes by multiplying 74 times 152/100:
[tex]\frac{152}{100}\times74=112.48[/tex]Therefore, Priya practiced for 112.48 minutes.
Which exponential function matches the values in the table below?3521612967776y=21631y = 6xy=6(67y=(6
Verify each equation
option A
For x=3 ------> y=216(3^3)=
find thevsurface area of a square pyramid wuth side length 3 km and slant height 5 km
The Total Surface Area = 4 triangles + 1 square
The TSA of the Pyramid = 4(1/2 bh) + LxL
[tex]\begin{gathered} d^2=3^2+3^2 \\ d^2=9+9 \\ d=\sqrt[]{18}\text{ =}\sqrt[]{9\times2}=\sqrt[]{9}\text{ }\times\sqrt[]{2}\text{ =3 }\sqrt[]{2} \end{gathered}[/tex][tex]\begin{gathered} 5^2=h^2+(\frac{3}{2})^2 \\ 25-\frac{9}{4}=h^2 \\ 25-2.25=h^2 \\ h=\sqrt[]{22.5}\text{ =1.5km} \end{gathered}[/tex]TSA of the pyramid =
[tex]4(\frac{1}{2}\times5\times3)+(3^2)=(2\times15)+9=30+9=39km^2[/tex]A teacher buys packs of notebooks to give to their students. The tape diagram represents the ratio of brown notebooks to red notebooks. Brown notebooks Red notebooks Based on the ratio, if there are 24 red notebooks, what is the number of brown notebooks?
The number of brown notebooks is 40.
What is the ratio?
A ratio displays the multiplicity of two numbers. For example, if there are eight oranges and six lemons in a bowl of fruit, the orange-to-lemon ratio is eight to six. Similarly, the lemon-to-orange ratio is 6:8, and the orange-to-fruit ratio is 8:14.
We have,
24 red notebooks,
∴ 5/3 = x/24.
Cross-multiply, and we now have
120 = 3x.
Divide both sides by 3,
x = 120/3
x = 40
x = 40 brown notebooks.
Hence, the number of brown notebooks is 40.
To learn more about the ratio visit,
https://brainly.com/question/2914376
#SPJ1
(6×10 to the ninth power)divided by (2.4×10 to the third power)
Answer:
2.5×10 to the sixth power
Step-by-step explanation:
6÷2.4=2.5
10^9÷10^3=6
combine like terms algebra
Solve the equation 20 + 0.44x + 4 = 19 + 1.69x.
A. x = 4
B. x = 2.14
C. x = 5
D. x = 34.4
Answer: A
Step-by-step explanation: The starting equation is 24 + 0.44x = 19 + 1.69x,
First, combine the x's on the RHS, and the integers on the LHS.
1.69x - 0.44x = 1.25x
24 - 19 = 5
So the equation will be 1.25x = 5
Divide both sides by 1.25 to isolate the x.
x = 4
what is 1 1/2 divided by 1/6
Answer: 66/2 or in simplest form, 33/1
Step-by-step explanation:
11/2 divided by 1/6
*Keep the first fraction, flip the sign to multiplication, reciprocal or flip the fraction*
= 11/2 x 6/1
=66/2
=33/1
(2x+1)(x-2)(x+3)
please help
Answer: 2x^3 + 3x^2 - 11x - 6
Step-by-step explanation: simplified