5.) figure 12.16 shows the floorplan for a modern one story house. Bob calculates the area of the floor of the housing this way: 36•72-18•18 = 2268 feet squared. what might Bob have in mind? Explain why Bob’s method is a legitimate way to calculate the floor area of the house, and explain clearly have one or both of the moving and additivity principles on area apply in this case
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From the given image, the Area of the floor can be calculated by removing/subtracting the area of the two triangles from the area of the rectangle.
Area of a rectangle is;
[tex]\begin{gathered} A_r=lb \\ A_r=36.72 \end{gathered}[/tex]Area of the two triangles;
[tex]\begin{gathered} A_t=\frac{1}{2}bh+\frac{1}{2}bh=\frac{1}{2}(18.18)+\frac{1}{2}(18.18) \\ A_t=18.18 \end{gathered}[/tex]The Area of the floor is;
[tex]\begin{gathered} A=A_r-A_t \\ A=36.72-18.18 \\ A=2592-324 \\ A=2268ft^2 \end{gathered}[/tex]Related Questions
laws of exponent : multiplication and power to a poweranswer and help me step by step
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All the numbers multiply in the normal way, and the powers of a power need to be multiplied.
[tex]72c^4d^8e^{10}[/tex]Perform a web search for images for the term graph of sales trends. Choose an image where there are both increasing and decreasing trends. Upload the image you found and discuss the time period(s) when the sales trend is increasing, and when it is decreasing. Also indicate any periods where the trend stayed constant (that is, it did not change).
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Imagine you have a newsstand and you start to pay attention to how many magazines you sell each month for one year to understand which months you sell more and which months you sell less. So what you want is to understand the trends of your business.
So, after a year, you are able to draw a graph that represents all sales for this year per month as follows:
So, as we can see above, We have the sales of your newsstand from January to August. The x-axis indicates the months of the year and the y-axis indicate the number of magazines sold. We can see for January you sold 15 magazines and the number increased for February and Mars. Between Mars, April and May, it stayed constant and from May to August it decreased. It is represented by the line in red, where we have first an increasing trend, after a constant trend and finally a decreasing trend. So that is how it works, and now you can understand and explain how a graph of sales trends works and which kind of images you have to look for.
got a square thats 23cm and 57cm .what is the perimeter
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The perimeter of the shape is obtained by summing up all its 4 sides
=> 23 + 23 + 57 + 57
Perimeter = 46 + 114
perimeter = 160 cm
For which equation is x = 5 a solution ?
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Given x = 5
We will find which equation will give a solution x = 5
1) x/2 = 10
so, x = 2 * 10 = 20
So, option (1) is wrong
2) x - 7 = 12
x = 12 + 7 = 19
So, option 2 is wrong
3) 2 + x = 3
x = 3 - 2 = 1
So, option 3 is wrong
4) 3x = 15
x = 15/3 = 5
So, the answer is option 3x = 15
Each expression below represents the area of a rectangle written as a product tha area model for each expression on your paper and label its length and then we nation showing that the area written as a product is equal to the area wimen as the the parts de prepared to share your equations with the class. a. (x+3)(2x + 1) ca(224) d. (2x + 5)(x + y + 2) • (20 - 1999 (2x-1) (2x-1) g. 2(325) ( 2+ y + 3) 2
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We have the expression:
[tex]x(2x-y)[/tex]It can be thougth as the area of a rectangle with sides x and (2x-y).
We can also think of the the difference between an area of a rectangle with sides x and 2x and a rectangle with sides x and y:
[tex]x(2x-y)=x\cdot2x-x\cdot y=2x^2-xy[/tex]Answer: x(2x-y) = 2x^2-xy
In a coordinate plane, the midpoint of AB is (2,5) and A is located at (-5,10). If (x,y) are the coordinates of B, find x and y.
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In a coordinate plane, the midpoint of AB is (2,5) and A is located at (-5,10). If (x,y) are the coordinates of B, find x and y.
Remember that
the formula to calculate the midpoint between two points is equal to
[tex]M=(\frac{x1+x2}{2},\frac{y1+y2}{2})[/tex]In this problem we have
M=(2,5)
(x1,y1)=A(-5,10)
(x2,y2)=B(x,y)
substitute the given values
[tex](2,5)=(\frac{-5+x}{2},\frac{10+y}{2})[/tex]step 1
Find the x-coordinate of B
equate the x-coordinates
so
2=(-5+x)/2
solve for x
4=-5+x
x=4+5=9
step 2
Find the y-coordinate of B
equate the y-coordinates
5=(10+y)/2
solve for y
10=y+10
y=0
therefore
the coordinates of B are (9,0)Question 25.Show if given 1-1 functions are inverse of each other. Graph both functions on the same set of axes and show the line Y=x as a dotted line on graph.
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Given:
[tex]\begin{gathered} f(x)=3x+1_{} \\ g(x)=\frac{x-1}{3} \end{gathered}[/tex]To check the given functions are inverses of each other,
[tex]\begin{gathered} To\text{ prove: }f\mleft(g\mleft(x\mright)\mright)=x\text{ and g(f(x)=x} \\ f(g(x))=f(\frac{x-1}{3}) \\ =3(\frac{x-1}{3})+1 \\ =x-1+1 \\ =x \end{gathered}[/tex]And,
[tex]\begin{gathered} g(f(x))=g(3x+1) \\ =\frac{(3x+1)-1}{3} \\ =\frac{3x+1-1}{3} \\ =\frac{3x}{3} \\ =x \end{gathered}[/tex]It shows that, the given functions are inverses of each other.
The graph of the function is,
Blue line represents g(x)
Red line represents f(x)
green line represents y=x
whats the absolute value between the points -45 and -11
Answers
For two real numbers u and v, |u-v| is the absolute value between the points:
|-45-(-11)|=|-34|=34
The senior classes at High School A and High School B planned separate trips to New York City.The senior class at High School A rented and filled 2 vans and 6 buses with 366 students. HighSchool B rented and filled 6 vans and 3 buses with 213 students. Each van and each bus carriedthe same number of students. Find the number of students in each van and in each bus.Answer: A van hasstudents and bus has students
Answers
Let V be the number of students that fit inside a van and B the number of students that fit inside a bus. Since 366 students fit in 2 vans and 6 buses, then:
[tex]2V+6B=366[/tex]Since 213 students fit in 6 vans and 3 buses, then:
[tex]6V+3B=213[/tex]Multiply the second equation by 2:
[tex]\begin{gathered} 2(6V+3B)=2(213) \\ \Rightarrow12V+6B=426 \end{gathered}[/tex]Then, we have the system:
[tex]\begin{gathered} 2V+6B=366 \\ 12V+6B=426 \end{gathered}[/tex]Substract the first equation from the second one and solve for V:
[tex]\begin{gathered} (12V+6B)-(2V+6B)=426-366 \\ \Rightarrow12V-2V+6B-6B=60 \\ \Rightarrow10V=60 \\ \Rightarrow V=\frac{60}{10} \\ \therefore V=6 \end{gathered}[/tex]Substitute V=6 into the first equation and solve for B:
[tex]\begin{gathered} 2V+6B=366 \\ \Rightarrow2(6)+6B=366 \\ \Rightarrow12+6B=366 \\ \Rightarrow6B=366-12 \\ \Rightarrow6B=354 \\ \Rightarrow B=\frac{354}{6} \\ \therefore B=59 \end{gathered}[/tex]Therefore, a van has 6 students and a bus has 59 students.
The area of a square backyard is 79 ft?. The owner is looking to get fencing to enclose the yard, so they need to find the approximate length of each side of the backyard AND what is the perimeter of the backyard?
Answers
According to the given question we have the following:
The area of a square backyard is 79 ft
Therefore if the area of a square backyard is 79 ft that means that length of each side would be the following:
length of each side=area of a square backyard/2
length of each side=79 ft/2
length of each side=39.5
Therefore if 39.5 is lenght of each side, the perimeter of the backyard would be calculated as follows:
perimeter of the backyard=l+l+l+l
perimeter of the backyard=39.5+39.5+39.5+39.5
perimeter of the backyard=158
Find the missing side or angle.Round to the nearest tenth.b=15a=30c=29A=[ ? 1°
Answers
STEP 1
The given parameters are a=30, b=15 and c=29
The corresponding cosine rule needed to find the angle A is denoted below
[tex]A=\cos ^{-1}\mleft[\frac{b^2+c^2-a^2}{2bc}\mright]^{}[/tex]STEP 2
Substitute the given parameters into the equation.
[tex]\begin{gathered} A=\cos ^{-1}\mleft\lbrace\frac{15^2+29^2-30^2}{2\times15\times29}\mright\rbrace \\ A=\cos ^{-1}\mleft\lbrace\frac{225+841-900}{870}\mright\rbrace \\ A=\cos ^{-1}\mleft\lbrace\frac{166}{870}\mright\rbrace \\ A=\cos ^{-1}0.1908 \\ A=79.0^0 \end{gathered}[/tex]Learn A STORY OF UNITS Lesson 4 Homework Helper 4.2 5. Mikal's backpack weighs 4,289 grams. Mikal weighs 17 kilograms 989 grams more than his backpack. How much do Mikal and his backpack weigh in all?
Answers
We have that the backpack weighs 4,289 grams = 4.289 kg.
Since Mikal weigh 17.989, we have that the total weight is:
[tex]17.989+4.289=22.278[/tex]therefore, Mikal and his backpack weigh 22.278 kg
It took Carmen 4 hours to drive 200 miles. Using context clues from the problem, what formula can be used to find George's rate of speed?
Answers
From the information given, we can find th rate of speed with the equation;
[tex]\text{distance = rate x time}[/tex]Or;
[tex]d=rt[/tex]Use your scatter plot of the temperature in 'n de in degrees North 2. The vertical intercept ans1°F The horizontal intercept ans2 °N
Answers
From the graph, the vertical intercept is 120°F
The slope, m, of the line that passes through the points (x1, y1) and (x2, y2) is computed as follows:
[tex]m=\frac{y_2-y_1}{x_2-x_!}[/tex]From the graph, the line passes through the points (0, 120) and (55, 60), then its slope is:
[tex]m=\frac{60-120}{55-0}=-\frac{12}{11}[/tex]The slope-intercept form of a line is:
y = mx + b
where m is the slope and b is the y-intercept. In this case, the equation is
y = -12/11x + 120
Substituting with y = 0, we get:
[tex]\begin{gathered} 0=-\frac{12}{11}x+120 \\ -120=-\frac{12}{11}x \\ (-120)\cdot(-\frac{11}{12})=x \\ 110=x \end{gathered}[/tex]The horizontal intercept is 110°N
juan is mailing a box like the one pictured below to his sister
Answers
Given:
Given a rectangle with
[tex]\begin{gathered} h=5cm \\ l=12cm \\ w=6cm \end{gathered}[/tex]Required:
To find the volume.
Explanation:
The formula for surface area is
[tex]SA=2lw+2lh+2wh[/tex]Here
[tex]\begin{gathered} =2(12)(6)+2(12)(5)+2(6)(5) \\ =144+120+60 \\ =324 \end{gathered}[/tex]Final Answer:
[tex]324cm^2[/tex]what is the rate of change of the cube’s surface area when its edges are 50 mm long?
Answers
The first thing we are going to do is identify the volume and surface of the cube and their respective derivatives or rate of change
[tex]\begin{gathered} V\to\text{volume} \\ S\to\text{surface} \\ l=\text{side of a square} \end{gathered}[/tex][tex]\begin{gathered} V=l^3\to(1) \\ \frac{dV}{dt}=3l^2\frac{dl}{dt}\to(2) \end{gathered}[/tex][tex]\begin{gathered} S=6l^2\to(3) \\ \frac{dS}{dt}=12\cdot l\cdot\frac{dl}{dt}\to(4) \end{gathered}[/tex]From the exercise we know that:
[tex]\begin{gathered} \frac{dV}{dt}=300\frac{\operatorname{mm}^3}{s}\to(5) \\ 3l^2\frac{dl}{dt}=300\frac{\operatorname{mm}^3}{s}\to(2)=(5) \\ \frac{dl}{dt}=\frac{300}{3l^2}\frac{\operatorname{mm}^3}{s}\to(6) \end{gathered}[/tex]The exercise asks us to calculate the rate of change of the surface (4) so we substitute the differential of length (6) in (4)
[tex]\begin{gathered} \frac{dS}{dt}=12\cdot l\cdot(\frac{300}{3l^2}\frac{\operatorname{mm}^3}{s}) \\ \frac{dS}{dt}=\frac{1200}{l}\frac{\operatorname{mm}}{s} \end{gathered}[/tex]what is the rate of change of the cube’s surface area when its edges are 50 mm long?
[tex]\begin{gathered} l=50\operatorname{mm} \\ \frac{dS}{dt}=\frac{1200}{50\operatorname{mm}}\frac{\operatorname{mm}^3}{s} \\ \frac{dS}{dt}=24\frac{\operatorname{mm}^2}{s} \end{gathered}[/tex]The answer is 44mm²/sSolve for x: |x - 2| + 10 = 12 A x = 0 and x = 4B x = -4 and x = 0C x = -20 and x=4 D No solution
Answers
|x - 2| + 10 = 12
|x - 2| = 12 -10
|x - 2| = 2
There are 2 solutions:
x-2 = 2 and x-2 = -2
Solve each:
x = 2+2
x = 4
x-2=-2
x =-2+2
x=0
solution: x=0 and x = 4
Two monomials are shown below.18x³y 30x22What is the greatest common factor (GCF) of thesemonomials?
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The given monomials are:
[tex]\begin{gathered} 18x^3y \\ 30x^2y^2 \end{gathered}[/tex]Factorizing each term, we get,
[tex]\begin{gathered} 18x^3y=2\times3\times3\times x^2\times y \\ 30x^2y^2=3\times2\times5\times x^2\times y^2 \end{gathered}[/tex]Therefore, the GCF is,
[tex]\text{GCF}=6x^2y[/tex]how many minutes until the heart beats 200 times
Answers
From the given table, we can read that the 200 beats is associated with the entry: "5 minutes", so that is the answer we pick.
which agrees with the first option in the provided list of possible answers.
graph the slope connecting (2,3) and (4,0)
Answers
SOLUTION
STEP 1: Write the given points
[tex](2,3)\text{ }and\text{ }(4,0)[/tex]STEP 2: Find the slope
[tex]\begin{gathered} \mathrm{Slope\:between\:two\:points}:\quad \mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1} \\ \left(x_1,\:y_1\right)=\left(2,\:3\right),\:\left(x_2,\:y_2\right)=\left(4,\:0\right) \\ m=\frac{0-3}{4-2} \\ m=-\frac{3}{2} \end{gathered}[/tex]The graph of the slope is seen below:
13. Graph the inequality. xs-3 X>8 10 9
Answers
You have teh following inequality:
x ≤ -3
consider that the previous inequality includes all number lower and equal to -3, that is, -3,-4,-5,.., until - infinity.
Then, the graph is:
For the following inequality:
x > 8
consider that the solutions are all numbers greater than 8 without including it.
Then, for the graph, you have:
There are gallon of orange juice and gallon of cranberry juice in the refrigerator. How many gallons of juice are there in all? A 8 10 B. 112/2 C 8 12 17/12
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Answer:
2 gallons of juice
Step-by-step explanation:
your welcome
HELP HELP HELP PLEASE!!!!!!!!!!
Answers
The slope of the given table is m = 5/4 or 1.25
The given table has various values of x and y
So given : y₂ = 30 and y₁ = 45
likewise x₂ = 8 and x₁ = 4
Thus the points are
P₁ = ( 4, 45 ) and P₂ = ( 8, 30 )
Since both points are positive thus these points lie in the first quadrant
Also to calculate the slope of a graph we use the formula
m or slope = y₂ - y₁ / x₂ - x₁
On substituting the above mentioned values
we will get
m or slope = 45 - 30/ 8 - 4
this further implies that
m or the slope = 5 /4 = 1.25
Thus the slope of the given values is 1.25
To know more about slope and coordinate geometry you may visit the link which is mentioned below:
https://brainly.com/question/16302642
#SPJ1
5.) The elements of f(x) are (-7,3).(-1, 6) and (8,-3). What is the range of the function?
Answers
The range of a function is all values of y the function have.
So, looking at the elements (-7, 3), (-1, 6) and (8, -3), the y-coordinates of these points are 3, 6 and -3.
So the range of f(x) is:
[tex]\text{range}=\mleft\lbrace-3,3,6\mright\rbrace[/tex]write and slove six less then the product of a number n and 1/4 is no more than 96 fill in the boxs
Answers
ANSWER:
[tex]n\leq408[/tex]STEP-BY-STEP EXPLANATION:
With the statement we deduce the following inequality
[tex]\frac{1}{4}\cdot n-6\leq96[/tex]Solving for n
[tex]\begin{gathered} 4\cdot\frac{1}{4}\cdot n-4\cdot6\leq4\cdot96 \\ n-24\leq384 \\ n\leq384+24 \\ n\leq408 \end{gathered}[/tex]having a bit of a problem with this logarithmic equation I will upload a photo
Answers
SOLUTION
We are asked to solve the equation
[tex]4^{5x-6}=44[/tex]44 cannot be written in index form. So to solve this, we will take logarithm of both sides of the equation
We will have
[tex]\log 4^{5x-6}=\log 44[/tex]Solving for x, we have
[tex]\begin{gathered} \log 4^{5x-6}=\log 44 \\ \\ 5x-6\log 4=\log 44 \\ \\ \text{dividing both sides by log4} \\ \\ 5x-6=\frac{\log 44}{\log 4} \\ \\ 5x=\frac{\log44}{\log4}+6 \end{gathered}[/tex]The exact solution becomes
[tex]x=\frac{(\frac{\log44}{\log4}+6)}{5}[/tex]The approximate solution to 4 d.p
[tex]\begin{gathered} x=\frac{(\frac{\log44}{\log4}+6)}{5} \\ \\ x=\frac{(\frac{1.64345}{0.60206}+6)}{5} \\ \\ x=\frac{8.72971}{5} \\ \\ x=1.7459 \end{gathered}[/tex]Hello can you assist me please i need to solo e and Identity sine cosine or tangent and identify opposite hypnose or adjeact #12
Answers
Solution (12):
Given the triangle;
The opposite side is labelled as x and the adjacent side is 17.
Using the tangent trigonometry ratio, we have;
[tex]\tan\theta=\frac{opposite}{adjacent}[/tex]Thus;
[tex]\begin{gathered} \tan(51^o)=\frac{x}{17} \\ \\ x=17\tan(51^o) \\ \\ x=20.99 \\ \\ x\approx21 \end{gathered}[/tex]What is the Slope of HI ? Justify your answer .Please help
Answers
Solution:
Given:
A coordinate plane with two similar triangles.
To get the slope of HI, because the two triangles are similar, their hypotenuses will always have the same slope.
Hence, the slope of HI is also the slope of DE.
[tex]\begin{gathered} \text{Considering }\Delta DEF,\text{ using the points (8,32) and (12,24)} \\ \text{where;} \\ x_1=8 \\ y_1=32 \\ x_2=12 \\ y_2=24 \end{gathered}[/tex]
Using the formula for calculating slope (m),
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Substituting the values of the points gotten from triangle DEF,
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{24-32}{12-8} \\ m=\frac{-8}{4} \\ m=-2 \end{gathered}[/tex]Since the slope of triangle DEF is the hypotenuse of the right triangle DEF, then the slope HI is also the hypotenuse of triangle HIJ and both hypotenuses have the same slope since both triangles are similar.
Therefore, the slope of HI is -2.
Use a calculator to find an angle θ on the interval [0∘,90∘] that satisfies the following equation.tanθ=3.54
Answers
Answer:
θ = 74.23°
Explanation:
The inverse function of the tangent is arctangent and it can be written as:
[tex]\arctan (x)=\tan ^{-1}(x)[/tex]So, if tan θ = 3.54, then:
[tex]\theta=\tan ^{-1}(3.54)[/tex]Then, using the calculator, we get:
[tex]\theta=74.23\text{ degrees}[/tex]So, the answer is θ = 74.23°
1000=10 to the power 310,000= 10 to the power 4100,000=10 to the power 51,000,000= 10 to the power 6the next line is
Answers
According to the information, the question looks to construct the pattern given, at the left we can see that there is a 0 added in every line and at the right the exponent is added +1.
the next line in the pattern is
[tex]10,000,000=10^7[/tex]