The width of the living room on the new blueprint is 15 feet.
How to calculate the width?Based on the information, the scale of the original blueprint will be:
= 2 in / 5 ft
The width of the original blueprint is 6 inches, the actual width of the living room will be:
2/5 = 6/x
where x = width of living room
Cross multiply
x = 5 × 6 / 2
x = 15 feet.
The width is 15 feet.
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Use the parent function f(x) and the description of the transformation to write the new function g (x) Rotate the graph f(x) = - 4x + 5 until it has the same steepness in the opposite direction. This represents reflecting the graph across the y-axis. Therefore the new function is g(x) = What is the answer
Given:
The given function is, f (x) = -4x + 5.
The objective is to reflect the graph across the y - axis and find the new function.
Explanation:
The general transformation formula for reflection over y-axis is,
[tex]g(x)=f(-x)[/tex]To find f(-x):
The required transformation can be calculated as,
[tex]\begin{gathered} g(x)=f(-x) \\ g(x)=-4\mleft(-x\mright)+5 \\ g(x)=4x+5 \end{gathered}[/tex]Hence, the new function is g(x) = 4x + 5.
A northbound train and a southbound train meet each other on parallel tracks heading in opposite directions. The northbound train travels 12 miles per hour faster than the southbound train. After 2 hours, they are 240 miles apart. At what speeds are the two trains traveling?
please help me, I'm gonna fail my test tomorrow
Answer:
Speed of northbound train = 66
Speed of southbound train = 54
Step-by-step explanation:
First, let's make the variables simpler:
Speed of southbound train = x
Thus:
Speed of northbound train = y = x + 12
Distance = speed · time
240 = 2 ( x + x + 12 ) = 2 ( 2x + 12 ) = 4x + 24
216 = 4x
x = 54
Now, plug in x to find the speed of the northbound train (y):
y = 54 + 12 = 66
tweleve is no less than the sum of a number n and 3
Please help I dont understand!!!!!
Answer: This is a linear pair of angles because they are two adjacent angles that have a common side and whose other sides point in opposite directions.
Please help me thanks lol
Answer:
I would say yes they are
Step-by-step explanation:
because you multiply the small one's numbers by 2 and get the big triangle
Answer:
they are similar! :)
Step-by-step explanation:
the best way to figure this out is just by looking to see if they have anything in common. in this case, the larger figure is just two times more on each side than the smaller figure.
1. The Mariaskis' home is located in a community where the rate of
assessment is 45% of the market value. The tax is $65 per $1,000 of
assessed value. The Mariaskis' home has a market value of $97,400.
a. What is the assessed value?
b. What is the yearly real estate tax?
a.) The Assessed value is $43,830
b.) Annual Tax is $2,848.95
Define marked price
'Marked price' is the general price of the thing without any discount. 'discount' is a percentage of the marked price.
Given,
Assessment rate = 45%
Tax rate is $65 per $ 1000 of assessed value
Marked value = $97,400
a.)
To obtain assessed value,
calculate the 45% of $97,400 like that
45/100 = x/97,400
cross multiply the ratios
100x = 45 * 97,400
x = (45 * 97,400) / 100
x = 45 * 974
x = 43,830
Hence,the Assessed value is $43,830
b.)
Find yearly real estate tax,
Assessed value = $43,830
Tax rate is = 65 / 1000 of assessed value
= 0.065 * 43830
= 2,848.95
Hence, the annual tax is $2,848.95
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what is the slope of the line ?
Answer:
Step-by-step explanation:
5/2
Answer: f(x)= 2x-3
Step-by-step explanation: The formula for slope is y=mx+b, where m is equal to the slope of the line and b is equal to the y-intercept. We can find the slope by looking at the line OR solving algebraically using the following calculations:
(y2-y1)/(x2-x1)
Pick 2 points on the line and plug in.
(x1,y1)-->(2,1) and (x2,y2)-->(3,3)
(3-1)/(3-2)=2/1=2
So, the slope of the line is 2. m=2.
To find the y-intercept, we can solve algebraically or look at the graph.
y=2x+b
Plug in a point from the graph to find b, the y-intercept.
3=2(3)+b
3=6+b
-3=b
So, the y-intercept is b.
Now, we plug our values into the slope intercept equation, y=mx+b
y=2x-3
Again, you look look at the graph and see where x=0 is to find the y intercept. To find the slope you can use rise/run and count to see that to get from one point on the graph to the next, you count up 2 (rise 2) and to the right 1 (run 1) which gives you 2/1. 2/1 is equal to 2, giving you the slope of 2.
Hope this helped :))
What are the new vertices of quadrilateral KLMN if the quadrilateral is translated two units to the right and four units upward? A. K = (-2,0), L' = (1,0), M = (1,-3), N = (-2,-3) B. K = (-2,-2), L' = (1,-2), M = (1,-5), N = (-2,-5) C. K = (-0,0), L' = (3,0), M = (3,-1), N = (0,-1) D. K = (-2,2), L' = (1,2), M = (1,-1), N = (-2,-1)
K' ( -2, 2) , L' (1,2) , M' (1,-1) , N' (-2,-1)
Firstly, we needt to identify the coordinates of the vertices of the quadilateral
Afterwards, we then perform the translation
The translation simply means we add 2 to the x-value and add 4 to the y-value
So if we had coordinates of a vertex as (x,y); upon translation, we will have (x + 2, y+ 4)
Let us identify the vertices;
K'
K (-4,-2)
L (-1,-2)
M (-1,-5)
N (-4,-5)
After translation, we have;
K' ( -2, 2) , L' (1,2) , M' (1,-1) , N' (-2,-1)
Please help and provide an explanation for why the answer is f(x) = 3/2x + 7
What is the equation of the line that passes through Point (-4, 1) and has a Slope of 3/2.
Answer:
see below
Step-by-step explanation:
the point-slope equation is
y-1 = 3/2 (x+4)
Answer:
[tex]y=\frac{3}{2}x+7[/tex]
Step-by-step explanation:
To write the equation of a line, two information are needed.
Slope (also known as gradient)A pair of coordinates (or a point) on the lineThe slope can be calculated using the gradient formula as long as two pairs of coordinates are given. This question provides the slope, hence we can substitute its value into the equation right away.
In slope-intercept form, the equation of a line is given by y= mx +c, where m is the slope and c is the y-intercept. The slope gives us the steepness of the line, while the y-intercept is the y value in which the line cuts through the y-axis (vertical axis).
y= mx +c
Given that slope= [tex]\frac{3}{2}[/tex], m= [tex]\frac{3}{2}[/tex].
Substitute the value of m:
[tex]y=\frac{3}{2}x+c[/tex]
Next, find the value of c by substituting a pair of coordinates.
When x= -4, y= 1,
[tex]1=\frac{3}{2} (-4)+c[/tex]
1= -6 +c
Add 6 to both sides:
c= 1 +6
c= 7
Substituting the value of c:
[tex]\bf{y=\frac{3}{2}x +7 }[/tex]
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Find the equation of the line with slope −35 and y-intercept (0,−3).
Answer:
y = -35x -3
Step-by-step explanation:
We can use the formula y = mx + c to find the equation of the line.
Here,
m ⇒ slope
c ⇒ y-intercept
From these, they have already given the slope of the line.
m ⇒ -35
And now we have to find the c ( y-intercept ) of the line using the given coordinate,
( 0 , -3 ) ⇒ ( x , y )
So, to find the y-intercept you have to replace x, y & m with 0, -3 & -35 respectively, and solve for c.
Let us solve it now.
y = m x + c
-3 = -35 × 0 + c
-3 = 0 + c
-3 = c
And now we can write the equation of the line like this.
y = m x + c
y = -35x -3
Answer:
Equation of line is given as y =mx + c, where m is the slope and c is the y-intercept.
Since slope is -35, equation of line is y = -35x + c.
Substitute (0,-3) into equation to find c.
-3 = -35(0) + c
c = -3
Hence, equation is y = -35x - 3.
Question 3 (1 point)
(03.06 LC)
Determine if the sequence is arithmetic or geometric, and find the common difference or ratio
Arithmetic, Common Difference = -9
The Correct option is (b).
What is Common Difference?
The common difference of an arithmetic sequence is the difference between any of its terms and its previous term. An arithmetic sequence goes from one term to the next by always adding (or subtracting) the same amount. The number added (or subtracted) at each stage of an arithmetic sequence is called the "common difference", because if we subtract (that is if you find the difference of) successive terms, you'll always get this common value. Most often, "d" is used to denote the common difference.
Given,
x = 1 2 3 4
f(x)= 81 72 63 54
Now, According to the question:
2nd term - 1st term = 72 - 81 = -9
3rd term - 2nd term = 63 - 72 = -9
4th term - 3rd term = 54 - 63 = -9
Hence, Arithmetic, Common Difference = -9
The Correct option is (b).
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HELP PLEASE!
f(x)= ³ √x+8. Find the inverse of f(x).
Answer: (D)
the answer would be D
Step-by-step explanation:
giving ten points since thats all i have
if test scores for an exam were normally distributed with a mean of 75 and a standard deviation of 5, find the probability that a randomly selected student scored less than 82.
the probability that a randomly selected student scored less than 82.
Then the value is P( X< 82)=0.9192
From the question we are told that
The sample size is n = 24
The mean is =75
The standard deviation is =5
Generally the probability that a randomly chosen student scored is less than 82 is mathematically represented as
P( X < 82) = P ( Z< 82-75/5)
=P(Z <1.4)
=0.9192
From the z table the area under the normal curve corresponding to 1.4 is 0.9192
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each side of a square is increasing at a rate of 8 cm/s. at what rate is the area of the square increasing when the area of the square is 81 cm2?
The area of square is increasing with the rate of 144 cm/s2.
What is rate of expansion of solid ?For physics, The term "thermal expansion" refers to a material's change in length, width, height, or volume when its temperature is raised or lowered. Solids exhibit particularly noticeable thermal expansion due to their closely packed atoms. There are numerous uses for thermal expansion of solids in daily life.
A solid's atoms vibrate more quickly around their fixed positions when it is heated. As a result, there is little relative growth in the size of solids during heating. In order to prevent buckling when exposed to heat from the sun, metal train tracks feature tiny gaps.
CalculationL = length of a side
A = L2
dA/dt = 2L dL/dt
dL/dt = 8 cm/s
A = 81 cm2 ⇒ L = √A = √81 cm = 9 cm
dA/dt = 2(9cm)(8 cm/s) = 144 cm/s2
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Challenge An arts academy requires there to be 4 teachers for every 92 students and 3 tutors for every 24 students. How many students does the academy have per teacher? Per tutor? How many tutors does the academy need if it has 72 students?
Answer:2
Step-by-step explanation:25 students per a teacher and 33 students per a tutor.if the academy has 77student they need 2 tutors
WILL GIVE 20 POINTS.
Match each picture to its name.
Answer:
1. PQ
2. PQ + qr= pr
3. the arrow going both ways with p q
4. point p
5. the arrowing going one way with p q
Step-by-step explanation:
I took the test
Day 10xASE CertifiedBrakesASE CertifiedA/C Repair143223ASE CertifiedEngine Tune-Ups3Not ASECertifiedA manager that owns 3 localarea Car MaintenanceGarages was researchingcertifications of mechanicsthat worked for hercompany. Consider thefollowing Venn diagram. What is the probability that a randomly selected mechanic that is certified in A/C repair given that the mechanic is certified to do tune-ups ?
The probabilities from the venn diagram are:
Let A be the event that the Mechanic is AC repairman and T be the event that he does tune ups.
[tex]P(A\cap T)=\frac{2}{13}[/tex]The probability that he does tune ups is:
[tex]P(T)=\frac{3}{13}[/tex]Hence the required probability is given by:
[tex]P(A|T)=\frac{P(A\cap T)}{P(T)}=\frac{\frac{2}{13}}{\frac{3}{13}}=\frac{2}{3}[/tex]Hence the probability is 2/3.
The histogram shows information about the weights of some of the parcels handled by a delivery company in one month.
Zoe says:
"There are fewer parcels weighing between g and g than parcels weighing between g and g."
Is Zoe correct?
Show how you decide.
(4 marks)
From the histogram of the distribution, it is found that Zoe is not correct, as there are more people weighing between 300 g and 450 g than people weighing between 450 g and 700 g.
What is an histogram?An histogram is a graph that shows the number of times each element of x was observed in the distribution. When the input is an interval of values, as is the case in this problem, it shows the number of observations that is in each interval.
Hence, from the histogram in this distribution, it is found that:
There are approximately 75 people weighing between 300 g and 450 g.There are 50 people weighing between 450 g and 700 g.75 is a greater amount than 50, hence Zoe's statement is not correct, as there are more people weighing between 300 g and 450 g than people weighing between 450 g and 700 g.
What is the missing information?The complete problem is given by the image at the end of the answer.
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Rory is adding a sidewalk to his front yard. The picture shows the dimensions of the
sidewalk.
How much cement, in cubic feet, does Rory need to build the sidewalk?
A. 156
B. 96
C. 60
D. 4608
Answer:
348 ft
Step-by-step explanation:
First split the sidewalk into two rectangles. then multiply the LxWxH (length times width times height) of both rectangles. 8 times 6 times 6 = 288 ft. then 10 times 2 times 2 = 60. then add the two volumes of the rectangles to result in 348 cubic ft
50 POINTS!
A line goes through the points (3, -4) and (-1, 8). Write the equation of the line in point-slope form. Show your work for full credit. (Show the steps for how you went from the two points, above, to having the equation in point-slope form. All calculations must be written down.)
can someone show how they do this instead of just only giving the answer.
Answer:
y= -3x + 5
Step-by-step explanation:
m= (y2-y1)/(x2-x1)
m= [8-(-4)]/(-1-3)
m=12/-4
= -3
y= mx + b
-4=(-3)(3) + b
-4=9+b
b=5
therefore, y= -3x+5
The heartbeat of a horse is about 42 beats per minute. About how many times would it beat in ten minutes?
A. 400 beats
B. 450 beats
C. 475 beats
D. 500 beats
The number of heartbeat in ten minutes is 420 beats
What are unit rates?Unit rates are the rates of a quantity to one of another quantity
How to determine the number of heartbeats?From the question, the given parameters are:
Number of heartbeats per minute = 42 beats per minute -- this represents the unit rateNumber of minutes = 10 minutesThe number of heartbeats in these ten minutes is then calculated as
Total heartbeats = Number of heartbeats per minute x Number of minutes
Substitute the known values in the above equation
So, we have
Total heartbeats = 42 x 10
Evaluate
Total heartbeats = 420
Hence, the total heartbeat is 420 beats
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NEED DONE ASAP WILL MARK BARINLIEST
Including both end zones, a football field is 4,320 inches long. What is this value expressed in scientific notation?
A
4.32×10−4
B
4.32×10−3
C
4.32×103
D
4.32×104
Answer:39.2 40.2 444.96
Step-by-step explanation:
Una hoja de papel rectangular tiene un área de 84 pulgadas,el ancho del papel es 5 pulgadas menos que el largo¿cual es el ancho,en pulgadas de la hoja de papel ?
Answer: I think the width is 7.
Step by step explanation:
So let's say the length is 12. This means I need to subtract 5 from it, since the width is 5 inches less than the length. Now that we know this, that means the width is 7, which is the area.
I hope this helps.
A gym membership costs $25 to join and $14 each month. Write and use an algebraic
expression to find the cost of the gym membership for 6 months.p
The algebraic expression to find the cost of the gym membership for 6 months is given by 25+6×14.
What is algebraic expression?
An algebraic expression is one that has been constructed using integer constants, variables, and algebraic operations. A good example of an algebraic expression is 3x2 2xy + c. Any mathematical operation that involves variables, such as addition, subtraction, multiplication, or division, can have its solutions calculated using algebraic expressions. Monomial, binomial, and polynomial expressions are the three different categories of algebraic expressions.
Given, the cost of joining membership = $25
The cost of each month = $14
Cost of 6 months = 6 multiplied by 14
Cost of gym membership for 6 months = 25+6×14
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[tex]6x^{2} -7=9x+8x^{2}[/tex]
27/50 as a percentage
Answer: 54%
Step-by-step explanation:
How do
you
create equations and use them to solve
problems?
Answer:
define the unknown quantity as =variable. Then use the given info to write down an equation in terms of the unknown quantity. At the end, solve the equation for the unknown.
I am not sure how to solve this
There are a total of 235 books in the library. On Monday, 113 books were checked out. On Tuesday, fifty-six books were checked back in. How many books are there in the library on Wednesday morning?
Answer:
178
Step-by-step explanation:
235-113=122
122+56=178
Answer:
178 books
Step-by-step explanation:
235 minus 113 books that werr checked out and plus 56 books that came back in total it's 178, if nobody stole anything :)