The scale factor of a similarity transformation is the ratio of the lengths of the corresponding sides of the two similar figures.
What is scale factor?The scale factor is a ratio between two corresponding lengths, areas, or volumes of two similar figures. It is used to compare the size of one figure to another, as well as to enlarge or reduce the size of a figure. The scale factor is expressed as a ratio, such as 1:2, where the first number is the original size and the second is the new size.
It is usually represented as a decimal or fraction, and can be calculated by dividing the length of one of the sides of one figure by the length of the corresponding side of the other figure. For example, if we have two triangles with corresponding sides that measure 3 units and 6 units, then the scale factor of the dilation is 0.5 (3/6). This means that the second triangle is half the size of the first.
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7. A kids furniture warehouse ships small tables and chairs in certain combinations to consumers in the United States. The weight of 3 tables and 5 chairs is 62.5lbs and the weight of 3 tables and 2 chairs is 52lbs. Create and solve a system of equations to find out how much each table and chair weighs.
The weight of each small tables and chairs in the United States is 15lbs and 3.5lbs respectively.
Simultaneous equationLet
Weight of tables = xWeight of chairs = yCost of 3 tables and 5 chairs is 62.5lbsCost of 3 tables and 2 chairs is 52lbs3x + 5y = 62.5
3x + 2y = 52
Subtract the equation to eliminate x5y - 2y = 62.5 - 52
3y = 10.5
y = 10.5/3
y = 3.5 lbs
Substitute y = 3.5 into
3x + 2y = 52
3x + 2(3.5) = 52
3x + 7 = 52
3x = 52 - 7
3x = 45
x = 45/3
x = 15 lbs
Therefore, the weight of each small tables and chairs in the United States is 15lbs and 3.5lbs respectively.
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use the substitution method to solve the system of equaltions. choose the correct ordered pair. 2y+4x=18 and 2y-3x=4
The solution of the system of equation is x = 7 and y = 12.5.
How to solve equation by substitution?2y + 4x = 18
2y - 3x = 4
2y = 4 + 3x
y = 2 + 3 / 2 x
Hence, let's substitute the value of y in equation(1)
2( 2 + 3 / 2 x) + 4x = 18
4 + 3x + 4x = 18
4 + 7x = 18
7x = 14
x = 14 / 2
x = 7
2y - 3(7) = 4
2y - 21 = 4
2y = 25
y = 25 / 2
y = 12.5
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jordan bought a radio for $120.He paid for it with 2 coins and $5 bills.If there were half as many coins as bills, how many $2 coins were there and how many $5 bills were there
There are 20 $5 bills and 10 $2 coins.
How to find the number of $2 coins and $5 coins using equation?He bought a radio for $120. He paid for it with 2 coins and $5 bills.
let
the number of $5 bills = x
the number of $2 coins = y
Therefore,
y = 1 / 2 x
2y + 5x = 120
2(1 /2 x) + 5x = 120
x + 5x = 120
6x = 120
x = 120 / 6
x = 20
y = 1 / 2 × 20
y = 10
Therefore, there are 20 $5 bills and 10 $2 coins.
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A 1500 pound car is stopped in traffic on a hill that is at an incline of 10°. determine the force that is required to keep the car from rolling down the hill.
Answer: about 260 Lb
Step-by-step explanation:
For a population with an unknown distribution, the form of the sampling distribution of the sample mean is _____. Group of answer choices approximately normal for small sample sizes exactly normal for large sample sizes exactly normal for small sample sizes approximately normal for large sample sizes
For a population where the distribution is unknown, the sampling distribution of the sample mean will be b which is approximately normal for all sample sizes.
Given options regarding sample sizes.
We have to choose the correct option which shows the sample mean characteristics when the distribution is unknown.
Based on the central limit theorem the sampling distribution of the sample mean for either skewed variable ir normally distributed variable can be approximated given the mean and standard deviation.
The central limit theorem is said to be true when n greater than or equal to 30.
When n is greater than 30 ,z test is used, when n is less than 30 ,t test is used.
Hence for a population where the distribution is unknown ,the sampling distribution of the sample mean will be approximately normal for all sample sizes.
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Question is incomplete as it includes options in a right way:
1)exactly normal for large sample,
2) approximately normal for all sample sizes,
3) exactly normal for all sample sizes.
What is the focus of a parabola with a standard form of y = 1/4x^2 - x - 1?
Include an explicit reasoning, just giving an answer won’t be helpful
Answer:
(2, -1).
Step-by-step explanation:
y = 1/4x^2 - x - 1
First convert to vertex form:
y = 1/4(x^2 - 4x) - 1
y = 1/4[(x - 2)^2 - 4] - 1
y = 1/4(x - 2)^2 - 2
The formula for the focus of the parabola y = a(x - h)^2 + k is (h, k+1/4a)
So here it is:
(2, -2+1/ 4*1/4)
= (2, -1).
A walking path across a park is represented by the equation y=-3x - 3. A
new path will be built perpendicular to this path. The paths will intersect at
the point (-3, 6). Identify the equation that represents the new path.
OA. y=-3x-6
O B. y=x+7
OC. y=3x+15
O D. y=-x+5
166
10
MAR
FREN
10-
10-
10
Answer:
y = (1/3)x + 7
Step-by-step explanation:
The general structure form of a line in slope-intercept form is:
y = mx + b
In this form, "m" represents the slope and "b" represents the y-intercept.
The slope of a perpendicular line is the opposite-signed, reciprocal of the original line's slope. Therefore, if the slope of the original line is m = -3, the new slope is m = 1/3.
The y-intercept can be found by plugging the new slope and the values from the point (-3, 6) into the slope-intercept form equation.
m = 1/3
x = -3
y = 6
y = mx + b <----- Slope-intercept form
6 = (-3)(1/3) + b <----- Insert values
6 = -1 + b <----- Multiply -3 and 1/3
7 = b <----- Add 1 to both sides
Now, that you have the slope and y-intercept, you can construct the equation of the perpendicular line.
y = (1/3)x + 7
For a right triangle with one leg = 3.24 cm and a hypotenuse = 7.16 cm, find the length of the missing leg
Answer:
[tex]a=\sqrt{40.768}[/tex]
Step-by-step explanation:
Given a leg and a hypotenuse we can find the third side by substituting the known values using Pythagorean theorem, let the unknown be a.
[tex]a^2+3.24^2=7.16^2[/tex]
Now all we must do is solve for a:
[tex]a^2+3.24^2=7.16^2\\a^2+10.4976=51.2656\\a^2=40.768\\a=\sqrt{40.768}[/tex]
Three museums charge an entrance fee based on the number of visitors in the group. the table lists the fees charged by the museums. at which museum is the entrance fee proportional to the number of visitors?
a.
museum a
b.
museum b
c.
museum c
d.
museum a and museum b
The entrance fee is proportional to the number of visitors at A)museum a.
In arithmetic, two sequences of numbers, often experimental statistics, are proportional or at once proportional if their corresponding factors have a regular ratio, that's called the coefficient of proportionality or proportionality consistent.
The definition of proportional is something that has an incredibly correct dating of length or that is appropriate. An example of something proportional is a woman's tiny toes to her quick stature. An instance of something proportional is the quantity of pay a worker receives for the hours that they installed.
While something is proportional to something else, it does no longer suggest the values are equal, simply that they trade with admiration for each other. The regular of proportionality serves as a multiplier.
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Answer:
Museum C
Step-by-step explanation:
If you divide them all (like 3/4) you get .75
The two polygons are similar. Find the values of x and y.
Answer: [tex]x=11, y=9[/tex]
Step-by-step explanation:
Corresponding sides of similar figures are proportional, so:
[tex]\frac{x-2}{6}=\frac{15}{10}\\\\\frac{x-2}{6}=\frac{3}{2}\\\\x-2=9\\\\x=11[/tex]
[tex]\frac{y+3}{8}=\frac{15}{10}\\\\\frac{y+3}{8}=\frac{3}{2}\\\\y+3=12\\\\y=9[/tex]
Perform the indicated equation
Answer:
1
Step-by-step explanation:
When dividing fractions i use the method KFC(keep flip change) :
Keep the first fraction :
[tex]\frac{14a^{2} }{10b^{2} }[/tex]
Flip the second fraction :
[tex]\frac{15b^{2} }{21a^{2} }[/tex]
Change the function :
÷ → ×
Now write your new equation :
[tex]\frac{14a^{2} }{10b^{2} }[/tex] × [tex]\frac{15b^{2} }{21a^{2} }[/tex]
Now multiply the numerators together and the denominators together :
14a² × 15b² = 210a²b²
10b² × 21a² = 210a²b²
Now make this into a fraction again :
210a²b² / 210a²b²
Anything divided by itself is always 1 so :
210a²b² / 210a²b² = 1
Hope this helped and have a good day
30 times 4 times the ten power of three
Answer [tex]=7085760[/tex]
Step-by-step explanation:
Use order of operations and evaluate the exponent first
[tex]30*4*3^{10}[/tex]
[tex]30*4(59049)[/tex]
[tex]30*236192[/tex]
[tex]=7085760[/tex]
Answer: 1920
Step-by-step explanation:
4x4x4=64
64x30=1920
A swimming pool is 10 m wide and 25 m long. It is 1.2 m deep at one end and 2.2 m deep at the other end. The floor slopes uniformly from one end to the other.
a)Explain why the shape of the pool is a prism. 1.2 m
b)The pool is filled with water at a rate of 2 m³ per minute. How long will it take to fill the pool?
At a rate of 2 m³ per minute, it would take 212.5 minutes to fill this swimming pool.
The shape of the pool.Based on the information provided, we can logically deduce that the shape of this pool is a prism because it is deep (2.2 m) at one end and shallow (1.2 m) at the other end.
How to calculate the time?First of all, we would determine the volume of this swimming pool as follows:
Volume = 1/2 × (1.2 + 2.2) × 10 × 25
Volume = 1/2 × (3.4) × 250
Volume = 1.7 × 250
Volume = 425 m³.
For the time, we have:
Time = volume/rate
Time = 425/2
Time = 212.5 minutes.
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m is inversely proportional to the square of (p-1).
When p = 4, m = 5.
Find m when p = 6.
Answer:
9/5
Step-by-step explanation:
First we have to find the constant k
m = k/(p-1)^2 (p-1)^ goes on the bottom of the fraction because of the inverse.
5 = k/(4-1)^2
5 = k/3^2
5 = k/9 Multiply both side by 9
45 = k We know can use this constant to solve our problem
m = 45/(6-1)^2
m = 45/5^
m = 45/24
m = 9/5
How long must a ladder be to reach the top of a 12-foot wall if the bottom of the ladder is placed 3 feet from the base of the wall
Answer: 13 feet
Step-by-step explanation:
Answer:
12.37 ft
Step-by-step explanation:
Hypotenuse(c): the ladder
Cathetus: the wall (a=12) and the floor (b=3)
Equation:
[tex]c^{2} =a^{2} +b^{2}[/tex]
[tex]c^{2} =(12)^{2}+ (3)^{2} =144+9[/tex]
[tex]c^{2} =153[/tex]
[tex]c=\sqrt{153}[/tex]
[tex]c=12.37[/tex]
The ladder is 12.37 feet long
Hope this helps
Which function has a minimum and is transformed to the right and down from the parent function, f(x) = x²?
O g(x)=-9(x + 1)²-7
Og(x) = 4(x-3)² +1
O g(x)=-3(x-4)²-6
Og(x)= 8(x-3)²-5
Answer:
Step-by-step explanation:
Discussion
A: incorrect. the minus turns the parabola upside down and you would get a maximum, not a minimum.
B: incorrect. The + 1 moves the parabola upwards not downwards.
C: incorrect. The - 3 turns the parabola upside down. You get a maximum, not a minimum.
D: correct. The parabola moves right (x - 3)^2 which anti intuitive, but it is correct. - 5 moves the parabola down. +8 the plus makes a minimum.
Noah has a summer tree-trimming business. Based on experience, Noah knows that his profit, P, in dollars, can be modelled by = −32 + 150 − 1200, where x is the amount he charges per tree.
1. How much does he need to charge if he wants to break even?
2. How much does he need to charge if he wants to make a profit of $600?
Answer:
Addition form: x = 75 + √3 (675 − P) / 3
or
Subtract form: x = 75 − √3 (675 − P) / 3
Find a linear differential operator that annihilates the given function. (Use D for the differential operator.) cos 2x
Let [tex]y=\cos(2x)[/tex], with first two derivatives
[tex]Dy = -2\sin(2x)[/tex]
[tex]D^2y = -4\cos(2x)[/tex]
Consider the linear ODE
[tex]aD^2y + bDy + cy = 0[/tex]
Substitute [tex]y[/tex] and its derivatives and solve for the unknown coefficients [tex]a,b,c[/tex].
[tex]-4a\cos(2x) - 2b\sin(2x) + c\cos(2x) = 0[/tex]
[tex]\implies \begin{cases}-4a+c=0 \\ -2b=0 \end{cases}[/tex]
[tex]\implies b=0 \text{ and } c= 4a[/tex]
Then the minimal ODE with this solution is
[tex]aD^2y + 4ay = 0 \implies \boxed{D^2y + 4y = 0}[/tex]
The Renaissance and the Reformation are often described as eras that had many great advancements. In your opinion, what were the most important changes and advancements that occurred
It's common to hear people say that the Renaissance and Reformation saw numerous significant developments.
Why was Reformation important to the Renaissance?While the Reformation paved the way for the division of religion, the Renaissance paved the way for growth in art and architecture. The main distinction between the Renaissance and the Reformation is this.What impact did the Renaissance have on the Reformation?
According to Palmer, the intellectual activities of the Renaissance stimulated the market for books, inspired people to read more, and inspired them to consider how to alter the present, all of which contributed to the Reformation. Rereading the Bible was one of them, as Luther did.Why was the Renaissance important?
The Renaissance period cultivated a new change in art, knowledge, and culture.
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Suppose the risk-free rate is 3.2 percent and the market portfolio has an expected return of 9.9 percent. the market portfolio has a variance of .0282. portfolio z has a correlation coefficient with the market of .18 and a variance of .3185. according to the capital asset pricing model, what is the expected return on portfolio z?
Beta = Correlation x (Variance of Z)^0.5 / (Variance of Market)^0.5
Beta = 0.18 x (0.3185)^0.5 / (0.0282)^0.5
Beta = 0.604927
CAPM equation:
Expected return = Risk free rate + Beta x (Market return - Risk free rate)
Expected return = 3.2% + 0.604927 x (9.9% - 3.2%)
Expected return = 7.25% is the answer.
Portfolio return refers to the return or loss realized on an investment portfolio that includes multiple types of investments. The portfolio is intended to provide returns based on the defined objectives of the investment strategy and the risk tolerance of the type of investor covered by the portfolio.
The basic formula for expected return is to multiply the weight of each asset in the portfolio by the expected return and then add up all these numbers. In other words, the expected return of a portfolio is a weighted average of the returns of the individual components.
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HELP HELP HELP HELP
HELP HELP HELP HELP
Step-by-step explanation:
find the slope:
[tex]\frac{y2-y1}{x2-x1}=\frac{-4+2}{1+3} =\frac{-2}{4} =-\frac{1}{2}[/tex]
Now our equation looks like:
[tex]y=-\frac{1}{2} x+b[/tex]
To solve for b, plug in one of the coordinates
[tex]-4=-\frac{1}{2} (1)+b[/tex]
[tex]-4=-\frac{1}{2} +b[/tex]
[tex]b=-3.5[/tex]
Put our equation together to get y = -1/2x-3.5
System of Linear Programming:
z=-3x + 5y
x+y> -22
x-y-4
x - y ≤ 2
Minimum value of z:
The minimum value of z is -12.
Given that the system of linear programming
z=-3x+5y
x+y≥-22
x-y≥-4
x-y≤2
Firstly, we will convert the given constraints into equality as
x+y=-22
x-y=-4
x-y=2
Now, we will take the equation x+y=-22 and taking x as 0 as find y and taking y as 0 to find x, we get
If x=0 then y is
0+y=-22
y=-22
If y=0 then x=-22
So, the points lie on the line x+y=-22 is (0,-22) and (-22,0).
Further, we will take the equation x-y=-4 and taking x as 0 as find y and taking y as 0 to find x, we get
If x=0 then y=4
If y=0 then x=-4
So, the points lie on the line x-y=-4 is (0,4) and (-4,0).
Furthermore, we will take the equation x-y=2 and taking x as 0 as find y and taking y as 0 to find x, we get
If x=0 then y=-2
If y=0 then x=2
So, the points lie on the line x-y=2 is (0,-2) and (2,0).
now, we will find the feasible region of the given constraints as shown in figure.
We will find that each constraint will contain origin or not by substituting (0,0), we get
0+0≥-22 containing origin
0-0≥-4 containing origin
0-0≤2 containing origin
From the graph we can see that the minimum value of x is -13 and minimum value of y is -12.
z=-3x+5y
z=-3x+3y+2y
z=-3(x-y)+2y
minmum value of x-y from the given constraints is
-4≤x-y≤2
From here minimum value of x-y is -4
So, z=-3(-4)+2y
z=12+2y
For the minimum value of z the value of y should be minimum.
From the graph we can see the minimum value of y=-12
So, z=12+2(-12)
z=12-24
z=-12
Hence, the minimum value of z for the system of Linear Programming:
z=-3x + 5y, x+y≥-22, x-y≥-4, x - y ≤ 2 is -12.
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Linda is filling the mold above with water and freezing it for an ice project. If a = 8 cm and b = 7 cm, what will be the volume of the frozen figure?
The volume of the frozen figure is 736 cm³
Volume of a prismFrom the question, we are to determine the volume of the frozen figure
In the given diagram,
The volume of the frozen figure = a³ + 1/2(a²b)
From the given information,
a = 8 cm
b = 7 cm
∴ Volume of the frozen figure = 8³ + 1/2(8² ×7)
Volume of the frozen figure = 512 + 1/2(448)
Volume of the frozen figure = 512 + 224
Volume of the frozen figure = 736 cm³
Hence, the volume of the frozen figure is 736 cm³
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Find 20% of 150
A. 20
B. 130
C. 120
D. 30
For this, multiply 150 × .20 = 30
Therefore, 20% of 150 is 30.
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Translate the following into an algebraic expression:
22 decreased by y%
Answer:22-0.22y
Step-by-step explanation: we have to decrease 22 by y%
we need to calculate what is y% of 22. y% of 22 simply means y% into 22 that is y% x 22
= 0.01(y) x 22
= 0.22y
= 22 - 0.22y
Select the correct equation.
The focus and directrix of a parabola are shown. What is the equation of the parabola?
Check the picture below, so the parabola looks more or less like that one, with a "p" distance of 2 units that is positive, whilst the vertex, which is always half-way between the focus point and the directrix is where you see it there, thus
[tex]\textit{horizontal parabola vertex form with focus point distance} \\\\ 4p(x- h)=(y- k)^2 \qquad \begin{cases} \stackrel{vertex}{(h,k)}\qquad \stackrel{focus~point}{(h+p,k)}\qquad \stackrel{directrix}{x=h-p}\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix}\\\\ \stackrel{"p"~is~negative}{op ens~\supset}\qquad \stackrel{"p"~is~positive}{op ens~\subset} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\begin{cases} h=-1\\ k=2\\ p=2 \end{cases}\implies 4(2)( ~~ x-(-1) ~~ )~~ = ~~(y-2)^2\implies 8(x+1)=(y-2)^2 \\\\\\ x+1=\cfrac{1}{8}(y-2)^2\implies \boxed{x=\cfrac{1}{8}(y-2)^2-1}[/tex]
Answer: UR WELCOME
Step-by-step explanation: ANSWER ON EDMENTUM
A grocery store sells a bad of 4 oranges for $1.04. how much would it cost for 11 oranges?
If a grocery store sells a bag of 4 oranges for $1.04 then it will cost $2.86 for 11 oranges.
Given that a grocery store sells a bag of 4 oranges for $1.04 means revenue is $1.04 with no profits.
We have to find the cost of 11 oranges. We have assumed that there are no profits as we are require to find cost. But there is huge difference between cost and profits.
We know that average cost is total cost divided by number of items.
Cost of 4 oranges=$1.04
cost of 1 orange=1.04/4
=$0.26 per orange
Cost of 11 oranges=0.26*11
=$2,86.
Hence if a grocery store sells a bag of 4 oranges for $1.04 then it will cost $2.86 for 11 oranges.
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Solve the equation 2x^3-5x^2+x+2=0 given that 2 is a zero of f(x)= 2x^3-5x^2+x+2
The polynomial equation [tex]2x^{3} - 5 x^{2} + x + 2 = 0[/tex] given that 2 is zero of
f(x) = [tex]2x^{3} - 5 x^{2} + x +2[/tex]
According to the question,
f(x) [tex]=2x^{3} - 5 x^{2} + x + 2[/tex]
[tex]f(2)= 2(2)^{3} - 5 (2)^{2} + 2 + 2 \\= 2(8) - 5(4) +4\\= 16 - 20 + 4\\= -4 + 4\\= 0.[/tex]
Hence, the polynomial equation [tex]2x^{3} - 5 x^{2} + x + 2 = 0[/tex] given that 2 is zero of f(x) [tex]=2x^{3} - 5 x^{2} + x + 2[/tex].
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Translate to algebra numbers, the difference of a number times 3 and 6 equals 9.
Answer:
The equation is ×=-3
Step-by-step explanation:
Let x be the number
Difference between a number tines 3 and 6 is 9
3x-6x=9
-3x=9
x=-3
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determine the slope of the line
Answer:
slope = 2
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 3, 0) and (x₂, y₂ ) = (0, 6) ← 2 points on the line
m = [tex]\frac{6-0}{0-(-3)}[/tex] = [tex]\frac{6}{0+3}[/tex] = [tex]\frac{6}{3}[/tex] = 2