Final answer:
To find the scale factor for enlarging a children's book from 20 cm by 24 cm to 25 cm by 30 cm, divide the enlarged dimension by the original corresponding dimension, resulting in a scale factor of 1.25.
Explanation:
We are asked to find the scale factor used to enlarge a children's book from dimensions of 20 cm by 24 cm to a larger version with dimensions of 25 cm by 30 cm. To find the scale factor, we need to divide one dimension of the enlarged book by the corresponding dimension of the original book. We can take either the length or the width to find the scale factor.
Let's use the width for this example:
Original width = 20 cm
Enlarged width = 25 cm
Scale factor = Enlarged width / Original width
Scale factor = 25 cm / 20 cm
Scale factor = 1.25
Therefore, a scale factor of 1.25 should be used to enlarge the book from the original dimensions to the new dimensions.
What is the inverse of the function f(x) = 2x + 1?
h(x) = 1/2 x – 1/2
h(x) = 1/2 x + 1/2
h(x) = 1/2 x – 2
h(x) = 1/2 x + 2
What is the exact answer?
Answer:
[tex]h(x)=\frac{x}{2}-\frac{1}{2}[/tex]
Step-by-step explanation:
Hello
Step1
Let f(x)=y
f(x) = 2x + 1
(1)y= 2x + 1
to find the inverse of f(x)
Replace every x with a y and replace every y with an x
y= 2x + 1
replacing
x=2y+1
Step 2
Now solve the equation for y
x=2y+1
subtract 1 on both sides
x-1=2y+1-1
x-1=2y
divide boths dies by 2
(x-1)/2=2y/y
[tex]\frac{x-1}{2} =\frac{2y}{2} \\y=\frac{x-1}{2}[/tex]
let this last equation h(x)= inverse of f(x)
[tex]h(x)=\frac{x-1}{2}\\h(x)=\frac{x}{2}-\frac{1}{2}[/tex]
Have a great day
What is the area of 74.8 and 22.6?
If ON is a midsegment of KLM, find LM.
A.2
B.3
C.4
D.5
Answer:
LM= 4
Step-by-step explanation:
In the triangle KLM, ON is the mid segment of KLM
WE use triangle Mid segment theorem
MN= twice of ON
MN= 2 times of ON
4x= 2(x+1)
distribute 2 inside the parenthesis
4x= 2x+2
Subtract 2x on both sides
4x-2x= 2x+2-2x
2x= 2
divide by 2 on both sides
x= 1
To find length of MN, we plug in 1 for x
MN= 4x= 4(1)= 4
HELP!! Not hard, just confusing.. ΔABC is reflected across the x-axis and then translated 4 units up to create ΔA′B′C′. What are the coordinates of the vertices of ΔA′B′C′ ?
A′(-3, 3), B′(-1, 1), C′(-2, 3)
A′(3, -3), B′(1, -1), C′(2, -3)
A′(3, -5), B′(1, -7), C′(3, -5)
A′(-3, 3), B′(-1, 1), C′(-2, -3)
Answer:
1st one : A′(-3, 3), B′(-1, 1), C′(-2, 3)
Step-by-step explanation:
below
What is the fifth root of -32?
The fifth root of -32 is -2. To find it, think of a number that, when raised to the power of 5, gives the original number.
The fifth root of -32 is -2. To find the fifth root of a number, we can think of it as finding a number that, when raised to the power of 5, gives us the original number. In this case, -2 * -2 * -2 * -2 * -2 = -32.
Use elimination to solve the system of equations.
2x+6y=-8 and 5x-3y=88
What Rate Of Simple Interest Is Needed For $700 To Double,In 3 Years?
Cory earns $20 for every lawn he mows and $9 for every hedge he trims. He uses the expression 20x + 9y to keep track of his earnings.
Part A: Identify the coefficients and variables in the expression.
Part B: How many terms are in the expression, what are they, and how do you know?
Part C: Which term in the expression shows the total earned from trimming hedges?
please help.
if p(x,y) is the point on the unit circle defined by real number theta, then csc theta= _____. a. x/y. b. y/x. c. 1/x. d. 1/y.
Answer:
Option d is correct
[tex]Csc \ \theta =\frac{1}{y}[/tex]
Step-by-step explanation:
Here P(x,y) is the point on unit circle ( unit circle has radius 1 and center (0,0))
Now in a diagram we can see that
OA= x
AP= y
radius OP =1
∠POA =θ
Now in ΔAOP
[tex]Csc\ \theta =\frac{hypotenuse }{opposite \ side} \\Csc\ \theta =\frac{OP}{AP}[/tex]
[tex]Csc \ \theta =\frac{1}{y}[/tex] ( since OP =1 and AP =y)
Answer:
1/y
Step-by-step explanation:
apex
What is 1,295.014 rounded to the nearest hundredth?
For a circle of radius 4 feet, find the arc length s subtended by a central angle of 26 degrees.
Answer:
The arc's length is 1.8 ft
Step-by-step explanation:
For calcaulate the arc length S we used the formula below:
[tex] S=\frac{\pi.\alpha(\º)}{180}*R[/tex]
Here alpha is the arc angle in degrees and R is the circle radius. Thus, if alpha is equal to 26 and R equals to 4 ft:
[tex] S=\frac{\pi.26}{180}\ *\ 4ft[/tex]
[tex] S=0.45\ *\ 4ft[/tex]
[tex] S=1.8\ ft[/tex]
What is the surface area of a piece of pipe that is open at both ends, has a radius of 6 inches, and a height of 18 inches? (Use 3.14 for π.)
The surface area of an open-ended pipe with a radius of 6 inches and a height of 18 inches is 678.24 square inches. The calculation is based on the formula for the circumference of the circle, which is multiplied by the height of the cylinder.
To calculate the surface area of a pipe that is open at both ends, we need to find the area of the outer surface. Since the pipe is a cylinder without the top and bottom circles, the surface area is simply the circumference of the circle (which is the edge of the openings) times the height of the cylinder. The formula for the circumference of a circle is C = 2πr, where r is the radius.
The radius is given as 6 inches and the height is 18 inches, therefore:
Circumference (C) = 2πr = 2 × 3.14 × 6 inches = 37.68 inches.The surface area (SA) of the pipe is C × height = 37.68 inches × 18 inches = 678.24 square inches.A regular 24 sided polygon is rotated with this center of rotation at its center what is the smallest degree of rotation needed to map the polygon back onto itself
Please help me solve this word problem:
In a round-robin chess tournament, each player is paired with every other player once. The function shown below, models the number of chess games, "N", that must be played in a round-robin tournament with "t" chess players. In a round-robin chess tournament, 55 games were played. How many players entered the tournament?
N=t^2-t divided by 2.
Answer:
t = 11
Step-by-step explanation:
From the equation that gives, the number of games you can get the number t of players who participated in the ronund-robin tormeo, is:
[tex]N = \frac{t ^ 2-t}{2}[/tex]
[tex]55 = \frac{t ^ 2-t}{2}[/tex]
[tex]110 = t ^ 2-t[/tex]
[tex]t ^ 2-t -110 = 0[/tex]
[tex](t-11) (t + 10) = 0[/tex]. Then
[tex]t - 11 = 0\\t = 11\\t + 10 = 0\\t = -10[/tex]
Since t cannot take negative values, then t = 11.
In a survey conducted by a union, members were asked to rate the importance of the following issues: (1) job security, (2) increased fringe benefits, and (3) improved working conditions. Five different responses were allowed for each issue. Among completed surveys, how many different responses to this survey were possible? ...?
Final answer:
To calculate the number of different responses in the survey, we multiply the number of potential responses for each issue. With 5 options for each of the 3 issues, there are 5 x 5 x 5 = 125 different possible combinations.
Explanation:
To determine the number of different responses to the survey conducted by a union, we need to calculate the total possible combinations that can occur when members are asked to rate the importance of three issues: (1) job security, (2) increased fringe benefits, and (3) improved working conditions. Since there are five different responses allowed for each issue, we would use a combination formula.
Each member can choose from 5 different responses for each of the 3 issues. This is a situation where we use the 'fundamental counting principle' where you multiply the number of options for each independent choice to get the total number of possibilities:
For job security: 5 possible responsesFor increased fringe benefits: 5 possible responsesFor improved working conditions: 5 possible responsesThe total number of different responses to the survey is 5 x 5 x 5, which equals 125.
So, members have 125 different ways to respond to the survey based on how they rate the importance of each issue.
If you were to use the substitution method to solve the following system, choose the new equation after the expression equivalent to y from the first equation is substituted into the second equation.
12x – y = –4
4x – 3y = –6
Answer
4x – 3(–12x – 4) = –6
4(12x + 4) – 3y = –6
4(–12x – 4) – 3y = –6
4x – 3(12x + 4) = –6
...?
Answer:
the answer to this question is 4x - 3(12x + 4) = -6 hope this helps
what is the range of the relation. (–2,7) (7,2) (2,7)
A. {-2,2,7}
B. {-2,7}
C. {2,7}
D. {2}
Domain:{−2,7,2}
Range:{7,2}
A hole is poked in a balloon so that every minute the balloon loses 3/10ft 3 of air. What is the total change in the number of cubic feet of air in the balloon after 5/9 min?
(2s+5)/(s^2+6s+34) inverse Laplace transform
The inverse Laplace transform of (2s+5)/(s^2+6s+34) is found by completing the square in the denominator and then matching the result to a known form in the Laplace transform table.
Explanation:The question asks for the inverse Laplace transform of the function (2s+5)/(s^2+6s+34). To find the inverse Laplace transform, we usually decompose the given function into a form that matches entries in the Laplace transform table. A common technique involves completing the square for the quadratic denominator, which enables us to match the form with the inverse transform for exponential or trigonometric functions as per standard Laplace tables.
In this case, the denominator can be rewritten as (s+3)^2 + (5^2 - 3^2) to make it resemble the denominator of the Laplace transform of a damped sine or cosine function. Next, we would separate the original function into partial fractions if necessary or directly find a corresponding entry in the Laplace transform table. Unfortunately, without further simplification, we cannot provide the exact inverse Laplace transform but you should use the approaches mentioned along with your extended Laplace table or use the convolution theorem if the function can be expressed as a product of functions.
Rite cut riding lawnmower obeys the demand equation p=-1/20x+1060. The cost of producing x lawnmowers is given by the function c(x)=120x+5000
a)Express the revenue R as a function of x
b)Express the profit P as a function of X
c)Fine the value of x that maximizes profit. What is the maximum profit?
d)What price should be charged to maximize profit? ...?
The revenue function is R = -1/20x^2 + 1060x and the profit function is P = -1/20x^2 + 940x - 5000. The value of x that maximizes profit is 9400, and the maximum profit is calculated by substituting this value into the profit function. The price to charge to maximize profit is $590.
Explanation:a) To express revenue (R) as a function of x, we multiply the price (p) by the quantity (x):
R = p * x
Substituting the demand equation (p = -1/20x + 1060):
R = (-1/20x + 1060) * x
Simplifying:
R = -1/20x^2 + 1060x
b) Profit (P) is given by subtracting the cost (c(x)) from the revenue (R):
P = R - c(x)
Substituting the expressions for R and c(x):
P = (-1/20x^2 + 1060x) - (120x + 5000)
Simplifying:
P = -1/20x^2 + 940x - 5000
c) To find the value of x that maximizes profit, we take the derivative of the profit function with respect to x and set it equal to zero:
dP/dx = -1/10x + 940
Solving for x:
-1/10x + 940 = 0
x = 9400
d) To find the price that maximizes profit, we substitute the value of x (9400) into the demand equation:
p = -1/20(9400) + 1060
simplifying:
p = 1060 - 470
p = $590
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a) First, we must express the revenue, denoted as 'R'. Revenue is simply the price per item multiplied by the quantity of items sold. Given the demand equation 'p', we can express the revenue as follows:
R = p * x = ( -1/20 * x + 1060 ) * x
This simplifies to:
R = x * (1060 - 0.05*x)
b) Profit is revenue minus cost. We use the revenue equation from part a) and the given cost equation 'c = 120x + 5000'. Plug these into the profit equation:
P = R - c = ( x * (1060 - 0.05*x) ) - ( 120x + 5000 )
This simplifies to
P = x * (1060 - 0.05*x) - 120*x - 5000
c) To maximize profit, we need to find the derivative of the profit function and then solve for x when this derivative is equal to zero (this will find the quantity that maximizes profit). After doing this, we find that the quantity that maximizes profit is x = 9400.
If we substitute x = 9400 into the profit function, we get the maximum profit which turns out to be 4413000.
d) The price that should be charged to maximize profit is found by substituting the value of x that gave us the maximum profit into the price function. In this case, substituting x = 9400 gives us the price = 590.
Therefore, in order to maximize profit, 9400 lawnmowers should be produced and sold at a price of 590 per lawnmower, which will yield a profit of 4413000.
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Convert 3/20 to a percent
To write a fraction as a percent, first remember that a percent is a ratio of a number to 100. If we want to convert [tex]\frac{3}{20}[/tex] to a percent, we need to find a fraction equivalent to [tex]\frac{3}{20}[/tex] that has a 100 in the denominator. We can do this by setting up a proportion.
[tex]\frac{3}{20}[/tex] = [tex]\frac{n}{100}[/tex]
Now, we can use cross products to find the missing value.
3 × 100 = 300
20 × n = 20n
300 = 20n ← Divide both sides by 20.
15 = n
Therefore, [tex]\frac{3}{20}[/tex] as a percent would be 15%.
Convert to scientific notation: 0.000678
What number between 30 and 40 has only itself as factors?
A)14 is 30 percent of what number?
B) 72 is what percent of 180?
If AZ is a midsegment of WXY, find XZ
A.7
B.9
C.12
D.14
State the X- and Y- intercepts of each function.
2/3x - 1/3y = 2
the ratio of length to width in a rectangle is 3:1. If the perimeter of the rectangle is 112 feet, what is the length of the rectangle?
Length of the rectangle= 42 feet
Width of the rectangle =14 feet
What is rectangle?A rectangle is a closed two-dimensional figure with four sides. The opposite sides of a rectangle are equal and parallel to each other and all the angles of a rectangle are equal to 90°.
Given,
Ratio of length to width of rectangle = 3:1
Let width be x then length will be 3x
Perimeter of the rectangle = 112 feet
2(Length + Width) = 112
2(3x + x) = 112
2(4x) = 112
8x = 112
x = 112/8
Width x = 14 feet
length = 3x = 3×14 = 42feet
Hence, 42 feet is length and 14 feet is width of the rectangle.
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if 2tanA=3tanB,then prove that tan(A-B)=sin2B/(5-cos2B) ...?
The mean for average temperature in Buffalo ,New york , is 47.5°. The temperture fluctuates 23.5° above and below the mean temperture . If t=1 present January ,the phase shift of the sine function is 4
a) Write the funtion for the average monthly tempperature in Buffalo
b) According to your modle ,what is the average tenperature in March ?
c) According to your modle ,what is the average tenperature in August ?
The formula for the circumference C of a circle with radius r is C = 2πr. Which of the following is a formula for π (pi) of the circle in terms of the circumference and radius?
A. PI=C+2r
B: C-2r
C: PI=2R/C
D: PI/C/2R
...?
Answer: D. [tex]\pi=\dfrac{C}{2r}[/tex]
Step-by-step explanation:
Given : The formula to find the circumference is given by :-
[tex]C=2\pi r[/tex], where r is the radius of the circle.
To find the formula for [tex]\pi[/tex] , we need to divide 2r on both of the sides in the above equation, we get
[tex]\pi=\dfrac{C}{2r}[/tex] , where r is the radius of the circle.
Hence, the correct formula for [tex]\pi[/tex] : Option D [tex]\pi=\dfrac{C}{2r}[/tex]