The dilation of the circle with a scale factor 1/r and center at (a,b) will transform the circle into a point at (a,b).
A dilation is a transformation that results in an image with the same shape as the original but a different size. • An enlargement is a dilation that produces a larger image. • A reduction is a dilation that produces a smaller image.
To solve this we will use the transformation formula for a dilation with center (a,b) and scale factor
k, (x,y) --> (a + k(x-a), b + k(y-b)).
Substituting in our values, we get
(x,y) --> (a + (1/r)(x-a), b + (1/r)(y-b)).
Setting this equal to (a,b), we get
(a + (1/r)(x-a) = a, b + (1/r)(y-b) = b).
Solving for x and y gives x = a and y = b. Therefore, the dilation of the circle with a scale factor of 1/r and center at (a,b) will transform the circle into a point at (a,b).
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A school is arranging chairs in rows for an assembly. $11$ chairs make a complete row, and right now there are $110$ chairs total. The school wants to have as few empty seats as possible, but all rows of chairs must be complete. If $70$ students will attend the assembly, how many chairs should be removed?
The number of chairs that should be removed, for there to be as few empty seats as possible but for all rows of chairs to be complete, is 33 chairs.
How to find the chairs to be removed ?The number of chairs that make up a row is 11 chairs and there are to be 70 students in attendance. The number of rows that would take the students is therefore:
= Number of students / Number of rows
= 70 / 11
= 6. 36
= 7 rows rounded up
The number of rows needed is 7 rows which means the number of chairs would be:
= 7 rows x 11 chairs per row
= 77 chairs
The number of chairs to be removed is:
= Total chairs - Chairs needed
= 110 - 77
= 33 chairs
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what number is in the same ratio to 64 as 5 is to 8
Answer: 102.4
Given ratio 5:8
Let's assume the answer to be x
5÷8 should be equal to 64÷x
∴ x= (64×8) ÷ 5
=102.4
The number that has the same ratio to 64 as 5:8 is gotten as; 40
How to Calculate Ratio?
We have the ratio 5:8.
Now, we want to find the number that has the same ratio to 64 as 5:8. Thus, we will use proportion to get this;
x/64 = 5/8
Cross multiply to get;
x = 64 * 5/8
x = 40
B. ) For Service B, is the additional charge per mile greater or less than 30 cents per
mile of the trip? Explain your reasoning.
The additional charge per mile for Service B is less than 30 cents per mile of the trip. This is because the rate for Service B is 20 cents per mile plus a flat fee of $10, which works out to less than 30 cents per mile for longer trips.
For a trip of 10 miles, Service B would cost
(10 x 0.20) + 10
= $12.
For a trip of 20 miles, Service B would cost
(20 x 0.20) + 10
= $22.
Therefore, the additional charge per mile for Service B is
(12/10)
= 1.2 for the 10 mile trip and
(22/20)
= 1.1 for the 20 mile trip.
Both of these are less than 30 cents per mile.
The additional charge per mile for Service B is less than 30 cents per mile of the trip because the rate for Service B is 20 cents per mile plus a flat fee of $10, which works out to less than 30 cents per mile for longer trips. To demonstrate this, for a 10 mile trip, the total cost would be $12, and for a 20 mile trip, the total cost would be $22. This works out to an additional charge per mile of 1.2 and 1.1 cents respectively, which are both less than 30 cents per mile.
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Can you let me know the answer please
Answer:
y ≤ [tex]\frac{1}{3}[/tex] x - 4
Step-by-step explanation:
the first step is to obtain the equation of the line.
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, - 4) and (x₂, y₂ ) = (3, - 3) ← 2 points on the line
m = [tex]\frac{-3-(-4)}{3-0}[/tex] = [tex]\frac{-3+4}{3}[/tex] = [tex]\frac{1}{3}[/tex]
the line crosses the y- axis at (0, - 4 ) ⇒ c = - 4
y = [tex]\frac{1}{3}[/tex] x - 4 ← equation of the line
----------------------------------------------
the shaded region below the line indicates the values that are less than y
the solid line indicates that y can equal the values on the line (≤ )
the solution is then
y ≤ [tex]\frac{1}{3}[/tex] x - 4
need help on both these , preciate it .
Therefore ,we can conclude from answering the offered question that the region of the circle, triangle, and square is where the darkest area is. A=210-123 = 87 square units
Triangle - what is it?A triangle is a polygon since it has three sides plus three vertices. It is one of the basic geometric forms. An illustration of a triangle with the sides A, B, and C is Triangle ABC. A distinct plane or triangle in Geometrical are discovered when the three aspects are not collinear. Three sides & three corners define a triangle as a polygon. The triangle's corners are defined as the locations where three sides converge. 180 degrees is the result of multiplying three triangle angles.
Here,
The total of the circle, triangle, and square's surface areas.
The region of the darkish area is comprised of the areas of the Circle, Triangle, and Square.
=>A = 210 – 123 = 87 square units
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Use the diagram to find.. (Trigonometry)
Answer:
Step-by-step explanation:
b and f
What are the 3 triangles called?
The types of 3 triangles are called-
equilateral,isosceles, andscalene.Explain the classification of the 3 triangles?Scalene triangle:
The scalene triangle has sides that are all measured differently.In such a triangle, no side will be the same length as any other side.Every interior angle in a scalene triangle is also unique.Isosceles triangle:
The lengths for two of the sides in such an isosceles triangle are equal.The angles that are opposite their equal sides are therefore equal.An isosceles triangle, in other words, has two equal sides with two equal angles.Equilateral triangle:
Each side of an equilateral triangle has an equal length.Each internal angle in this scenario will be 60 degrees in length.An equilateral triangle is often referred as an equiangular triangle since its angles are equal.To know more about the classification of the 3 triangles, here
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How do you create a function in forex?
A trader can create their own automated trading strategies in forex by writing a script or program in a programming language, such as MQL4 or Python. This script will contain instructions to execute trades according to specific criteria defined by the trader. They can then backtest the strategy to see how it performs.
1. Decide on a trading strategy. This could include things like setting entry and exit points, calculating position sizes, and setting stop losses and take profits.
2. Choose a programming language that is compatible with the trading platform you are using, such as MQL4 or Python.
3. Write the script or program that will contain the instructions for the trading platform to follow in order to execute the trading strategy.
4. Test the script or program to make sure it works properly.
5. Run a backtest to see how the trading strategy performs.
6. If the results of the backtest are satisfactory, you can deploy the trading strategy on the trading platform.
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GIVING BRAINLIEST AND 50 POINTS
Answer:
2x + 2
Step-by-step explanation:
Combine all the like terms:
-5x + 7x -12 + 14 = 2x + 2
Answer:
2x + 2
Step-by-step explanation:
(- 5x - 12) + (14 + 7x) ← remove parenthesis
= - 5x - 12 + 14 + 7x ← collect like terms
= (- 5x + 7x) + (- 12 + 14)
= 2x + 2
Factor Completely 4q^6+8q^3
Answer:
4[tex]q^{3}[/tex]( q³ + 2)
Step-by-step explanation:
4[tex]q^{6}[/tex] + 8q³ ← factor out 4q³ from each term
= 4q³ (q³ + 2)
Answer:
4q^3(q^3 + 2)
Step-by-step explanation:
The GCF of the exponents is 3, and the GCF of the bases is 4q. So divide both numbers by 4q ^ 3 and get
4q ^ 6 / 4q ^ 3 = q ^ 3
8q ^ 3 / 4q ^ 3 = 2
so you get
4q^3 (q ^ 3 + 2)
Find out the answer to 4x+12=63
[tex]12 \frac{3}{4} [/tex]
or 12.75
Answer:
x=12.75
Step-by-step explanation:
Follow the steps within the image.
-Hope this helped
An office manager is planning to set up three computer workstations and a file cabinet in a space that is 27 feet wide. The file cabinet takes up 3 feet. What is the width of the space available for each computer station?
Answer:
The width of the space available for each computer station is 8 feet-------------------------------
The width of the space for computer stations is:
27 - 3 = 24 feetEach computer station has a space of:
24/3 = 8 feetFind the surface area and volume for this following pyramid
We calculated volume of pyramid = 160 cubic inches and surface area = 214.59 square inches.
what is pyramid?
A three-dimensional geometrical figure having flat polygon base along with a number of lateral triangular shaped faces.
How to calculate the volume and surface area of the pyramid?The given pyramid is a rectangular pyramid having length 10 inch and width 8 inch. The height of pyramid is 6 inches.
length, l = 10 inch
width, w = 8 inch
height, h = 6 inch
Now the volume will be, V = 1/3 × l × w ×h
V = 1/3 × 10 × 8× 6
hence, the volume = 160 cubic inches
We calculate the surface area of the given pyramid,
formula for surface area, SA = l × w + 1/2 × w ×√(4h²+l²) + 1/2 × l ×√(4h²+w²)
SA = 10 × 8 + 1/2 × 8 ×√(4×6²+10²) + 1/2 ×10×√(4×16²+8²)
Surface area = 214.593 square inches
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Write a statement to represent the expression h-9
expression h-9 is represented as statement 'h decreased by 9'.
What is subtraction?Subtraction is an operation used to find the difference between numbers. When you have a group of objects and you take away a few objects from it, the group becomes smaller. For example, you bought 9 cupcakes for your birthday party and your friends ate 7 cupcakes. Now you are left with 2 cupcakes. This can be written in the form of a subtraction expression: 9 - 7 = 2 and is read as "nine minus seven equals two".
Given expression
h-9
Here h is a variable, 9 is constant and - is the symbol of subtraction.
the phrase "decreased by" tells us to use subtraction.
Statement for the above expression
h decreased by 9.
Hence, the statement 'h decreased by 9' represents expression h - 9.
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Hello can someone please help me with this please What is the best possible geometric model for a set of rail tracks?
Ray ----Point ---- Line --- Plane
Fine the measure of an angle that is supplement to ABC if m < ABC is 82?
100 ---- 8---------278------
Fine the measure of an angle that is complementary to ABC is 32?
328------148------58------32
The intersection of two lines is a ?
Quadrilateral--------Point--------Line--------Plane
A rail track is composed by multiple lines, however all the lines are in the same plane, hence a plane is the best geometric model for the rail track.
How to obtain the supplement of an angle?Two angles are supplementary if the sum of their measures is of 180º, hence the supplement of an angle is obtained subtracting 180º by the angle measure.
This means that the supplement of ABC = 82º is given as follows:
180º - 82º = 98º.
How to obtain the complement of an angle?Two angles are complementary if the sum of their measures is of 90º, hence the complement of an angle is obtained subtracting 90º by the angle measure.
This means that the supplement of ABC = 90º is given as follows:
90º - 32º = 58º.
Where do two lines intersect?Two lines intersect at a single point, which is the solution to the system of equations involving the two lines.
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Kiran reads 5 pages in 20 minutes. He spends the same amount of time per page. how long will it take him to read 11 pages? helpppp its a table too. time in minutes 20. the number of pages:5 1 11.
Answer:
44 minutes
Step-by-step explanation:
Kiran reads 5 pages in 20 minutes, if we divide we will know that he reads 1 page in 4 minutes.
Multiply 4 by 11 to find out how long it will take him to read 11 pages.
11 times 4 = 44
It will take Kiran 44 minutes to read 11 pages.
What are 2 types of domain names?
TLDs are the most common type of domain name and are typically three or more characters after the final dot in a domain name. ccTLDs are two-letter domains that represent a specific country or region.
Domain names are used to identify websites on the internet. There are two main types of domain names: top-level domains (TLDs) and country code top-level domains (ccTLDs).
TLDs are the most common type of domain name and are typically three or more characters after the final dot in a domain name. Examples of TLDs include .com, .org, .net, .edu, and .gov.ccTLDs are two-letter domains that represent a specific country or region. Examples of ccTLDs include .us for the United States, .au for Australia, .ca for Canada, .uk for the United Kingdom, and .fr for France.
When registering a domain name, users should choose a TLD or ccTLD that best suits their needs. For example, if they are targeting a global audience, they should consider a .com TLD. If they wish to target a specific country, they should consider a ccTLD.
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What is the coefficient of x3y4 in 2x 3y2 5?
The coeficient of x^3+y^4 in the algebraic expression is the number 2
What is an algebraic expression?
An algebraic expression is a set of numbers and letters that make up an expression that has a meaning, the letters are variables and the numbers are coefficients or independent terms, algebraic expressions can be part of an equation and model mathematical processes.
In the given expression we have the following:
2x^3+ 2y^4
As we are asked for the coefficient of the variable "y" then we must take the number that is just before the letter which in this case is the number 2.
2 is the coefficient of x^3+y^4
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What kind of line is y 2x 3?
Answer: It is a straight line
Step-by-step explanation:
Need this question quick 20 points
On solving the provided question we can say that the rectangular form of the equation is y = -1
What is equation?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.
Ф = [tex]\pi[/tex]/2
y = - 1
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Is 5 a polynomial or not?
Because 5 is represented by the polynomial 5x0, the answer is yes.
A polynomial is a mathematical statement made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables.
An example of a polynomial of a single indeterminate x is x² − 4x + 7.
An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable).
Sums of terms of the form kxn, where k is any number and n is a positive integer, make up polynomials.
For instance, the polynomial 3x+2x-5.
By noticing which formulas only contain the operations of addition, subtraction, multiplication, and non-negative integer exponents, the polynomials may be located. Expressions with additional operations are considered non-polynomial expressions.
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In the figure below, there are three right trangles. Complete the following.
A
C
D
B
(a) Write a similiarity statement relating the three right triangles.
ACDA~A~A
(b) Complete each proportion.
BD
BC
BC
DA
DC
=
0
BD
X
5
Part (a)
Let one of the angles be [tex]\theta[/tex]. After solving for all of the other angles using the triangle sum theorem, we see that [tex]\triangle CDA \sim \triangle BDC \sim \triangle BCA[/tex].
Part (b)
[tex]\frac{BD}{BC}=\frac{BC}{CA}, \frac{DA}{DC}=\frac{DC}{DB}[/tex]
Which of the following sets of numbers could not represent the three sides of a triangle? [12,17,26] [12,20,29} {7,20,25} {7,16,24}
Answer:
The fourth one could not represent the three sides of a triangle
Step-by-step explanation:
because the two sides of the triangle must be larger together than the third side and 7+16=23<24, so the fourth one could not represent the three sides of a triangle.
Answer:
C
Step-by-step explanation: The third one down. There are two ways you know this.
1. If you had two boards that where 6 cm and 20 cm and tried to make a triangle with the third side = 27, the two little boards would lie flat on the 27 cm board.
2. The other three answers all make the smaller two sides larger than the third larger side.
A coordinate plane. The x- and y-axes each scale by one. A graph of a line intersects the points negative one, zero and zero, one. A coordinate plane. The x- and y-axes each scale by one. A graph of a line intersects the points negative one, zero and zero, one. What is the slope of the line?
The slope of the line on the given coordinate plane is equal to 1.
How to calculate the slope of a line?In Mathematics, the slope of a straight line can be calculated by using this this mathematical expression;
Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope, m = (y₂ - y₁)/(x₂ - x₁)
From the information provided in the graph, we have the following data points on the line:
Points on x-axis = (-1, 0).
Points on y-axis = (0, 1).
Substituting the given points into the slope formula, we have the following;
Slope, m = (y₂ - y₁)/(x₂ - x₁)
Slope, m = (1 - 0)/(0 - (-1))
Slope, m = 1/(0 + 1)
Slope, m = 1/1
Slope, m = 1
In conclusion, we can logically deduce that the slope of this line is equal to 1.
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How do you find the sides of a 45 45 90 triangle when given the hypotenuse?
The value of the legs of the triangle would be hypotenuse/√2 and trignometric angle are 45 degree
You can use basic trigonometry to solve this problem. We know that the sine of the angle made by the hypotenuse and the base is equal to the ratio of perpendicular height and the hypotenuse, given that the angle is 45° the perpendicular will be equal to ⇒ hypotenuse × sin(45°).
That is perpendicular=hypotenuse/√2
Similarly, the cosine of the angle made by the hypotenuse and the base is equal to the ratio of base length and the hypotenuse, given that the angle is 45° the base will be equal to ⇒ hypotenuse × cos(45°)
That is base=hypotenuse/√2
Therefore, the value of the legs of the 45°-45°-90° triangle would be hypotenuse/√2.
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At the movie theatre, child admission is $5.70 and adult admission is $9.60. On Monday, three times as many adult tickets as child tickets were sold, for a total sales of $1345.50. How many child tickets were sold that day
The total number of child ticket and adult ticket that were sold was: 270 and 810 respectively.
How many child tickets were sold that day?On Monday, three times as many adult tickets as child tickets were sold at the movie theatre.The adult admission was $9.60, and the child admission was $5.70.The total sales for the day were $1345.50.In order to find out how many child tickets were sold that day, the total sales for the adult tickets must first be calculated. Since three times as many adult tickets were sold, the number of adult tickets can be calculated by dividing the total sales by three. This results in $448.50.To calculate the total sales for the child tickets, the total sales must be subtracted from the adult ticket sales.This results in $897.00. Since the price of the child tickets was $5.70, the total number of child tickets sold can be calculated by dividing the total sales by this price.This results in 157 child tickets sold.To learn more about the application of linear equations refer to:
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A stone was thrown into a pond from 8 feet above the surface of the water in the pond. Justin wrote 8 feet to represent the height from which the stone was thrown. What does 0 represent in this situation
H)
find the exact value of sec 7pi / 4
Answer: sqrt(2)
Step-by-step explanation:
Remember that sec x = 1/cos x.
That means that sec 7pi/4 = 1/cos(7pi/4)
cos(7pi/4) = -cos(7pi/4 - pi)
= -cos(3pi/4)
cos(3pi/4) is a special angle which evaluates to -sqrt(2)/2.
Hence, -cos(3pi/4) evaluates to simply sqrt(2)/2
Since cos(7pi/4) is equal to -cos(3pi/4),
cos(7pi/4) is equal to sqrt(2)/2.
Lastly, sec 7pi/4 = 1/cos(7pi/4) , which is the reciprocal of sqrt(2)/2, that is 2/sqrt(2).
Rationalizing the answer 2/sqrt(2) gives sqrt(2)
Solve the following quadratic equation, leaving your answer in exact form:
2e²-8e +7= 0
Pls can anyone help it would rrly help out
Answer:
The two answers would be 0 and ln (7)
Step-by-step explanation:
Hope it helps:)
Charles and Paul each have a computer repair business.
Charles charges a diagnostic fee of around 60$ plus 12$ per hour spent on computer repairs.
Y= 12x+60
Paul charges a diagnostic fee of 40$ plus 16$ per hour spent on computer repairs.
The situation is graphed in the picture
Y= 16x+40
*Which statement BEST describes the system of equations?
A. For repairs requiring 2 hours of work, the total amount charged by Charles will be 72$ and the total amount charged by Paul will be 84$
B. For repairs requiring 8 hours of work, the total amount charged by Charles will be 168$ and the total amount charged by Paul will be 156$
C. For repairs requiring 5 hours of work, the total amount charged by both Charles and Paul will be 100$
D. For repairs requiring 5 hours of work, the total amount charged by both Charles and Paul will be 120$
(This is just too much to look at for me so If anyone can figure it out I greatly appreciate it)
For repairs that take five hours to complete, Charles and Paul will each charge a total of $120.
What is the graph's equation?In order to put the equation in y-intercept (y=mx+b) form and determine the equation of a graphed line, first determine the slope and y-intercept. The slope is the ratio of the y-to-x change.
What are the three techniques for graphing equations?For charting linear functions, there are three fundamental techniques. The first method involves tracing a line through a set of points that have been plotted. The second method makes use of the slope and y-intercept. Applying transformations to the identity function f(x)=x f(x) = x is the third step.
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