Answers
The perimeter and area of the original square are 4s and s², respectively, and the perimeter and area of the dilated square are 192 and 2304, respectively.
What is area of square ?
Area of square can be defined as the square of given side.
Given ,
Let's assume that the side length of the original square is 's'. The perimeter of the original square is then 4s and its area is s².
The perimeter of the dilated square will be 4 times longer than the original square, so it will be 4 * 4s = 16s.
The area of the dilated square will be 4 times greater than the original square, so it will be 4^2 * s² = 16s².
Here s is 12
so ,
16s = 16 * 12 = 192
16s*s = 16 * 12 * 12 = 2304
Therefore, The perimeter and area of the original square are 4s and s², respectively, and the perimeter and area of the dilated square are 192 and 2304, respectively.
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Related Questions
Help, Solve it by using Elmination, Linear Equation
Answers
Answer:
The mistake they made was that they subtracted [tex]2y[/tex] from [tex]2y[/tex] and got [tex]0y[/tex]. Instead of subtracting, they should have added it.
Step-by-step explanation:
Given:
[tex]8x+2y=44\\5x+2y=35[/tex]
We can combine the system of equations into a single equation:
[tex]13x+4y=79[/tex]
From this step, we can conclude that the answer for part b is incorrect. The mistake they made was that they subtracted [tex]2y[/tex] from [tex]2y[/tex] and got 0y. Instead of subtracting, they should have added it.
We can continue solving the system of equations by writing y in terms of x.
[tex]8x+2y=44\\2y=44-8x\\y=22-4x[/tex]
now substitute this into the single equation:
[tex]13x+4y=79\\13x+4(22-4x)=79\\13x+88-16x=79\\-3x+88=79\\-3x=-9\\x=3[/tex]
Since we now know that [tex]x=3\\[/tex], we can substitute this into the equation we made for y.
[tex]y=22-4x\\y=22-4(3)\\y=22-12\\y=10[/tex]
The solution for the system of equations is [tex]x=3[/tex] and [tex]y=10\\[/tex].
Help, please thank you, and have a wonderful day
Answers
2 terms
4
X^3/2
1/2
Examine the right triangle below. Let a = 15, b = 20, and c = 25. What is the
sin B=, rounded to the nearest hundredth?
Answers
The value of sin B rounded to the nearest hundredth is 0.80.
What are Trigonometric Functions?Trigonometric functions are defined as the real functions which are simply the functions of an angle of a triangle. They are basically the periodic functions which relate an angle in a right angled triangle to the ratios of the length of two sides.
The right triangle represented in the question is given below.
We know that sine of an angle in a right angled triangle is the ratio of it's opposite side to hypotenuse.
In the triangle ABC, AB is the hypotenuse and AC is the opposite side of B.
Sin B = AC / AB
Sin B = b / c
Sin B = 20 / 25
Sin B = 0.8
Hence the value of sine of B is 0.8.
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convert 31,750 feet into miles
Answers
To convert 31,750 feet to miles, divide the number of feet by the number of feet per mile:
31,750 feet / 5,280 feet/mile = 6 miles
please help me with this.
Answers
Following are the values of the functions -
1) f(a) = 8a - 4
2) f(a+h) = 8a+ 8h - 4
3)[tex]\frac{f (a+h)-(a) }{h}= 8[/tex]
Describe function.An expression or relationship with one or more variables is called a function. Both its inputs and outputs are numerous. There is just one output per input. The function explains how the inputs and outputs are related.
To evaluate f(a), we simply substitute the value of "a" into the function:
1) f(a) = 8a - 4
To evaluate f(a+h), we substitute the value of "a+h" into the function:
2) f(a+h) = 8(a+h) - 4
f(a+h) = 8a+ 8h-4
To find the expression for [tex]\frac{f (a+h)-(a) }{h}[/tex], we divide the result by h: L(a+h)-f(a) h we can subtract f(a) from f(a+h) and then
3) [tex]\frac{f (a+h)-(a) }{h}[/tex]
[tex]= \frac{ (8a+8h-4-(8a-4)}{h} \\= \frac{8h}{h}= 8[/tex]
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Rui is a professional deep water free diver. His altitude (in meters relative to sea level), x xx seconds after diving, is modeled by: d ( x ) = 1 2 x 2 − 10 x d(x)= 2 1 x 2 −10xd, left parenthesis, x, right parenthesis, equals, start fraction, 1, divided by, 2, end fraction, x, squared, minus, 10, x How many seconds after diving will Rui reach his lowest altitude?
Answers
Answer: look at the image for the answer and explanation
Step-by-step explanation:
X =
Evaluate.
-(-2)+√(-2)²-4(1)(-8)
2(1)
= 2 + (²)
X =
Enter the number that
belongs in the green box.
Answers
The value of the equation for x is 32
What is PEDMAS?PEDMAS is described as a mathematical acronym that represents the important operations during calculations.
The alphabets represents;
ParenthesesExponentsDivisionMultiplicationAdditionSubtractionFrom the information given, we have;
-(-2)+√(-2)²-4(1)(-8)
expand the brackets
2 + -2 -4(-8)
multiply the values
2 -2 + 32
Add the values
32
Hence, the value is 32
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Help me with this question…..
Answers
Answer:
A.
Step-by-step explanation:
Since [tex]5[/tex] can rewritten as [tex]\sqrt{25}[/tex] and [tex]6[/tex] rewritten as [tex]\sqrt{36},[/tex] we can see which options go between [tex]\sqrt{25}[/tex] and [tex]\sqrt{36}.[/tex] The only square root that goes between is [tex]\sqrt{29}.[/tex] Therefore the answer is [tex]\boxed{A.}[/tex] (or [tex]\sqrt{29}.[/tex])
rewrite the equation in vertex form. y^2-4y-x+9=0
Answers
In the vertex form the equation can be rewritten as x = 1×(y - 2)² + 5
The equation is given in the standard form y²-4y-x+9 = 0 and we have to convert it into vertex form
So basically, the general vertex form of any equation is x = a(y - k)² + h
⇒ y²-4y-x+9 = 0
Shifting the x to RHS,
⇒ x = y²- 4y + 9
Writing y²- 4y in the form of (a-b)²,
⇒ x = y²- 4y + 4 + 5
⇒ x = 1×(y - 2)² + 5,
Hence the equation is now converted to vertex form
⇒ where a = 1, k = 2 and h = 5
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Determine whether the ordered pair is a solution to the system of equations or inequalities y<4x-1; y>x. Yes or no?
(1,3)
(0,0)
Answers
Answer:
Step-by-step explanation:
To determine whether an ordered pair is a solution to a system of equations or inequalities, we need to substitute the values for x and y into each equation or inequality and see if the resulting expression is true. If it is true for all of the equations or inequalities, then the ordered pair is a solution to the system.
Here's the step-by-step process for each ordered pair:
(1,3):
Substitute x = 1 and y = 3 into y < 4x - 1: 3 < 4(1) - 1 = 3 < 3, which is true.
Substitute x = 1 and y = 3 into y > x: 3 > 1, which is true.
Since both inequalities are true, the ordered pair (1,3) is a solution to the system y < 4x - 1 and y > x.
(0,0):
Substitute x = 0 and y = 0 into y < 4x - 1: 0 < 4(0) - 1 = -1, which is false.
Substitute x = 0 and y = 0 into y > x: 0 > 0, which is false.
Since at least one inequality is false, the ordered pair (0,0) is not a solution to the system y < 4x - 1 and y > x.
Consider the line 9x-8y=-9.
Find the equation of the line that is parallel to this line and passes through the point (−3, 4).
Find the equation of the line that is perpendicular to this line and passes through the point (-3, 4).
Equation of parallel line:
Equation of perpendicular line:
1
=
X
0=0
5
Answers
Find the equation for the line through the points (2,3) and (7,1)
Answers
Answer:
Step-by-step explanation:
m=3-1/2-7= -2/5
c⇒ -2
y=mx+c
y=-2/5x-2
This is a sketch of y = sin x.
The vertex A is at (90°, 1).
Write down the coordinates of the vertex A of the curve with equation
a) y = sin x + 2
b) y=-sin x
Answers
Vertex A: (90°, 3) and Vertex B: (90°, -1) of the sine function.
EquationsThe vertex A of the curve y = sin x + 2 is obtained by shifting the vertex of y = sin x upward by 2 units. Since the vertex of y = sin x is (90°, 1), the vertex of y = sin x + 2 will be:
A = (90°, 1 + 2) = (90°, 3)
Therefore, the coordinates of the vertex A of the curve y = sin x + 2 are (90°, 3).
b) The curve y = -sin x is obtained by reflecting the curve y = sin x about the x-axis. Since the vertex of y = sin x is (90°, 1), the vertex of y = -sin x will be:
A = (90°, -1)
Therefore, the coordinates of the vertex A of the curve y = -sin x are
(90°, -1).
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Draw a rectangular fraction model to explain your thinking. 1/2 of 2/3 = 1/2 of_ third(s) =_ third(s)
Answers
A rectangle that has been divided into equal parts is referred to as a rectangular fraction. Depending on how many equal pieces you divide the whole into, the equal parts may be divided into halves, thirds, fourths, and so on.
1/2 of 2/3 is equal to 1/3
What is the equation?
The equation is defined as a mathematical statement with at least two terms that contain variables or values that are equal.
To represent the multiplication of 1/2 and 2/3, we can draw a rectangle and divide it into equal parts.
1) First, we draw a rectangle.
2) Then, we divide it into 2 equal parts horizontally.
3) Next, we divide each half vertically into 3 equal parts.
4) Now we can see that each small rectangle represents 1/6 of the whole rectangle.
So, 1/2 of 2/3 is equal to 1/2 of 1/3.
Therefore, 1/2 of 2/3 is equal to 1/3.
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The area of a rectangular red sticker is 33 millimeters.The perimeter is 28 millimeters. what are the dimensions of the sticker?
Answers
The dimensions of the sticker are 11 millimeters and 3 millimeters.
What is Area and Perimeter?Area of a two dimensional shape is the total region which is bounded by the object's shape.
Perimeter of a straight sided figures or objects is the total length of it's boundary.
Given is a sticker which is rectangular in shape.
Area of the sticker = 33 millimeters²
Perimeter of the sticker = 28 millimeters
Area of a rectangle = Length × Width
Perimeter of a rectangle = 2(Length + Width)
Let x be the length and y be the width of the rectangle.
x y = 33
2(x + y) = 28 ⇒ 2x + 2y = 28 ⇒ 2y = 28 - 2x ⇒ y = 14 - x
Substituting y = 14 - x in x y = 33,
x(14 - x) = 33
14x - x² = 33
-x² + 14x - 33 = 0
x² - 14x + 33 = 0
Factorizing the quadratic equation,
(x - 11) (x - 3) = 0
x - 11 = 0 or x - 3 = 0
x = 11 or x = 3
If x = 11, then y = 33/11 = 3
If x = 3, y = 33/3 = 11
Hence the dimensions are 11 millimeters and 3 millimeters.
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a student gets paid to sell raffle tickets at the school basketball game. He earns $15 a day, plus an extra $0.25 for each raffle ticket he sells and $2 for each hour he works at the game. If d= days, r= raffle tickets, and h= hours, what function can he use to calculate his earnings?
Answers
The function can be used to calculate his earnings, 15d + 0.25r + 2h
What are functions?Function is a relation between a set of inputs and a set of outputs which are permissible. In a function, for particular values of x we will get only a single image in y. It is denoted by f(x).
The function that the student can use to calculate his earnings is:
Earnings = 15d + 0.25r + 2h
where:
d = number of days worked
r = number of raffle tickets sold
h = number of hours worked at the game
The first term, 15d, represents the base pay of $15 per day worked.
The second term, 0.25r, represents the additional earnings of $0.25 per raffle ticket sold.
The third term, 2h, represents the additional earnings of $2 per hour worked at the game.
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PLEASE HELP
Draw a pie chart for the given data:
Rugby Team
England
France
Ireland
Scotland
Wales
Frequency
20
5
15
25
25
Answers
Step-by-step explanation:
you draw a circle ⭕ then you do lines inside the circle the you write the numbers aside
Write equivalent expressions.
-4y+8
Select all that apply.
A: -4(y-2)
B: -4(-2+4y)
C: (2-y)4
D: 4(-y+8)
Answers
A and C are equivalent expressions for a given expression.
What does an expression mean?
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
The given expression is -4y+8.
Given options are:
A. -4(y-2)
By simplifying it we will get -4(y-2) = -4y+8
So, both are equivalent.
B. -4(-2+4y)
By simplifying it we will get -4(-2+4y) = 8-16y
So, both are not equivalent.
C. (2-y)4
By simplifying it we will get (2-y)4 = 8-4y
So, both are equivalent.
D. 4(-y+8)
By simplifying it we will get 4(y-8) = 4y-32.
So, both are not equivalent.
A, and C are equivalent expressions for a given expression.
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Which of the symbols correctly relates the two numbers below? Check all that
apply.
A. =
B. >
C. Z
☐ D. <
E. >
OF. s
364? 225
Answers
The symbols which correctly relate the numbers 364 and 225 are '>' and '≠'.
The solution has been obtained by using concept of relational symbols.
What are relational symbols?
Relational symbols are used in mathematics to represent mathematical relations, which combine with one or more other mathematical objects to construct complete mathematical statements. These are the relational symbols for equality and comparison in arithmetic and common mathematics.
We are given 2 numbers as 364 and 225.
It is clearly visible that both the numbers are not same so, the symbol '≠' depicts the relationship between the two numbers.
Also, we know that the number 364 is greater than 225. So the another symbol depicting relation between the numbers is '>'.
Hence, the symbols which correctly relate the numbers 364 and 225 are '>' and '≠'.
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Question: Which of the symbols correctly relates the two numbers below? Check all that apply.
364? 225
A. =
B. >
C. ≥
D. <
E. ≤
F. ≠
consider the following: Point (3,5), and Line y-1=0. Write the slope intercept form of the equation of the line through the given point an parallel to the given line.
Answers
Step-by-step explanation:
please see the attached picture
In ΔDEF, e = 9.2 cm, m m∠F=72° and m m∠D=61°. Find the length of f, to the nearest 10th of a centimeter.
Answers
The length of side f is 12.0 inches
How to determine the length of side fFrom the question, we have the following parameters that can be used in our computation:
In ΔDEF, e = 9.2 cm, m m∠F=72° and m m∠D=61°
The sum of angles in a triangle is 180 degrees
Using the above as a guide, we have the following:
E = 180 - 72 - 61
E = 47
Using the law of sines, we have
f/sin(F) = e/sin(E)
substitute the known values in the above equation, so, we have the following representation
f/sin(72) = 9.2/sin(47)
So, we have
f = sin(72) * 9.2/sin(47)
Evaluate
f = 12.0
Hence, the length is 12.0 inches
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Solve: 6(x + 5) = -2(x-3)
Answers
Answer:
Step-by-step explanation:
6(x+5) = 6x+30
-2(x-3)=-2x+6
6x+30=-2x+6
8x+30=6
8x=-24
x=-3
Answer: x = -3
Step-by-step explanation:
6(x + 5) = -2(x-3)
1. Distribute: 6x + 30 = -2x + 6
2. Add 2 to both sides: 8x + 30 = 6
3. Subtract 30 on both sides: 8x = -24
4. Divide by 8 on both sides: x = -3
Only using positive exponents, what is the simplified form of the expression p−6q7r/p2q−2
Answers
Step-by-step explanation:
Here is it. I hope it will help
Determine the more basic function that has been shifted, reflected, stretched, or compressed q(x) = -1/x + 1
Answers
The more basic function that has been shifted, reflected, stretched, or compressed to create q(x) = -1/x + 1 is the function f(x) = 1/x.
What do you understand by the team function?The transformation applied to f(x) to obtain q(x) is divided into several steps:
Reflection: The negative sign in front of 1/x reflects the graph of f(x) across the x-axis, causing the y-values to change sign.
Vertical shift: Adding "+1" to -1/x raises the graph of f(x) by one unit.
Horizontal shift: Although there is no explicit horizontal shift in q(x), we can see that the graph of q(x) has a vertical asymptote at x=0, whereas the graph of f(x) does not. This means that the graph of q(x) has been shifted to the right by one unit.
The more basic function that has been shifted, reflected, stretched, or compressed to create q(x) = -1/x + 1 is the function f(x) = 1/x.
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HELPPP PLEASE I NEED HELP
Answers
The rule A(x,y) ⇒ (-y,x) describes a transformation. The correct option is D.
What is a transformation of rotation?The concept of rotation in mathematics has its roots in geometry. Any rotation is a movement of a certain area while maintaining at least one point. It may be used to describe, for instance, how a rigid body moves around a fixed point.
Our point A(x,y) becomes A' when a point is rotated 90 degrees counterclockwise about the origin (-y,x). To put it another way, flip x, and y, making y negative.
The transformation is described by the rule A(x,y) (-y,x). The right answer is D.
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Factorise:
(a - 2b)^3 + (2a - b)^3
Answers
Answer:
Step-by-step explanation:
To factorise the expression, we can use the factor theorem which states that if a polynomial p(x) has a factor (x - r), then p(r) = 0.
We can use this theorem to find the factors of the polynomial expression:
(a - 2b)^3 + (2a - b)^3
We can write (a - 2b)^3 as (a - 2b)(a^2 - 4ab + 4b^2). Using the factor theorem, we see that:
(a - 2b)(a^2 - 4ab + 4b^2) = 0 when a = 2b
Similarly, we can write (2a - b)^3 as (2a - b)(4a^2 - 4ab + b^2). Using the factor theorem, we see that:
(2a - b)(4a^2 - 4ab + b^2) = 0 when a = b/2
Now we have two equations: a = 2b and a = b/2, which we can use to solve for a and b in terms of each other. We see that:
a = 2b = b/2
Multiplying both sides by 2, we get:
2a = b
We can substitute this back into the original expression:
(a - 2b)^3 + (2a - b)^3 = (a - 2(2a))^3 + (2a - (2a))^3 = (-3a)^3 + (0)^3 = -27a^3
So the factorised form of the expression is:
(a - 2b)^3 + (2a - b)^3 = -27a^3.
Work Shown:
Use the sum of cubes factoring rule
x^3 + y^3 = (x+y)(x^2 - xy + y^2)
In this case,
x = a-2by = 2a-bSo,
x^3 + y^3 = (x+y)(x^2 - xy + y^2)
(a-2b)^3 + (2a-b)^3 = (a-2b+2a-b)((a-2b)^2 - (a-2b)(2a-b) + (2a-b)^2)
(a-2b)^3 + (2a-b)^3 = (3a-3b)((a^2-4ab+4b^2) - (2a^2-ab-4ab+2b^2) + (4a^2-4ab+b^2))
(a-2b)^3 + (2a-b)^3 = (3a-3b)((a^2-4ab+4b^2) - (2a^2-5ab+2b^2) + (4a^2-4ab+b^2))
(a-2b)^3 + (2a-b)^3 = (3a-3b)(a^2-4ab+4b^2 - 2a^2+5ab-2b^2 + 4a^2-4ab+b^2)
(a-2b)^3 + (2a-b)^3 = (3a-3b)(3a^2-3ab+3b^2)
(a-2b)^3 + (2a-b)^3 = 3*3(a-b)(a^2-ab+b^2)
(a-2b)^3 + (2a-b)^3 = 9(a-b)(a^2-ab+b^2)
The answer has been fully confirmed with WolframAlpha.
3ab2 +1
3a²b-1
(a = 2 ; b = -2)
EVALUATE THE EXPRESSION
Answers
Answer:
3ab2+1 = -23
3a^2b-1 =-25
Step-by-step explanation:
Question is attached below!
Thanks! :)
Answers
The parameters for the home mortgage, and the monthly payment, PMT, for the mortgage are as follows;
Part 1;
P = $175,000, APR = 7%, n = 12, Y = 30
Part 2;
The monthly payment for the mortgage, PMT ≈ $1,164.28
What is a mortgage?A mortgage is a loan agreement, with the possession of the collateral presented for the loan such as a house being bought with the loan amount, being relinquished by the debtor, upon default
Part 1
The value of the mortgage = $175,000
The fixed Annual Percentage Rate, APR = 7%
The duration of the payment = 30 years
The principal amount of the mortgage, P = $175,000The annual percentage rate, APR = 7% = 0.07The number of payment (periods), per year, n = Monthly = 12The number of years of the loan, Y = 30Part 2; The monthly payment PMT loan formula can be presented in the following format;
[tex]PMT = \frac{P\times \frac{APR}{n} }{1-\left(1+\frac{APR}{n}\right)^{(-n\cdot Y)} }[/tex]Therefore;
[tex]PMT = \frac{175000\times \frac{0.07}{12} }{1-\left(1+\frac{0.07}{12}\right)^{(-12\times 30)} } \approx 1164.28[/tex]
The monthly payment for the mortgage is, PMT ≈ $1,164.28
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A magician shuffles a standard deck of playing cards and allows an audience member to pull out a card, look at it, and replace it in the deck. Three additional people do the same. Find the probability that of the 4 cards drawn, at least 1 is a face card. (Round your answer to one decimal place.
Answers
The probability that at least 1 of the 4 cards drawn is a face card is 0.6.
How to find probability of 4 cards drawn?A typical deck contains 52 cards in total. There are 51 cards left in the deck after the first spectator draws a card. The replacement card leaves 52 cards in total, which is the same as before. The number of cards remains 52 for all four draws since each succeeding audience member will draw a card and replace it.
Finding the likelihood that none of the four cards are face cards and subtracting it from one will give us the chance that at least one of the four cards is a face card.
A deck of cards has 12 face cards (4 jacks, 4 queens, and 4 kings). Consequently, the likelihood that a single draw will not provide a face card is:
P(not a face card)=(52 - 12)/(52)=(40/(52)=(10/13).
The likelihood that none of the four draws will produce a face card is:
P(no face cards are present) = (10/13)4 = 0.432
As a result, the likelihood that at least 1 of the four cards revealed is a face card is as follows:
P(none are face cards) = 1 - P(at least one is a face card) = 1 - 0.432 = 0.568
The chance, rounded to one decimal place, is roughly 0.6.
Consequently, there is a 0.6 percent chance that at least one of the four cards will be a face card.
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3. If an angle measures 2π radians, what is the measure of the angle in degrees?
Answers
Answer:
360 degrees
2 pi radians, means you have 2 pi of something and they are radians. It is the same 360 degrees. A radius is the line from the side of the circle to the center.
Reason: pi radians is 180 degrees. Double each value to find that 2pi radians is 360 degrees. It's a full revolution of a circle. Use a unit circle if necessary.
