===========================================================
Explanation:
The preimage (-6,-2) shifts to the image point (-4,-4)
Focus on the x coordinates. The jump from -6 to -4 is an increase of 2. So we have x become x+2
Now focus on the y coordinates. The jump from -2 to -4 is -2, so y becomes y-2
The translation rule we use is [tex](\text{x},\text{y})\to (\text{x}+2,\text{y}-2)[/tex] which shifts the point 2 units to the right and 2 units down.
-----------------
Let's apply this rule to the point (3,-1)
[tex](\text{x},\text{y})\to (\text{x}+2,\text{y}-2)\\\\(3,-1)\to (3+2,-1-2)\\\\(3,-1)\to \boldsymbol{(5,-3)}\\\\[/tex]
The preimage (3,-1) shifts to the image (5, -3)
Cynthia Besch wants to buy a rug for a room that is 19 ft wide and 33 ft long. She wants to leave a uniform strip of floor around the rug. She can afford to buy 275 square feet of carpeting. What dimensions should the rug have?
The dimensions of the rug that Cynthia Besch should buy are 11 ft wide and 25 ft long, which gives an area of 275 ft².
How are the dimensions determined?The dimensions of the rug include the width and the length.
Cynthia is budget-constrained to buy 275 ft² only.
When we factorize 275, we have 1, 5, 11, 25, 55, and 275.
The possible combinations of width and length to get 275 ft² and also ensure that a uniform strip of the floor is left around the rug are 11 ft and 25 ft. This width and length are less than the room's width and length and satisfy the requirement for a uniform strip.
The strip from the room's width and length must be 8 ft each (from all sides).
Data and Calculations:Width of room = 19 ft
Length of room = 33 ft
Area of room = 627 ft²
Dimensions:Width of rug = 11 ft(19 - 8)
Length of rug = 25 ft (33 - 8)
Area = 275 ft² (11 x 25)
Thus, the dimensions of the rug that Cynthia Besch should buy are 11 ft wide and 25 ft long.
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Anna has 55 coins in her piggy bank. She notices that she only has dimes and pennies. If she has exactly
four times as many pennies as dimes, how many pennies are in her piggy bank?
Answer: 44 Pennies
Step-by-step explanation: The ratio of pennies to dimes is 4:1. Add both numbers up to get 5 and divide 55 by 5 to get 11. multiply 4 and 1 from the ratio by 11 to get 44 and 11. This is the number of pennies and dimes.
What's the length of segment LM?
Answer:
6
Step-by-step explanation:
17 is the total length
11 is part of the length
17-11 =6
What value of x is in the solution set of 2(3x - 1) ≥ 4x - 6?
-10
-5
-3
-1
Answer:
-1
Step-by-step explanation:
[tex]2(3x-1) \geq 4x-6 \\ \\ 6x-2 \geq 4x-6 \\ \\ 2x \geq -4 \\ \\ x \geq -2[/tex]
Answer:
-1 is the answer
Step-by-step explanation:
The sum of three lengths of a fence rages from 31 to 40 inches. Two side lengths are 9 and 12 inches. If the length of the third side is x inches, write and solve a compound inequality to show the possible lengths of the third side
Answer:
10 ≤ x ≤ 19
Step-by-step explanation
The sum of the three lengths is 9 + 12 +x = 21 + x
We know the sum ranges from 31 to 40
So we get the inequality
31 ≤ 21 + x ≤ 40
Subtracting 21 from each part of this inequality give
31-21 ≤ x ≤40-21
10 ≤ x ≤ 19
The compound inequality to show the possible lengths of the third side is 10 ≤ x ≤ 19.
What is inequality?A statement of an order relationship-greater than, greater than or equal to, less than, less than or equal to- between two numbers or algebraic equations.
Now it is given as,
Range of sum of three lengths of a fence = 31 to 40 inches
Length of two sides = 9 and 12 inches
Length of third sides = x inches
So, length of sum of three lengths of a fence = 9 + 12 + x
⇒ length of sum of three lengths of a fence = 21 + x
∵ Range of sum of three lengths of a fence = 31 to 40 inches
31 ≤ length of sum of three lengths of a fence ≤ 40
⇒ 31 ≤ 21 + x ≤ 40
Subtracting 21 we get.
10 ≤ x ≤ 19
Thus, the compound inequality to show the possible lengths of the third side is 10 ≤ x ≤ 19.
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A total of $35,000 is to be invested, some in bonds and some in certificates of deposit (CDs). If the amount invested
in bonds is to exceed that in CDs by $1,000, how much will be invested in each type of investment?
The amount invested in CDs is S
The amount invested in bonds is
The amount invested in each type of investment should be $17,000 and $18,000, respectively, as this problem is based on simple interest.
What is a simple mathematical interest?Calculating the amount of interest that will be owed on a sum of money at a certain rate and for a specific period of time is possible using simple interest. Contrary to compound interest, where we add the interest of one year's principal to the next year's principal to compute interest, the principal amount under simple interest remains constant.
based on the facts provided;
Calculating the investment amount:
Since the certificate of deposit is assumed to be x in this instance, the bond should be $35,000 - x.
The formula now should be
($35,000 - x) - x = $1,000
$35,000 - 2x = $1,000
$34,000 = 2x
x = $17,000
So, the bond should be
= $35,000 - $17,000
= $18,000
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Calculate the average GPA for Andy after each of his four years of high school if he gets a good start his Freshman year?
Answer:
Freshman Sophomore Junior Senior
3.5 3.25 3.0 3.2
Step-by-step explanation:
Average GPA = Total GPA / number of years
Freshman Year (1 year): 3.5 = 3.5
Sophomore Year (2 years) = (3.5 + 3.0) = 6.5/2 = 3.25
Junior Year(3 years) = (3.5 + 3.0 + 2.5)/3 = 9.0/3 = 3.0
Senior Year(4 years) = (3.5 + 3.0 + 2.5 + 3.8) = 12.8/4 = 3.2
find the volume of a cylinder with radius 6 and height 16,pi= 3.142
The volume of the cylinder is 1809.5 cubic units.
What is the volume of a cylinder?The volume of a cylinder is equal to the product of the area of the circular base and the height of a cylinder. The volume of a cylinder is defined as the space occupied by the cylinder as the volume of any three-dimensional shape is the space occupied by it
V = πr²h
where 'r' is the radius of the base (circle) of the cylinder
'h' is the height of the cylinder
Given that a cylinder with a radius of 6 and height of 16.
Here r = 6 and h = 16,
the volume of a cylinder = πr²h
the volume of a cylinder = π(6)²×16
the volume of a cylinder = 1809.5 cubic units
Thus, the volume of the cylinder is 1809.5 cubic units.
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F(x) = 2x-1. Translation 3 units right followed by a vertical stretch by a factor of 2.
According to the parameters given, the rule again for graph of g after so transformations of a function F(x) = 2x - 1 is g(x) = -4x + 4.
What is defined by the term translation?A translation is a form of transformation in which every point in a figure moves the same distance within the same direction. are frequently alluded to as slides A translation can be described using words such as "moved up 3 more than 5 to the left" or even with notation.The graph for the given function defined by the equation;
F(x) = 2x - 1
Initially, the graph of g is a three-unit translation, so we have;
g(x) = f(x) + 3g(x) = 2x - 1 + 3 = 2x + 2Then comes a vertical stretch by such a factor of two and a reflection in the x axis.
The above means that graph must all be multiplied by 2 and that x values containing x are now considered to be -x.
g(x) = 4x + 4And an x-axis reflection yields;
g(x) = 4(-x) + 4g(x) = -4x + 4Thus, the rule for making the graph of function g(x) is by; g(x) = -4x + 4.
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9. Steven wants to buy a $595 bicycle. Steven has no money saved, but will be able to deposit $30 into a
savings account when he receives his paycheck each Friday. However, before Steven can buy the bike, he
must give his sister $65 that he owes her. For how many weeks will Steven need to deposit money into his
savings account before he can pay back his sister and buy the bike?
22 weeks
b.
21 weeks
d.
23 weeks
26 weeks
C.
a.
5
Answer:
22 weeks
Step-by-step explanation:
595+65=660
22x30=660
so he could buy a bicycle and owes his sister the money after 22 weeks
Can someone help me please
Using translation concepts, the graph of square CDEF after a rotation 270º counterclockwise around the origin is given at the end of the answer.
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
The rule for a rotation 270º counterclockwise around the origin is:
(x,y) -> (y,-x).
Hence the vertices of the rotated graph will be given as follows:
E': (-4,-3) -> (-3, 4).F': (-9,-3) -> (-3, 9).D': (-4,-8) -> (-8, 4).C': (-9,-8) -> (-8, 9).The graph with these vertices is given at the end of the answer.
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PLEASE! Need help for question 12&14
Answer:
12. BC = 8
14. JL = 18
Step-by-step explanation:
You want to apply the Segment Addition theorem to two problems.
The segment addition theorem tells you the whole is the sum of the parts. The equation for each problem reflects this fact. When given values are substituted, the answer becomes clear.
12.AB +BC = AC
7 +BC = 15
BC = 8 . . . . . . . . subtract 7
14.JK +KL = JL
8 +10 = JL = 18
__
Additional comment
It often helps to draw a diagram.
f(1)=30,f(n)=2•f(n-1)-50
The explicit formula of the sequence is Tn = 30 - 20(n - 1)
How to determine the explicit formula of the sequence?The recursive formula of the sequence is given as
f(1) = 30, f(n) = 2 • f(n - 1) - 50
The above means that
f(n) = 2 • f(n - 1) - 50
f(1) = 30
Substitute 2 for n
So, we have
f(2) = 2 • f(2 - 1) - 50
Evaluate the difference
So, we have
f(2) = 2 • f(1) - 50
Substitute f(1) = 30 in f(2) = 2 • f(1) - 50
f(2) = 2 • 30 - 50
Evaluate
f(2) = 10
Substitute 3 for n
So, we have
f(3) = 2 • f(3 - 1) - 50
Evaluate the difference
So, we have
f(3) = 2 • f(2) - 50
Substitute f(2) = 10 in f(3) = 2 • f(2) - 50
f(3) = 2 • 10 - 50
Evaluate
f(3) = -30
So, we have the first three terms to be
30, 10, -10
The above represents an arithmetic sequence, where
First term, a = 30
Common difference = -20
The nth term of the sequence is
Tn = a + (n - 1)d
So, we have
Tn = 30 - 20(n - 1)
Hence, the explicit formula of the sequence is Tn = 30 - 20(n - 1)
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Determine how long it will take for a principal amount of $1,500 to become double its initial value when deposited into an account paying interest at a rate of 13%, continuously compounded.
A.
5.33 years
B.
6.32 years
C.
11.25 years
D.
14.33 years
c is incorrect
A survey of 75 people found 45 like rabbits, 32 like hamsters, and 15 like both animals. How many people like neither animal?
Step-by-step explanation:
two people like neither animal
Answer:
13
Step-by-step explanation:
15+75-32-45
90-32-45
58-45
13
HELPPPP PLEASE John walks away from his house down a straight street. The graph shows John's distance from his house over time. Describe his trip. Find John's speed on each section of the walk.
John's speed on each section of the walk are 4 km per hour, 0 km per hour and 1.5 km per hour
How to find John's speed on each section of the walk?On the first section, we have the following points
(x, y) = (0, 0) and (1.5, 6)
The speed is calculated as
Speed = (y2 - y1)/(x2 - x1)
This gives
Speed = (6 - 0)/(1.5 - 0)
Evaluate
Speed = 4
On the second section, we have the following points
(x, y) = (1.5, 6) and (2, 6)
The speed is calculated as
Speed = (y2 - y1)/(x2 - x1)
This gives
Speed = (6 - 6)/(2 - 1.5)
Evaluate
Speed = 0
On the third section, we have the following points
(x, y) = (2, 6) and (6, 0)
The speed is calculated as
Speed = (y2 - y1)/(x2 - x1)
This gives
Speed = (0 - 6)/(6 - 2)
Evaluate
Speed = -1.5
Hence, John's speed on each section of the walk are 4 km per hour, 0 km per hour and 1.5 km per hour
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Zoie is painting a picture that is 15 by 27 inches. She plans to frame it in a frame x inches wide.
Write a polynomial that will be the area of the framed picture.
What will be the area of the picture with the frame if x=3?
If the width of the painting is w, then its length is 2w. Then, since the frame is 2 inches thick on each side of the painting, its width is w+4 and its length is 2w+4. So the area of the rectangle bounded by the frame (which includes both the area of the frame and the area of the painting) is (w+4)(2w+4).
The area of the painting is w×2w=2w2, and the area of the frame is 196 square inches, so the area of the two combined is 2w2+196. However, that is the same area as the other one I described, so we can then equate the two, i.e. (w+4)(2w+4)=2w2+196. You can then solve that equation for w, and hence find all of the relevant dimensions.
What’s 8^2x4^2 please help lol
Answer:
1024
Step-by-step explanation:
8^2=8x8=64
4^2=4x4=16
64x16=1024 :)
Answer: 1024
Step-by-step explanation: 8^2 times 4^2=80. When you square a number, you multiply it by itself. So, 8^2 = 8 times 8 which equals 64. 4^2 = 4 times 4 which equals 16. 64 times 16 = 1024.
Hello,
Does this exercise look correct?
10. Rebecca goes to a bank with $2000 she has saved over the summer. The bank advertises a 3% interest rate when opening a savings account. The bank compounds the money daily with an exponential formula of A(t) = Pe^rt, where P represents the initial amount deposited, e is Euler's constant (approximately 2.71828), r is the rate in decimal form, and t is the total time. Rebecca wants to know how much money will be in her savings account after 10 years.
P = 2000
e = Euler's constant (2.71828)
r = 0.03
t = 10
A(t) = Pe^rt
A(10) = 2000 * 2.71828^ 0.03*10
A(10) = 2000 * 2.71828^ 0.3
A(10) = 2699.71707036 ≈ $2700
Answer: Yes it looks correct i also did it myself and got the same answer
Step-by-step explanation:
I need to prove x*0=0 with field axioms?
Hence proved, x*0 = 0.
A statement that is assumed to be true is referred to as a postulate, axiom, or assumption. It is used as the foundation for further deductive reasoning and arguments.
Given many of the typical formulations of the Peano axioms, for example, this is the base case for the definition of multiplication, so it’s an axiom, not a theorem.
x*o = 0
By using an example as rings:
Therefore, By definition of negotiation
= x + (-x)
0 = x · 1 + ( - x) where 1 is the multiplicative identity,
Now,
= x · ( 0 + 1) + ( - x)
Therefore by distributive law,
= x · 0 + x · 1 + (-x)
Where 1 is the multiplicative identity.
By definition of negotiation,
= x · 0 + x + (-x)
= x · 0 + 0
Where 0 is the additive identity.
= x · 0
Therefore, x*0 = 0
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What Is the correct answer?
The correct answer is x/ 7 = 9. Option D
What are algebraic expressions?Algebraic expressions are simply defined as expressions comprising of terms, variables, coefficients, constants and factors.
They are also made up of mathematical operations such as addition, subtraction, multiplication, division, bracket, etc.
It is important to note that quotient represents division.
Example;
The quotient of 1 and 2 is 1/ 2
The quotient of 3 and 4 is 3/ 4
From the information given, we have that;
The quotient of a number and 7 is 9
Let the number be x
We have;
x/ 7 = 9
Thus, the correct answer is x/ 7 = 9. Option D
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There are 48 people at a party. There are seven times as many adults as children. There are twice
s many females as males. If there are 5 girls (female children) at the party, how many men (male
adults) are there?
48 persons are present at the gathering. There are seven times more adults than children in the world. The number of women is two times that of men. If there are five females (young women) in attendance. The total number of male adults are15
The total number of people are in the party is equal to 48
Let the number of children be x
So, the number of adults in the party is equal to 7 x
x + 7 x =48 ( This is a linear equation)
So, the number of children in the comes to be 6
Number of adults in the party = 6 * 7 = 42
Now let the number of males be y
So total number of females = 2 y
Y+2y = 48 ( This is a linear equation)
Y=16
Therefore, the number of males is 16 and the number of females is 32
The number of children in the party is 6 and the female child is equal to 5
Then, the number of male children =6-5 = 1
So total number of males in the party is equal to 16
Adult males =total number of males - number of male children
=16 - 1 = 15
Hence the total number of male adults =15
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Which equation represents the ellipse with vertices located at (3,-3) and (3,-13) and foci at (3,-5) and (3,-11)?
Check the picture below, so the ellipse looks more or less like so.
[tex]\textit{ellipse, vertical major axis} \\\\ \cfrac{(x- h)^2}{ b^2}+\cfrac{(y- k)^2}{ a^2}=1 \qquad \begin{cases} center\ ( h, k)\\ vertices\ ( h, k\pm a)\\ c=\textit{distance from}\\ \qquad \textit{center to foci}\\ \qquad \sqrt{ a ^2- b ^2} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\begin{cases} h=3\\ k=-8\\ a=5 \end{cases}\implies \cfrac{(x-3)^2}{b^2}+\cfrac{(y-(-8))^2}{5^2}=1 \\\\\\ \stackrel{\textit{we also know that}~\hfill }{c=3\hspace{3.5em} 3=\sqrt{5^2 - b^2}} \implies 3^2=5^2-b^2\implies b=\sqrt{5^2-3^2} \implies \boxed{b=4} \\\\\\ \cfrac{(x-3)^2}{4^2}+\cfrac{(y-(-8))^2}{5^2}=1\implies \cfrac{(x-3)^2}{16}+\cfrac{(y+8)^2}{25}=1[/tex]
Find the horizontal limit(s) of the following function:
f(x)=2x3−8x2−9x/11−10x−5x3
The horizontal limit of the given function is given as follows:
y = -2/5.
What is a limit?A limit is given by the value of function f(x) as x tends to a value. For a standard function, we just calculate the numeric value of a function.
However, in this problem, an horizontal limit means that x goes to infinity, hence it we replace and calculate the numeric values we would have a fraction of infinity divided by infinity as a result, which is an undetermined limit.
Then, we use the algorithm to solve an infinity limit, in which we consider just the term with the highest exponent of both the numerator and of the denominator.
Hence:
[tex]\lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow \infty} \frac{2x^3}{-5x^3} = \lim_{x \rightarrow \infty} -\frac{2}{5} = -\frac{2}[5}[/tex]
Because the limit of a constant is the constant, hence the horizontal limit of the given function is given as follows:
y = -2/5.
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SOMEONE HELP PLS ILL MARK BRAINLIEST
Answer:
Statements:
1) -2(x-4)=2x+12
2) -2x+8=2x+12
3) -4x+8=12
4) -4x=4
5) x=-1
Reasons:
1) Given
2) Distributive Property
3) Combine like terms/Subtraction Property of Equality (subtract 2x from both sides).
4) Subtraction Property of Equality
5) Division Property of Equality
What’s next in this pattern and what would be the conjecture of this pattern? Please I really need help fast
The next in the pattern is ← and the conjecture is a rotation by 90 degrees in the clockwise direction
How to determine the next in the pattern?The pattern is given as:
↑, →, ↓
In the above pattern, we can see that each arrow is rotated 90 degrees in the clockwise direction
When the arrow ↓ is rotated in this direction, we have:
←
Hence, the next in the pattern is ← and the conjecture is a rotation by 90 degrees in the clockwise direction
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Magic Mirror has $428,210 in capital and $87,498 in
liabilities. Find the assets.
The total asset of Magic mirror is $515,708
How to find the asset of magic capital?Magic Mirror has $428,210 in capital and $87,498 in liabilities.
The capital is also know as the equity which means the company's net worth.
Liabilities are everything a business owes, now and in the future.
Assets are everything a business owns. Assets may be current or fixed assets
Therefore,
Total Assets - Total Liabilities = Capital
Where
Total Liabilities = $87,498Total assets = ?Capital = $428,210Hence,
Total Assets = $87,498 + $428,210
Total Assets = $515,708
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What is the solution for Elena's equation
Answer:
Step-by-step explanation:
The equation which has exactly one solution is .
The equation which has exactly infinitely many solutions is .
At a workshop , each of the 100 participants hugs each other participants once. Find the total number of hugs?
Answer:
10000
Step-by-step explanation:
100 hugs x 100 hugs
= 10,000 hugs.
What is the solution to the inequality? |x−2|≥9
Due to modulus there can be two answers, one with greater than equal to and one with less than equal to. So the answer is 11 and -7.
Solve the inequality |x−2|≥9
Inequality is a Mathematical statement that shows the relation between two expressions using the inequality symbol. The expressions on both sides of an inequality sign are not equal. It means that the expression on the left-hand side should be greater than or less than the expression on the right-hand side or vice versa.
a) |x−2|≥9 = x-2≥ 9
=> x≥ 9+2
=> x≥ 11
b) |x−2|≥9 = x-2≥ -9 (when sign the negative the greater than equal to sign changes to less than equal to sign)
= x ≤ -9+2 ≤-7
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