Answer:
(-10, 12).
Step-by-step explanation:
A dilation with a scale factor of 2 centered at the origin expands distances from the origin by a factor of 2. If a point in the plane is represented by the coordinates (x, y), then the point obtained by a dilation centered at the origin with scale factor k is represented by (kx, ky).
So, if the original point is (-5, 6), then after the dilation of 2 centered at the origin, the new point is represented by (2 * -5, 2 * 6) = (-10, 12).
So the coordinates of (-5, 6) after a dilation of 2 centered at the origin are (-10, 12).
estimate the population in the year 2040
well, in 2007 it was 12000, so initially that's what it was, and in 2019 it went to 23000, so that's 12 years later, and in 2040, that'll be 33 years later.
[tex]\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 23000\\ P=\textit{initial amount}\dotfill &12000\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &12\\ \end{cases} \\\\\\ 23000 = 12000(1 + \frac{r}{100})^{12}\implies \cfrac{23000}{12000} =\left(1+ \cfrac{r}{100} \right)^{12} \\\\\\ \cfrac{23}{12}=\left(\cfrac{100+r}{100} \right)^{12}\implies \sqrt[12]{\cfrac{23}{12}}=\cfrac{100+r}{100}[/tex]
[tex]100\sqrt[12]{\cfrac{23}{12}}=100+r\implies 100\sqrt[12]{\cfrac{23}{12}}-100=r\implies \boxed{5.57\approx r} \\\\[-0.35em] ~\dotfill\\\\ \qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &12000\\ r=rate\to 5.57\%\to \frac{5.57}{100}\dotfill &0.0557\\ t=years\dotfill &\stackrel{year~2040 }{33}\\ \end{cases} \\\\\\ A \approx 12000(1 + 0.0557)^{33} \implies \boxed{A \approx 71782}[/tex]
product p of three numbers x ,y,and z
Answer:
p = x(y)(z)
Step-by-step explanation:
product is multiplication.
multiplication has no specific order.
If joes shoes cost 44 dollars and 20 cents and joe has 10
dollars and 68 cents. How much money does joe need?
Answer: 44.20-10.68=33.52
He need 33.52$
Step-by-step explanation:
a restaurant uses square tables with sides of length 1.3m, and round tablecloths with diameter 2m. Determine the percentage of each tablecloth which overhangs its table.
Answer:
46.21%
Step-by-step explanation:
The area of the table top is 1.3 x 1.3 = 1.69 m²
The area of the circular tablecloth is given by πr² where r is the radius of the table cloth
Give diameter of tablecloth is 2m, radius r = 2/2 = 1 m
Area of tablecloth = π · 1² = π
So the excess area of the tablecloth which overhangs
= π - 1.69 = 1.45 m² (taking π = 3.14)
So the fraction of the tablecloth that overhangs
= Excess area of tablecloth ÷ total area of tablecloth
= 1.45 /π
= 0.4621
As a percentage this would be
0.4621 x 100
= 46.21%
The vertex of this parabola is at (5,-4). Which of the following could be its
equation?
The possible equation of the parabola is y = (x - 5)^2 - 4
How to determine the possible equationfrom the question, we have the following parameters that can be used in our computation:
Vertex = (5, -4)
The vertex form of a parabola is given by:
y = a(x - h)^2 + k
where (h, k) is the vertex of the parabola and "a" is a constant that determines the shape of the parabola.
We are given that the vertex of the parabola is (5,-4). Substituting these values into the vertex form, we get:
y = a(x - 5)^2 - 4
Let a = 1
So, we have
y = (x - 5)^2 - 4
Hnce, the possible equation is y = (x - 5)^2 - 4
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please help meee
here is the picture
Answer:
f(-2) = 46
f(-1) = 17
f(0) = 2
f(1) = 1
f(2) = 14
Step-by-step explanation:
F(-2) = 46
F(-1)= 17
F(0)= 2
F(1)= 1
F(2)= 14
One cubic foot holds 7.48 gallons of water, and 1 gallon of water weighs 8.33 pounds. How much does 4.4 cubic feet of water weigh in pounds? In tons?
Answer:
4.4 cubic feet of water weighs approximately 273.5016 pounds or 0.13676 tons.
Step-by-step explanation:
To find the weight of 4.4 cubic feet of water in pounds, we need to find the number of gallons it contains and then multiply it by the weight of one gallon of water.
1 cubic foot = 7.48 gallons
So, 4.4 cubic feet = 4.4 * 7.48 = 32.912 gallons
And the weight of 32.912 gallons of water in pounds is:
32.912 gallons * 8.33 pounds/gallon = 273.5016 pounds
To convert this weight to tons, we divide the weight in pounds by 2000:
273.5016 pounds / 2000 = 0.13676 tons
So, 4.4 cubic feet of water weighs approximately 273.5016 pounds or 0.13676 tons.
Calculate the area of the triangle
find the length of the x
a^2 + b^2 = c^2
12x^2 + b^2 = 13^2
144 + b^2 = 169
b^2 = 25
b = 25; x = 5
use the formula
a = (1/2)(24)(5)
a = (1/2)(120)
area = 60
Find
(M.
f(x)=√√√x²-1
g(x)=√√√x-1
a. √√x+1
b. √√x-1
C.
d.
-X+1
1
X+1
The function operation (f/g)(x) in the functions f(x) = √( x² - 1 ) and g(x) = √( x - 1 ) is √( x + 1).
What is the function operation (f/g)(x) in the function?A function is simply a relationship that maps one input to one output.
Given the functions in the question;
f(x) = √( x² - 1 )g(x) = √( x - 1 )(f/g)(x) = ?To evaluate (f/g), replace the function designators in f/g with the actual functions.
(f/g)(x) = f(x) / g(x)
(f/g)(x) = ( √( x² - 1 ) ) / ( √( x - 1 ) )
Now, rewrite 1 as 1²
(f/g)(x) = ( √( x² - 1² ) ) / ( √( x - 1 ) )
Factor using difference of square
(f/g)(x) = ( √( (x - 1)(x + 1 ) ) / ( √( x - 1 ) )
Combine into a single radical
(f/g)(x) = √( ( (x - 1)(x + 1) ) / ( x - 1 ) )
Now, cancel out the common factors (x-1)
(f/g)(x) = √( (x + 1) / 1 )
(f/g)(x) = √( x + 1)
Therefore, the function operation (f/g)(x) is √( x + 1).
Option A) √( x + 1) is the correct answer.
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mr ramirez bought a watermelon that weighs 12 pounds for a picnic he cuts it into pieces that each weigh 1.5 pounds. how many pieces of water melon can mr ramiez cut?
Equivalence means to be same, whether it be value, temperature, size, etc.
Let's make an equation to solve this problem. We first would need to take the total (12 pounds) and divide that total by the amount each slice must weigh (1.5 pounds) to get an equal number of slices.
12 ÷ 1.5 = 8To check our work, we can take number of slices (8), and multiply that by the weight of each slice (1.5 pounds) to get the original weight of the watermelon.
8 × 1.5 = 12Now, we know for sure that Mr. Ramirez can make 8 watermelon slices each weighing 1.5 pounds if he has a 12-pound watermelon.
CJ has three more pet pigs than Jacqui has. Let’s write an expression to represent how many pigs CJ has. To do that, we follow these steps:
Identify the constants and the variables.
There is one known number or constant here: it is 3. CJ has 3 more pigs than Jacqui. That number, 3, won’t change. The variable is the number of pets Jacqui has. Let’s call that j.
Identify the operations.
The phrase “more than” tells us we need to add. There are no other operations in this expression.
Rewrite the phrase as an expression.
“Three more pet pigs than Jacqui has” is 3 + j.
Last year, Shailyn read four fewer books than Oswaldo. Which expression shows how many books Shailyn read last year?
Answer: Let's follow the same steps as in the previous example:
Identify the constants and the variables.
The known constant here is 4. Shailyn read 4 fewer books than Oswaldo. Let's call the number of books Oswaldo read "o".
Identify the operations.
The phrase "four fewer" tells us we need to subtract.
Rewrite the phrase as an expression.
"Four fewer books than Oswaldo" is o - 4.
So, the expression that shows how many books Shailyn read last year is o - 4.
Step-by-step explanation:
Write an equation to describe the sequence below. Use n to represent the position of a term
In the sequence, where n = 1 for the first term.
-25, -50, -100,...
Write your answer using decimals and integers.
a,
Blank 1:
Blank 2:
Submit
C
C
An equation to show the sequence is -25n.
What is a geometric series?When all the terms of the geometric sequence are added, than that expression is known as geometric series.
The sum of terms of a geometric sequence;
Now, lets suppose its initial term is , multiplication factor will be r
and let it has total n terms, then, its sum is given as:
[tex]S_n = \dfrac{a(r^n-1)}{r-1}[/tex]
(sum till nth term)
We are given that;
The first term of sequence=-25
D= -50-(-25)
=-25
Now,
an = a + (n-1)d
=-25+(n-1)-25
=-25-25n+25
=-25n
Therefore, the answer of the sequence will be -25n.
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Sets A and B are subsets of the universal set U.
These sets are defined as follows.
U= {f, k, m, q, x,y}
A={f, k, m, y}
B = {f, m,q}
Find the following sets.
Write your answer in roster form or as Ø.
(a) AUB' =
(b) A' B' =
(a) The union set is AUB'={f, k, m, x, y}.
(b) The union set is A'UB'={q,k, x, y}.
What is the union of two sets?The union of two sets is also a set. This set contains all the elements of both two sets.
The universal set is U= {f, k, m, q, x,y} and two subsets are A={f, k, m, y} and B = {f, m,q}.
(a)
B' is the complementary set of B. So, find the elements of B'=U-B.
B'= {f, k, m, q, x,y}-{f, m,q}
={k, x,y}
Now, find the union set AUB'.
AUB' ={f, k, m, y}U{k, x,y}
={f, k, m, x, y}
Therefore, the required answer is AUB'={f, k, m, x, y}.
(b)
Also, A' is the complementary set of A. So, find the elements of A'=A-B.
A'= {f, k, m, q, x,y}-{f, k,m, y}
={q,x}
Now, find the union set A'UB'.
A'UB' ={q,x}U{k, x,y}
={q,k, x, y}
Therefore, the required answer is A'UB'={q,k, x, y}.
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Endpoints of a diameter are (−5,−11) and (−1,1) Find the standard form of the equation for the circle with the following properties.
Answer:
Standard form of the equation for the circle
(x + 3)² + (y + 5)² = 40
Step-by-step explanation:
The equation of a circle in standard form is
[tex]\boxed{(x - a)^2 + (y-b)^2= r^2}[/tex]
where (a, b) is the center of the circle and r is the radius
To find center of circle
The end points of the diameter are (-5, -11) and (-1, 1)
The center of the circle is midway between these two points
The x-coordinate of the midpoint = (-5 + -1)/2 = -6/2 = -3
The y-coordinate of the midpoint is (-11 + 1) /2 = -10/2 = -5
So the center of the circle is at (-3, -5)
To find the radius,
Calculate the distance from (-3, -5) to any of of the endpoints.
Let's take the endpoint (-1, 1) and find its distance from (-3, -5)
The distance between any two points (x₁, y₁) and (x₂, y₂) is calculated from the formula
[tex]d^2 = {(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2[/tex]
Substituting
(x₁, y₁) = (-1, 1)
(x₂, y₂) = (-3, -5)
and r for distance
we get
[tex]r^2 = {(-3 - (-1))^2 + (-5 - 1)^2[/tex]
[tex]r^2 = {(-2)^2 + (-6)^2}[/tex]
[tex]r^2 = {{4} + {36}}[/tex]
[tex]r^2 = {40}[/tex]
So the center (a, b) is (-3, -5) and r² =40
Plugging this into the circle equation:
(x - (-3))² + (y - (-5))² = 40
(x + 3)² + (y + 5)² = 40
PLEASE HELP!!! PLEASE IM BEGGING SOMEONE TO HELP ME GHIS IS DUE TOMORROW
Answer:
D
Step-by-step explanation:
It's the most random and produces no bias.
Answer:
D
Step-by-step explanation:
Find the value of X
Please help! Asap
Answer:
Step-by-step explanation:
Rob loaded 9 trucks in 1 hour find his loading speed per hour
Answer:
9 trucks/hour
Step-by-step explanation:
If he loaded 9 trucks in one hour, his loading speed is 9 trucks per hour.
Xin is going to invest in an account paying an interest rate of 5.8% compounded annually. How much would Xin need to invest, to the nearest hundred dollars, for the value of the account to reach $2,290 in 16 years?
The amount that should be invested in order to have $2,290 in 16 years is $929.11.
What is compound interest?
The interest on a deposit calculated using both the initial principle and the accrued interest from prior periods is known as compound interest. In other words, compound interest is interest that is earned on interest.
Here, we have
Given: Xin will invest in an account paying an interest rate of 5.8% compounded annually.
Amount to invest = Future value / (1 + r)ᵗ
Where:
r = interest rate
t = time
X = $2,290 / (1 + 0.058)¹⁶
X = 2,290 / 2.46474
X = $929.11
Hence, the amount that should be invested in order to have $2,290 in 16 years is $929.11.
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A car travels 55 mph and passes a truck travelling 50 mph. How long will it take the car to be
more than 23 mi ahead?
Answer:you never asked for like in what minutes or hours?
Step-by-step explanation:
The car, traveling at a speed 5 mph faster than the truck, will take more than 4.6 hours to be more than 23 miles ahead.
Explanation:This question pertains to relative speed. When the car is traveling at 55 mph and the truck at 50 mph, the car is effectively moving away from the truck at (55 mph - 50 mph) = 5 mph. To calculate the time it will take for the car to be more than 23 miles ahead, we can use the formula: Time = Distance/Speed. So the time it would take is Time = 23 miles / 5 mph = 4.6 hours. Therefore, it will take the car more than 4.6 hours to be more than 23 miles ahead.
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2. What is the equation of the parabola that passes
through the points (-1,0), (7, 0) and (3,-16)?
3. What is the equation of the parabola that passes
through the points (-4,9), (-3, 2) and (0,-7) and (4,9)?
The equations of the parabolas are y = x² - 6x - 7 and y = x² - 7
How to determine the equation of the parabolasParabola 1
Given that
The points (-1,0), (7, 0) and (3,-16)
The equation is represented as
y = ax² + bx + c
So, we have
a - b + c = 0
49a + 7b + c = 0
9a + 3b + c = -16
Make c the subject in a - b + c = 0
c = b - a
So, we have
49a + 7b + b - a = 0
9a + 3b + b - a = -16
48a + 8b = 0
8a + 4b = -16
Multiply 8a + 4b = -16 by 2
48a + 8b = 0
16a + 8b = -32
Subtract
32a = 32
So, we have
a = 1
Recall that 48a + 8b = 0
So, we have
48 + 8b = 0
This gives
8b = -48
Divide
b = -6
Also, we have
c = b - a
This gives
c = -6 - 1
c = -7
So, the equation is
y = x² - 6x - 7
Parabola 2
Given that
The points (-4,9), (-3, 2) and (0,-7) and (4,9)
The equation is represented as
y = ax² + bx + c
So, we have
16a - 4b + c = 9
9a - 3b + c = 2
c = -7
16a + 4b + c = 9
The equations become
16a - 4b = 16
9a - 3b = 9
16a + 4b = 16
Add (1) and (3)
32a = 32
So, we have
a = 1
Subtract (1) and (3)
-8b = 0
So, we have
b = 0
So, the equation is
y = x² - 7
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Need help on algebra please
Answer:
Step-by-step explanation:
The value of a motorcycle changes according to the equation V=5,000(1.03)t^, where V= value in dollars and t= time in years.
Use the dropdowns to complete the statements.
In the equation, the number 5,000 represents the ________ of the motorcycle. The value of the motorcycle is __________ at a rate of ________ per year.
In the equation, the number 5,000 represents the initial value of the motorcycle. The value of the motorcycle is increasing at a rate of 3% per year.
What are Exponential Functions?Exponential functions are functions where the independent variable, x is in the exponent.
The given exponential equation is,
V = 5,000 (1.03)^t
Here V represents the value of the motorcycle in t years.
When t = 0,
V = 5000 (1.03)⁰ = 5000
So 5000 represents the initial value of the motorcycle.
V = 5,000 (1 + 0.03)^t
At t = 0, V = 5000
At t = 1, V = 5000 (1.03)¹ = 5150
At t = 2, V = 5000 (1.03)² = 5304.5
So the value of the motorcycle is increasing.
The rate is 0.03 or 3%.
Hence, 5,000 represents the initial value of the motorcycle and the value of the motorcycle is increasing at a rate of 3% per year.
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Timothy, Laurence and Mike went to a bookstore to buy some books. The ratio of the number of books bought by Laurence and Mike were 2: 7. Timothy and Laurence bought a total of 20 books while Timothy and Mike bought a total of 35 books. How many books did Timothy buy?
Answer:
[tex]\mbox{\large \textsf{Timothy bought 14 books}}[/tex]
Step-by-step explanation:
Let's use first letters of names to represent the number of books bought by that person. This makes it easier to explain.
Therefore, the books bought by each of the three persons are T(imothy), L(aurence) and M(ike)
We will now convert each of the word description into math equations and solve
We are given that the ratio of the number of books bought by Laurence and Mike were 2: 7
We can write this as:
[tex]\dfrac{L}{M} = \dfrac{2}{7}\\\\[/tex]
Multiplying both sides by M:
[tex]L = \dfrac{2}{7}M\cdots\cdots(1)[/tex]
Timothy and Laurence bought a total of 20 books can be represented as
[tex]T + L = 20\cdots\cdots(2)[/tex]
Timothy and Mike bought a total of 35 books can be represented as
[tex]T + M = 35\cdots\cdots(3)[/tex]
Eq (3) - Eq (2):
[tex]T + M - (T + L) = 35 - 20\\\\T + M - T - L = 15\\\\M - L = 15 \cdots\cdots (4)[/tex]
Substituting for [tex]\displaystyle L = \frac{2}{7}M[/tex] from equation (1) into equation (4) we get
[tex]M - \dfrac{2}{7}M = 15\\\\\dfrac{5}{7}M = 15\\\\M = \dfrac{7}{5} \times 15\\\\M = 21\\\\[/tex]
Given [tex]\displaystyle M = 21[/tex] using equation (3), [tex]\displaystyle T + M = 35[/tex] we get
[tex]T + 21 = 35\\\\T = 35 - 21\\\\\textrm{or}\\\\T = 14[/tex](Answer)
If we wanted to find out how many books Laurence bought use Eq(1)
[tex]L = \dfrac{2}{7}M\\\\L = \dfrac{2}{7} \times 21\\\\L = 6\\\\[/tex]
A positive integer is twice another. The difference of the reciprocals of the two positive integers is frac(1,10). Find the two integers.
The two integers are 5 and 10.
What do you mean by Integers?
An integer is a number with no decimal or fractional part and it includes negative and positive numbers, including zero.
Integer is a Latin word which means 'whole' or 'intact'. This means integers do not include fractions or decimals.
A number is positive if it is greater than zero, so it said to be positive integers
A number is negative if it is less than zero, so it said to be negative integers.
A number line is a visual representation of numbers on a straight line. This line is used for the comparison of numbers that are placed at equal intervals on an infinite line that extends on both sides, horizontally.
Given:
Let x be the positive number
2x be the other positive number
Find the first integer
[tex]\frac{1}{x} - \frac{1}{2x} = \frac{1}{10}[/tex]
[tex]\frac{2x - x}{2x^2} = \frac{1}{10}[/tex]
[tex]\frac{x}{2x^2} = \frac{1}{10}[/tex]
[tex]\frac{1}{2x} = \frac{1}{10}[/tex]
2x = 10
x = 5
Therefore, the first positive integer is 5.
Find the other integer
2x = 2(5) = 10
Therefore, the other integer is 10.
To check:
[tex]\frac{1}{x} - \frac{1}{2x} = \frac{1}{10}[/tex]
[tex]\frac{1}{5} - \frac{1}{10} = \frac{1}{10}[/tex]
[tex]\frac{2}{10} - \frac{1}{10} = \frac{1}{10}[/tex]
[tex]\frac{1}{10} = \frac{1}{10}[/tex]
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Counting back from 18, what number follows 17?
Answer:
16
Step-by-step explanation:
As the question states, we are counting downwards which means with every interval we are going back -1. Therefore, 17 - 1 = 16
An electric clock is stopped by a power failure. What is the probability that the second hand is stopped between the 4 and the 9?
Answer: the answer is 5/12
Can someone please help me do this
The vertices of the image of triangle ABC are A''(x, y) = (- 6, 8), B''(x, y) = (- 8, 4) and C''(x, y) = (- 4, 4).
How to determine the image of a triangle set on Cartesian plane
Any triangle can be generated by three points that are not collinear, in this problem we need to determine the image of a triangle, which is the result of two rigid transformations: (i) Reflection over the y-axis, (ii) Dilation centered at the origin with a scale factor of 2, whose definitions are shown below:
Reflection over the y-axis:
(x, y) → (- x, y)
Dilation centered at the origin with a scale factor of 2:
(x, y) → (2 · x, 2 · y)
If we know that A(x, y) = (3, 4), B(x, y) = (4, 2), C(x, y) = (2, 2), then the image of the vertices are determined below:
Reflection over the y-axis
A'(x, y) = (- 3, 4), B'(x, y) = (- 4, 2), C'(x, y) = (- 2, 2)
Dilation centered at the origin with a scale factor of 2
A''(x, y) = (- 6, 8), B''(x, y) = (- 8, 4), C''(x, y) = (- 4, 4)
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If the scale factor of figure A to figure B is 3:8 find x
x^{2}-2x+ and completing the square ( Algebra 2 )
x^2 - 2x + 1 is the required quadratic equation using the completing the square
Perfect square trinomials using the completing the square
Given the quadratic expression below
x^2 - 2x
We need to determine the constant that will make the expression a perfect square.
The constant will be the half of the square of coefficient of 'x'
Coefficient of 'x' = -2
Half of the coefficient of 'x' = -2/2 = -1
Square of the coefficient = (-2/2)^2
Square of the coefficient = 1
Hence the complete quadratic expression using the completing the square is x^2 - 2x + 1
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A candle is burning. It starts out 12 inches long. After 1 hour, it is 10 inches long. After 3 hours, it is 5.5 inches
1. Explain one reason why it might be reasonable to model the relationship between time and height of the candle with a linear function.
2. Explain one reason it might NOT be reasonable to model this relationship with a linear relationship
The reasons for (1) and (2) are added below
Why it is reasonable to use a linear functionOne reason why it might be reasonable to model the relationship between time and height of the candle with a linear function is that the rate of change of the candle's height appears to be constant over time.
Why it is unreasonableOne reason why it might NOT be reasonable to model this relationship with a linear function is that the candle's height cannot continue to decrease indefinitely.
This means that the candle's height is bounded and cannot continue to decrease linearly forever.
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