What is the image of (0, 4) after a dilation by a scale factor of 3 centered at the
origin?

the first question answer is 15/17

Step-by-step explanation:

Using the formula V = Pe^(rt), we have:

P = $741

r = 0.058 (since the interest rate is 5.8%)

t = 13

So, V = 741e^(0.05813) = $1613.87 (rounded to the nearest cent)

Therefore, the amount of money in the account after 13 years is $1613.87.

Answer:

Step-by-step explanation:

The solution to the given rational expressions is (z - 2)/(z^(2)+4z-12).

To subtract rational expressions with common denominators, we simply subtract the numerators and keep the same denominator.

In this case, our common denominator is (z^(2)+4z-12),  so we can subtract/add the numerators:

So, we will subtract the numerators, (z) - (2), and keep the same denominator:
(z)/(z^(2)+4z-12)-(2)/(z^(2)+4z-12) = (z - 2)/(z^(2)+4z-12)

Now, we can simplify the numerator by combining like terms:
(z - 2)/(z^(2)+4z-12) = (z - 2)/(z^(2)+4z-12)

Since the numerator and denominator cannot be simplified any further, this is our final answer:
(z - 2)/(z^(2)+4z-12)

Therefore, the solution to the subtraction of the given rational expressions is (z - 2)/(z^(2)+4z-12).

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Answer:

Step-by-step explanation:

you have 22 bucks and your mom took 2

22-2=20

My Answer:

22-2= 20, right? She can't drink anymore wine if you (shown as "i") used the remaining 20$. Tell me if this makes sense. No wine (none) is consumed if you have no money left.

Answer from Artificial Intellegence (to get another view on the question so you can figure out the best answer):

If you had 22 bucks and your mom took 2 dollars for her weekly wine tasting, you would have 20 dollars left. If you have 0 dollars left, this means your mom spent all of the remaining 20 dollars on wine. Assuming each wine bottle costs the same, we can divide the remaining 20 dollars by the cost of one wine bottle to find how many wine bottles your mom bought for her weekly wine tasting. Without knowing the exact cost of one wine bottle, we can't determine the exact number of wine bottles your mom drank.

Answer:

[tex](5x-1)(x+4)[/tex]

Step-by-step explanation:

Given:

[tex]5x^2 +19x-4[/tex]

Factor the expression by grouping. First, the expression needs to be rewritten as [tex]5x^2 +ax+bx-4[/tex]. To find a and b, set up a system to be solved.

[tex]a+b=19[/tex]

[tex]ab=5(-4)=-20[/tex]

Since [tex]ab[/tex] is negative, a and b have the opposite signs. Since [tex]a+b[/tex] is positive, the positive number has greater absolute value than the negative. List all such integer pairs that give product [tex]-20[/tex].

[tex]-1,20[/tex]

[tex]-2,10[/tex]

[tex]-4,5[/tex]

Calculate the sum for each pair.

[tex]-1+20=19[/tex]

[tex]-2+10=8[/tex]

[tex]-4+5=1[/tex]

The solution is the pair that gives sum [tex]19[/tex].

[tex]a=-1[/tex]

[tex]b=20[/tex]

Rewrite [tex]5x^2+19x-4[/tex] as [tex](5x^2-x)+(20x-4)[/tex].

Factor out x in the first and 4 in the second group.

[tex]x(5x-1)+4(5x-1)[/tex]

Factor out common term [tex]5x-1[/tex] by using distributive property.

[tex](5x-1)(x+4)[/tex]

Therefore, [tex](5x-1)(x+4)[/tex].

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Answer:

Step-by-step explanation:

I'm guessing you need the volume of the bead with the hole.

We need to get the volume of two objects; a cube and a cylinder. We need the cylinder for the hole.

V(square) = 6^3

V(square) = 216 mm^3

V(cylinder) = pi(r^2)(h)

pi(1.5^2)(6)

Radius is half the diameter, and 6 represents the height, since it's as long as the cube.

V(cylinder) = 42.41 or 13.5pi

We need to do V(s) - V(c) to find the volume of the bead.

216 - 13.5pi = 173.588 or 173.59 or 173.6

I hope this helps!

The approximate area of Central Park is about 450 square blocks.

The given dimensions of the park stated in the question are

Length of Central Park = 50 blocks

Width of Central Park = 9 blocks

The approximate area of Central Park is the product of its length and width:

So, we have

Area of Central Park = Length x Width

When the given values are substituted into the the equation mentioned above, we obtain the subsequent expression

Area = 50 * 9

Evaluate

Area = 450

Hence, the approximate area is about 450 square blocks.

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An ellipse has an equation equal to 9x^2-144x+16y^2+96y+495=0, the eccentricity of the curve is √7/4.

To compute the eccentricity of the curve of an ellipse, we must first complete the square for both x and y terms to put the equation in standard form.

Complete the square for x terms:
9x²- 144x + 495 = -16y² - 96y
9(x² - 16x) + 495 = -16(y² + 6y)
9(x²- 16x + 64) + 495 - 9(64) = -16(y² + 6y)
9(x - 8)² + 39 = -16(y² + 6y)

Complete the square for y terms:
9(x - 8)² + 39 = -16(y² + 6y)
9(x - 8)² + 39 = -16(y² + 6y + 9) + 16(9)
9(x - 8)² + 39 - 16(9) = -16(y + 3)²
9(x - 8)² - 105 = -16(y + 3)²

Move constant term to the right side of the equation and divide by -105:
9(x - 8)² - 16(y + 3)² = 105
-9(x - 8)²/105 + 16(y + 3)²/105 = 1
(x - 8)²/(105/9) + (y + 3)²/(105/16) = 1

Identify the values of a^2 and b^2:
a² = 105/9
b² = 105/16

Compute the eccentricity using the formula e = √(1 - (b²/a²)):
e = √(1 - ((105/16)/(105/9)))
e = √(1 - (9/16))
e = √(7/16)
e = √7/4

Therefore, the eccentricity of the curve is √7/4.

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The sequence of transformations that maps DOG to D'O'G' is a rotation of about 90 degrees of the origin, followed by a translation of 5 units right.

Rotation is a physical phenomenon where an object spins around an axis. It is a type of circular motion where an object moves in a circular path around a central point.

To accomplish this transformation, first, the point representing the letter D is rotated 90 degrees clockwise around the origin so that it is now pointing in the same direction as the letter O. After that, the point representing the letter D is translated 5 units to the right, resulting in the final transformation of DOG to D'O'G'.

Thus, the sequence of transformations that maps DOG to D'O'G' is a rotation of about 90 degrees of the origin, followed by a translation of 5 units right.

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1) the probability that all three of them hit the target is 3/10,  none of them hit the target 1/40, only John hits the target 3/40, 2) a red marble is chosen from plastic X is 2/9, a white marble is chosen from plastic Y is 4/15, a red marble is chosen is 2/9,  a marble is chosen from plastic Y if it is known that it is red is 2/5.

1. a) The probability that all three of them hit the target is the product of their individual probabilities:
P(all three hit the target) = P(John hits the target) × P(Sam hits the target) × P(Grey hits the target)
= (3/4) × (1/2) × (4/5)
= 12/40
= 3/10

b) The probability that none of them hit the target is the product of their individual probabilities of not hitting the target:
P(none hit the target) = P(John doesn't hit the target) × P(Sam doesn't hit the target) × P(Grey doesn't hit the target)
= (1 - 3/4) × (1 - 1/2) × (1 - 4/5)
= (1/4) × (1/2) × (1/5)
= 1/40

c) The probability that only John hits the target is the product of his probability of hitting the target and the other two's probabilities of not hitting the target:
P(only John hits the target) = P(John hits the target) × P(Sam doesn't hit the target) × P(Grey doesn't hit the target)
= (3/4) × (1 - 1/2) × (1 - 4/5)
= (3/4) × (1/2) × (1/5)
= 3/40

2. The tree diagram for this game is as follows:

       Die
      /   \
     /     \
    /       \
   /         \
  /           \
 /             \
<3             >=3
/ \           / \
X   Y         X   Y
/ \ / \       / \ / \
R W R W      R W R W

a) The probability that a red marble is chosen from plastic X is the product of the probability of the die outcome being less than 3 and the probability of choosing a red marble from plastic X:
P(red from X) = P(die < 3) × P(red from X)
= (2/6) × (4/6)
= 8/36
= 2/9

b) The probability that a white marble is chosen from plastic Y is the product of the probability of the die outcome being greater than or equal to 3 and the probability of choosing a white marble from plastic Y:
P(white from Y) = P(die >= 3) × P(white from Y)
= (4/6) × (2/5)
= 8/30
= 4/15

c) The probability that a red marble is chosen is the sum of the probabilities of choosing a red marble from plastic X and from plastic Y:
P(red) = P(red from X) + P(red from Y)
= (2/9) + (4/15)
= 10/45
= 2/9

d) The probability that a marble is chosen from plastic Y if it is known that it is red is the probability of choosing a red marble from plastic Y divided by the probability of choosing a red marble:
P(Y | red) = P(red from Y) / P(red)
= (4/15) / (2/9)
= 12/30
= 2/5

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There is no solution to this problem.

To find the three consecutive odd integers, we need to use algebra. Let's first represent the three consecutive odd integers as x, x+2, and x+4. Then we can set up an equation based on the given information:

(x+2)(x+4) - (x)(x+2) = 34

Simplifying the equation gives:

x^2 + 6x + 8 - x^2 - 2x = 34

Combining like terms gives:

4x + 8 = 34

Subtracting 8 from both sides gives:

4x = 26

Dividing by 4 gives:

x = 6.5

However, since we are looking for odd integers, there is no solution to this problem. Therefore, the answer is NO SOLUTION.

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There are three types of triangle according to sides and angles each.

The triangle is a type of polygon having three sides, angles and vertices.

Classification of triangles :-

Based on sides :-

1) Scalene triangle :- A triangle with all different measurements of sides and angles are called a Scalene triangle.

2) Isosceles triangle :- A triangle with two of the sides and angles are congruent called an Isosceles triangle.

3) Equilateral triangles :- A triangle with all the same measurements of sides and angles is called an Equilateral triangle.

Based on angles :-

1) Acute angled triangle :- A triangle with all the angles less than 90°, are called acute angled triangle.

2) Obtuse angled triangle :- A triangle with all the angles greater than 90° and less than 180°, are called Obtuse angled triangle.

3) Right angled triangle :- A triangle with one angle equals 90° is called a Right angled triangle.

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The Quick Meals Diner served 131 child plates and 157 adult plates.

Let's use a system of two equations to represent the given information:

c + a = 288     (1)   // The number of child and adult plates served add up to 288

2.5c + 8.2a = 1614.9   (2)   // The total amount collected is the sum of the prices of all plates served

where c represents the number of child plates served and a represents the number of adult plates served.

We can use equation (1) to solve for c in terms of a:

c = 288 - a

Substituting this expression for c into equation (2), we get:

2.5(288 - a) + 8.2a = 1614.9

720 - 2.5a + 8.2a = 1614.9

5.7a = 894.9

a = 157

So, 157 adult plates were served. Substituting this value into equation (1), we get:

So, 157 adult plates were served. Substituting this value into equation (1), we get:

So, 131 child plates were served.

Therefore, The result is 131 child plates and 157 adult plates.

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The product of ((4)/(3)x-6) and ((5)/(6)x+(5)/(3)) as a trinomial in simplest form is (10/9)x^2 + (-10/9)x + (-10).

To express the product of ((4)/(3)x-6) and ((5)/(6)x+(5)/(3)) as a trinomial in simplest form, we need to multiply the two expressions together and then simplify. Here are the steps:

1. Distribute the first term of the first expression to the second expression: (4/3)x * (5/6)x + (4/3)x * (5/3) = (20/18)x^2 + (20/9)x
2. Distribute the second term of the first expression to the second expression: -6 * (5/6)x + -6 * (5/3) = (-30/6)x + (-30/3)
3. Combine the like terms: (20/18)x^2 + (20/9)x + (-30/6)x + (-30/3) = (20/18)x^2 + (-10/9)x + (-30/3)
4. Simplify the fractions: (10/9)x^2 + (-10/9)x + (-10)

So the product of ((4)/(3)x-6) and ((5)/(6)x+(5)/(3)) as a trinomial in simplest form is (10/9)x^2 + (-10/9)x + (-10).

The product of ((4)/(3)x-6) and ((5)/(6)x+(5)/(3)) as a trinomial in simplest form is (10/9)x^2 + (-10/9)x + (-10).

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Answer:

12

Step-by-step explanation:

Its easy and right

Answer:

2

Step-by-step explanation:

For 4 and 6, the common factors are 1 and 2. Since 2 is the highest among the given factors, HCF will be 2 for 4 and 6.

Answer:

it’s 159 sorry

Step-by-step explanation:

10 to the second power is 10x10 which is 100 then 8 to the second power is 8x8 which is 64. 164-5 is 159, I apologize.

The manufacturer should ship 0 refrigerators to warehouse A and 80 refrigerators to warehouse B to minimize costs. The minimum cost is $800.

The objective of the problem is to minimize the cost of shipping the refrigerators to the two warehouses while also meeting the requirements of shipping at least 100 refrigerators and hiring at least 300 workers. This can be formulated as a linear programming problem with the following decision variables:

x1 = the number of refrigerators shipped to warehouse A
x2 = the number of refrigerators shipped to warehouse B

The objective function is the total cost of shipping the refrigerators:

minimize 12x1 + 10x2

The constraints are the requirements of shipping at least 100 refrigerators, hiring at least 300 workers, and the maximum capacity of each warehouse:

x1 + x2 >= 100
4x1 + 2x2 >= 300
x1 <= 75 (100 - 25)
x2 <= 80 (100 - 20)

Using the graphical method, we can plot the constraints and find the feasible region. The optimal solution will be at one of the corner points of the feasible region.

After plotting the constraints and finding the feasible region, we can evaluate the objective function at each of the corner points to find the minimum cost. The corner points and their corresponding costs are:

(75, 0) -> 12(75) + 10(0) = $900
(0, 80) -> 12(0) + 10(80) = $800
(50, 100) -> 12(50) + 10(100) = $1700
(60, 90) -> 12(60) + 10(90) = $1740

The minimum cost is $800, which occurs when 0 refrigerators are shipped to warehouse A and 80 refrigerators are shipped to warehouse B.

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The answer of the given question based on the Equation is given the solution to the given equation is n = 21/4.

A quadratic equation is type of equation in an algebra that involves variable (usually represented by x) that  raised to the second power (i.e., squared). The general form of the quadratic equation are given,

[tex]ax^2+bx+c = 0[/tex]

The highest power of  variable is 2, hence , name "quadratic".

To solve this equation, we can start by simplifying each of the terms on both sides of the equation:

3n + √(n² + 8) + 3√(n² + 8) - √(n² + 8) = 8

Combining like terms, we get:

3n + 3√(n² + 8) = 8

Subtracting 3√(n² + 8) from both sides, we get:

3n = 8 - 3√(n² + 8)

Dividing both sides by 3, we get:

n = (8/3) - (√(n² + 8)/3)

Now, we can rearrange this equation to isolate the radical term on one side of the equation:

√(n² + 8)/3 = (8/3) - n

by Squaring both the sides of equation, we get:

n² + 8 = 64/9 - (16n/3) + n²

Simplifying this equation, we get:

16n/3 = 56/9

Dividing both sides by 16/3, we get:

n = 21/4

Therefore, the solution to the given equation is n = 21/4.

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Answer:50

Step-by-step explanation:5+5=10 and 5 groups of 10 is 50

Answer:30

Step-by-step explanation:

5x5=25

25+5

30

The formula holds for k + 1.

What is mathematical induction?

Mathematical induction is a method of mathematical proof used to establish the truth of a statement for an infinite set of values.

To prove the formula for every positive integer n:

3 + 11 + 19 + 27 + ... + (8n - 5) = n(4n - 1)

using mathematical induction, we need to show two things:

Step 1: Base Case

When n = 1, we have:

3 = 1(4(1) - 1)

Simplifying the right-hand side gives:

3 = 3

So the formula holds for n = 1.

Step 2: Inductive Step

Now assume that the formula holds for some positive integer k, which means:

3 + 11 + 19 + 27 + ... + (8k - 5) = k(4k - 1)

We need to show that the formula also holds for k + 1. That is, we need to show that:

3 + 11 + 19 + 27 + ... + (8(k+1) - 5) = (k+1)(4(k+1) - 1)

Starting with the left-hand side of this equation:

3 + 11 + 19 + 27 + ... + (8(k+1) - 5)

= (3 + 11 + 19 + 27 + ... + (8k - 5)) + (8(k+1) - 5) (by adding the next term)

= k(4k - 1) + (8k + 3) (by substituting the formula for k)

[tex]= 4k^2 - k + 8k + 3[/tex]

[tex]= 4k^2 + 7k + 3[/tex]

Now, we simplify the right-hand side of the equation:

(k+1)(4(k+1) - 1)

= (k+1)(4k + 3)

[tex]= 4k^2 + 7k + 3[/tex]

We can see that the left-hand side and the right-hand side are equal.

Hence, the formula holds for k + 1.

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Step-by-step explanation:

Toby's loan amount is $450 and the finance charge is $50 every two weeks. He rolls over the loan 4 times.

Total cost = $450 + ($50 x (1 + 4))

Total cost = $450 + ($50 x 5)

Total cost = $450 + $250

Total cost = $700

Therefore, the total cost of Toby's payday loan is $700.

Tabitha's loan amount is $300 and the finance charge is $40 every two weeks. She rolls over the loan 6 times.

Total cost = $300 + ($40 x (1 + 6))

Total cost = $300 + ($40 x 7)

Total cost = $300 + $280

Total cost = $580

Therefore, the total cost of Tabitha's payday loan is $580.

Sariah's loan amount is $500 and the finance charge is $45 every two weeks. She rolls over the loan 7 times.

Total cost = $500 + ($45 x (1 + 7))

Total cost = $500 + ($45 x 8)

Total cost = $500 + $360

Total cost = $860

Therefore, the total cost of Sariah's payday loan is $860

Answer:

#6.

Loan amount = $450

Finance charge = $50 every two weeks

Number of rollovers or renewals = 4

Total Cost = 450 + (50 x (1 + 4))

Total Cost = 450 + 250

Total Cost = $700

The total cost of Toby's loan is $700.

#7.

Loan amount = $300

Finance charge = $40 every two weeks

Number of rollovers or renewals = 6

Total Cost = 300 + (40 x (1 + 6))

Total Cost = 300 + 280

Total Cost = $580

The total cost of Tabitha's loan is $580.

#8.

Loan amount = $500

Finance charge = $45 every two weeks

Number of rollovers or renewals = 7

Total Cost = 500 + (45 x (1 + 7))

Total Cost = 500 + 360

Total Cost = $860

The total cost of Sariah's loan is $860.

Answer: x=6, y=8

Using elimination means that we eliminate one of the variables in both equations which help find out the other variable, which we then substitute to find the whole equation.

    3x-4y=-14

+   3x+2y=-2

=>-4y=-14

+   2y=-2

=>-2y=-16

=>y=8

So to find x,

3x-4(8)=-14

=3x=-14+32

=x=18/3 so x=6

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No, 5x^2+y=0 is not a direct variation.

Direct variation is a relationship between two variables, x and y, where y is directly proportional to x, meaning that as x increases, y increases in proportion to x, and as x decreases, y decreases in proportion to x.

The equation 5x^2+y=0 does not satisfy this relationship since y is not directly proportional to x. As x increases or decreases, y may change in a non-proportional manner due to the presence of the constant term.

An example of a direct variation equation is y = kx, where k is a constant. In this equation, y is directly proportional to x, with a constant of proportionality k.

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We can conclude that -

The exponential function is of the form -

f(x) = eˣ

Given is to write the exponential growth and exponential decay equation.

{ 1 } -

The general exponential growth equation is -

[tex]$f(x)=a(1+r)^{x}[/tex]

{ 2 } -

The general exponential decay equation is -

[tex]$\frac {dN}{dt}= -\lambda N[/tex]

Option {A} and option {E} represent the exponential decay. Option {B}, {E} and {D} represent exponential growth.

Therefore, we can conclude that -

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Throughout the hour, 70 percentage of customers add chocolate creamer to their coffee.

Find the proportion of consumers who selected chocolate creamer and add up all of the customers who visited throughout the hour to determine the appropriate percentage.

The number of clients who selected chocolate creamer is calculated by dividing the total number of customers by 100.

Here it is,

For one hour, the manager of a coffee shop counted the number of patrons who added vanilla or chocolate creamer to their coffee.

The question given is:

                         Vanilla      Chocolate    

Age 18 - 30            2               6

Age 30 +                4               8      

2 + 4 + 6 + 8 Equals 20 clients in this instance.

6 + 8 = 14 is the number of clients who select chocolate creamer.

Customers that used chocolate creamer made up: [14/20] / 100 = 70%

As a result, 70% of consumers at that time add chocolate creamer to their coffee.

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The complete question is:

The manager of a coffee shop recorded the number of customers who put vanilla creamer or chocolate creamer in their coffee during one hour and classified them by age. The results are shown in the table. Coffee Creamer. Vanilla. Chocolate. Age 18 to 30. 2, 6. Age 31 plus. 4, 8 What percentage of these customers put chocolate creamer in their coffee during this hour?

Answer:

70%

Step-by-step explanation:

i did the quiz lol

The point where the two lines come together (1,1). Hence, x = 1 and y = 1 are the answers to the system of equations.

Algebraically speaking, an equation is a statement that shows the equality of two mathematical expressions. For instance, the two equations 3x + 5 and 14, which are separated by the 'equal' sign, make up the equation 3x + 5 = 14.

The technique of solving a system of equations involves calculating the unknown variables while maintaining the equations balanced on both sides. We solve an equation system by identifying the value of the variable that makes the condition of all the provided equations true.

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The polynomial p(x) in the form p(x) = (x+1)q(x), where q(x) is a polynomial of degree n-1.

Algebraic expressions called polynomials include coefficients and variables. Indeterminates are another name for variables. For polynomial expressions, we can do mathematical operations like addition, subtraction, multiplication, and positive integer exponents but not division by variables.

x2+x-12 is an illustration of a polynomial with a single variable. There are three terms in this example: x2, x, and -12.

Since we know that p(-1)=0, we can use this information to substitute -1 into p(x), giving us:

p(-1) = 0

We can then rearrange this equation to get:

0 = p(-1) = (x+1)q(x)  

This gives us the form of p(x) that we are looking for:

p(x) = (x+1)q(x)

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