Write an equivalent expression by factoring for 6a + 15

To  find the center of dilation,We'll fix our compass to a distance that is closer to the overall distance but still greater than halfway between vertex L and point C. Start with the compass's point on vertex L while maintaining the same distance, and then draw a curve that intersects the line connecting L and C.

Centre of dilation  of an image in mathematics refers to a change that results in an image with the same shape but a different size, either larger or smaller. A dilation can only be built with two bits of information.

An operation that moves, flips, or otherwise alters a figure to produce a new figure is called a transformation. Rigid transformations maintain size, whereas non-rigid transformations do not. A dilatation enlarges or reduces a figure while maintaining its original shape. To put it another way, the dilatation resembles the original. Every dilatation has a scale factor and a centre. The scale factor indicates how much the figure stretches or contracts, and the centre serves as the point of reference for the dilation (much like the vanishing point in a perspective drawing). A scale factor is usually identified by a label and is never zero. Additionally, the dilatation would be if the original figure were labelled, for example.

The point from which the image is dilated is known as the centre of dilatation (or point of dilation).

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The maximum price per egg that the supermarket may charge is $0.245 per egg, which is the difference between the pricing per egg for the 2 distinct cartons.

The answer to the query is

The following details are available to us:

We'll first calculate the cost per egg for each of the two different-sized cartons in order to determine the cost per egg that lies between the two costs.

We are aware that the cost of one product is determined by dividing the total cost by the quantity of products.

The price of an egg between 0.24 as well as 0.25 must now be determined.

Note that there is a 0.01 difference between the two fees.

To precisely determine the middle charge, we will split it by two:

0.01/2 = 0.005

This can be added to $0.24 or subtracted from $0.25.

$0.24 + $0.005 = $0.245

So, $0.245 is the maximum price the supermarket can charge per egg.

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The complete question is-

A carton of 12 eggs costs $3.00. A carton of 18 eggs costs $4.32. Suppose a supermarket wants to sell the eggs individually. Is there a price the supermarket can charge per egg that is between the prices per egg for the two different-sized cartons? Explain

The general solution of the linear equation 3x + 2y = 5 is y = (-3/2)x + 5/2.

To find the solution of the linear equation 3x + 2y = 5, we can use the method of isolating one variable and then substituting that value back into the equation.

3x + 2y = 5

First we can try to isolate y:

2y = -3x + 5

then we divide by 2

y = -(3/2)x + 5/2

So one solution of the equation is (x,y) = (-(3/2)x + 5/2)

Therefore, the solution of the linear equation 3x + 2y = 5 is y = -(3/2)x + 5/2.

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The number of cubic yards of each component needed are 3.99 cubic yards of cement, 7.97 cubic yards of sand  and 15.94 cubic yards of gravel

Ratio is used to compare two or more quantities. It is used to indicate how big or small a quantity is when compared to another

Since a total of 18.6 cu yd of concrete is required and the total amount of these components must be 1½ times the volume of concrete needed. We can say:

total amount of these components = 1½ × 18.6 cu yd = 27.9 cu yd

Also, since the ratio of cement to sand to gravel for this application is 1:2:4. We have:

Total share = 1 + 2 + 4 = 7

cement = 1/7  × 27.9 =  3.99 cubic yards

sand  = 2/7  × 27.9 =  7.97 cubic yards

gravel = 4/7  × 27.9 =  15.94 cubic yards

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Answer:

Step-by-step explanation:

I will assume you want the y-axis intercepts

arrange each equation into the form  y = mx + b  <==b  is  y-axis intercept

2x+y =1

y = -2x+1    <====  y axis intercept = 1

x -2y = 8

2y = x-8

y = 1/2x -4       <====  - 4 is the y axis intercept

Another way to find the y-axis intercept is to realize this occurs when x = 0

  put x = 0 into the equations to find the intercept value

2x+y =1

2(0) + y = 1

y =1    <=====intercept

x-2y = 8

0 - 2y = 8

y = -4   <=====intercept

To find the where the two lines intersect, equate them

-2x+1 = 1/2x-4

5 = 2.5x

x = 2    then y = -2x+1 = -3      point of intersection (2,-3)

The points  (4.5,1.5), (0.5, – 1.5), and (1.5, – 2.5) have been graphed on the coordinate plane (Refer to the graph attached below.)

The Cartesian coordinate system on a plane is a system of coordinates that uniquely identifies each point by a pair of numerical coordinates.

These numerical coordinates are the signed distances from two fixed perpendicular oriented lines to the point, measured in the same unit of length.

A graph having one x-axis and one y-axis is referred to as a cartesian plane (also known as an X-Y graph).

The orientation of these two axes is perpendicular.

The graph's exact center is marked by the origin (O).

So, we have the points:

(4.5,1.5), (0.5, – 1.5), and (1.5, – 2.5)

Now, the graph is as follows:

(Refer to the graph attached below)

Therefore, the points  (4.5,1.5), (0.5, – 1.5), and (1.5, – 2.5) have been graphed on the coordinate plane (Refer to the graph attached below.)

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Answer:A,D,E,F

Step-by-step explanation:A(x) = x4 - 2x³ - 21x² +22x + 40= A,D,E,F

The new coordinates of the point in the transformed shape would be (-1/2x, -1/2y).

A point is transformed when it is moved from where it was originally to a new location. Translation, rotation, reflection, and dilation are examples of different transformations.

A scale factor of -1/2 around the center point (0,0) would reflect the shape across the origin and also shrink it by a factor of 1/2.

The transformation can be represented by the matrix:

[-1/2 0]

[ 0 -1/2]

This matrix would be applied to the coordinates of each point in the shape to obtain the new coordinates of the transformed shape.

So, if a point in the shape had coordinates (x, y), the new coordinates of the point in the transformed shape would be (-1/2x, -1/2y).

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The question seems to be incomplete the correct question would be:

Enlarge shape q by a scale factor of -1/2 around the center point (0,0). if a point in the shape had coordinates (x, y), what are the new coordinates?

Answer:

DC = 99

Step-by-step explanation:

BD perpendicular AC

AD/BD = BD/DC

=> DC =DB^2/AD

         =33^2/11=99

{calculate}

In mathematics, an algebraic expression is an assertion built up from integer constants, variables, and algebraic operations. This article is all about to Monomials, Binomials, and Polynomials.

1. Monomial

An algebraic expression that carries only one non-zero term is known as a monomial. A monomial is a just like a type of polynomial, like, binomial and trinomial, which is an algebraic expression having only a one single term, which is a non-zero.

It comprises of only a single term which makes it easy to do the operation of addition, subtraction, and multiplication.

2. Binomial

An algebraic expression that comprises of two non-zero terms is known as a binomial. It is expressed in the form equation ax ^m + bx ^n where a and b number, x is variable, m and n are nonnegative distinct integers.

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A relation R  is a subset of the Cartesian product. Or simply, a bunch of points (ordered pairs). In other words, the relation between the two sets is defined as the collection of the ordered pair, in which the ordered pair is formed by the object from each set.

a group of some elements of the input set which are passed to a function to obtain some elements of the output set. It is the inverse of the Image. It is denoted as;

f: X → Y.

N be the set of Natural numbers and the relation R be defined as;

R = {(a ,b) : b=a2, a ,b ∈ N}. State whether R is a relation function or not.

From the relation R = {(a ,b) : b=a2, a ,b ∈ N}, we can see for every value of natural number, their is only one image. For example, if a=1 then b =1, if a=2 then b=4 and so on.

Therefore, R is a relation function here.

f:A→B, and D⊆B, the preimage  D of under  f is defined as

[tex]f^-1[/tex](D)={x ∈ A∣ f(x)∈D}.(5.4.5)

Hence, [tex]f^-1[/tex](D) is the set of elements in the domain whose images are in C. The symbol [tex]f^-1[/tex](D) is also pronounced as “f inverse of D.”

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The ratio to describe the number of jeans shared by Hallie and Mattie is obtained as 2 : 3.

The ratio of two numbers a and b can be written as a : b = a/b.

The ratio of two quantities is the unit rate of one quantity with respect to the other.

Here,

The number of jeans donated by Hallie and Mattie are given as 4 and 6 respectively.

It can be written in terms of ratio as 4 : 6.

It can be simplified as,

⇒ 4 : 6

⇒ 4/6

⇒2/3

⇒ 2 : 3

Hence, the number of jeans donated can be written in terms of ratio as 2 : 3.

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Answer:

A and B

Step-by-step explanation:

theres one input for each ouput

An exponential function is a mathematical function of the form f(x) = a×bˣ, where a and b are constants and x is the input variable. To find the exponential function of a data set, you can use the method of least squares.

This method finds the best-fitting exponential function for a given set of data points by minimizing the sum of the squares of the differences between the data points and the function.

The first step in finding the exponential function of a data set is to plot the data points on a graph. Next, you need to re-arrange the exponential function into the form y = a×bˣ, where y is the dependent variable and x is the independent variable.

Then you can use the method of least squares to find the values of a and b that best fit the data. The value of a represents the y-intercept of the function, and the value of b represents the growth rate or decay rate of the function.

Once you have found the values of a and b, you can use the exponential function to make predictions about the data set. It is also possible to use software packages like R or Python to do this process.

In conclusion, finding the exponential function of a data set involves using the method of least squares to find the best-fitting exponential function for a given set of data points.

This is typically done by plotting the data points, re-arranging the exponential function, and using the method of least squares to find the values of a and b that best fit the data. The function can then be used to make predictions about the data set.

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Answer:

Step-by-step explanation:

In conclusion, it can be argued that Abby Sunderland was too young to sail solo. Despite her ambitious and determined nature, her lack of experience and maturity put her at a significant risk during her solo sailing journey. The fact that she had to be rescued twice during her attempt highlights the dangers of attempting such a feat at such a young age. While it is admirable to have the courage to pursue one's dreams, it is important to consider the potential consequences and weigh them against the potential benefits. In this case, it can be argued that the risks far outweighed the potential rewards.

The linear equation [ ( 2x PLUS y ) EQUALS 10 ] has only one solution.

A linear equation is an algebraic equation having the form y=mx+b, involving only a constant and a first-order (linear) term, where b is the y-intercept and m is the slope. Occasionally, the above is called a 'linear equation of two variables,' where x and y are the variables.

Now solve the given linear equation which is:

[ ( 2x + y ) = 10  ]

Now solve this equation in order to determine the number of solutions it has,

( 2x + y ) = 10

( 2x + (10 - 2x)) = 10

( 2x + 10 - 2x) = 10

( 2x + 10 - 2x) = 10

(10) = (10)

Since 10 = 10 is correct, therefore, the equation  ( 2x + y ) = 10 has only one solution.

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The Correct answer is option a. 7-9.42, P-value = 0.002 which is derived based on the given data about alcohol consumption.

The chi-square test of homogeneity is a statistical test used to determine whether there is a significant difference between the observed frequencies of two categorical variables.

In this case, the test statistic would be the chi-square value calculated using the observed frequencies of alcohol consumption in the sample of smokers and non-smokers, and the P-value would be the probability of obtaining a chi-square value as extreme or more extreme than the calculated value under the assumption that the null hypothesis is true (i.e. no difference in alcohol consumption between smokers and non-smokers).

In this case, the test statistic would be 7.942 and the P-value would be 0.002 which implies that there is a significant difference in alcohol consumption between smokers and non-smokers.

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Rose gets 12 refills by a coffee shop.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

A coffee shop sells a mug for $8.95. Each refill costs $1.50.

And, Last month Rose spent $26.75 on a mug and refills.

Let number of refills she get = x

So, We can formulate;

⇒ $8.95 + $1.50x = $26.75

⇒ 8.95 + 1.50x = 26.75

⇒ 1.50x = 26.75 - 8.95

⇒ 1.50x = 17.80

⇒ x = 17.8 / 1.5

⇒ x = 12

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The distance between the line and the point is 8 units.

When two parallel lines intersect, a two-dimensional coordinate plane called the cartesian plane is created. The horizontal line is the X-axis, while the vertical line is the Y-axis. If the sign of x is positive, the coordinate point (x, y) in the Cartesian plane indicates that the point is on the right of the origin; otherwise, it indicates that the position is on the left of the origin.

Given a line L,

and the equation of a line is y = 1

actual equation of line is ax + by +c = 0

equation of line is 0x + y - 1 = 0

here a = 0, b = 1 and c = -1

and point T(-1, -7)

distance between line and the point is d = [tex]\frac{|ax_1 + by_1 + c|}{\sqrt{a^2 + b^2} }[/tex]

x₁ = -1, y₁ = -7

|ax₁ + by₁ + c| = |0(-1) + 1(-7)  +(-1)|

|ax₁ + by₁ + c| = 8

√(a² + b²) = √(0² + (1)²) = 1

distance between line and the point is d = 8/1 = 8 units

Hence the distance is 8 units.

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Answer:

3 small postcards; 4 large postcards

I know this. Hope it helps :)

Answer:

4 large post cards and 3 small ones

Exponents can be classified into four types: integer, rational, irrational, and complex exponents. They represent repeated multiplication, roots, and advanced concepts such as complex numbers.

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Answer:

-4x

Step-by-step explanation:

3-7=-4 just add a x

The probability that this dancer raised less than £10 is; 19/30

Probability is defined as the number of successful outcomes divided by the total number of outcomes. Thus;

Probability = number of successful outcomes/total number of outcomes

From the attached table, we see that;

£4.99 of less: Number of dancers are 15

£5 to £9.99: Number of dancers are 23

£10 to £14.99: Number of dancers are 12

£15 to £19.99: Number of dancers are 7

£20 to £24.99: Number of dancers are 3

Thus, we see that the total number of dancers = 15 + 23 + 12 + 7 + 3 = 60 dancers.

If a dancer is chosen at random, the probability that the dancer raised less than £10 = (23 + 15)/60 = 38/60 = 19/30

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Complete question is;

A group of dancers raised some money for a charity here is some information about the money raised

One of the dancers is chosen at random to give the money raised to the charity

What is the probability that this dancer raised less then £10

Answer:

ez

Step-by-step explanation:

(x,y)=(16/185,-2/185)

Answer:

50 km : 12 km

Step-by-step explanation:

600 km : 12 km

=50 km : 1 km.

First step in finding the percent markdown is to find the percentage change in sales price.

In order to find the percentage change in sales price, use the percent change equation.

(New - Old)/(Old) * 100 = % Change

Now input 141.27 for the New price and 175.80 for the Old price.

(141.27 - 175.80)/(175.80) * 100 = % Change

-34.53/175.80 * 100 = % Change

-0.2* 100 = % Change

20 = % Change

Hence, the percentage change in sales price is 20%

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Answer:

i need more information to answer your question

Step-by-step explanation:

Answer: 21d^7

Step-by-step explanation:(7x3) x d^(5+2)
= 21 d^7

Answer:

(7d^5)(3d^2)

7*3 = 21

5+2 = 7

21d^7

The number of small sized bowls on the counter = 68 bowls

The number of medium sized bowls on the counter = 82 bowls

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

From the data given,

Let the number of small bowls on the counter be = x

Let the number of medium bowls on the counter be = y

The total number of bowls is = 150

So , the equation will be

x + y = 150   be equation (1)

The amount the small bowl can hold = 4 ounces

The amount the medium bowl can hold = 6 ounces

The total amount of all the bowls on the counter = 764 ounces

So , the equation will be

4x + 6y = 764   be equation (2)

Now , on simplifying the equation (1) and equation (2) ,

Multiply equation (1) by 4 , we get

4x + 4y = 600   be equation (3)

Subtracting equation (3) from equation (2) , we get

2y = 164

Divide by 2 on both sides , we get

y = 82

Therefore the number of medium sized bowl is 82 bowls

Substituting the value of y in equation (1) , we get

x + y = 150

x + 82 = 150

Subtracting 82 on both sides , we get

x = 68

Therefore , the number of small sized bowl is 68 bowls

Hence,

The number of small sized bowls on the counter = 68 bowls

The number of medium sized bowls on the counter = 82 bowls

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