What is the scale factor of the dilation triangle ABC was dilated?

Initial value of the linear function through A and B is 3.

The starting output value, or the y-value when x = 0, is the initial value. The rate of change is the rate at which the input or, in the case of a graph, the rate at which y changes in relation to x. A function's starting value in mathematics denotes the function's y-intercept. The constant in an equation can also be used to determine initial values. In graph functions, understanding the y-intercept is beneficial. By substituting 0 0 for x x and finding y y, you may verify the starting value.

Given,

Points

A (1,3)

B (6,13)

Linear function,

f(x) = ax + b

Equating,

f(x) = x + 3

Let x = 0

f(x) = 3

As we know,

The graph of a linear function is a straight line. The following is the form of a linear function. a + bx = y = f(x). One independent variable and one dependent variable make up a linear function. X and Y are the independent and dependent variables, respectively.

Initial value of the linear function through A and B is 3.

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Answer: 12 3/5

Step-by-step explanation:

1 3/4 x 7 1/5 = 12.6= 12 3/5

For the number given as - {n} = 998001, its corresponding square root is 999.

In mathematics, a square root of a number [x] is a number [y] such that - y² = x. in other words, a number y whose square is x. For example, 4 and −4 are square roots of 16.

y² = x

y = ±√(x)

Given is to find the square root of a number as follows -

998001

The given number is -

998001

We can write it as -

x² = 998001

x = ± 999

Therefore, we get the value of [x] as 999.

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557,568 inch³ of refrigerant can be held by the tubing.

Here we have to find how much a refrigerant can hold.

Data given:

outer diameter (d) = 78inch

outer radius(r) = 39 inch

inner diameter (d') = 34 inch

inner radius (r') = 17inch

Height (h) = 12 feet

= 12 × 12

= 144 inch

the formula to find the volume of the cylinder:

volume= пr²h

So here we get

Refrigerant hold = Volume of the outer cylinder - the volume of the inner cylinder

= πr²h - πr'²h

= πh(r² - r'²)

= π ×144 ( 39² - 17²)

= π × 144 ×56 × 22

= 22/7 × 144 × 56 × 22

= 557,568 inch³

Therefore the refrigerant can hold 557,568 inch³.

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A full size scale is a type of scale in which the representative factor is 1 is to 1

A scale factor is defined as the ratio of the scale of a given original object to the scale of a new object that is its representation but of a different size.

To determine the scale factor, first identify the corresponding sides on the two figures.

Then, divide the new figure's measurement by the original figure's measurement. The resulting value is your scale factor, or how many times your new figure is larger or smaller than the original.

A full size scale is a scale in which the length of the drawing is proportional to the actual length of the object.

As a result, its representative fraction is 1:1 by definition. The drawing is drawn in full size scale with the actual measurement

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Answer:

The average rate of change of a function over an interval is found by taking the difference between the function's values at the endpoints of the interval and dividing by the length of the interval. In this case, we have:

f(1) = -3(1)^3 + 7(1) = -3 + 7 = 4

f(3) = -3(3)^3 + 7(3) = -27 + 21 = -6

The average rate of change over the interval from x=1 to x=3 is therefore (-6 - 4) / (3 - 1) = -10 / 2 = -5.

To label your answer, you could write something like: "The average rate of change of the whale's movement over the interval from x=1 to x=3 seconds is -5 meters/second."

the average rate of change of the function on the interval from x = 0 to x = 5 is 580.8

Average rate of change of a function f(x) between x-values x1 and x2 = (f(x2) -f(x1)/ (x2 -x1)

For this given function f(x)=12(3)x then it will mean that

f(x) = 12.3^x and x-values 0 and 5, the average rate of change is

the average rate of change = (f(5) -f(0))/(5 -0) = (2916 -12)/5 = 580.8

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P(Z3)=0.1170 is the likelihood of earning at least 1 gram of extra cereal.A probability seems to be a number that expresses the possibility or probability that a specific event will take place.

The probability is computed by dividing the total possible outcomes by the number of possible ways the event could occur. Probabilistic and odds are two distinct ideas. Odds are the likelihood that something will occur and the variety of outcomes that can result in success. the overall number of outcomes that could occur. For instance, there is only one way to receive a head and there are a total of two possible outcomes, hence the probability of flipping the coin and getting heads is 1 in 2.

Y=1.8945 grams.

Y = 0.8405 grams.

The z-score is the result of dividing the standard deviation by the value that has been decreased by the mean:

z= σx−μ = 0.85053−1.9845≈1.19

Table A can be used to determine the relevant value:

P(Z≥3)=P(Z>1.19)=1−P(Z<1.19)=1−0.8830=0.1170

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The 5 transformations of a linear function are translation , reflection , dilation , vertical transformation and horizontal transformation.

In the question ,

we have to write the different types of transformation .

A transformation is defined as an alteration in the parent function’s graph .

there are basically 3 main types of transformations .

(i) the first type is Translations ,

the translation causes the graph to shift left, right, up, or down so many units.

(ii) the second type is Reflection ,

the Reflections cause the graph to rotate/flip over the x-axis or y-axis.

(iii) the third type is Dilation ,

In dilation the shape of a graph is changed by a certain factor. that is the graphs will look narrower or wider .

the other two transformations are

(iv) vertical transformation : it affects the y axis .

(v) horizontal transformation : it affects the x axis .

Therefore , the 5 types of transformation are explained above.

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=======================================================

Explanation:

Segments JK, KL, and JL are tangent to the circle.

We can break those segments into smaller pieces and notice we have these 3 pairs of congruent tangents:

Let's use the first equation to solve for x.

MJ = NJ

5x-8 = 8x-35

5x-8x = -35+8

-3x = -27

x = -27/(-3)

x = 9

Use the same idea to find y.

KN = KO

7y-9 = 2y+11

7y-2y = 11+9

5y = 20

y = 20/5

y = 4

Now compute the length of segment KO.

KO = 2y+11 = 2*4+11 = 19 units

Subtract this from LK to find LO

LO = LK - KO

LO = 32 - 19

LO = 13

This makes segment LM to be also 13 units long.

Now use the value of x to find sides MJ and NJ

MJ = 5x-8 = 5*9-13 = 32

NJ = 32 as well

--------------------------------------------------------------

We have these pieces:

which give us

Therefore, the perimeter of triangle JLK is:

JK+KL+JL = 51+32+45 = 128 units

Answer: 1

Step-by-step explanation:

The equation of the Least squares regression line is:

y(hat) = a + bx ,

⇒y(hat) = 1136+14.673x,

y(hat) = cost per hour and x= number of seats

If the data show a slimmer relationship between the two variables, the line that best fits this linear relationship is called the least-squares regression line, which minimizes the vertical distance between the data points and the regression line. The term "least squares" is used because it is the smallest sum of squared errors, also known as "variance".

In regression analysis, the dependent variable is plotted on the vertical Y-axis and the independent variable is plotted on the horizontal X-axis. These labels form the equation of the best-fit line determined by the least-squares method.

Operating costs are related to the day-to-day maintenance and management of your business. Operating expenses include direct cost of goods sold (COGS) and other operating expenses, often referred to as selling, general and administrative expenses (SG&A). These costs include rent, labor costs, other overhead costs, raw material costs, and maintenance costs. Operating expenses do not include non-operating expenses related to financing such as interest, investments and foreign currency translation. Operating expenses are deducted from revenue to determine operating profit and reflected in the company's income statement.

     Operating cost=Cost of goods sold + Operating expenses

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The phrase that best defines “figurative language is A. writing that is meant to be imaginative and vivid rather than literal

The use of figurative language, as opposed to literal language, serves the following purpose: it allows the reader to imagine what the author means when he writes a sentence or a statement. Figurative speech strengthens and deepens an author's work.

Figurative language is the use of words in unconventional ways to convey a complicated meaning, colorful writing, clarity, or evocative comparison. It employs a common sentence to allude to something without directly stating it.

Types of Figurative Language include:

In conclusion, the correct option is A.

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The Dimensions are 16.402 in wide by 8.401 in tail

Can the perimeters of two dissimilar shapes match each other?

Perimeter of custom windows = Perimeter of (rectangle+ semicircle)

Perimeter of rectangle = 2xy

Perimeter of semicircle = 1/2 πx²

A = 2xy + 1/2 πx²

2x + 2y + πx = 60

y = (60 - 2x -πx) / 2

A = 2x([60 - 2x - πx] /2) + 1/2(πx²)

0 = 60 - 4x - πx

x = 60 / (π+4)

x = 8.401

Hence,  Dimensions are 16.402 in wide by 8.401 in tail.

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Answer:

You would be saving the same amount of money either way.

Step-by-step explanation:

It's the commutative property.

1) The line's equation is y = 4 because it passes through the coordinates (-5,4).

2)  The equation of the line is y= 2x + 4

What is slope ?

A line's steepness is determined by its slope. In mathematics, slope is determined by "rise over run" (change in y divided by change in x).

1) A line with a slope of 0 is considered to be horizontal.

The equation is y=4 because along a horizontal line, the y-values remain constant.

The line's equation is y=4 because it passes through the coordinates (-5,4).

2) (x1,y1) = (-2,0) , m=2

y-y1=m(x-x1)

y-0 = 2 (x-(-2))

y=2(x+2)

y= 2x + 4

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Answer: 25% i believe

Step-by-step explanation:

The probability that it lands inside the triangle is,

P = 25%

The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.

Since, the probability is equal to,

P = size of the event space/size of the sample space

Here, In this problem

size of the sample size = area of the rectangular dartboard = 648 square centimeters

And, size of the event space = area of the triangular part = 162 square centimeters.

Hence, the probability that it lands inside the triangle is,

P = 162 / 648

P = 0.25

P = 25%

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Answer:

x = 4[tex]\sqrt{3}[/tex]

Step-by-step explanation:

using the sine ratio in the right triangle and the exact value

sin60° = [tex]\frac{\sqrt{3} }{2}[/tex]

sin60° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{x}{8}[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] ( cross- multiply )

2x = 8[tex]\sqrt{3}[/tex] ( divide both sides by 2 )

x = 4[tex]\sqrt{3}[/tex]

It is true that a multiple linear regression model interprets the slope differently than a simple linear regression model.

The link between two variables is determined through simple linear regression. The slope of a straight line used to represent linear regression indicates how changing one variable impacts another variable.

For the complex relationships between data, multiple linear regression is used. More than one variable may contribute to the explanation of this relationship.

One y-intercept and numerous slopes (one for each variable) make up a multiple regression formula. The formula is understood in the same way as a simple linear regression formula, however more than one variable influences the relationship's slope.

Therefore, the statement is true.

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Answer:

0

Step-by-step explanation:

Slope=(y2-y1)/(x2-x1)

=(4-(-3))/(10-c)=7/10

=7/(10-c)=7/10

c=0

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

The given equation is

y = (2/3)x + 3

The slope of the line is the change in y coordinates with respect to the change in x coordinates.

This is the linear equation in the the slope intercept form

y = mx + b

Where m is the slope of the line

b is the y intercept

y is the y coordinates

x is the x coordinates

The value of x = -2

Substitute the value of x in the equation

y = (2/3) × -2 + 3

Do the arithmetic operations

= -4/3 + 3

Add the numbers

= 5/3

Therefore, the solution is 5/3

I have solved the question in general, as the given question is incomplete

The complete question is:

What is the solution of the equation y = (2/3)x + 3x, when x = -2?

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The average rate of change between x = -3 and x = 1 is; 9/4

The average rate of change is calculated as the slope of the line between the two given points on the graph.

Now, looking at the graph, we can see that the coordinates of the two given points are;

(-3, -6) and (1, 3)

The formula to calculate the average rate of change which is the slope is;

m = (y₂ - y₁)/(x₂ - x₁)

m = (3 - (-6))/(1 - (-3))

m = 9/4

Thus, that is the average rate of change in conclusion

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Answer:

2

Step-by-step explanation:

A 14 seater matatu makes 1420 = <<1420=280>>280 shillings per trip during normal hours.

It makes 1430 = <<1430=420>>420 shillings per trip during rush hours.

Since the matatu made 10 trips and earned 3540 shillings, then it made 10-3540/280 = <<10-3540/280=12>>12 trips during normal hours.

This means it made 10-12 = <<10-12=2>>2 trips during rush hours. Answer: {2}.

Synthetic division is a yet another way to divide a polynomial by the factor, where k is a constant.

What is a synthetic division?

Synthetic division is usually used to find factors of polynomials of degree 3 that cannot be factored by grouping the polynomial.

Synthetic division is also used to find factor polynomials of degree 4 or higher.

We use synthetic division if and only if no other methods will work since there is a trial and error aspect to using it.

Taking an example:

We have to find the roots of the polynomial, [tex]f(x)= x^3+3x^2-4[/tex]

Substituting x=1 in the above equation, we get,

f(1)= [tex]1^3+3-4[/tex]=0

Thus, (x-1) is a root of the above polynomial.

Dividing the given function by (x-1)

[tex]x^3+3x^2-4/x-1\\=x^2+4x+4\\=(x+2)^2[/tex]

Thus, the roots of the given polynomial are given as, (x-1) and [tex](x+2)^2[/tex].

Hence, this is the synthetic division to find out the roots of the polynomial.

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The population grew to the number 7,723 in 27 years past 1940, i.e., 1967.

What is the linear function?

In mathematics, the term linear function refers to two distinct but related notions: In calculus and related areas, a linear function is a function whose graph is a straight line, that is, a polynomial function of degree zero or one.

We have,

The population of a small town, P, as a function of time, t, in years past 1940 is:

P = 2,323 + 200t

Let t be the year in which the population reached a count of  7,723. Solve for t:

P = 2,323 + 200t

7,723 = 2,323 + 200t

7,723 - 2,323 = 200t

5,400 = 200t

t = 5400/200

t = 27 years

Hence, The population grew to the number 7,723 in 27 years past 1940, i.e., 1967.

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The distance between Kim and Louise is 340.75 feet.

Algebra is a study of mathematical expressions, in which numbers and quantities are represented in formulas and equations by letters and other universal symbols.

Given that,

The distance of Kim from the ground level, who is standing on the deck at point K  = 140.75 feet.

Also, the distance of  Louise at point L, who is standing below Kim's position, = 200 feet.

The distance between point K and L,

= 200 + 140.75

= 340.75 feet

The required distance between K and L is 340.75 feet.

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The equation relating C and S is given as follows:

C(S) = 5000 + 200S.

The graph of the equation is then given by the image shown at the end of the answer.

The first step in defining the function is verifying the input and the output variables, as follows:

Then from these variables, we identify the type of function, which is linear, as for each additional ton of sugar, the cost increases by a fixed amount.

This fixed amount is of $200, hence it represents the slope of the function. The fixed fee of $5,000 to rent trucks is the intercept, hence the equation is defined as follows:

C(S) = 5000 + 200S.

And then the graph starting at (0,5000) and connecting point (10, 7000) is given at the end of the answer.

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The Z - score for the given shaded region under the standard normal distribution = - 0.61

A normal distribution with a mean of zero and a standard deviation of one is known as the standard normal distribution. The standard deviation shows how far a given measurement deviates from the mean, and the standard normal distribution is centered at zero.

According to the given information

P(Z > z)  =  0.73

            =  1 - P(Z < z) = 0.73

            =  P(Z < z ) = 1 - 0.73

            =  P(Z < z ) = 0.27

            =  P(Z <-0.61 ) = 0.27  

z  = -0.61  (using standard normal (Z) table  )

The Z - score for the given shaded region under the standard normal distribution = - 0.61

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