The equation of line L1, is y=5x+1

The equation of line L2, is 2y-10x+3=0

The new coordinates of House B and House C are
B' ( 3 , -5 ) and C' ( 4 , -4 ) respectively

What is Translation?

A translation moves a shape up, down, or from side to side, but it has no effect on its appearance. A transformation is an example of translation. A transformation is a method of changing a shape's size or position. Every point in the shape is translated in the same direction by the same amount.

Given data ,

Let the 3 houses be A , B ,C

The coordinate of House A = A ( 1 , -1 )

​The coordinate of House B = B ( 1 , -2 )

The coordinate of House C = C ( 2 , -1 )

Now , the houses are relocated to new coordinates with

The new coordinate of House A = A' ( 3 , -4 )

The translation of Point A can be expressed in the form of x and y coordinate as there is a translation occurred with a scale factor

So ,

A ( x₁ , y₁ ) to A' ( x₂ , y₂ )

A ( 1 , -1 ) to  A' ( 3 , -4 )

x₂ = x₁ + 2

y₂ = y₁ - 3

From the figure , we can clearly see that the coordinates of the houses A , B and C are translated by a scale factor and the new coordinates are

x₂ = x₁ + 2

y₂ = y₁ - 3

Therefore ,

B ( x₁ , y₁ ) to B' ( x₂ , y₂ )

B' ( x₂ , y₂ ) = B' ( 3 , -5 )

C ( x₁ , y₁ ) to C' ( x₂ , y₂ )

C' ( x₂ , y₂ ) = C' ( 4 , -4 )

Hence , the new coordinates of House B and House C are B' ( 3 , -5 ) and C' ( 4 , -4 ) respectively

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The solution of the given system of equations is (-1, -2).

We are aware that a linear system of equations can be solved using a substitution method.

The intersection of the two lines represents the system's solution.

The given equations are-

y = 3x+1 ...eq 1

y = -2x-4  ...eq 2

Put the value of eq 1 in eq2 .

3x+1  = -2x-4

3x + 2x = -4 - 1

5x = -5

x = -5/5

x = -1

Put the x in eq 1.

y = 3(-1)+1

y = -2

Thus, the solution of the given system of equations is (-1, -2).

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The complete question is-

What is the solution to the system of equations-

y=3x+1 ;

y=-2x-4

Answer:

1

Step-by-step explanation:

Replace the variable letter with the number.

t + d / 8 - 6

6 + 8 / 8 - 6

6 + 1 - 6

7 - 6

1

The option that is the graph of (g – f)(x) is; On a coordinate plane, a straight line with a positive slope goes through points (negative 2, negative 6), (0, 0), and (2, 6).

We are given the function as;

f(x) = -x

Now, the line passes through the points (0,0),(-6,6) and (6,-6) is;

The function given as; g(x) = 2x

This line passes through the points (-3,-6),(0,0) and (3,6).

Before we graph (g - f)(x), we have to first simplify it to get;

The graph of of (g - f)(x)

(g - f)(x) = g(x) - f(x)

= 2x - (-x)

= 3x

At x = 0, we have;

(g - f)(0) = 3(0) = 0

At x = 2, we have;

(g - f)(2) = 3(2) = 6

At x = -2, we have;

(g - f)(-2) = 3(-2) = -6

At x = -6, we have;

(g - f)(-6) = 3(-6) = -18

Looking at the options, option C is true

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The sample statistic when the nursing administrator went through a sample of hospital records is 217.

A statistic is a metric used to describe a sample. Estimation or hypothesis testing can be used to determine how likely it is that a sample statistic differs from the population parameter.

A sample is an analytic subset of a larger population in statistics. The use of samples enables researchers to conduct studies with more manageable data and more quickly. Randomly drawn samples have little bias if they are large enough, but obtaining such a sample can be costly and time-consuming.

A sample statistic is a piece of statistical data derived from a small number of items. A sample is merely a subset of a population. Therefore, the 217 of the patients had been admitted for heart issues is the sample.

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The percentage is the indicating hundredth is  12.5%.

A specific number in every hundred is what is meant by the percentage. It is a fraction with 100 as the denominator, and one percent is used to symbolize it.

Using the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %.

Given:

A student was marked tardy five different times in a 40-day period.

Percentage of 5 among 40

= (5/40) x 100

= 12.5%

Hence, The percentage of times the students marked will be 12.5%".

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Answer:

An equation is a proposition of two expressions that are equal.

Step-by-step explanation:

Answer:

snap to solve

Step-by-step explanation:

u can use snap to solve to get ur answers

Answer:

Step-by-step explanation:

cost price = $640

sell price = $940

percentage = ?

Rate * Base = Amount

Percent * Sell Price = Cost Price

P * 940 = 640

P940 = 640

P940/940 = 640/ 940

P = 0.66666667

Percent = (0.66666667 × 100)/100 = 66.666667

Correct Answer is 66 2/3%

The slope of the line shown in the graph is 4.5 .

In the question ,

it is given that ,

the amount of grapes is represented on x axis . and

the cost for that grape in the grocery store is represented on y axis .

to find the slope we need two points on the line ,

from the graph we can take two points as (1 , 4.5) and (2 , 9) ,

the slope can be calculated using the formula

slope = (change in y coordinate)/(change in x coordinate)

slope = (9 - 4.5)/(2 - 1)

slope = 4.5/1

slope = 4.5 .

Therefore , The slope of the line shown in the graph is 4.5 .

The given question is incomplete , the complete question is

The graph below shows the cost of grapes at a grocery store. What is the slope of the line?

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Answer:

a. )

Step-by-step explanation:

There are 15 balls  ......  two are green with a star

2 out of 15 = 2/15 = .1333

The time it takes the object to attain maximum height is 2 seconds

To find the time it takes the object to attain maximum height, we have to use the quadratic equation to do so. The formula can be given as

t = -b/2a

But let's write and define our quadratic equation with it's variables.

S = 64t - 16t²

To attain maximum height;

t = -b/2a

a = -16, b = 64,c = 0

Substituting the values

t = -64/2(-16)

t = 2

The time is 2 seconds

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Answer:

191=266+109x

Step-by-step explanation:

It says 191 is the same as 266 added to the product of 109 and _____. i am guessing you meant to say a variable.

Answer:

13.5

Step-by-step explanation: that's the minimum of dimensions for the box

Answer:

4

Step-by-step explanation:

Solution by separating parts

Rewriting our equation with parts separated

=1 + 1/2 + 2 + 1/2

Solving the whole number parts

1 + 2 = 3

Solving the fraction parts

1/2 +1/2 = 2/2

Reducing the fraction part, 2/2,

2/2 = 1/1

Simplifying the fraction part, 1/1,

1/1 = 1

Combining the whole and fraction parts

3 + 1 = 4

Answer:

4 miles

Step-by-step explanation:

1 1/2 = 1.5
2 1/2 = 2.5

1.5 + 2.5 = 4 miles

The length of NM is 10 units

What are similar triangles?

If two triangles' corresponding angles and sides are identical and their corresponding sides are proportional, or if the ratios between the lengths of the corresponding sides are comparable, then two triangles are said to be similar.

Similar triangles are triangles with the same shape but different sizes. Examples of related objects are all equilateral triangles and squares with any side length.

The triangles ONP and LNM are similar triangles.

So, the following is true.

(ON/LN)=(NP)/(NM)

(3.6/6)=(6)/(NM)  ( LN=LO+ON=2.4+3.6=6 )

3.6 NM=6*6 =36

NM=36/3.6 = 10

So, the length of NM is 10 units

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Answer:

Step-by-step explanation:

Perimeter formula from Area =

4√Area units.

4√250 =

4 × 15.8 =

63.2 cm

Answer:

25%

Step-by-step explanation:

divide the number by the total then multiply by 100 and add a percent sign

350/1400*100=25%

Answer of the given question are respectively,

[tex]-x^2y , 2w ,\\\\h^6 , -14a^5b^2\\x^6 , 4m^8\\9x^4/14 , y^2\\-5/x^2 , 1/2k\\7 , 1[/tex]

Exponent:

                          A quantity representing the power to which a given number or expression is to be raised, usually expressed as a raised symbol beside the number or expression.

        Example:

                             [tex]2^3[/tex] = 2 × 2 × 2

Combine like term:

 1. [tex]9x^2y -10x^2y[/tex] = [tex]-x^2y[/tex]

 2. Subtract 6w from 8w

          8w -6w = 2w

Rule:

          [tex]x^{a} * x^{b} = x^{a+b} \\\\[/tex]

1.

        [tex]h^2 * h^4 = h^{2+4} \\ \\\\= h^6[/tex]              

2.  

        [tex](-2a^2b).(7a^3b)\\\\-14 a^{2+3} b^{1+1} \\\\= -14 a^5 b^2[/tex]

Rule:

       [tex](x^a)^b = x^{ab}[/tex]

  1.  [tex](x^2)^3 = x^6[/tex]

  2.

         [tex](-2m^3)^2 * m^2 \\\\4m^6*m^2\\\\4m^8[/tex]

Rule:

           [tex]x^a/x^b = x^{a-b}[/tex]

1.

   [tex]27x^5/42x\\\\= 9x^4 /14[/tex]

2.

          [tex](y^3)^2/y^4\\\\y^6/y^4\\\\y^2\\[/tex]        

Rule:

            [tex]x^{-a}= 1/x^a[/tex]

1.

    [tex]-5x^{-2} \\\\= -5/x^2[/tex]

2.

    [tex]4k^2/8k^3\\\\= k^{-1} /2\\\\= 1/2k[/tex]

Rule:

           [tex]x^0 =1[/tex]

1.

         [tex]7x^0\\\\= 7[/tex]

2.

         [tex](w^4)^2/w^8\\\\w^8/w^8\\\\w^0\\\\=1[/tex]

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Answer:

[tex]33[/tex]

Step-by-step explanation:

Define functions:

[tex]r(x) = 2x+1\\s(x) = -x^2[/tex]

Substitute [tex]s(x)[/tex] into [tex]r(x)[/tex]:

[tex]2(-x^2) + 1[/tex]

Solve for value:

[tex]= 2((-4)^2)+1\\= 2(16) + 1\\= 32 + 1\\= 33[/tex]

** assuming that the function of [tex]s(x)[/tex] the x value is squared with the negative sign.

(16, 36)  is the image point .

What is  image point?

Reflecting (-6, -4) in the line y= - x yields the point (4, 6).

Dilating (4, 6) by a factor of 4 gives the point (16, 36).

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Answer:

First, find the number of boys: [tex]78-60=18[/tex]

The ratio of the number of girls to boys would be 60 : 18.

Answer: 6

Step-by-step explanation:

Angles opposite congruent sides in a triangle are congruent, so both angles are equal to [tex](13x-6)^{\circ}[/tex].

Since angles in a triangle add to [tex]180^{\circ}[/tex], so:

[tex]36+2(13x-6)=180\\\\2(13x-6)=144\\\\13x-6=72\\\\13x=78\\\\x=6[/tex]

Answer:

13685

Step-by-step explanation:

8050 + .7(8050)

8050 + 5635

13685

A student 6ft tall is standing 20ft away from a 35ft tall flagpole.

The flagpole is 60ft away from a building.

From the students point of view, the flagpole is lined up perfectly with the top of the building.

What's the height of the building?

Respuesta:

5 millas

Explicación paso a paso:

Si hay 2 personas y cuesta 12 dólares primero restarás 2 dolars por cada persona dejándote con 10 dólares. Después de eso, dividirá 10 por 2 para las millas porque cada milla cuesta 2 dólares. que te llevará a 5 millas

GRACIAS

Using the normal distribution, it is found that:

a) The probability that a randomly selected person spent more than ​$​25 is of 0.3446 = 34.46%.

b) The probability that a randomly selected person spent between ​$12 and ​$​21 is of 0.3307 = 33.07%.

c) The middle 95% of the amounts are between $13.2 and $32.8.

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation for the costs of the meal are given as follows:

[tex]\mu = 23, \sigma = 5[/tex]

The probability that a randomly selected person spent more than ​$​25 is one subtracted by the p-value of Z when X = 25, hence:

Z = (25 - 23)/5

Z = 0.4

Z = 0.4 has a p-value of 0.6554.

1 - 0.6554 = 0.3446 = 34.46%.

The probability that a randomly selected person spent between ​$12 and ​$​21 is the p-value of Z when X = 21 subtracted by the p-value of Z when X = 12, hence:

X = 21:

Z = (21 - 23)/5

Z = -0.4

Z = -0.4 has a p-value of 0.3446.

X = 12:

Z = (12 - 23)/5

Z = -2.2

Z = -2.2 has a p-value of 0.0139.

0.3446 - 0.0139 = 0.3307 = 33.07%.

The normal distribution is symmetric, meaning that the bounds of the middle 95% of values are given as follows:

-1.96 = (X - 23)/5

X - 23 = -1.96 x 5

X = $13.2

1.96 = (X - 23)/5

X - 23 = 1.96 x 5

X = $32.8

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The slope of the function y = 2 + 34x is 34 and the y-intercept of the function y = 2 + 34x is 2.

First, let us understand the slope intercept form;

The slope intercept form is simply a way of writing a line's equation so that the slope (steepness) and y-intercept (where the line crosses the vertical y-axis) are obvious.

We know that the slope intercept form of a line is y = mx + c where m is the slope of the line and b is the y-intercept of the line.

We are given:

y = 2 + 34x

y = 34x + 2

Compare with y = mx + c, we will get;

m = 34

b = 2

So, the slope is 34 and the y-intercept is 2.

Thus, the slope of the function y = 2 + 34x is 34 and the y-intercept of the function y = 2 + 34x is 2.

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Answer:

I believe the answer is c

Answer:

  240 cm by 288 cm

Step-by-step explanation:

You want the dimensions of a 150 cm by 180 cm poster enlarged by the ratio 8:5.

The enlargement ratio, expressed as a fraction, multiplies each of the original dimensions to get the new dimensions. The new dimensions are ...

  (8/5)·150 cm by (8/5)·180 cm = 240 cm by 288 cm

The function modelled for the given condition is [tex]y = -16x^{2} + 6x +22[/tex] and the time after which the skier is 5 feet above the water is 1.23 seconds.

A competitive water skier's heights y, x seconds after soaring off a ramp.

For x = 0, y = 22

for x = 0.25, y = 22.5

For x = 0.75, y = 17.5

For x = 1, y = 12

For x = 1.1, y = 9.24

The general equation of a quadratic equation is y = [tex]ax^{2} + bx +c[/tex]

Putting x = 0 and y = 22 in the equation, we get :

[tex]y = ax^{2} +bx +c[/tex]

c = 22

Now, putting x = 1 and y =12, we get,

12 = a*1 + b*1 + 22

a +b = 12 - 22 = -10 equation (1)

Putting x = 0.25, y = 22.5,

22.5 = a* [tex]22.5^{2}[/tex] +b*22.5 +22

506.25 a +22.5b = 0.5 equation(2)

Solving equation (1) and equation(2), we get :

a = -16 and b = 6 and c = 22

So, the quadratic equation becomes,

[tex]y = -16x^{2} + 6x +22[/tex]

Now, Time when the skier is 5 feet above the water,

[tex]x = \frac{3 +\sqrt{281} }{16} = 1.23 seconds[/tex]

Hence, the function modelled for the given condition is [tex]y = -16x^{2} + 6x +22[/tex] and the time after which the skier is 5 feet above the water is 1.23 seconds.

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