A line passes through the points (0, 0) and (–17, –11). What is its equation in slope-intercept form?

Write your answer using integers, proper fractions, and improper fractions in simplest form

[tex](\stackrel{x_1}{8}~,~\stackrel{y_1}{7})\hspace{10em} \stackrel{slope}{m} ~=~ 4 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{7}=\stackrel{m}{ 4}(x-\stackrel{x_1}{8}) \\\\\\ y-7=4x-32\implies {\Large \begin{array}{llll} y=4x-25 \end{array}}[/tex]

Answer:

y = 4x -25

Step-by-step explanation:

y = 4x + b

we must find the y intercept

plug in the point

7 = 4(8) + b

7 = 32 + b

subtract 32 from both sides

-25 = b

the y intercept is -25

plug in -25 for b

y = 4x - 25

The simplified form of the expression 52 + 1/5(-1/2)  is [tex]\frac{519}{10}[/tex]

A fraction is a ratio of two integers.

The integers are always in two parts separated by a division line. the part above the division line is called the numerator and the part below the division line is called the denominator.

52 + 1/5(-1/2)

Multiply out the fraction

we have

52 + (-1/10)

52 - 1/10

to make 52 have the same denominator as 1/10 we multiply 52 by 10/10 so that it becomes

520/10 - 1/10

simplifying the numerator we have,

[tex]\frac{520 - 1}{10}[/tex] =  [tex]\frac{519}{10}[/tex]

In conclusion the solution to 52+1/5(-1/2) is  [tex]\frac{519}{10}[/tex]

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The matching numbers are:

1) 0.0000225 = 2 x 10⁻⁵

2) 219,000 = 2 x 10⁵

3) 3,40,000 = 3 x 10⁶

4) 297,000 = 3 x 10⁵

5) 0.0000034 = 3 x 10⁻⁶

What are Exponents?

The exponent of a number indicates how many times a number has been multiplied by itself. For instance, 34 indicates that we have multiplied 3 four times. Its full form is 3 3 3 3. Exponent is another name for a number's power. A whole number, fraction, negative number, or decimal are all acceptable.

We have to match the following terms :

1) 0.0000225 = 2 x 10⁻⁵
we can write 0.0000225 as
2.25 / 100000
or, 2.25 / 10⁵
then, 2.25 x 10⁻⁵

2) 219,000 =  2 x 10⁵
as the numbers after 2 are 5
therefore we write 10⁵

3) 3,40,000 = 3 x 10⁶
as the numbers after 3 are 6
therefore we write 10⁶

4) 297,000 = 3 x 10⁵
we round off 297 as 300
as the numbers after 3 are 5
therefore we write 10⁵

5) 0.0000034 = 3 x 10⁻⁶
we can write 0.0000034 as
3.4/ 1000000
or, 3.4 / 10⁶
then, 3.4x 10⁻⁶

Hence, the matching numbers are:
1) 0.0000225 = 2 x 10⁻⁵
2) 219,000 = 2 x 10⁵
3) 3,40,000 = 3 x 10⁶
4) 297,000 = 3 x 10⁵
5) 0.0000034 = 3 x 10⁻⁶

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Answer:

31

Step-by-step explanation:

Answer:

Step-by-step explanation:

-2y = -x -1
2y = x+1
y = 1/2x+1/2

Working together, they can mow the yard in 48 minutes.

Given data;

A lawn can be mowed by Wilma in 120 minutes. In 80 minutes, Vanessa can cut the same lawn. When working together, how long does it take Wilma and Vanessa to mow the lawn?

Let 't' is their time in minutes working together.

Add their rates of working to get their rate working together,

Wilma's rate: [ 1 lawn ] / [ 120 min ]

Vanessa's rate: [ 1 lawn ] / [ 80 min ]

Rate working together: [ 1 lawn ] / [ t min ]

1/120 + 1/80 = 1/t

Multiply both sides by 240t;

2t + 3t = 240

5t = 240

t = 48

It takes them 48 min to mow the lawn working together.

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The value of y is  x/2 + c/5  

Given,

In the question:

5x - 7y = 3y - 2c

To find the value of y.

Now, According to the question:

The equation is given as:

5x - 7y = 3y - 2c

Combine the like terms:

-7y - 3y = -5x - 2c

Calculate the sum or difference:

-10y = -5x - 2c

y = -5x/-10 - 2c/-10

Calculate the product or quotient :

y = x/2 + c/5

Hence, The value of y is  x/2 + c/5

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Answer:

7, 7/1

Step-by-step explanation:

The ratio 7:49 can be simplified to 1:7.

I agree with Andrea that Δ AEG ≅ Δ AFG by the AAS congruence postulate

Triangles are said to be congruent when the sides and angles equal in accordance to to the triangle congruency rules

Some of the rules include

The problem requires the prove by Angle - angle - Side = AAS to ensure that the the triangles are congruent

The AAS have it that the two triangles being compared should have their two angles and the side not included being equal

The Angle - Angle - Side = AAS, here include

< FA,G - < AFG - AG

< EAG - < AEG - AG

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Total number of outcomes in rolling a die 3 times = [tex]6^3[/tex]  =216

What is outcome of an event?

Suppose an event is happening. The result of the event is called outcome of the event.

For example : let the event be throwing of a die. One of the outcome of the event is getting a 4 on the die

Number of outcomes of rolling a die first time = 6

Number of outcomes of rolling the die second time = 6

Number of outcomes in rolling a die third time = 6

Total number of outcomes in rolling a die 3 times = [tex]6 \times 6 \times 6[/tex]

                                                                                   = [tex]6^3[/tex]

                                                                                   = 216

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A shaded region above a solid boundary line matches the graph of the inequality y <|x-2| + 1.

What is inequality?

Inequality is a relationship between two expressions or values that is not equal to each other.

This inequality may be written in two ways:

(a) y < x - 2 + 1

   or

   y < x - 1

(b) y < -x +2 + 1

   or

    y < -x + 3

A graph of the inequality is shown below. The shaded region satisfies the inequality.

Hence, a shaded region above a solid boundary line matches the graph of the inequality y <|x-2| + 1.

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Answer:

18 orders in 2 days 9 orders in 1 day

Answer:

Step-by-step explanation:

9x2=18 which is 2 days so 9x1= 9 which is one day

Number of Atlantic cods caught in the year 2001 is; 40300 t

Percentage can be calculated by dividing the value by the total value, and then multiplying the result by 100. This is expressed as;

Percentage = (value / total value) * 100%

Now, we are told that;

Number of Atlantic cods caught in 1991 = 310000 t

We are told that in the year 2001, there were 87% less caught. Thus;

Number by which it was reduced = 310000 * 87% = 269700

Thus;

Number of Atlantic cods caught in the year 2001 = 310000 - 269700

Number of Atlantic cods caught in the year 2001 = 40300 t

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Answer:

  (s, f) = (4.5, 2.25)

Step-by-step explanation:

You want the solution to the simultaneous equations ...

Writing these in general form, we have ...

  3s +2f -18 = 0

  2s +3f -15.75 = 0

Using the "cross-multiplication method" for solution, we find ...

  ∆1 = (3)(3) -(2)(2) = 5

  ∆2 = (2)(-15.75) -(3)(-18) = 22.5

  ∆3 = (-18)(2) -(-15.75)(3) = 11.25

  s = ∆2/∆1 = 22.5/5 = 4.5

  f = ∆3/∆1 = 11.25/5 = 2.25

The solution is (s, f) = (4.5, 2.25).

__

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According to the Pythagoras theorem, the value of x is 13.76

Pythagoras theorem:

“In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“ is known as Pythagoras theorem.

Given,

Here we have the triangle with the side values.

Now, we have to find the value of x through this given values.

In order to calculate the value of x,

First, we need the value of the side KM.

Let us consider the value of KM is y.

Then according to the concept of Pythagoras theorem,

The value of y is calculated as,

=> (12.3)² = y² + (5.4)²

=> 151.29 = y² + 29.16

=>  y² = 122.13

=> y = 11.05

Therefore, the value of the hypotenuse  x is calculated as,

=> x² = (11.05)² + (8.2)²

=> x² = 122.13 + 67.24

=> x² = 189.37

=> x = 13.76

Therefore, the value of x is 13.76.

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Step-by-step explanation:

volume = base area × height

= (1/2×12×16)×10

=960cm3

surface area:

1. triangle area = 1/2×12×16=96cm2

2.bottom area = 12×10=120cm2

3.side area = 16×10=160cm2

4.slope area = 10×20=200cm2

5.add everything and remember you have two triangle

surface area= 96×2+120+160+200 =672cm2

Answer:

k = 13

Hope this helps : )

Step-by-step explanation:

To solve the equation, we need to first isolate the variable by doing the inverse operation which in this case is dividing since 7 is being multiplied with the variable k.

1. Divide 7 on both sides of the equal sign.

7k = 91

7 7

2. Answer.

The 7 cancels out so we are left with k = 13 since

91 ÷ 7 = 13

k = 13

3. Check.

Plug in the variable "k."

7(13) = 91

91 = 91 ✓

The percentage of items that have not been sold is: 60%

In mathematics, the percentage is calculated by dividing the given value by the total which is then multiplied by 100.

Percent in itself stands for out of 100.

Let the total number of items= i

Let the percentage be represented as= p

Then,

         i=100 (Given in the question)

Let the number of items sold in the first hour be= a

Let the number of items sold in the second-hour be= b

Since,

         p= Given Value/Total value x100

thus,

        a/100x100=30%

        The hundreds cancel out.

Thus, a=30 -(i)

The number of items sold in the second hour= b

b=10 (provided in the question) -(ii)

Let the total number of items sold be=T

The total number of items sold= a+b

From (i) and (ii)

Total number of items sold=30+10

Thus,

        Total number of items sold=40 -(iii)

Number of items that have not been sold(n)=100-(a+b)

                                                                        =100-T

                                                                        = 100-40

                                                       From (iii)

                                                                     n = 60 -(iv)

Then,

          Percentage of items that have not been sold = n/100x100

                                                                From -(iv)              

                                                                                      = 60/100x100

          Canceling hundred by hundred                      

                                                                                      = 60%

Thus,

          Answer: The percentage of items that have not been sold is: 60%

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If (x, y) represents the location of any point on the original square, the ordered pair which represents the coordinates of the corresponding point on the resulting square is: (0.4x, 0.4y).

In Geometry, dilation simply refers to a type of transformation which changes the size of a geometric object and the location of its points based on the scale factor, but not its shape.

In Geometry, a scale factor can be defined as the ratio of two corresponding side lengths or diameter in two similar geometric objects (shapes) such as equilateral triangles, square, quadrilaterals, polygons, etc., which can be used to either enlarge or reduce their size.

Generally speaking, the transformation rule for the dilation of a geometric object (square) based on a specific scale factor is given by this mathematical expression:

(x, y)      →    (SFx, SFy)  = (0.4x, 0.4y)

Where:

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Complete Question:

A square with the perimeter of 20 units is graphed on a coordinate grid. The square is dilated by a scale factor of 0.4 with the origin as the center of dilation.

If (x, y) represents the location of any point on the original square, which ordered pair represents the coordinates of the corresponding point on the resulting square?

answer choices

(0.4x, 0.4y)

(x + 20, y + 20)

(x + 0.4, y + 0.4)

(20x, 20y)

Answer:

a) ln(Length), ln(Time)

c)log(Length), log(Time)

e)Length, Time²

Step-by-step explanation:

Answer:

the person above me is correct!

Step-by-step explanation:

The possible outcomes must contain at least three tails, not 33 because a coin is flipped eight times. Then, the possible outcomes that contain at least three tails are 219.

The possible outcome is the possible result of an event. The possible outcomes that contain at least three tails mean the possible outcomes with exactly three tails and more than three. So, the calculation is:

Hence, the possible outcomes that contain at least three tails are 219.

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From the given triangle, the order of the sides DEF from shortest to longest is DE, DF, and EF.

Triangle:

The polygon with three edges known as sides and three vertices are known as triangle.

Given,

Here we have the triangle with their corresponding angle.

Now, we have to order the sides from shortest to longest.

Here in the given triangle we know the angles of m∠D = 61, m∠E = 60, and m∠F = 59.

By knowing this measures we can order the sides from shortest to longest, because angles are the opening between to sides, which means if the angle is wide, its opposite side that is in front of the angle is wide too, if the angle is narrow, its opposite side will be narrow.

In this case, the opposite side of ∠D will be the longest, because it is the largest angle. And the opposite side of m∠E will be the second longest, and finally the opposite side of ∠F will be the smallest.

From values, the shortest to longest the order is written as DE, DF and EF.

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Equation represents the population of the city 'p' in thousand of people in x years when in 2005 projected population is 450,000 and increases by 4,000 people each year is given by p = 4x + 450.

Total population in 2010 is equal to 470,000 people.

As given in the question,

Let 'p' represent the population in thousands of people.

Let x represents the number of years.

Population projected in 2005 = 450,000 people

                                                 = 450 ( in thousand people)

Population increases by 4000 people each year that is equal to 4 (in thousand of people)

Required equation to represent the population in x years ( in thousand of people ) is given by:

p = 4x + 450

Population in 2010 is equal to :

p = 4 ( 2010 - 2005) + 450

 = 4(5) + 450

= 20 + 450

= 470 ( in thousand of people)

= 470,000 people

Therefore, equation represents the population of the city 'p' in thousand of people in x years when in 2005 projected population is 450,000 and increases by 4,000 people each year is given by p = 4x + 450.

Total population in 2010 is equal to 470,000 people.

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The system of equations represents their transportation costs is:

50 − 2. 5x = y

40 − 2x = y

The correct option is  (A)

Given,

In the question:

Kaisorn deposits $50. 00 onto her public transportation card.

It costs her $2. 50 per trip to ride the subway.

Thom deposits $40. 00 on his public transportation card.

It costs him $2. 00 per trip to ride the subway.

Now, According to the question:

x → represents  the number of trips

y → represents the amount remaining in each account

According to the given condition:

The system of equations represents their transportation costs is :

50 − 2. 5x = y

40 − 2x = y

Hence, The system of equations represents their transportation costs is:

50 − 2. 5x = y

40 − 2x = y

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Answer:

[tex]y=|x|-4[/tex]

Step-by-step explanation:

The vertex of the graph is at (4, 0).

This eliminates all of the options except for [tex]y=|x|-4[/tex].

La ecuación exponencial 9ˣ⁺¹ + 3 = 28.3ˣ tiene una solución en x ≈ 1.922.

Aquí tenemos una ecuación exponencial en forma implícita, esto es, que la variable x no está en términos implícitos de las constantes de la ecuación.

Esta forma se puede resolver mediante métodos gráficos, a partir de la graficación del siguiente sistema de ecuaciones:

f(x) = 9ˣ⁺¹ - 28.3ˣ - 3

g(x) = 0

La solución es todo punto tal que f(x) = g(x).

A continuación, se grafica cada ecuación en un plano cartesiano mediante una herramienta gráfica. De acuerdo con la imagen, la solución de la ecuación es x ≈ 1.922.

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Answer:

Step-by-step explanation:

d- down four then right three