The three townships of Springfield, Wyandot, and
Johnsonville form an equilateral triangle as shown
below. Write and solve an equation to determine the
value of x.
Wyandot
(62) mi
18.6 mi
Johnsonville
Springfield
X=

Answer:x-int=4 1/4   y-int=-5 1/3

Step-by-step explanation:[tex]4x-3y=17\\ +3y =+3y\\ 4x=3y+17\\4x/4=3y/4 +17/4\\x=\frac{3}{4}x+ 4 \frac{1}{4} \\\\4x-3y=17\\-4x=-4x\\-3y=-4x+17\\-3y/-3=-4x/-3+17/-3\\y=\frac{4}{3}x -5\frac{1}{3}[/tex]

Answer: 5

Step-by-step explanation: if you do something to one side of the equation, it has to be done to the other side.

in this case, they divided the left side (3x+5y) by 5

so so make both sides equal, you'd have to divide the right side (25) by 5 as well which would give you 5

Answer:

Step-by-step explanation:

(

1

)

.

plugging the

4

into

g

(

x

)

and then putting what you get from that in to

f

(

x

)

(

2

)

.

plug

g

(

x

)

into

f

(

x

)

and then plug in the

4

Option 1:

Plug

4

into

g

(

x

)

:

g

(

x

)

=

−

2

(

4

)

−

6

=

−

8

−

6

=

−

14

Then plug

g

(

x

)

into

f

(

x

)

:

f

(

x

)

=

3

(

−

14

)

−

7

=

−

42

−

7

=

−

49

Option 2:

Plug

g

(

x

)

into

f

(

x

)

:

f

(

x

)

=

3

(

−

2

x

−

6

)

−

7

=

−

6

x

−

18

−

7

=

−

6

x

−

25

Finally plug

4

into our current

f

(

x

)

:

f

(

x

)

=

−

6

(

4

)

−

25

=

−

24

−

25

=

−

49

Rise and Run of line's ratio gives the Slope of the line.

Rise of a line is the how many units you move up or down to reach from one point to another point. Run of a line is the how many units you move left or right to reach from one point to another.

>Slope of a line is the ratio of the rise to the run of the line.

Let us assume the graph of y = x.

Now in the graph we take three points

let point 1 be (3,3) = (x1,y1)

    point 2 be (5,5)= (x2,y2)

    point 3 be (5,3)= (x3,y3)

Now the rise is y2  -  y1 which is 2

Now the run is x2 - x1 which is 2

Slope is [tex]\frac{rise}{run}[/tex]  = [tex]\frac{2}{2} =1[/tex], we know that slope of line y=x is 1 and here we get the same so it is proved that slope of line is  [tex]\frac{rise}{run}[/tex] .

Rise and Run of line's ratio gives the Slope of the line.

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Answer:

p + 166 = 249

p = 83 pages

Step-by-step explanation:

We know that she has to finish 249 pages novel and read 166.

So, let p represent the number of pages left to read; we have the equation

p + 166 = 249

Now let's solve by subtracting 166 from both sides

p = 83 pages

So, Emma had 83 pages left to read by friday

The continuous data that is presented as a frequency distribution makes up the median of the grouped data.

The center number in the set of data, known as the median, is what divides the data set's upper and lower halves. Since the data is divided into class intervals, the middle value is unknown when calculating the median of grouped data.

Let us understand this with the help of a median class example.

Consider the data as 48, 20, 59, 69,73. We have to calculate the median.

Arranging in ascending order we get, 20, 48, 59, 69, 73.

Here the number of observations is n = 5.

To find the median of odd data we will use the formula:

[(n+1)/2] = (5+1)/2 = 3.

Therefore, median = 3rd observation.

Median = 59.

Hence we got the idea of the median with the example of class.

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The

tools

used to make a

chart

are  Info-gram, tableau, Grafan, Chartist

What is a chart?

A

chart

can be defined as a

graphical

representation for

data

visualization, such that the data is represented with symbols as bars  lines in line chart, or slices in a pie chart"

It is used to represent tabular numeric data and  functions or other kinds of quality structure, providing different information.

The tools used in a chart includes;

Info-gram

tableau

Grafana

Chartist,

FusionCharts,

Datawrapper

ChartBlocks

Hence, a

chart

is a graphic representation of data.

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The value of the v is 11.5 units.

What is a Line Segment?

A line segment is a portion of a straight line that is defined by two points. It is a one-dimensional geometric figure with no width or area. Line segments can be drawn in many ways, including straight, curved, or jagged. The length of a line segment is the distance between the two points that define it. Line segments are commonly used to measure distances, form shapes, and construct geometric figures. Line segments can be used to define polygons, circles, and other shapes. Line segments are also used in mathematics to represent vectors and calculate angles. Line segments are a fundamental element of geometry and are used in a variety of applications, including navigation, construction, engineering, and computer graphics.

We have,

PS= RS = 31,

PQ = 2v,

and QR = v + 23,

v = ?

If PS= RS = 31,

then  PQ = QR,

so, 2v = v + 23,

v = 23/2

v = 11.5 unit

Hence, the value of the v is 11.5 units.

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Answer:

40 orange marbles

Step-by-step explanation:

We know for every 12 marbles, we have 5 orange marbles and 7 green marbles

Now we have 56 green marbles. To get from 7 to 56, we take 7 times 8.

So, we do the same take 5 times 8 = 40 orange marbles

So, it contains 40 orange marbles!

Answer:

1) x = 29; m∠3 = 6º

2a) scalene

2b) acute

Step-by-step explanation:

1) We can first solve for m∠3, as it is supplementary to 174º.

174º + m∠3 = 180º

m∠3 = (180 - 174)º

m∠3 = 6º

Then, we can solve for x by setting the sum of the measures of the interior angles of the triangle to 180º.

m∠1 + m∠2 + m∠3 = 180º

↓ substitute in given and solved values

(3x + 2)º + (5x - 60)º + 6º = 180º

↓ combine like terms

8xº - 52º = 180º

↓ add 52 to both sides

8xº = 232º

↓ divide both sides by 8º

x = 29

2a) We know that this triangle is not equilateral, as the measure of one of its interior angles (m∠3) is 6º. However, the triangle may be isosceles if m∠1 = m∠2. We can check for that by substituting x into each angle measure expression.

m∠1 ≟ m∠2

(3x + 2)º ≟ (5x - 60)º

↓ substitute in x-value

3(29)º + 2º ≟ 5(29)º - 60º

↓ simplify

(87 + 2)º ≟ (145 - 60)º

89º ≠ 85º

m∠1 ≠ m∠2; the triangle is not isosceles. Therefore, it must be scalene.

2b) All of the triangle's angles are less than 90º. Hence, it is an acute triangle.

The evaluated value of the expression b² - 4ac when a = -2, b = -4 and c = 1 is 24.

To evaluate an algebraic expression means to find the value of the expression when the variable is replaced by a given number.

To evaluate an algebraic expression, you have to substitute a number for each variable and perform the arithmetic operations.

Therefore, let's evaluate b² - 4ac when a = -2, b = -4 and c = 1.

Hence,

b² - 4ac = (-4)² - 4(-2)(1) = 16 + 8 = 24

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To find the degree of a polynomial function, count the number of terms in the expression. To find the number of turning points, take the degree of the polynomial and subtract 1. The number of turning points will be equal to that number.

To find the degree of a polynomial function, the first step is to count the number of terms in the expression. For example, if the expression is 3x^2 + 4x + 2, then the degree is 2 because there are three terms.The second step is to subtract 1 from the degree of the polynomial. In the example, subtracting 1 from 2 gives us 1. Therefore, the polynomial has 1 turning point.A turning point is a point on the graph of the polynomial where the slope of the tangent line is 0. This means the graph changes direction at the turning point. In the example, the graph changes direction at the point (1, 5).In summary, to find the degree and the number of turning points in a polynomial function, count the number of terms in the expression to find the degree, then subtract 1 from the degree to find the number of turning points.

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Equation 6x² - 5x- 6 has the elements (2x-3) (3x+2) .Quadratics can be defined using an equation of a second-degree polynomial.

The mathematical action known as "squaring," which is typically used to describe a quadratic problem, involves multiplying a variable by itself. This lexicon is based on the idea that the area of a square is equal to the product of the lengths of its sides. The Latin term quadratum, which means square, is where the word "quadratic" comes from.

here

= 6x² - 5x- 6

= 6x² - 9x + 4x - 6

=  2 ( 2x - 3 ) + 3x ( 2x - 3 )

= (3x+2) ( 2x - 3 )

So , Equation 6x² - 5x- 6 has the elements (2x-3) (3x+2) .

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The probability of making exactly 4 shots is 4/5, in where 4 is outcomes Favour to me and 5 is total possible outcomes.

The probability is measured as the ratio of favorable outcomes of a particular event to the total possible outcomes of that event. The value of probability should be lies between 0 to 1.

The term favorable outcome uses to determine the probability in mathematics. It is the possibility of happening expected incident of a particular event.

the ways in how i can make exactly 4 shots in the game = my favorable outcomes/total possible outcomes

                                                             =4/5

hence, the result is 4/5.

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The formula for the volume of cylinder with base area B and height H is V = B × H.

A cylinder is a 3-dimensional shape having two parallel circular bases joined by a curved surface.

The volume of a cylinder is expressed as;

V = π × r² × h

Area of a circle which is the base of a cylinder = πr²

Given that;

Plug the given values into the above formula.

V = π × r² × h

V = πr² × h

V = Base area × Height

V = B × H

Therefore, formula for the volume is V = B × H.

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Answer:

Step-by-step explanation:

.035*16=.56 solution has decreased for this part

16 divided by 3.5⁶66677⁷54776367

Step-by-step explanation:

4_35665567

Step-by-step explanation:

the domain of a function is the interval or set of all valid x (input) values.

the range of a function is the interval or set of all valid y (function result) values.

the graph shows us that the x values are continuously between -5 and +3.

and the end points are filled, so, they are to be included as valid points (via the <= or >= signs).

so, the domain is

-5 <= x <= 3

After 6 years the population of goats on the small island reaches 1000.

It is the rate of increases of population per individual in the population. The term related to time period and entire population.

given, initial population of goat on the smallest island, N° =2,

after t years the population of goats on this island, N= 1000

the maximum goat carrying capacity of this island, K= 1500

per capita growth rate, r = 0.5 per year

now, we use logistic growth equation, dN/dt = r×N[(K-N)/K]

                                                           dN/dt = 0.5×1000{1500-1000)/1500}

                                                                    dN/dt= 166.67

                                                             ∫dN/166.67 = ∫dt

                                                         by integrating both sides

                                               N/166.67 = t+c , where c is the

                                                     integration constant

                                                    at time t=0, N°=2

                                                        c= 0.012

                                                 N/166.67 =t+0.12

                                    as N=1000 , t= 5.99 years

hence, after 6 years the population of goat on the island reaches 1000.

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The third number in this sequence is 23.

The sum of three consecutive odd numbers can be written as (2n-1) + (2n+1) + (2n+3) = 69, where n is a positive integer. Expanding the left side gives us 6n+1 = 69, which means n = 11. The third number in the sequence is (2n+1) = (2 × 11+1) = 23. Therefore, the third number in the sequence is 23.

In the given sequence, 1, –3, 9, –27, 81,..., each number is multiplied by -3 to get the next one in the sequence. Since the absolute values of the numbers in the sequence are increasing, the sequence is diverging to an infinite value, either positive or negative. Therefore, it can be concluded that the given sequence is a divergent sequence.

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Answer:

2 / 27

Step-by-step explanation:

2/9 * 1/3   =  (2*1) / (9*3) = 2/27

(A) The expression for each plane are as follows;

Plane A; 1300 + 17x

Plane B; 1092 + 21x

B). The equation to show when the two planes would be at the same altitude is; 1300 + 17x = 1092 + 21x.

It follows from the task content that the initial altitudes of plane A and B are 1300 and 1092 respectively.

Since plane A gains altitude at 17 meters per second; The expression for the altitude after x seconds is;

1300 + 17x

Also, since plane B gains altitude at 21 meters per second; The expression for the altitude after x seconds is;

1092 + 21x

Ultimately, at the point when the two planes are at the same altitude; the equation which is true about the situation is;

1300 + 17x = 1092 + 21x.

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To find the vertical asymptote, take the limit of the function as x approaches infinity or negative infinity. To find the horizontal asymptote, take the limit of the function as x approaches the endpoints of the domain.

To find the vertical asymptote of a function, take the limit of the function as x approaches either infinity or negative infinity. This will give the value at which the output of the function approaches infinity or negative infinity, respectively. To find the horizontal asymptote, take the limit of the function as x approaches the endpoints of the domain. If the limit of the function as x approaches the endpoint is finite, then the horizontal asymptote is the value of the limit. If the limit of the function as x approaches the endpoint is infinite, then the horizontal asymptote is undefined. If the limit of the function as x approaches the endpoint is undefined, then the horizontal asymptote is undefined.

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-2 is the zero of the polynomial 3x²+ 4x + 2k for the value of k equals to -2.

As given in the question,

Given polynomial is equal to :

3x²+ 4x + 2k

-2 is the zero of the given polynomial 3x²+ 4x + 2k

Compare with the standard quadratic equation ax² + bx + c

Let 'α' be the zero whose value is equal to -2.

And 'β' be the another zero.

Sum of the zeros of the polynomial = -b/ a

⇒ α + β = -4 / (3)

⇒α + β = -4/3 ___(1)

Product of the zeros = c/a

⇒αβ = 2k / 3

⇒(-2)β = 2k/3

⇒β = -k/3

Substitute the value of α and β in (1)

-2 + -k/3 = -4/3

⇒-k/3 = -4/3 + 2

⇒ -k/3 =2/3

⇒ k = -2

Therefore , the value of k for the given polynomial with the given condition is equal to -2.

The above question is incomplete , the complete question is :

For what value of k , - 2 is a zero of the polynomial 3x²+ 4x + 2k?

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Answer:

cos(x) = r/t

sin(x) = s/t

tan(x) = s/r

Step-by-step explanation:

Background info:

This question becomes simple when we remember SohCahToa.

Soh stands for Sine = Opposite/ Hypotenuse

Cah stands for Cosine = Adjacent/ Hypotenuse

Toa stands for Tangent = Opposite/ Adjacent

Solving:

1. Cosine of angle x (think Cah)

The adjacent side is r and the hypotenuse is t.

so the answer is r/t

2. sine of angle x (think Soh)

The opposite side is s and the hypotenuse is t.

so the answer is s/t

3. Tangent of angle x (think toa)

The opposite side is s and the adjacent side is r.

so so the answer is s/r

The above quadratic equation has two solutions, as shown by the question Yes.

A second-order polynomial equation with a single variable, x, is known as a quadratic equation.

ax2 + bx + c = 0 is a quadratic equation in standard form.

x stands for an unknown (an variable)

With respect to known numbers, a, b, and c, where a 0

The polynomial's number of solutions is influenced by the equation's highest possible power given in the question.

The roots or zeros of the expression on the left-hand side of the equation are the values of x that fulfill the equation.

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SSS Stands on Side - Side - Side

SAS Stands on Side - Angle - Side

ASA Stands for Angle - Side - Angle.

There are three theorems that may be used to determine whether two triangles are similar: Angle - Side - Angle (ASA), Side - Angle - Side (SAS), and Side - Side - Side (SSS).

SSS, which stands for "side, side, side," denotes that there are two triangles with identical angles on all three sides. The triangles are congruent if their third sides are the same as those of another triangle.

That is what the SAS regulation says. The triangles are congruent if the two sides and included angle of one triangle are the same as the two sides and included angle of another triangle. Any angle that is created by two specified sides is an included angle.

According to the ASA postulate of Euclidean geometry, two triangles are similar if their two corresponding angles are congruent and one side is equal to the corresponding side of the other triangles.

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domains =  all real numbers , (−∞,∞)and also the range is = all real numbers , (−∞,∞)

Range: the discrepancy between the top and bottom numbers. To get the range, locate the greatest observed value of the variable and deduct the least observed value the minimum. The data points between the two extremes of the distribution are not taken into consideration by the range; just these two values are considered. Between the lowest and greatest numbers, there is a range. Values at the extremes make up the range. The data set 4, 6, 10, 15, 18, for instance, has a range of 18-4 = 14, a maximum of 18, a minimum of 4, and a minimum of 4.

domains =  all real numbers , (−∞,∞)and also the range is = all real numbers , (−∞,∞)

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Answer: x = 3/4

Step-by-step explanation:

1/3x + 3 = 4 - x

Subtract 3 from both sides

1/3x = 1 - x

Then times 3 from both sides

x = 3 - 3x

Add 3x on both sides

4x = 3

Divided by 4, both side

x = 3/4