Write the equation of the line in slope-intercept form
2y=-12x-16

Answer: M = (5, 6)

Formula for midpoint:

[tex]\sf (x_m, y_m) = \left(\dfrac{x_1+x_2}{2}, \dfrac{y_1+y_2}{2}\right)[/tex]

Here given:

Find midpoint M by substituting values:

[tex]\sf M = \left(\dfrac{6+4}{2}, \dfrac{7+5}{2}\right)[/tex]

[tex]\sf M = \left(\dfrac{10}{2}, \dfrac{12}{2}\right)[/tex]

[tex]\sf M = \left(5, 6\right)[/tex]

Given:-

To find:-

Answer:-

Here we are interested in finding the midpoint of a line segment whose endpoints are given to us . Say if a line segment has endpoints [tex](x_1,y_1) [/tex] and [tex](x_2,y_2)[/tex] , then the midpoint of the line is given by ,

[tex]\implies Midpoint= \bigg(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\bigg) \\[/tex]

And here , we have;

So on substituting the respective values, we have;

[tex]\implies (x_m , y_m ) =\bigg(\dfrac{ 6+4}{2},\dfrac{7+5}{2}\bigg) \\[/tex]

[tex]\implies (x_m , y_m ) =\bigg( \dfrac{10}{2} , \dfrac{12}{2}\bigg) \\[/tex]

[tex]\implies\underline{\underline{ (x_m , y_m ) = (5,6)}}\\[/tex]

Hence the midpoint is (5,6) .

and we are done!

The equation in the form ax+ by=c a>0 where a and b are not both zero and a, b, and c are integers with greatest common actor  of 1 represent either linear or non linear function. Hence, this statement is true.

The formula for a linear function is f(x) = mx + b, where m and b are real values. Isn't it resembling the slope-intercept form of a line, represented by the equation y = mx + b? Yes, this is the case as the graph of a linear function is a line.

Here,

• 'm' is the slope of the line.

• 'b' is the y-intercept of  line.

• 'x' is the independent variable.

• 'y'  is the dependent variable.

As the name suggests, a nonlinear function is one that is NOT linear. To put it another way, a nonlinear function's graph is not a line, which means that its graph can be anything other than a line.

Given that, ax+ by=c a>0 where a and b are not both zero and a, b, and c are integers with a greatest common factor of 1

ax+ by -c=0     [by transpose]

The general form of linear equation is ax+ by +c z +d=0

So, it is a binary first order equation of 'x' and 'y'.

Therefore, ax+ by=c a>0 where a and b are not both zero and a ,b, and c are integers with a greatest common factor of 1 can represent either a linear or non linear function.

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Answer:

true

Step-by-step explanation:

when naming or labeling a line it matters which points you use

The distance from the line y = -3 to the point (5,2) is 5 units.

Distance from the line ax+by+c=0 from the point (m,n) is calculated by

[tex]distance=\frac{|am+bn+c|}{\sqrt{a^{2} +b^{2} } }[/tex]

In the given question

the equation of the line is [tex]y=-3[/tex] ⇒ [tex]y+3=0[/tex]

equation of line becomes 0.x+1.y+3=0

given the point (5,2)

Substituting the values in the distance formula we get

[tex]d=\frac{0*5+1*2+3}{\sqrt{0^{2} +1^{2} } }[/tex]

[tex]=\frac{2+3}{1} \\ \\ =\frac{5}{1} \\ \\ =5[/tex]

Therefore , the distance from the line y = -3 to the point (5,2) is 5 units.

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The domain of the function 13. is {-4≤x≥2} and the range of the function is {2≤x≥6} and The domain of the function 14. is {0.5≤x≥1.75} and the range of the function is {0.25≤x≥1.5}

The domain of the function means all the possible value that can be put in the function or the value of inputs

The range of the function means all the possible values that can be the result of various inputs or the value of output

On the graph the x coordinates represent the domain of the function that is possible inputs and y axis represent the range of the function that is all possible outcomes

The first problem (13.)

the  highest point's coordinates can be reed as (-4, 6) and the coordinates of lowest point are (0,2) . There is one more significant point , the second endpoint, whose coordinates are (2,3)

So, The domain of the function is {-4≤x≥2} and the range of the function is {2≤x≥6}

The Second problem (14.)

the  highest point's coordinates can be reed as (1.75, 1.5) and the coordinates of lowest point are (0.5, 0.25) .

So, The domain of the function is {0.5≤x≥1.75} and the range of the function is {0.25≤x≥1.5}

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Answer: Hope it help

Step-by-step explanation:

The equation which describes this situation in terms of the cost of each shirt (x) and the cost of each pair of pants (y) is, 5x+3y=190

Equation: There are numerous ways in which one may define an equation. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an ‘equal’ sign. The most basic and simple algebraic equations consist of one or more variables in math.

Glenn is shopping for school clothes

Number of shirts Glenn want to buy=  He plans to get one of each of the same shirt in five different colors which is equal to 5

x is the cost of each shirt

that means cost of 5 shirts = 5x

Number of pair of pants he want to buy=  three pairs of the same pant each in a different color which is equal to 3

y is the cost of each pair of pants

that means the cost of three pair of pants = 3y

The total cost for his clothes is $190

The equation which describes this situation in terms of the cost of each shirt (x) and the cost of each pair of pants (y) is, 5x+3y=190

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Answer: Side lengths: 7.2, 7.2[tex]\sqrt{3}[/tex], 14.4

Step-by-step explanation:

Take sin of 60 to calculate side opposite to angle 60

sin 60=[tex]\frac{\sqrt{3} }{2}[/tex]

cos 60=1/2  

7.2 / 1/2=

7.2 * 2=14.4

[tex]\frac{\sqrt{3} }{2}[/tex]*14.4=

[tex]\frac{14.4\sqrt{3} }{2}[/tex]=7.2[tex]\sqrt{3}[/tex]

The hypotenuse:

[tex](\frac{\sqrt{3} }{2})^2[/tex]+(1/2)^2=

3/4 + 1/4 = 1

1 * 14.4 =14.4

Side lengths: 7.2, 7.2[tex]\sqrt{3}[/tex], 14.4

Step-by-step explanation:

The 30-60-90 triangle is one of the most important trigonometry concept you will learn throughout your secondary schooling.

Attached below is a triangle that you should memorize for easy practice. The way this triangle is formed can be proven trigonometrically and/or with the unit circle, but that's not what this question is asking for.

When comparing the numbers on the attachment and your question, we can generate that the side 7.2=x, because the side with the 60 degree angle and right angle contains the variable x.

Since we have x now, all we would have to do is to plug in the x values and solve the question.

The hypotenuse (longest side of the triangle) = 2x = 2(7.2) = 14.4

The side opposite to the 60 degree angle (left most side)= [tex]x\sqrt{3}[/tex] = [tex]7.2\sqrt{3}[/tex] = 12.6

I hope this helped!

Answer:

all real x other than 2

Step-by-step explanation:

[tex]\frac{3x-6}{x-2}=3 \\ \\ 3x-6=3x-6[/tex]

Thus, the equation is true for all x in its domain, which is all real x other than 2.

Answer: a scale model is a representation or copy of an object that is larger or smaller than the object being represented, (sorry if this wasnt what you were asking)

Step-by-step explanation:

The distance between the pair of points X(-2,5) and Y(1,11) is [tex]\sqrt{45}[/tex] units.

We can find the distance between the points X and Y by using distance formula.

The distance formula is used to find the distance between two defined points on a graph (in the absence of a scale).

Here the two points are  X(-2,5) and Y(1,11).

The distance formula for points (a,b) and (c,d) is given by :-[tex]\sqrt{(d-b)^2+(c-a)^2}[/tex]

Here,

(a,b) represents the point X(-2,5), and

(c,d) represents the point Y(1,11)

Putting the values of (a,b) and (c,d) in the distance formula, we get,

[tex]\sqrt{(11-5)^2+(1-(-2))^2}[/tex]

[tex]\sqrt{6^2+3^2} \\ \sqrt{36+9}\\ \sqrt{45}[/tex]

Hence, the distance is [tex]\sqrt{45}[/tex] units.

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I think the answer is -2.5n + 6.5.

How to work it out:

Answer:

15. False, m<1 and m<3 are not vertical

16. False, m<2 and m<4 are vertical, so they must be the same

17. True, they are supplementary

18. True, they are also supplementary

19. 90 - 35 = 55

20. m<7 = m<4, so it's 42 degrees

21. 126-90 = 36 degrees

22. 115-90 = 25, which gives us the angle of m<4, which is vertical to m<7, which means m<7 is also 25.

Brainliest answer please.

The solution set of this inequality is x = -8

What is inequality ?

inequality

   12 < -3(x+4)

  12 <  -3x - 12

  12 + 12 < - 3x

     24  <  -3x

     - 8 < x

The solution set of this inequality is x = -8

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Answer:

Not a function; D: {2, 9}; R: {8, 4, 7}

Answer:

Dependent

18.46%

Step-by-step explanation:

All possible combinations for Sadie taking two marbles out from the hat:

[tex](6+2+2+4+2)×[(6+2+2+4+2)-1] [/tex]

[tex] = 16 \times 15[/tex]

[tex] = 240[/tex]

All the possible combinations that the first marble is brown and the second marble is not purple:

[tex]2 \times (6 + 2 + 1 + 4)[/tex]

[tex] = 2 \times 13[/tex]

[tex] = 26[/tex]

The probability:

[tex] \frac{240}{26} \times 100\%[/tex]

[tex] = \frac{240}{13} \times 50\%[/tex]

[tex] = \frac{1200}{13} \%[/tex]

[tex]≈18.46%[/tex]

Answer:

0.2, 3 out of 9, 41%, 6/13

Step-by-step explanation:

6/13 = 0.46

3 out of 9 = 3/9 = 0.33

41% = 0.41  (change percent to decimal by dividing it by 100)

0.2

Now compare:

Least to greatest:  0.2, 3 out of 9, 41%, 6/13

An infinite geometric series is the outcome of an unlimited geometric sequence.

The infinite geometric series be 2/5 +4/25 + 8/125 + . . . . then the sum of the infinite geometric series is 2/3.

An infinite geometric series is the outcome of an unlimited geometric sequence. This series wouldn't have a finish. It is possible to calculate the sum of all finite geometric series. The terms in the sequence will grow steadily larger, but adding the larger numbers together will not provide a solution if the common ratio of an infinite geometric series is greater than one.

Given:

a(first term) = 2/5

r(common difference) = 2/5

Since, |r| < 1 the infinite series converges.

[tex]S_\infty[/tex] = a/1-r ; -1 < r < 1

[tex]S_\infty[/tex] = (2/5)/(1-2/5)

simplifying the above equation, we get

[tex]S_\infty[/tex] = (2/5)/(3/5) = 2/3

The sum of the infinite geometric series is 2/3.

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Answer:

A collection of different things

Step-by-step explanation:

I looked up the definition

The total of a geometric series is an unlimited number of terms with a fixed ratio between them.

If S n= a₁ + a₁r+ a₁ r²+ . . +a₁ rⁿ⁻¹ then rSn = a₁r + a₁ r²+ . . +a₁ rⁿ⁻¹+a₁ rⁿ.

The sum of a geometric series Sn  is given by:

[tex]$S_n=a(\frac{1-r^{n} }{1-r} )[/tex]

Given:

Sum of first n terms of the Geometric progression be

Sn = a₁ + a₁r + a₁ r² + . . + a₁ rⁿ⁻¹  ---(1)

On multiplying by r on both sides,

r Sn = a₁r + a₁ r² + . . + a₁ rⁿ⁻¹ + a₁ rⁿ  ----(2)

So, (2) − (1) gives,

[tex]rS_n-S_n=ar^{n} -a[/tex]

[tex]S_n(r-1)=a(r^{n} -1)[/tex]

Therefore, the sum of n terms of a GP is:

[tex]$S_n=a(\frac{1-r^{n} }{1-r} )[/tex]

Let the expression be r S n = a₁r + a₁ r² + a₁ r³ + . . . . + a₁rⁿ

Sum of first n terms of the Geometric progression is:

Sn = a₁ + a₁r + a₁ r² + . . + a₁ rⁿ⁻¹  

On multiplying by r on both sides, we get

rSn = a₁r + a₁ r²+ . . +a₁ rⁿ⁻¹+a₁ rⁿ  

Therefore, rSn = a₁r + a₁ r²+ . . +a₁ rⁿ⁻¹+a₁ rⁿ  

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The student's error is that the common ratio would not be equal to 3/2.

What is Common Ratio:

The general form of representing a geometric progression is a1, (a1r), (a1r2), (a1r3), (a1r4) ,... where a1 is the first term of GP, a1r is the second term of GP, and r is the common ratio.

Common Ratio Formula:

Common ratio,

r =a n / a n−1

where,

an  is the nth term of the geometric progression.

an−1 is the (n - 1)t h term of the geometric progression.

Now,

[tex]S_{infinity} = 2a_{1} \\\\= a_{1} / 1-r\\\\2a_{1} = a_{1} / 1-r\\\\= 1-r = 1/ 2\\\\r = 1/2 - 1\\\\r = 1/2[/tex]

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The value of the given expression will be 57 if the value of h = -7.

So, let the value of expression be 'x'.

SUbstitute h = -7 in the expression as follows:

Therefore, the value of the given expression will be 57 if the value of h = -7.

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The complete question is given below:
If h = -7, the expression has a value of _.

39(2) + 3h = x

By looking at the graph:

Domain: (-6, 1] U (1, 5]

Range:  (-3, 2] U [3, 7)

The domain is the set of inputs (horizontal axis) and the range is the set of the outputs (vertical axis).

By looking at the horizontal axis we can see that the first part goes from x = -6 to x = -1, this interval is (-6, 1]

(at x = -6 there is a open circle, so x = -6 does not belong to the domain)

Similarly, the second interval is (1, 5]

Then the domain is D: (-6, 1] U (1, 5]

To get the range we do the same thing, but we need to look at the vertical axis. The first interval goes from y = -3 to y = 2 and then y = 3 to y = 7, the range is:

R: (-3, 2] U [3, 7)

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The geometric mean can be determined by multiplying the terms from part c and the first term of the sequence from part a and taking their square root.

The first term of the sequence from part a is 2 and the term from part c is 512.

Geometric mean of a sequence is the average value of a set of numbers, determined by multiplying the terms together and taking their root.

In general form, the geometric mean for a n number of terms is n√x1*x2*x3*…*xn

Since there are two terms 2 and 512, we will take the square root of the product.

Geometric mean=√2*512=√1024=32

For the geometric sequence as it is the mean, the term will be the 2nd term of the sequence

Hence, the geometric mean of the two chosen positive number 2 and 512 is 32 which is the 2nd term.

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Answer: x=-11

Step-by-step explanation:

5(x+5)=2x-8

5x+25=2x-8

5x+25-25=2x-8-25

5x=2x-33

3x=-33

x=-11

The value of x in the given expression is -11.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Given that; Five times the sum of x and 5 is 8 less than twice x.

WE are asked to Solve for x.

Then the expression form as;

5(x+5)=2x-8

Now solve for x;

5x+25=2x-8

Subtract 25 on both sides;

5x+25-25=2x-8-25

5x=2x-33

3x=-33

x=-11

Therefore, the value of x in the given expression is -11.

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Considering the expression of a line and how to obtain it having 2 points, you obtain:

A linear equation o line can be expressed in the form y = mx + b

where

Knowing two points (x1, y1) and (x2, y2) of a line, the slope m of said line can be calculated using the following expression:

m= (y2 - y1)÷ (x2 - x1)

Substituting the value of the slope m and the value of one of the points in the expression of a linear equation, y = mx + b, the value of the ordinate to the origin b can be obtained.

In this case, you want to obtaina linear equation giving the sales y in terms of the year x. You know:

So, being (x1,y1)= (2011, 32.266) and (x2,y2)= (2012, 33.278), the slope m can be calculated as:

m= (33.278 - 32.266)÷ (2012 - 2011)

Solving:

m=1.012

Considering point 1 and the slope m, you obtain:

32.266= 1.012×2011 + b

32.266= 2035.132 + b

32.266- 2035.132= b

- 2002.866= b

Finally, the linear equation giving the sales y in terms of the year x is y=1.012x - 2002.866

You can use the equation to predict the sales for 2013 as follow:

y=1.012×2013 - 2002.866

Solving:

y=1.012×2013 - 2002.866

y= $34.29 billion

Finally, the sales in 2013 will be $34.29 billion.

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Answer:

15+3b

6f+10

Step-by-step explanation:

Those are your answers

Answer:

15 + 3b

6f + 10

Step-by-step explanation:

  Multiply 3 with 5 and multiply 3 with b and then add the results of the multiplication.

3*(5 + b) = (3*5) + (3*b)

              = 15 + 3b

2*(3f + 5) = (2*3f) + (2*5)

               = 6f + 10

The sum of the 8 terms of a series 5,13,21, . . , 61 is 264

The given series is:

          5,13,21, . . . . . . , 61

Notice that this is an arithmetic series with:

first term, a(1) = 5

number of terns, n = 8

common difference, d = a(2) - a(1) = 13 - 5 = 8

last term, a(8) = 61

The sum of the first n terms in an arithmetic series is given by the formula:

S(n) = n/2 [a(1) +a(n)

Substitute n = 8, a(1) = 5, a(n) = 61:

S(8) = 8/2 (5 + 61)

       = 4 . 66

       = 264

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The first ten terms of the Fibonacci sequence are 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89 and so on.

The Fibonacci numbers, sometimes known as Fn in mathematics, are a series of numbers. Each number in the Fibonacci sequence is composed of the sum of the two numbers before it. Typically, the sequence begins with 0 and 1.

means

0 + 1 = 1

1 + 1 = 2

1 + 2 = 3

2 + 3 = 5

3 + 5 = 8

5 + 8 = 13

8 + 13 = 21

13 + 21 = 34

21 + 34 = 55

34 + 55 = 89

Hence,the first ten terms of the Fibonacci sequence are 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89 and so on.

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[tex]\Large \boxed{\sf 0, 1, 1, 2, 3, 5, 8, 13, 21, 34}[/tex]

A series of integers known as the Fibonacci sequence begins with a zero, is followed by a one, another one, and then a series of increasing numbers. Each number in the series equals the sum of the two numbers before it. Every succeeding pair of Fibonacci numbers has a quotient resembling the golden ratio.