Find the value of r so that the line that passes through each pair of points has the given slope:
(r, -2) (10, 1) and the slope of the line is 1/4

Answer:

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keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the line L above

[tex]\stackrel{\textit{slope for line L}}{(\stackrel{x_1}{-1}~,~\stackrel{y_1}{-5})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{4})} ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{4}-\stackrel{y1}{(-5)}}}{\underset{run} {\underset{x_2}{6}-\underset{x_1}{(-1)}}} \implies \cfrac{4 +5}{6 +1}\implies \cfrac{9}{7} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{9}{7}} ~\hfill \stackrel{reciprocal}{\cfrac{7}{9}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{7}{9}}}[/tex]

so we're really looking for the equation of a line whose slope is -7/9 and that it passes through (9 , 3)

[tex](\stackrel{x_1}{9}~,~\stackrel{y_1}{3})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{7}{9} \\\\\\ \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}{3}=\stackrel{m}{- \cfrac{7}{9}}(x-\stackrel{x_1}{9}) \\\\\\ y-3=- \cfrac{7}{9}x+7\implies {\Large \begin{array}{llll} y=- \cfrac{7}{9}x+10 \end{array}}[/tex]

multiply ecerything that is in the brackets by 3

[tex]3(x) + 3(2) + 7 \\ = 3x + 6 + 7 \\ = 3x + 13[/tex]

ATTACHED IS THE SOLUTION

Answer:

[tex]\frac{9x^{2}}{y^{2}}[/tex]

Step-by-step explanation:

First you need to do what is inside the parenthesis

Dividing by a variable with the same base means the powers subtract so if we do this for x we get.

[tex]\frac{x^{\frac{1}{2}}}{x^{-\frac{1}{2}}}=x^{\frac{1}{2}-(-\frac{1}{2})}=x^{1}=x[/tex]

That brings us to

[tex](\frac{3xy^{-\frac{1}{2}}}{y^{-\frac{1}{2}}})^2[/tex]

Then we need to do a similar process for the y variable.

[tex]\frac{y^{-\frac{1}{2}}}{y^{\frac{1}{2}}}=y^{-\frac{1}{2}-(\frac{1}{2})}=y^{-1}=\frac{1}{y}[/tex]

Which brings us to

[tex](\frac{3x}{y})^2[/tex]

From here we just need to square the top and the bottom of the fraction which brings us back to our final answer with

[tex]\frac{9x^2}{y^2}[/tex]

Answer:

[tex]\dfrac{9x^2}{y^2}[/tex]

Step-by-step explanation:

Given expression:

[tex]\left(\dfrac{3x^{\frac{1}{2}}y^{-\frac{1}{2}}}{x^{-\frac{1}{2}}y^{\frac{1}{2}}} \right)^2[/tex]

Separate the variables inside the parentheses:

[tex]\implies \left( 3 \cdot \dfrac{x^{\frac{1}{2}}}{x^{-\frac{1}{2}}} \cdot \dfrac{y^{-\frac{1}{2}}}{y^{\frac{1}{2}}}\right)^2[/tex]

[tex]\textsf{Apply the exponent rule} \quad \dfrac{a^b}{a^c}=a^{b-c}:[/tex]

[tex]\implies \left( 3 \cdot x^{(\frac{1}{2}-(-\frac{1}{2}))} \cdot y^{(-\frac{1}{2}-\frac{1}{2})}\right)^2[/tex]

[tex]\implies \left( 3 \cdot x^{1} \cdot y^{-1}\right)^2[/tex]

[tex]\textsf{Apply the exponent rule} \quad (a^b)^c=a^{bc}:[/tex]

[tex]\implies 3^2 \cdot x^{(1 \cdot 2)} \cdot y^{(-1 \cdot 2)}[/tex]

[tex]\implies 9x^2y^{-2}[/tex]

[tex]\textsf{Apply the exponent rule} \quad a^{-n}=\dfrac{1}{a^n}:[/tex]

[tex]\implies \dfrac{9x^2}{y^2}[/tex]

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Answer:

The slope is 1/4

Step-by-step explanation:

hope it helps

Answer:

x = 21

Step-by-step explanation:

Given line a is parallel to line b we can form the following equation to find the value of x:

6x + 12 + 2x = 180 (because these are supplementary angles and their sum is equal to 180)

add like terms

8x + 12 = 180 subtract 12 from both sides

8x = 168 divide both sides by 8

x = 21

Answer:

The answer would be 92.8 but since we're rounding it'll be 90

Step-by-step explanation:

Answer: The area of a circle is 286.37cm².

Step-by-step explanation: The answer to this question can be solved by finding the value of the radius from the circumference and substituting it into the area.

Following are the steps to solve this problem:-

Step 1.  The circumference of the circle is 60cm.

The formula for the circumference of a circle is 2[tex]\pi \\[/tex]r.

Step 2. Calculating the value of radius (r) is 2[tex]\pi[/tex]r=60 cm.

                                                                2x 3.14xr =60cm.

                                                                r= 9.55cm

Step 3. Calculate the area of a circle by using the formula [tex]\pi[/tex]r²

Substituting the valur r( from step 2 ) in the formula

                                                  3.14x9.55x9.55= 286.37cm²

Thus, the answer is 286.37cm²

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Solution:

If

The general form of the coordinates of an ordered pair is

From the given expression;

The x-coordinate is -7

The y-coordiates is -2

Hence, the corresponding ordered pair is

Answer: wowwww LOL

Step-by-step explanation:

Thanks Mr Shady, the f r e e p o. i n t s are now mine.

The value of the given expression g = h+9/5 is 127.

So, g = h+9/5:

Insert the values in the expression as follows:

Therefore, the value of the given expression g = h+9/5 is 127.

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The correct question is given below:

Evaluate the expression when g = 30 and h = 14.

g = h+9/5

The rate at which the water level dropped each hour is 5 / 34 inches per hour.

In order to determine the rate  at which the water level dropped each hour , divide the total decrease in the water level by the total time it took for the water to decrease.

Division is the process of  grouping a number into equal parts using another number. The sign used to denote division is ÷. Division is one of the basic mathematical operations.

Change in water level per hour = total decrease / change in time

Change in time = 11 - 8 : 10 = 2 : 50 am = 2 hours 5/6 minutes

Change in water level per hour = 5/12 ÷ 2 5/6

5/12  ÷ 17/6

5 / 12 x 6 / 17 = 5 / 34 inches per hour

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Answer:

u = 4

Step-by-step explanation:

32 = 5u + 3u = 8u ( divide both sides by 8 )

4 = u

Step-by-step explanation:

u=4 after you add or combine like terms , you then divide both sides by the same factor

Answer: 5.184 ft

Step-by-step explanation:

The inequality that represents the legal driving speeds, s, in kilometers per hour is 45 >= s <= 70.

It should be noted that an inequality is simply used in mathematics to show that the expression or equation aren't equal.

From the information, the highway has a minimum speed limit of 45 miles per hour and a maximum speed limit of 70 miles per hour.

Therefore, the inequality that represents the legal driving speeds is 45 >= s <= 70.

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1) The relationship between ∠1 and ∠3 is that they are corresponding angles.

2) The relationship between ∠8 and ∠4 is that they are alternate exterior angles

3) The relationship between ∠2 and ∠3 is that they are supplementary angles.

When it comes to congruent angles, we know that when two parallel lines are intersected by a third one, the angles that occupy the same relative position at each intersection are known to be corresponding angles to each other.

Now, in the first figure, we see that there are a total of eight angles and we also see that 2 parallel lines have been intersected by a third one. Thus, some of the angles will be congruent to others. In this case, we see that the relationship between ∠1 and ∠3 is that they are corresponding angles.

Now, in the second figure, we see that there are a total of eight angles and we also see that 2 parallel lines have been intersected by a third one. Thus, some of the angles will be congruent to others. In this case, we see that the relationship between ∠8 and ∠4 is that they are alternate exterior angles because they are formed on the outside of the parallel lines.

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functions has a graph with the largest positive x-intercept is c. f(x) = 2(x-8) +1

The core concept of mathematics' calculus is functions. The unique varieties of relations are the functions. In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.

A)

0= 2x + 10 - 1

-9 = 2x

-4.5 = x

B)

0= 8x + 64

-64 = 8x

-8 = x

C)

0 = 2x - 16 +1

0 = 2x -15

7.5 = x

D)

0 = 13x - 39

39 = 13x

3 = x

functions has a graph with the largest positive x-intercept is c. f(x) = 2(x-8) +1

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Answer:

  Multiplying both sides of the equation by 35 eliminates the fractions

Step-by-step explanation:

You want to know how to eliminate the fractions from the equation n/5+3/7=2.

The multiplication property of equality allows you to multiply both sides of an equation by the same number without changing the value of the variable. To eliminate fractions, the number we choose can be the least common denominator of the fractions.

Fractions with denominators 5 and 7 will have a least common denominator of 5·7 = 35. Multiplying the equation by 35 gives ...

  35(n/5 +3/7) = 35(2)

  7n +15 = 70

Multiplying both sides of the equation by 35 eliminates the fractions.

__

Additional comment

The solution to this 2-step equation is ...

  n = (70 -15)/7 = 55/7 = 7 6/7

The coordinates of the midpoint between point E(2, -8) and point F(-12, -6) on segment EF is ( -5, -7 ).

A midpoint is simply a point that divides a line segment into two equal halves.

The midpoint formula is expressed as;

M = ( (x₁+x₂)/2, (y₁+y₂)/2 )

Given the data in the question;

Point E(2, -8)

F(-12, -6)

Coordinates of midpoint = ?

To determine the midpoint, plug the given points into the midpoint formula above and simplify.

M = ( (x₁+x₂)/2, (y₁+y₂)/2 )

M = ( ( 2 + (-12) )/2, ( (-8) + (-6) )/2 )

M = ( 2 - 12 )/2, ( -8 - 6 )/2 )

M = ( -10 )/2, ( -14 )/2 )

M = ( -5 ), ( -7 )

M = ( -5, -7 )

Therefore, the midpoint of line segment EF is ( -5, -7 ).

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[tex](\stackrel{x_1}{7}~,~\stackrel{y_1}{5})\hspace{10em} \stackrel{slope}{m} ~=~ 2 \\\\\\ \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 {\Large \begin{array}{llll} y-\stackrel{y_1}{5}=\stackrel{m}{ 2}(x-\stackrel{x_1}{7}) \end{array}}[/tex]

Answer:

MK= 12.5

AngleJNK=117°

AngleJNM=63°

Step-by-step explanation:

Part A:

MN = 3x + 1

JL = 2x + 9

JL and MK are the diagonals

MN = 1/2 of MK

MK =2(3x +1)

MK = 6x + 2

Therefore, JL = MK

2x + 9 = 6x +2

Collect like terms

2x-6x = 2 - 9

-4x = - 7

x = 1.75

Substituting the value of x,

MK = 6(1.75) + 2

MK = 10.5 + 2

MK = 12.5

Part B

AngleJNK = (5x +2)°

AngleJNM = (3x-6)°

Sum of interior angles of a quadrilateral = 360

Therefore, 2(5x +2)° + 2(3x-6)° = 360

(10x + 4) + (6x - 12) = 360

Collect like terms

10x + 6x - 12 + 4=360

16x = 360 + 8

16x = 368

x = 368/16

x = 23

Substituting the value of x

For angleJNK = 5(23) +2 = 115+2 = 117°

For angleJNM = 3(23) - 6 = 69 - 6 = 63°

After solving the system of equations using Gaussian elimination we get the values as x = 5 , y = -11 and z=3

Given we have the system of equations as follows:

2x - y + 4z = 33

x + 2y - 3z = -26

-5 x - 3y +5z = 23

Rewrite the system in matrix form and solve it by Gaussian elimination.

[ 2  -1  4     [ 33

 1  2  -3   =  -26

-5  -3  5 ]      23 ]

Now divide row 1 by row 2.

[ 1  -0.5  2        [ 16.5

 1     2   -3    =  -26

-5    -3  5 ]         23 ]

Now R₂ - 1R₁ → R₂

and R₃ + 5R₁ → R₃

[ 1  -0.5  2        [ 16.5

 0   2.5  -5    =  -42.5

 0  -5.5 15 ]       105.5 ]

Divide row 2 by 2.5.

[ 1  -0.5  2        [ 16.5

 0     1   -2    =  -17

 0  -5.5 15 ]       105.5]

R₁+0.5R₂ → R₁

R₃ + 5.5R₂ → R₃

[ 1   0  1          [ 8

 0   1   -2    =  -17

 0    0   4 ]        12 ]

Divide R₃ by 4

[ 1   0  1          [ 8

 0   1   -2    =  -17

 0    0   1 ]         3 ]

Therefore, R₁-1R₃→R₁

R₂ + 2R₃ → R₂

[ 1   0  1          [ 5

 0   1   0    =    -11

 0    0   1 ]        3 ]

therefore x = 5, y=-11 and z = 3.

Hence we solved the system of equations using Gaussian elimination.

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In the illustration above, a circle with a few lines intersecting at various locations is shown. So, if we split the circle in half, the resulting semicircle has a vertical angle of 180 degrees. Since ∠ROP = 125°, ∠POS = 55° is obtained by taking 180° away from 125°. ∠POS and ∠QOR are equivalent terms. Also, ∠ROP = ∠QOS.

What is lines intersecting?

In a plane, intersecting lines are any two or more lines that cross one another. The point of intersection, which can be found on all intersecting lines, is where the crossing lines share a common point.

the characteristics of intersecting lines

The intersecting lines (two or more) never cross over at more than one location.

Any angle may be used to intersect the lines in any direction. Always larger than 0° and less than 180°, this angle is generated.

A pair of vertical angles are created by two intersecting lines. The vertical angles have the same vertex and are opposing angles (which is the point of intersection).

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Answer:

1

Step-by-step explanation:

60 Kilometers = 120 minutes

60 ÷ 120 = .5

.5 × 2 = 1

1 kilometer = 2 Minutes

The expression that shows how many inches tall Tess is t = i - 3.

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.

Addition, subtraction, multiplication, and division are all possible mathematical operations. As an illustration, the expression x + y has the terms x and y with an addition operator between them.

In this case, Tess is 3 inches shorter than Johnny. and Johnny is i inches tall. Since Tess is shorter, we will subtract.

Therefore, the expression will be:

t = i - 3

where t = Tess height.

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The carton can hold 8402.7cm3 or 8.4 litres of milk now

Initially, the width and length of the carton are 8.88cm each.

Now, the width and length of the carton are doubled. That is:

The width and length are 2 x 8.88cm = 17.76 cm each

But the height remains the same:  26.64cm

Volume of the carton = width x length x height

                                    = 17.76 x 17.76 x 26.64

                                    = 8402.7 cm3 = 8.4 litres

Therefore, the quantity of milk the carton can hold now is 8402.7 cm3 or 8.4 litres.

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Step-by-step explanation:

2pi = 360°

=>

10pi = 5×2pi = 5×360 = 1800°

The distance that is between the ball and the goal line after these five plays is D. 36 yards.

From the information, the Eagles gain 31 yards on a pass toward the goal line and on the next four plays, the Eagles lose 3, 5, 7, and 4 yards, respectively.

After the first day, the yards remaining will be:

= 48 - 31

= 17

Now, the total distance between the goal line and the ball will be:

= 17 + 3 + 5 + 7 + 4

= 36

Therefore, the total distance is 36 yards.

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