Kevin needs to order some new supplies for the restraunt where he works. the restraunt needs at least 492 glasses. there are currently 333 glasses. if each set on sale contains 18 glasses

[tex] \boxed{ \sf{ \bold{\purple{m} = \dfrac{2}{3}}}}[/tex]

[tex] \\ [/tex]

If a line passes through two points, then its slope can be calculated with the following formula:

[tex] \sf{\purple{m} = \dfrac{\blue{y_2}- \green{y_1}}{\red{x_2}- \orange{x_1}}} [/tex]

[tex] \\ [/tex]

Where:

[tex]\sf{\implies \purple{m} \: is \: the \: slope \: of \: the \: line.} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \sf{\implies (\orange{x_1} \: , \: \green{y_1}) \: are \: the \: coordinates \: of \: the \: first \: point.} \: \: \: \: \: \: \\ \sf{\implies (\red{x_2} \: , \: \blue{y_2}) \: are \: the \: coordinates \: of \: the \: second \:point.}[/tex]

[tex] \\ [/tex]

Plugging in our values, we get:

[tex] \sf{\purple{m} = \dfrac{\blue{ - 7}- \green{( - 1)}}{\red{ - 8}- \orange{1}}} = \dfrac{ - 7 + 1}{ - 9} = \dfrac{ - 6}{ - 9} [/tex]

[tex] \\ [/tex]

Now, let's simplify our result:

[tex] \sf{ \purple{m} = \dfrac{ - 6}{ - 9} = \dfrac{ \blue{ - 3 \times}2}{ \blue{ - 3 \times }3} = \boxed{ \dfrac{2}{3}}}[/tex]

[tex] \\ \\ [/tex]

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The letter of another angle that has the size 125° is "b" because it is vertically opposite to 125°

From the attached image, we see that;

​RS and TU are parallel lines.

​PQ is a straight line.

Now, vertically opposite angles are defined as the angles formed which are opposite each other when two lines meet at a point.

Now, from the given image, we can say that another angle of size 125° will be b. This is because b is vertically opposite to the angle 125°

Therefore we conclude that the letter of another angle that has the size 125° is "b" because it is vertically opposite to 125°

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The numbers in order from the least to the greatest is  5, -45/7, -2.2, 13/7, 2.5, √9, 3.5.

When ordering a number from the least to the greatest, the negative number is smaller than the positive numbers. The farther a negative number is from 0 on the number line, the smaller the number is. The farther a positive number i from 0 on the number line, the larger the number is.

To order a number from least to greatest, convert al the numbers to decimals. A decimal is a number that is made up of integers and non-integers. The integers are separated from the non integers by a decimal point.

√9 = 3

-30/6 = - 5

13 / 7 = 1.857

- 4 5/9 = -4.56

The numbers ordered from least to greatest is:- 5, -45/7, -2.2, 13/7, 2.5, √9, 3.5

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Answer:

Step-by-step explanation:

10)99

16)a)4/13

b)8/13

c) 7/13

Answer:

Frictional force (F(frict)) = 17.1 N

Normal force (F(norm)) = 78.0 N

Gravitational force (F(grav)) = 63.7 N

Acceleration (a) = 1.2 ms⁻²

Step-by-step explanation:

Newton's second law:

[tex]\boxed{F_{net}=ma}[/tex]

where:

Use trigonometry to resolve the 28.5 N force into its horizontal and vertical components since it is acting on the particle at 30°:

[tex]\implies F_x=28.5 \cos 30^{\circ}[/tex]

[tex]\implies F_y=28.5 \sin 30^{\circ}[/tex]

Due to the particle's mass, m, and the acceleration due to gravity, g:

[tex]\boxed{W=mg}[/tex]

Given:

[tex]\begin{aligned}W & = mg\\\implies W & = 6.5 \times 9.8\\W & = 63.7\;\sf N\end{aligned}[/tex]

The particle is moving parallel to the plane (the horizontal), so acceleration perpendicular to the plane is zero.

Resolving forces vertically (taking ↑ as positive):

[tex]\begin{aligned}F & = ma\\\implies R-W-28.5 \sin 30^{\circ}&=6.5 \times 0\\R-W-28.5 \sin 30^{\circ}&=0\\R & = W+28.5 \sin 30^{\circ}\\R & = 6.5(9.8)+28.5(0.5)\\R & = 63.7+14.25\\R & = 77.95\\R & = 78.0 \;\; \sf N\; (1\:d.p.)\end{aligned}[/tex]

When a moving object is acted on by a frictional force, fiction is limiting, and the frictional force F is at its maximum value:

[tex]\boxed{F = \mu R}[/tex]

(Where μ is the coefficient of friction and R is the normal reaction).

[tex]\begin{aligned}F & = \mu R\\\implies F & = 0.22 \times 77.95\\F & = 17.149\\F & = 17.1 \;\; \sf N\;(2\:d.p.)\end{aligned}[/tex]

Friction always acts in the opposite direction to motion (or potential motion).

Resolving forces horizontally (taking → as positive):

[tex]\begin{aligned}F & = ma\\\implies 28.5 \cos 30^{\circ}-F & = 6.5a\\28.5 \left(\dfrac{\sqrt{3}}{2}\right)-17.149 & = 6.5a\\\dfrac{57\sqrt{3}}{4}-17.149 & = 6.5a\\7.532724008 & = 6.5a\\a & = 1.158880617\\a & = 1.2\; \sf ms^{-2}\;\;(1\:d.p.)\end{aligned}[/tex]

For 2 hours the cost will be same.

Firstly forming the equation as per the given information in question. Let us assume the number of hours to be t.

Cost on choosing first campus -

Cost = 25 × t

Cost on choosing second campus -

Cost = 10 + 20 × t

Now, equating both the equations to find the required time..

25t = 10 + 20t

Shifting 20t to Left Hand Side of the equation

25t - 20t = 10

Performing subtraction to find the value of t

5t = 10

Shifting 5 to Right Hand Side of the equation at denominator

t = 10÷5

Performing division to find the value of t

t = 2

Therefore, the number of hours for which the costs are the same is 2.

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Here,  slope is 0 and y-intercept is zero too as line y=0

A line's steepness and direction are determined by the slope of the line. Without actually using a compass, determining a line's slope in a coordinate plane allows one to anticipate whether a line is parallel, perpendicular, or not.

The change in a line's y coordinate relative to its change in x coordinate is referred to as the line's slope. Δy is the net change in the y coordinate, while Δx is the net change in the x coordinate.  

Therefore,

m =  y₂-y₁/x₂-x₁ (where m denotes the slope) can be used to express how the y coordinate changes in relation to the x coordinate.

Be aware that tan ∅ = y/x

We also refer to this tan as the line's slope

We know that the equation for slope(m) and y - intercept(c) of a line is given by :

y = mx + c

As here y is 0

then, 0 = (0)x + 0

Therefore, slope is 0 and y - intercept is zero too

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Using translation concepts, the equation for the translated graph is given by:

g(x) = |x + 2| + 1.

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s range(involving values of y) or in it’s domain(involving values of x). Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis, or rotations of a degree measure around the origin.

From the graph, we have that the parent function was:

Hence, considering the parent function f(x) = |x|, the equation for the translated graph is given by:

g(x) = |x + 2| + 1.

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Answer:

6

Step-by-step explanation:

Let the amount of cars washed be x

120-12

---------- = x

18

108/18 =x

x=6

If m FH = (31x + 3°), m GH = (33x + 3°) and m ∠FHG = (28x − 3°) then the measure of ∠FGH is 48°.

Given: m FH = (31x + 3°), m GH = (33x + 3°) and m ∠FHG = (28x − 3°)

Based on the above information, we get

m FG = 2(m ∠FHG) = 2(28x - 3)°= (56x - 6)°

The arcs in the circle add up to 360 degrees, then

m FG + m FH + m GH = 360°

120x = 360°

x = 3

Substitute the value of x in  m ∠FHG in we get

28(3) - 3 = 81°

The measure can be found using the triangle sum theorem (all angles in a triangle must add up to 180°).

Firstly, it is known that ∠GFH would be an inscribed angle if the chord from F to G is drawn, and the arc GH would be twice its measure.

m GH = 33(3) + 3 = 102°

Half of that would be m ∠GFH = 51°

According to the triangle sum theorem all angles of the triangle must add up to 180°:

Therefore, m ∠GFH+ m ∠FGH +m ∠FHG= 180°

m ∠FGH = 48°

Therefore, the measure of ∠FGH is 48°.

The complete question is:

Given: circle k(O), m FH = (31x + 3°) m GH = (33x + 3°)

m ∠FHG = (28x − 3°) Find: m ∠FGH

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Answer:

The segment bisector of RS is KM and RS Lenght is 34CM

Step-by-step explanation:

17+17=34

150 is   the cost of renting a car from YourPal.

What is surface area of cuboid ?

Proxy car equation: y = 0.32x + 18

YourPal equation: y = 0.36x + 12

Set equations right sides equal to each other... meaning their cost, y, are equal

0.32x + 18 = 0.36x + 12

18 = 0.04x + 12  (subtract 0.32x from both sides of the equation)

6 = 0.04x            (subtract 12 from both sides of the equation)

150 = x               (divide both sides of the equation by 0.04)

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In the A.P. Series the 7th term is a 16.

According to the statement

We have to find that the 7th term of the A.P. series.

So, For this purpose, we know that the

An arithmetic progression or arithmetic sequence ( AP ) is a sequence of numbers such that the difference between the consecutive terms is constant.

From the given information:

a₁ = -8

an = an-1+4

Then

second term = -8+4

second term = -4

And

Third term = -4+4

Third term = 0

And

Fourth term = 0+4

Fourth term = 4

And

Fifth term = 4+4

Fifth term = 8

And

Sixth term = 8+4

Sixth term = 12

And

7th term = 12+4

7th term = 16.

So, In the A.P. Series the 7th term is a 16.

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Answer:

Perimeter = 2(Length + Width)     | Formula for perimeter

102 = 2(3m + m)                             | Plug in value of length and width

102 = 2(4m)                                    | Combine like terms

102 = 8m                                        | Distribute 2

8m = 102                                        | Flip LHS and RHS

m = 12.75m                                    | Divide by 8 on both sides

Answer m = 12.75 ft

Answer: 171.5

Step-by-step explanation: Changes made to your input should not affect the solution:

(1): "891.8" was replaced by "(8918/10)". 2 more similar replacement(s)

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

               y-((184/10)*x+(8918/10))=0

STEP

1

:

           4459

Simplify   ————

            5  

Equation at the end of step

1

:

        184         4459

 y -  ((——— • x) +  ————)  = 0

        10           5  

STEP

2

:

           92

Simplify   ——

           5

Equation at the end of step

2

:

        92         4459

 y -  ((—— • x) +  ————)  = 0

        5           5  

STEP

3

:

Adding fractions which have a common denominator :

3.1       Adding fractions which have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

92x + 4459     92x + 4459

——————————  =  ——————————

    5              5    

Equation at the end of step

3

:

      (92x + 4459)

 y -  ————————————  = 0

           5      

STEP

4

:

Rewriting the whole as an Equivalent Fraction :

4.1   Subtracting a fraction from a whole

Rewrite the whole as a fraction using  5  as the denominator :

         y     y • 5

    y =  —  =  —————

         1       5  

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

4.2       Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

y • 5 - ((92x+4459))     5y - 92x - 4459

————————————————————  =  ———————————————

         5                      5      

Equation at the end of step

4

:

 5y - 92x - 4459

 ———————————————  = 0

        5      

STEP

5

:

When a fraction equals zero :

5.1    When a fraction equals zero ...

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

 5y-92x-4459

 ——————————— • 5 = 0 • 5

      5    

Now, on the left hand side, the  5  cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :

  5y-92x-4459  = 0

Equation of a Straight Line

5.2     Solve   5y-92x-4459  = 0

Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).

"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.

In this formula :

y tells us how far up the line goes

x tells us how far along

m is the Slope or Gradient i.e. how steep the line is

b is the Y-intercept i.e. where the line crosses the Y axis

The X and Y intercepts and the Slope are called the line properties. We shall now graph the line  5y-92x-4459  = 0 and calculate its properties

Graph of a Straight Line :

Calculate the Y-Intercept :

Notice that when x = 0 the value of y is 4459/5 so this line "cuts" the y axis at y=891.80000

 y-intercept = 4459/5  = 891.80000

Calculate the X-Intercept :

When y = 0 the value of x is 4459/-92 Our line therefore "cuts" the x axis at x=-48.46739

 x-intercept = 4459/-92  = -48.46739

Calculate the Slope :

Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is 891.800 and for x=2.000, the value of y is 928.600. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of 928.600 - 891.800 = 36.800 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

   Slope     = 36.800/2.000 = 18.400

Geometric figure: Straight Line

 Slope = 36.800/2.000 = 18.400

 x-intercept = 4459/-92 = -48.46739

 y-intercept = 4459/5 = 891.80000

The answer type is interval and the interval is (-∞,5).

The value of x is the domain for which the function is defined. Function in this case can use value from (-∞,5).

Graphs can be used to specify the domain and set of functions. The domain of a graph is made up of all the input values displayed on the x-axis since the term "domain" refers to the set of potential input values. The range is the collection of potential output values, as displayed on the y-axis. Remember that the domain and range of the graph may be larger than the values seen if the graph extends beyond the area that is visible.

Consider the function y = f(x), which has the independent variable x and the dependent variable y. A value for x is said to be in the domain of a function f if it successfully allows the production of a single value y using another value for x.

Hence, The type of answer is interval and the values of interval is (-∞,5).

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Functions can be reflected on the x-axis, the y-axis, or both axes. For example, function reflection y= f(x) can be written as y= -f(x) or y= f(-x) even y= -f(-x). There are four types of function or graph transformations: reflection, rotation, translation, and dilation. In mathematics, especially geometry, mirror or mirroring means flipping, so basically, the mirroring of a function is the mirror image of a given function or graph. Hence the reflection function is commonly known as the reflection function.

The reflection of the given function should be similar in size and shape to the original function.

f(x)=x+1; x-axis

(consult the pictures attached)

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The equation of the line y = -3x + 17 would have a graph that is shown in the diagram attached below.

Given that the line y = -3x + b goes through the point B(5, 2), it means that the slope (m) of the line would be -3, while the line would intercept the y-axis at b.

To find the value of b, substitute (x, y) = (5, 2) into y = -3x + b:

2 = -3(5) + b

2 = -15 + b

2 + 15 = b

17 = b

b = 17

Thus, the equation of the line y = -3x + 17 would have a graph that is shown in the diagram attached below.

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Both Fahrenheit and Celsius scales will have the same reading at temperature -40⁰.

The equation to convert temperature reading from Celsius to Fahrenheit degree is:

     F = (9/5) C + 32

Where:

F = Fahrenheit reading

C = Celsius reading

The equation tells us that the ratio of increment in Fahrenheit to Celsius scale is 9 : 5, and there is an offset 32 degree in Fahrenheit scale.

Suppose a specific temperature has the same number reading on both scales, then:

F = C

Substitute this into the equation:

F = (9/5) C + 32

C = (9/5) C + 32

C - (9/5) C = 32

-4/5 C = 32

C = 32 . (-5/4) = -40

Hence, both Fahrenheit and Celsius scales have the same reading at temperature -40⁰.

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Answer:

Step-by-step explanation:

5y - 7z + 5x - Z - 8x + y =

6y - 8z -3x =

-3x + 6y -8z

The order from least to greatest is negative 7.7 repeating, negative seven and one sixth,  forty-four sixths and square root of 60

To determine the order from least to greatest is to arrange the values in an ascending order.

Given the values as;

This is expressed as;

√60 = 7. 75

-7. 7

44/ 6 = 7. 33

-7 1/6 = -43/ 6 = -7. 17

The order from least to greatest is -7. 7, -7. 17 , 7. 33 and 7. 75

Thus, the order from least to greatest is negative 7.7 repeating, negative seven and one sixth,  forty-four sixths and square root of 60

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Answer:

B

Step-by-step explanation:

-20+-32.5= -52.5

-52.5+ 40= -12.5

The required no . is 1 / q where q > 2 and q is natural no .

For instance , let's take 1 / 2 ,

1 / 2 is one possible solution to this .

1 / 2 is not irrational .

Opposite of 1 / 2 is 2 which is a natural no .

Clearly , 1 / 2 is not a whole no .

Even it is greater than - 13 .

All the conditions are satisfied , hence 1 / 2 is one possible solution to this problem .

All the nos . of the form 1 / q where q > 2 and q is natural no . will satisfy the conditions of the question .  

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Conversion a mixed number 9 7/

8

to a improper fraction: 9 7/8 = 9 7/

8

= 9 · 8 + 7/

8

= 72 + 7/

8

= 79/

8

To find a new numerator:

a) Multiply the whole number 9 by the denominator 8. Whole number 9 equally 9 * 8/

8

= 72/

8

b) Add the answer from previous step 72 to the numerator 7. New numerator is 72 + 7 = 79

c) Write a previous answer (new numerator 79) over the denominator 8.

Nine and seven eighths is seventy-nine eighths

Conversion a mixed number 2 3/

8

to a improper fraction: 2 3/8 = 2 3/

8

= 2 · 8 + 3/

8

= 16 + 3/

8

= 19/

8

To find a new numerator:

a) Multiply the whole number 2 by the denominator 8. Whole number 2 equally 2 * 8/

8

= 16/

8

b) Add the answer from previous step 16 to the numerator 3. New numerator is 16 + 3 = 19

c) Write a previous answer (new numerator 19) over the denominator 8.

Two and three eighths is nineteen eighths

Subtract: 79/

8

- 19/

8

= 79 - 19/

8

= 60/

8

= 4 · 15/

4 · 2

= 15/

2

For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of both denominators - LCM(8, 8) = 8. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 8 × 8 = 64. In the following intermediate step, cancel by a common factor of 4 gives 15/

2

.

In other words - seventy-nine eighths minus nineteen eighths is fifteen halfs.

Conversion a mixed number 24 4/

5

to a improper fraction: 24 4/5 = 24 4/

5

= 24 · 5 + 4/

5

= 120 + 4/

5

= 124/

5

To find a new numerator:

a) Multiply the whole number 24 by the denominator 5. Whole number 24 equally 24 * 5/

5

= 120/

5

b) Add the answer from previous step 120 to the numerator 4. New numerator is 120 + 4 = 124

c) Write a previous answer (new numerator 124) over the denominator 5.

Twenty-four and four fifths is one hundred twenty-four fifths

Conversion a mixed number 6 3/

5

to a improper fraction: 6 3/5 = 6 3/

5

= 6 · 5 + 3/

5

= 30 + 3/

5

= 33/

5

To find a new numerator:

a) Multiply the whole number 6 by the denominator 5. Whole number 6 equally 6 * 5/

5

= 30/

5

b) Add the answer from previous step 30 to the numerator 3. New numerator is 30 + 3 = 33

c) Write a previous answer (new numerator 33) over the denominator 5.

Six and three fifths is thirty-three fifths

Subtract: 124/

5

- 33/

5

= 124 - 33/

5

= 91/

5

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The value  −14 w+3 or 3w≥−27 is w ≥ 9W or w < - 7

An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made.

- 14 >w + ?

w < -17

3w>= -27

Consequently, w ≥ 9W or w < - 7

The direction of the inequality sign does not change if both sides of the inequality multiply or divide the same positive value.

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The amount of fiber in the banana will be 3.3 fibers.

From the information, Jason has a banana. He also has raisin bran cereal, which contains 3.6 grams of fiber and Jason eats 6.9 grams of fiber at breakfast.

Therefore, the equation to find the amount of fiber in the banana will be:

b = 6.9 - 3.6

b = 3.3

Therefore, the amount of fiber in the banana will be 3.3 fibers.

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Answer:

x+3=3+x

x+3=x+3

Step-by-step explanation: