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The distance between these two lines  y=1/2x+2 and x-2y=6 is 10/√5

Distance between two lines:

We know that, the parallel lines can be extended till infinity. The slopes of two parallel lines are equal.

Distance d between two parallel lines

y = mx + c1 and

y = mx + c2 is calculated by the

d = |C1–C2|/√(A² + B²)

Given,

Here we have the two line equation they are,

y=1/2x+2 and x-2y=6

And we need to find the distance between them.

To find the distance between the lines, then we ahve to make the equation into standard form, that is,

y = mx + c

Here the first equation is in standard form, so we have to convert the second one,

So, the second equation is written as,

x - 2y = 6

-2y = 6 - x

y = (6 - x)/-2

y = -3 + 1/2 x

y = 1/2 x - 3

Now, we have to derive the value of the following from the given equation, then we get,

Slopes are same m1 = m2 = 1/2 and c1 = 2 ,c2 = -3.

here a = 1/2, b = -1

Now, apply the values on the formula, then we get,

d = |2 - (-3)|/√(1/2)² + (-1)²

d = 5/√1/4 +1

d = 5/√5/4

d = 5/√5/2

d = 10/√5

Therefore, the distance between these two equation is 10/√5.

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The proof that shows that triangles PQR and TSR are similar by AA similarity theorem is explained below.

The AA similarity theorem proves that two triangles are similar if we can show that two of its corresponding angles are congruent to each other.

Therefore, for triangles PQR and TSR to be similar by the AA similarity theorem, they must have two corresponding congruent angles.

The proof below shows the triangles, ΔPQR ~ ΔTSR are similar to each other:

Statement                                             Reasons                                              

1. QR ⊥ PT                                             1. Given

2. ∠QRP and ∠SRT are right angles   2. Def. of perpendicular

3. ∠QRP ≅ ∠SRT                                  3. All right angles are ≅

4. ∠QPR ≅ ∠STR                                  4. Given

5. ΔPQR ~ ΔTSR                                   5. AA similarity theorem

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Answer:

nicholas' score is -120 points

Step-by-step explanation:

-85-35=-120

The  number of visits thay Liam can make to earn his first free movie ticket is 9 visit.

Let x represent the number of visits

Since he receives 50 rewards points just for signing up and earns 12.5 points for each visit to the movie theater. This will be illustrated as:

50 + 12.5x >= 160

12.5x >= 160 - 50

12.5x >= 110

Divide

x >= 110/12.5

x >= 8.8

Therefore, he will need at least 9 visit.

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Liam has a points card for a movie theater.

He receives 50 rewards points just for signing up.

He earns 12.5 points for each visit to the movie theater.

He needs at least 160 points for a free movie ticket.

Write and solve an inequality which can be used to determine xx, the number of visits Liam can make to earn his first free movie ticket.

The measure of the base of the triangle is 14 ft.

A triangle is a polygon with three sides.  The sum of angles in a triangle is 180 degrees.

Therefore, the area of a triangle can be calculated as follows:

area of a triangle  = 1 / 2 bh

where

Therefore,

area of the triangle = 28 ft²

height of the triangle = 4 ft

base of the triangle = ?

Hence,

area of the triangle  = 1 / 2 × b × 4

28 = 1 / 2 × b × 4

28 = 4b / 2

28 = 2b

divide both sides by 2

b = 28 / 2

b = 14

Therefore,

base of the triangle = 14 ft

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The measure of the base of the triangle would be; 14 ft.

A triangle is a polygon with three sides.  The sum of angles in a triangle is 180 degrees.

Therefore, the area of a triangle can be calculated by the formula;

The area of a triangle  = 1 / 2 b h

where

b = base

h = height

Thus,

The area of the triangle is 28 ft²

The height of the triangle = 4 ft

The base of the triangle =?

Hence,

Area = 1 / 2 × b × 4

28 = 1 / 2 × b × 4

28 = 4b / 2

28 = 2b

Then divide both sides by 2

b = 28 / 2

b = 14

Therefore, the base of the triangle is 14 ft

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If Johny receives £x, then Sara will receive £4x (Given ratio is 1:4).

In mathematics, a ratio shows how many times one number is contained in another.

For instance, if there are eight oranges and six lemons in a fruit plate, the orange to lemon ratio is eight to six (that is, 8:6, which is equivalent to the ratio 4:3).

Similarly, the ratio of oranges to total fruit is 8:14, while the ratio of lemons to oranges is 6:8 (or 3:4). (or 4:7). Numbers in a ratio can represent any quantity, including counts of people or objects, weights, lengths, times, and so on. Most of the time, both numbers have to be positive.

If Johny receives £x, then Sara will receive £4x (Given ratio is 1:4).

assumable, 4x - x = £69

or, 3x = 69

or, x = 69/3 = £21

Then Johny receives £21 and Sara receives £84 (4x£21).

Becky receives £(138-(21+84)) = £33 as well.

Her proportion in the ratio is equal to (33/138) x 100% (23.91%).

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The Z-score for the 40-week gestation period baby weights 2450 grams is -0.86 is smaller.

The provided deals with Z-scores. A Z-score shows how many standard deviations away from the mean an element is. A numerical evaluation of a value's relationship to the mean within a group of values is called a Z-score. Z-scores can also be favorable or unfavorable.

The score is above the mean, as indicated by the positive value.

The score is below average as indicated by the negative value.

Given the information,

The mean weight and standard deviation of newborns born after a gestation of 32 to 35 weeks are 2700 grams and 800 grams, respectively.

Consequently, the 33-week gestation baby's Z-score is 2250 grams.

Z = σx − μ​ = (2250−2700) / 800 ​= -450 / 800 ​= −0.5625

The goal is to calculate the Z-score for babies born at 33 weeks gestation.

There is sufficient data to infer, based on the Z-score, that the 33-week gestation period falls 0.56 standard deviations below the mean.

According to the data, babies that are born after a gestation of 40 weeks have a mean weight of 2900 grams and an average range of 445 grams.

Consequently, the baby's Z-score at 40 weeks of pregnancy, weighing 2450 grams, is

Z = σx − μ ​= 385 / 2450 − 2900 ​= 385 / -450 ​= -0.86

The goal is to calculate the Z-score for baby weights at 40 weeks of gestation.

There is sufficient data to infer, based on the Z-score, that the 40-week gestation time falls 0.86 standard deviations below the mean.

The infant weighs 2250 grams at 33 weeks gestation, and the Z-score is -0.56.

The baby weighs 2450 grams at 40 weeks of pregnancy, and the Z-score is -0.86.

Since the infant weighs 2450 grams during 40 weeks of gestation, the Z-score for that period is lesser at -0.86.

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Answer:

The correct graph would be D.

Step-by-step explanation:

Since the sign is greater than, we know that it will be a open circle. So, our answer is c. or d.

To solve this problem, distribute, and you get:

3x+9>x+33

Subtract 3x on both sides.

9>-2x+33

Subtract 33 on both sides

9-33=

-24

-24>-2x

Divide by -2 on both sides.

Since we divided by a negative, switch the signs.

12<x

Now, find a graph that is equal to 12<x.

The correct graph would be D.

Hope this helps! ~~

Answer: by gamelover

commission of each accessory = $2

commission of each phone = $9

Given:

Commission on 18 phones and 21 accessories = $204 commission on 6 phones and 14 accessories = $82.

To find:

the price of each phone and the price of each accessory.

Solution:

let the commission of each phone be P and the accessory be A.

according to the question,

18P + 21A = 204

6P + 7 A = 68 -----i

6P + 14 A = 82 ------ii

by substitution of i in equation ii,

68 - 7A + 14A = 82

7A = 14

A = 2

commission of each accessory = $2

to find the commission on each phone:

6P + 7 x 2 = 68

6P = 54

P= 9

commission of each phone = $9

Hence, the required answers are 2 and 9.

Answer:

1 ⅜

Step-by-step explanation:

⅝ + ¾ = 11/8 or 1 ⅜

For the given question, the line AC and DF are found to be parallel lines.

Parallel lines are two or more lines which lie within the same plane but never intersect.

The basic properties listed below make it simple to identify parallel lines.

For the given parts:

Part 19: Line AC || Line DF

57° + ∠B = 180° (linear pair)

∠B = 123°

∠B = 123° (corresponding angles are equal)

Thus, Line AC || Line DF

Part 20: Line AC || Line DF

∠B = 143°  (vertically opposite angles)

Then, ∠B + 37°  = 143° + 37°  = 180° (linear pair)

Thus, Line AC || Line DF

Part 21: Line AC || Line DF

62° + ∠B = 180° (linear pair)

∠B = 118°

And, ∠E = 62° (alternate interior angles)

So, ∠B + ∠E = 118° + 62° = 180° (linear pair)

Thus, Line AC || Line DF

Part 22: Line AC || Line DF

∠B = 180° - 115° = 65°

∠B = 65° (alternate interior angles)

Thus, Line AC || Line DF

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To find out if the system has a single solution, we have to check wheter its equations are not equivalent to one another and no equation contraticds the others.

If these are some cases, we will find out while we answer, because you will either find an equation that the variable can have any number or we will get to an equation that is wrong for any value of the variable.

To find the solution, we will have to reduce the system to two variable and then to one variable.

To do this, we can pick a variable to get rid of and pair equations so we can achieve this.

Let's get rid of variable y by elimination.

Firstly, we can see that the first equations can by simplifies by dividing it by 3:

Now, since we want to eliminate y, we need to match its coefficient with another equation, but with opposite sign.

The second equation has a coefficient of -2 on y, so if we multiply the first simplified equation by -2, we will get:

Now, we can add this equation with the second:

Now, we will do similarly but with the last equation. The coefficient of y on it is -4, so we multiply the first simplified equation by (-4):

And add the third equation to it:

Notice that we can change the sign of all terms on this equation:

Now, we have two equations and two variable:

However, notice that the left side of the equations are equivalent, because if we multiply the first equation by two, we will get the pair:

So, the left side is equivalent, but the right sides are different, this means that one equation contradicts the other, That is, there is no possible pair of x and z so that these equations are both true.

This means that there is no solution to this system of equations.

Answer:

8

Step-by-step explanation:

D=wp+4

D-4=wp

D-4/w=p

p=100-4/12

p=96/12

p=8

Answer:

Dp/(wp+4)=p

Step-by-step explanation:

Number 1 D=wp+4

p×D=wp×p+4×p

=Dp=wp²+4p

=Dp=p(wp+4)

=from here you will divide both sides (wp+4) to get your answer

Number 2. 100p/(12p+4)=p

so from here 4 will divide 100 25 times leaving the answer 25p/12p=p

The percentage decline in profits (to the nearest tenth) is 7.4%.

The smallest percentage fall in profits as a percentage of sales occurred in the food business between 1966 and 1970.  

A percentage is any quantity or ratio that may be expressed as a portion of 100. If we want to calculate a percentage of a number, we should first divide it by 100 before multiplying it by the remainder. The proportion, therefore, denotes a component per 100. The word percent denotes a percentage of 100.

Percentage = (Difference / Total) * 100

According to the question,

Decline percentage = ((2.7-2.5)/2.7)*100

                                 = 7.4%

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well, is simply the price plus tax, so

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{5.65\% of 15.99}}{\left( \cfrac{5.65}{100} \right)15.99} ~~ \approx ~~ 0.90~\hfill \underset{total~cost}{\stackrel{15.99~~ + ~~0.90}{\approx\text{\LARGE 16.89}}}[/tex]

The restaurant can make 992 pancakes in 2 hours

Given

The restaurant uses 124 cups every hour

Each cup can be used to make 4 pan cakes.

Since 1/4 cups of mix can make one pancake.

All the pancakes are in equal size

Since 4 pancakes can be made from one cup of mix

The restaurant uses 124 cups of mix which means

For an hour the restaurant produces 4 x 124 pancakes Which is equal to 496 pancakes

In two hours The restaurant can make double that of one hour

Hence 496 x 2

992

The restaurant can make 992 pancakes in two hours

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Answer:

A is actually correct :)

Step-by-step explanation:

1/5^6

:]

Step-by-step explanation:

(9)

9x + 5y = 35

-2x - 5y = 0

---------------------

7x 0 = 35

(10)

7x = 35

x = 5

(11)

we pick one of the 2 equations, e.g.

-2x - 5y = 0

-2×5 - 5y = 0

-10 - 5y = 0

-10 = 5y

y = -10/5 = -2

Using linear functions, it is found that:

A linear function is modeled as follows:

y = mx + b.

In which the parameters of the function are as follows:

For the cost functions in this problem, we have that:

Hence the functions are given as follows:

The costs will be the same when:

A(x) = B(x)

Hence:

50 + 10x = 60 + 8x

2x = 10

x = 5 GB are used.

If two functions have the same slope and different intercept they are parallel, that is, they never intersect, hence if company A starts charging $8 per GB, this will happen.

The costs will always be the same when the functions are equal, that is, if:

B(x) = A(x) = 50 + 10x.

Decreasing the flat fee to $50 and increasing the cost per GB to $10.

The complete problem is:

Liam is comparing the costs of phone plans at two different companies to determine which plan to buy. Company A charges $50 each month plus an additional $10 per gigabyte of data used. Company B charges $60 each month plus an additional $8 per gigabyte of data used. The following equation represents the cost of the phone plans for the two companies when they are equal, where g represents the amount of gigabytes of data used.

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Answer:C

Step-by-step explanation:

Answer:

13 1/3 pages

Step-by-step explanation:

Unit rate = 5 p / 3 h

5p / 3 h  * 8h = 13 1/3 page

Answer:

h = 2.5 cm

Step-by-step explanation:

the volume (V) of a triangular prism is calculated as

V = area of triangular end × length , that is

V = [tex]\frac{1}{2}[/tex] bh × l

given b = 4, l = 7 and V = 35 , then

[tex]\frac{1}{2}[/tex] × 4 × h × 7 = 35

14h = 35 ( divide both sides by 14 )

h = 2.5 cm

The model given is:

The term in the parentheses represents the change of rate of the model. If the number is the parentheses is less than 1, we call it exponential decay.

If the number in parentheses is bigger than 1, we call it exponential growth.

In this case, the correct option is "decaying"

The number in parentheses let's call it R, is:

Where r is the rate of change. To find it:

To convert to percentage, we convert by multiplying by 100::

The second answer is 0.45%

And since t is the time passed in hours, and has a "60" multiplying it, the last answer is: Every 60 hours

The final answer is:

The function is exponentially decaying at a rate of 0.45% evary 60 hours.

Based on the dimensions of the rectangle, the number of square inches that are in the rectangle are 23,040 inches ²

x

First, convert the units of the rectangle from feet to inches so that it is easier to find the area.

Length of rectangle in inches:

= 16 x 12 inches per ft

= 192 inches

Width of rectangle:

= 10 x 12 inches per ft

= 120 inches

The area is:

= 192 x 120

= 23,040 inches ²

In conclusion, there are 23,040 square inches in the rectangle.

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According to the formula of cylindrical volume, we can find out that the rate at which the height of the water level is changing is [tex]\frac{3}{200\pi } inch/min[/tex].

Water is increasing at a rate of ( 3/200π ) inch/min in a cylindrical tank.

It is given to us that, for a right cylindrical tank,

Radius of the base, r = 20 inch ----- (1)

The rate of water poured into the cylindrical tank,

[tex]\frac{dV}{dt}[/tex] = 6 cubic inch per min ------- (2)

We have to find out the rate of change of height when the water level is 12 inches high.

This implies, we need to calculate [tex]\frac{dh}{dt}[/tex].

To find out [tex]\frac{dh}{dt}[/tex] , we have to use the equation for the volume of a right cylinder.

Let us say, the volume of cylinder is represented as V

We know, the formula of volume of a cylinder is

[tex]V = \pi r^{2} h[/tex] ------(3)

Substituting the value of r from equation 1 in equation 3, we will get

[tex]V = \pi r^{2} h\\= > V = \pi 20^{2} h\\= > V = \pi 400 h[/tex] ----- (4)

Differentiate equation (4) with respect to time,

[tex]\frac{d}{dt} V = \frac{d}{dt}[ \pi 400 h]\\= > \frac{dV}{dt}= \pi 400\frac{dh}{dt}[/tex] ----- (5)

Substituting the value of [tex]\frac{dV}{dt}[/tex] from equation (2) in equation (5), we have

[tex]6 = \pi 400\frac{dh}{dt}\\= > \frac{dh}{dt} = \frac{6}{400\pi }\\= > \frac{dh}{dt} = \frac{3}{200\pi } inch/min[/tex]

Thus, [tex]\frac{3}{200\pi } inch/min[/tex]  is the rate at which the height of the water level is changing.

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Answer:

See below

Step-by-step explanation:

Step-by-step explanation:

I assume you need the equation in slope-intercept form :

y = ax + b

"a" is the slope, "b" is the y-intercept (the y-value when x = 0).

the slope is defined as ratio (y coordinate change / x coordinate change) when going from one point on the line to another.

let's use the 2 points, where the line intersects the x- and the y- coordinate axis : (0, 9) and (9, 0)

that gives us "b" already : the y-value when x = 0 is 9.

about the slope "a" :

x changes by +9 (from 0 to 9).

y changes by -9 (from 9 to 0).

the slope is then -9/+9 = -1/1 = -1

and the equation is

y = -x + 9

The rate of change of the graph of what the health club charges is; 43

The rate of change is simply the slope of the graph which is the change in y-values per change in corresponding x-values. Thus;

Rate of change here is;

Slope = (y₂ - y₁)/(x₂ - x₁)

We have two coordinates as; (3, 169) and (8, 384) which represents the graph of what the health club charges.

Thus;

Rate of change = (384 - 169)/(8 - 3)

Rate of change = 43

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Answer:

0.3016

Step-by-step explanation:

If we have an 8 letter code word...

Total number of possible letters = 26

The number of letters possible = 8

So...

26 ^ 8 = 0.3016

Hope this helps!

Answer:

[tex]\approx 0.30164[/tex]

Step-by-step explanation:

The Alphabet contains 26 characters, and to better understand this probability, let's do each letter one step at a time.

Any letter being chosen should have an equal probability of: [tex]\frac{1}{26}[/tex], and for the first letter we don't really have to worry about choosing a non-repeated letter, since it's impossible to have a non-repeated letter on the first letter... since it's the first letter, so no other letter has been chosen.

This means we have a probability of: 1 to get a non-repeated letter when we choose the first letter.

The probability when we choose the 2nd letter is different, since there is a possibility of choosing a repeated letter. As stated above, the probability of choosing any one letter should be equal for each letter and is: [tex]\frac{1}{26}[/tex]

Since we want to avoid this one letter we choose in the beginning, the probability of choosing it is: [tex]\frac{1}{26}[/tex], which means the probability of not choosing it is: [tex]\frac{25}{26}[/tex]

For the 3rd letter it follows the same pattern, assuming we have two non-repeated letters, the probability of choosing a repeated letter from the previous two is there combined probabilities of: [tex]\frac{1}{26} + \frac{1}{26} = \frac{2}{26}[/tex]. Since we want a non-repeated letter, we subtract this probability from one, because the entire probability will equal one.

This gives us a probability of: [tex]\frac{24}{26}[/tex] of choosing a non-repeated letter.

You'll notice a pattern, the numerator is decreasing by one! This makes sense since each time we choose a non-repeated letter, well the number of non-repeated letters will decrease by one.

This gives us the probability for each letter up to eight letters

[tex]\frac{26}{26}, \frac{25}{26}, \frac{24}{26}, \frac{23}{26}, \frac{22}{26}, \frac{21}{26}, \frac{20}{26}, \frac{19}{26}[/tex]

To get an eight letter code that has no no repeated letters, all these events have to occur. To find the collective probabilities of all these events happening, we simply multiply them, assuming they're independent which we have no reason to believe they aren't independent.

This gives us a total probability of approximately: [tex]0.30164[/tex]

Mac drives 2921 miles per week as compared to Tia

Comparing numbers is a technique for determining if one number is equal to, smaller than, or larger than the other numbers. To compare two numbers, we write them using several symbols. In our daily lives, we make comparisons of figures, such as the daily temperature, the cost of things used on a regular basis, our height and weight, etc. The number with more digits is greater than the number with fewer digits when they are natural numbers.

Miles drove by Tia = 127 miles a week

Miles driven by Mac = Miles driven by Tia*23

= 127*23

2921

So, Mac drove 2921 miles

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