Lucy used 3 3/4 cups of sugar for her lemonade stand. She divided the
sugar, in equal amounts, into 6 pitchers. How much sugar went into each
pitcher?

The line that passes through the pair of points has the given slope. ( − 2 , 8 ) , ( r , 4 ) , m = − 1 2, then the intersection with the domain is r = -5/3.

The line that passes through the pair of points has the given slope is,

( − 2 , 8 ) , ( r , 4 )  and m = -12

Slope, numerical measure of a line's inclination relative to the horizontal. In analytic geometry, the slope of any line, ray, or line segment is the ratio of the vertical to the horizontal distance between any two points on it (“slope equals rise over run”).

m = rise/run

[tex]m=\frac{y_{2} -y_{1} }{x_{2}-x_{1} }[/tex]

Where,

m = slope

[tex](x_{1} ,y_{1} )[/tex] = coordinates of first point in the line

[tex](x_{2} ,y_{2} )[/tex] =  coordinates of second point in the line

Then, we can find the [tex]m_{1}[/tex]

We can use these two values, ( − 2 , 8 ) , ( r , 4 )

x1 = -2

y1 = 8

x2 = r

y2 = 4

m = [tex]\frac{4-8}{r-(-2)}[/tex]

[tex]m = \frac{-4}{r+2}[/tex]

We can substitute m= -12 value into m= -(4/r+2)

So,

We can write,

-12 =  [tex]\frac{-4}{r+2}[/tex]

We can find the domain,

If the fraction is defined, the dominator can not be equal to zero.

2 + r ≠ 0

Rearrange variables to the left side of the inequality,

r ≠ -2

Append the inequality as the domain,

r ≠ -2

We can solve the equation,

-12 =  [tex]\frac{-4}{r+2}[/tex]

Multiply both sides of equation by the common denominator,

-12 (r+2) =  -4(r+2)/ (r+2)

Reduce the fractions,

-12 (r+2) = -4

Apply the distributive property,

-12r - 24 = -4

Rearrange variable to the left side of the equation,

-12r = -4 + 24

Calculate the sum or difference,

-12r = 20

Divide both sides of the equation by the coefficient of variables,

r = - 20/12

r = -5/3

Therefore,

The intersection with the domain is r = -5/3, so  the line that passes through the pair of points has the given slope. ( − 2 , 8 ) , ( r , 4 ) , m = − 12.

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Answer: 21 containers of ice cream

Step-by-step explanation: simple problem, take 126 and divide it by 6 to get your answer

The value of the numbers 3√5•√10+11√5•√10-√5 based on the information is D. 14✓50 - ✓5

It should be noted that based on the information given, we simply want to simplify 3√5•√10+11√5•√10-√5.

This will be illustrated as:

= 3√5•√10+11√5•√10-√5

It should be noted that the numbers inside the square roots will be multiplied. This will be:

= (3√5•√10) + (11√5•√10) -√5

= 3✓50 + 11✓50 - ✓5

= 14✓50 - ✓5

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I can help you with this equation, if you type it out correctly :). The input you made doesn´t make sense.

Answer:

7.719

Step-by-step explanation:

Answer: 3/24 or 1/8 of the pizza

Step-by-step explanation:..

The expression will be given as -4x² + 3x. Thus, option B is correct answer.

Area may be defined as the total amount of space which is covered by an entity. The area for a square will be given by the product of its sides and the area of the rectangle will be given as the product of its length and breadth. It is given that the area of Maria's garden is 8x² - 3x and the length and breadth of Jamal's garden are 4x - 2 and 3x respectively. The area of Jamal's garden is given by A = l×b  = (4x - 2) × 3x = 12x² - 6x.

Now, difference between Maria's garden and Jamal's garden is given by

(8x² - 3x) - (12x² - 6x)

= 8x² - 3x - 12x² + 6x

=> -4x² + 3x which is the required answer.

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The number of children is 123 and the number of adults is 150 for that day.

According to the question,

We have the following information:

273 people used the public swimming pool.

Price for children = $1.25

Price for adults = $2.50

The total amount received = $528.75

Now, let's take the number of children to be x and the number of adults to be y on that day.

So, we have the following expression:

x + y = 273

x = (273-y) .... (1)

1.25x + 2.50y = 528.75

Now, putting the value of x from equation 1:

1.25(273-y) + 2.50y = 528.75

341.25 - 1.25y + 2.50y = 528.75

341.25 + 1.25y = 528.75

1.25y = 528.75-341.25

1.25y = 187.5

y = 187.5/1.25

y = 150

Now, putting this value of y in equation 1, we will find the value of x:

x = 273-y

x = 273-150

x = 123

Hence, the number of children is 123 and the number of adults is 150 on that particular day.

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Due to different rates of change in each case, neither graph shows a proportional relationship.

A graph represents a proportional relationship if the output variable y in the y-axis can be written as a product of the input variable x in the x-axis and the constant of proportionality k, as follows:

y = kx.

For the first case, the rate of change is of:

k = 4/10 = 0.4.

For the second case, the rate of change is of:

k = 8/10 = 0.8.

Different rates, hence cannot be written as proportional relationship.

Hence the rates for each interval are given as follows:

Different rates, hence it is not a proportional relationship.

The graphs are missing and are given by the image inserted at the end of the answer.

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Answer: x < 2

Step-by-step explanation:

    To solve this, we will isolate the variable c.

   Given:

4c < 14 - 3c

   Add 3c to both sides of the equation:

7x < 14

   Divide both sides of the equation by 7:

x < 2

The scissor has intersecting lines with angles 1,2,3,4.The angles are ∠1=159° and ∠3 is 159°. We got the angle ∠2=21° and ∠4=21°.

Given that,

In the picture there is a scissor.

The scissor has intersecting lines with angles 1,2,3,4.

∠1=159° and ∠3 is 159°.

We have to find the angles ∠2 and ∠4.

Two straight lines that intersect at the same location are said to be intersecting lines. The junction point is the place where two intersecting lines meet. Four angles are created when two lines cross. The four angles added together always equal 360 degrees. There is a unique connection between the angles created when lines intersect.

The straight line has 180°

∠1+∠2=180°

159°+∠2=180°

∠2=180°-159°

∠2=21°

Now,

∠3+∠4=180°

159°+∠4=180°

∠4=180°-159°

∠4=21°

Therefore, the angle ∠2=21° and ∠4=21°.

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Answer:

c=-12

Step-by-step explanation:

Let's solve your equation step-by-step.

2/3c−2=2+c

Step 1: Simplify both sides of the equation.

2/3c−2=2+c

2/3c+−2=2+c

2/3c−2=c+2

Step 2: Subtract c from both sides.

2/3c−2−c=c+2−c

−1/3c−2=2

Step 3: Add 2 to both sides.

−1/3c−2+2=2+2

−1/3c=4

Step 4: Multiply both sides by 3/(-1).

(3/−1)*(−1/3c)=(3/−1)*(4)

c=−12

Answer:

c=−12

Answer: $10.50

Step-by-step explanation:

Cot of 1 slice a pizza = $1.75

Cost of 6 slices of pizza = 6 × $1.75

=$10.50

Hence, Robert will pay $10.50 for the 6 slices of pizza and $20 for the membership.

The equation to determine the number of hours worked by the plumber is 190 = 35 + 50x and the number of hours is 3.1 hours option (A) is correct.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that:

Jerald is having drain issues at his home and decides to call a plumber.

The plumber charges $35 to come to his house and $50 for every hour they work.

Let x be the number of hours:

190 = 35 + 50x

50x = 155

x = 3.1 hours

Thus, the equation to determine the number of hours worked by the plumber is 190 = 35 + 50x and the number of hours is 3.1 hours option (A) is correct.

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We can simplify the numerical expression to get:

(2/5)*(14 - 27) + (2⁵/16) = -16/5

Here we have the expression:

(2/5)*(14 - 27) + (2⁵/16)

Let's simplify the term in the right first, we know that:

2⁵ = 2*2*2*2*2 = 4*4*2 = 16*2 = 32

Replacing that we get:

(2⁵/16) = 32/16 = 2

Then we get:

(2/5)*(14 - 27) + (2⁵/16) = (2/5)*(14 - 27) + 2

Now we can simplify the term in the left:

(2/5)*(14 - 27) = (2/5)*(-13) = -26/5

Replacing that we get:

(2/5)*(14 - 27) + 2 = -26/5 + 2 = -26/5 + 10/5 = -16/5

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r and s are the parallel lines, if ∠4 equals ∠5.

Given,

The figure with,

Four lines: Line r, Line s, Line l and Line m.

Angles: ∠1, ∠2, ∠3, ∠4, ∠5, ∠6, ∠7 and ∠8

Here, we have to find the parallel lines when ∠4 = ∠5

Lets see:

Angle 1 and angle 4 are the same because the opposite angles created by two crossing lines are identical. As a result, angle 1 also equals angle 5.

The corresponding angles are identical when two parallel lines cross across a line. To put it another way, if r and s are parallel, the angles created when l intersects r and s are same. Angle 1 equals Angle 5, Angle 2 equals Angle 6, etc. We can infer that r and s are parallel since we know that angle 1 Equals angle 5.

So, we can conclude that if ∠4 equals ∠5, then r and s are the parallel lines.

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7 × 12 = 72 satisfies the closure property of multiplication, the other integer when the sum is - 38 and one integer is - 22 will be - 16 and the total score for Gopi will be 112 marks.

1)

Closure property of multiplication:

It states that if  two real numbers a and b are multiplied, then the product will be a real number as well.

We have 7 × 12 = 72

7, 12 and 72 all are real numbers.

So, it is a closure property under multiplication.

2)

Sum = - 38

a = - 22

We need to find b

a + b = - 38

- 22 + b = - 38

b = - 38 + 22

b = - 16

3)

1 correct answer = 4 marks

1 incorrect answer = - 2 marks

Number of correct answers = 32

Number of incorrect answers = 8

Total score = 32 × 4 + (- 2) × 8

= 128 - 16

= 112 marks.

Therefore, we get that, 7 × 12 = 72 satisfies the closure property of multiplication, the other integer when the sum is - 38 and one integer is - 22 will be - 16 and the total score for Gopi will be 112 marks.

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The reflective Property of Congruence states that any figure is congruent with itself, therefore line LR ≅ line RL and ∠CBA ≅ ∠ABC.

If it is possible to superimpose one geometric figure on the other so that their entire surface coincides, that geometric figure is said to be congruent or to be in the relation of congruence.

Reflexive Property of Congruence said that an angle line segment or any shape is congruent with itself.

For example, a line segment with a length of 5 meters will be the same as another line with 5 meters or a copy of that line so both will be congruent.

Line LR and RL are the same in length thus line LR ≅ line RL.

Angle CBA and angle ABC are the same thus ∠CBA ≅ ∠ABC.

Hence "The reflective Property of Congruence states that any figure is congruent with itself, therefore line LR ≅ line RL and ∠CBA ≅ ∠ABC".

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The diagram prove that  m ║n by the consecutive interior angles converse.

The diagram is to prove line m is parallel to line n.

Therefore,

m ║ n

Hence,

m∠1 = 115°, m∠2  = 65° is given.

m∠1 + m∠2 = m∠1 + m∠2 follows the reflexive property of equality.

The reflexive property of equality means that anything is equal to itself

m∠1 + m∠2 = 115° + 65° is the substitution property of equality

Supplementary angles add up to 180 degrees.

m∠1 + m∠2 = 180 is the definition of supplementary angles

∠1 and ∠2 are supplementary when simplify

m ║ n by consecutive interior angles converse.

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Answer: 80

Step-by-step explanation:

72.4 = 724/10

9.38=

938/10.

72.4/9.38

= 7.7

=8 approximately

The estimated quotient of 72.4 ÷ 9.38 is 8

Estimation is the process of calculating the approximate value to make the calculation easier and simple.

The rounding off a number is the process of putting a number up or down to the nearest whole number or the nearest tens, hundred, thousand, etc

First number is 72.4

Round the number to the nearest whole number

72.4 = 72

Second number is 9.38

Round the number to the nearest whole number

9.38 = 9

Divide the number 72 by 9

72/9 = 8

The quotient is 8

Hence, the estimated quotient of 72.4 ÷ 9.38 is 8

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Answer:

you could either make the fraction a decimal or my personal like is to make the decimal a fraction

Step-by-step explanation:

convert the fraction to a decimal or decimal to fraction

The △ABC is congruent to △DCB (△ABC ≅ △DCB) under the SAS condition.

So, △ABC ≅ △DCB:

So, △ABC ≅ △DCB is under SAS condition.

Therefore, the △ABC is congruent to △DCB (△ABC ≅ △DCB) under the SAS condition.

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The selling price of the car is 77,000.

First, let's define what a selling price is.

The selling price is the price the customer pays to purchase the good.

Selling price = Cost price – (100% Loss)/100

We are told that the car cost 70,000 and that 17,500 was lost (12%) in repairs and painting.

The car's total cost is equal to 70,000 + 17,500 = 87,500.

So, the car's cost price is 87,500.

Selling price = 100/12/100 x cost price

= 100/12/100 x 87,500

= 0.88 x 87,500

= 77,000

Consequently, the car is being sold for $77,000.

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Answer:

x = +/-[tex]\frac{\sqrt{291} }{3} -6[/tex]

Step-by-step explanation: