Michael and Sondra are mixing lemonade. In Michael’s lemonade, the ratio of lemons to water is 1:4. In Sondra’s lemonade, the ratio of lemons to water is 2:6. Several equivalent ratios for each mixture are shown in the ratio tables.

Michael
Lemons
Cups of Water
1 4
3 12
4 16
Sondra
Lemons
Cups of Water
2 6
4 12
6 18

Imagine that you want to compare Michael’s ratio to Sondra’s ratio. Which two ratios in the tables shown have a common denominator you could use to compare?

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According to the question an example of C = 3 and D = 2 supports the answer that Equation A gives a bigger value than Equation B.

Two equations are considered to be comparable when their roots and solutions line up. To create an equivalent equation, the identical quantity, symbol, or expression has to be added to or removed from both of the equation's two sides. We can also create a similar equation by dividing or multiplying each component of an equation with a nonzero value.

given,

To determine which equation would give a bigger value, we can compare the expressions obtained by expanding Equation A and simplifying Equation B.

Expanding Equation A, we get:

A = (C + D) x (C + D) = C² + 2CD + D²

Simplifying Equation B, we get:

B = 2 x (C + D) = 2C + 2D

To compare the values of A and B, let's choose some values for C and D that are greater than zero. Let's choose C = 3 and D = 2.

Plugging these values into Equation A, we get:

A = 3² + 2(3)(2) + 2² = 9 + 12 + 4 = 25

Plugging these values into Equation B, we get:

B = 2(3 + 2) = 2(5) = 10

Since A is greater than B for the values of C = 3 and D = 2, we can conclude that Equation A gives a bigger value than Equation B for positive values of C and D.

Therefore, an example of C = 3 and D = 2 supports the answer that Equation A gives a bigger value than Equation B.

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The equation of the circle graphed is (x + 4)² + (y + 5)² = 16

From the question, we have the following parameters that can be used in our computation:

The circle (see attachment for complete question)

Where, we have

Center = (a, b) = (-4, -5)

Radius, r = 4 units

The equation of the circle graphed is represented as

(x - a)² + (y - b)² = r²

So, we have

(x + 4)² + (y + 5)² = 4²

Evaluate

(x + 4)² + (y + 5)² = 16

Hence, the equation is (x + 4)² + (y + 5)² = 16

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Answer:

7.30

Step-by-step explanation:

number 13 is simple subtraction.

If two triangles are similar, then their side lengths are proportional.

RS / JK = RT / JL

5 / x = 4 / 7

4x = 35

x = 35/4 = 8.75

RT / JL = TS / LK

4 / 7 = 6 / (y + 2)

42 = 4(y + 2)

42 = 4y + 4

4y = 38

y = 38/4 = 9.5

LK = 9.5 + 2 = 11.5 cm

JK = x = 8.75

Hope this helps!

Answer:

the first page :

x =20

the second page :

x = 45

Step-by-step explanation:

first question

to find angle BOC subtract 110 from 180( because 180 degrees is a straight line)

angle BOC = 70 degrees

this means that the angle opposite to it is also 70 degrees ( DOA)

now to find x, add up 110, 70, 70, 90, x to get 360

110 + 70 + 70 + 90 + x = 360

x = 20

second question :

every thing adds up to 360 degrees.

90 + 5x + x = 360

6x = 270

x = 45

Part A: We can complete the model representing Sage's minutes by putting n and 7 in the box.

Part B: We can complete the model representing Tom's minutes by putting n and 7 in the box

Part C: An algebraic expression to represent the number of minutes Sage has left is S = n - 7, where S equals the remaining talk minutes for Sage and n is the initial number of talk minutes.

Part D. An algebraic expression to represent the number of minutes Tom has left is T = n - 7, where T equals the remaining talk minutes for Tom and n is the initial number of talk minutes.

Part E: Sage and Tom have the same number of talk minutes left on their cell phone plans because they started with the same amount and consumed the same amount at the end of the month.

An algebraic expression is a mathematical expression that consists of variables and constants, along with algebraic operations and equality or inequality symbols.

The basic algebraic operations include addition, subtraction, division, and multiplication.

Thus, algebraic expressions can be used to mathematically model or represent the number of minutes that Sage and Tom have left.

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A' - (-1,4)

B' - (-1,8)

C' - (-5,4)

hope this helps

Answer: You can buy a maximum of 15 gallons of gas for $54.

To see why, you can divide the total amount of money you have by the cost per gallon:

$54 ÷ $3.60/gallon = 15 gallons

Step-by-step explanation:

Answer:

The common difference in the given sequence is 5.

Step-by-step explanation:

The common difference in the sequence is 5 because they all add by 5 each time for example 5 + 5= 10 and 10+5=15

Answer:

6,930

Step-by-step explanation:

9,702 times 5 enemies=48,510

48,510 points divided by 7 lives=6930

In the given similar triangles below, we have to find the measure of Dwrite. Triangle 1, ABC, is similar to Triangle 2, DEF. The two triangles are similar because their corresponding angles are congruent and their sides are proportional.

In order to find the measure of Dwrite, we can use the concept of proportionality. The sides of similar triangles are proportional to each other.

This means that if we know the ratio of the sides of one triangle, we can use that ratio to find the corresponding sides of the other triangle. We can use this property to find the value of Dwrite.

To start, let's write down the ratio of the sides of Triangle 1 and Triangle 2. We can choose any two corresponding sides to do this, but we'll choose AB and DE because they are easiest to measure: AB/DE = 6/8.5We know that the measure of AB is 6, so we can solve for the measure of DE: DE = AB x (DE/AB)DE = 6 x (8.5/6)DE = 8.5Now we know that the measure of DE is 8.5.

We can use this to find the measure of Dwrite. We know that DE and Dwrite are corresponding sides of Triangle 2 and Triangle 1, respectively.

So we can write a proportion using the ratio of DE to Dwrite: DE/Dwrite = 8.5/xWe know that DE is 8.5, so we can substitute that in:8.5/Dwrite = 8.5/Now we can solve for x by cross-multiplying:8.5x = 8.5Dwrite = 1Therefore, the measure of Dwrite is 1.

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Four triangles can create a set of pattern blocks that includes a total of four rhombuses.

To understand why, it's essential first to understand what pattern blocks are. Pattern blocks are shapes that are commonly used in early childhood education to teach math concepts like geometry, spatial reasoning, and fractions. They come in different shapes, including triangles, squares, hexagons, trapezoids, and rhombuses.

To create a set of pattern blocks using triangles, one can use four equilateral triangles with the same side length. When these triangles are arranged together, they form a larger equilateral triangle, as each external side of each small triangle connects to a side of another triangle. This larger equilateral triangle can then be divided into four smaller rhombuses by using two diagonals (lines connecting opposite corners) to form a "X" shape. Each of these four smaller rhombuses is made up of two adjacent triangles and forms a diamond shape. Therefore, it can be said that four equilateral triangles can form a set of four rhombuses within an equilateral triangle pattern block set.

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Answer:

63/100 or 63%

Step-by-step explanation:

Answer:

The percent that represents the model is 63%

Step-by-step explanation:

The model is 100 squares, correct? Well, there are 63 shaded. We can easily put that into a percent because percents are always out of 100. In other words, if there was X/100, the X would be the percent. In this case, 63 is in the X spot because that is how many there are shaded, which makes the percent 63%.

Hope this helps <3

Answer:

5/6 quarts of water

Step-by-step explanation:

2/3 same as 4/6. 4/6 + 1/6 = 5/6

8 less than a number

what this simply means is that

the number is greater than 8

Let the number be n

this means n is greater than 8

n - 8

by the time you substract 8 from n then your answer will be positive

n could be 9 , 10 etc but ut must be greater than 8

Answer: Yes they are similar and the ratio is 1 to 3

Step-by-step explanation:

They are similar because they are the same shape and the ratio is 3 because you can multiply each side by 3 to get the other figure's length.

Answer:

Yes she is correct

Step-by-step explanation:

Suppose before we add and additional element x to a set A the number of subsets are n.

Now we can think of the subsets of the new set A union x as the subsets containing x and the subsets that are not containing x.

The subsets that are not containing x are exactly the former n subsets of A and the subsetes that are containing x is obtained by appending x to each of the n subsets. So we get another n subsets.

Therefore there are n + n =2n subsets which is double of the original subsets.

Therefore, there are n + n = 2n subsets which are doubled of the original subset.

Sets are the collection of well-defined elements. A set is represented by a capital letter symbol and the number of elements in the finite set is shown as curly bracket {..}.

A ratio is an ordered pair of numbers a and b, written as a/b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other.

Given

Every time they add an element to a set, the number of subsets doubles.

Let the number of sets be n

But every time they add an element to a set, the number of subsets doubles.

Then according to the condition,

n + n = 2n

Therefore, there are n + n = 2n subsets which are doubled of the original subset.

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Answer: Height = 20 inches, Width = 36 inches

Step-by-step explanation:

Let the height be \(h\) and the width be \(h+16\).

Using the formula for the perimeter of a triangle,

\(2(h+h+16)=112\\\\2(2h+16)=112\\\\2h+16=56\\\\2h=40\\\\h=20 \implies h+16=36\)

Answer:

x = 59

Step-by-step explanation:

Equations

The interior angles formed by the sides of a quadrilateral have measures that sum to 360°.

The image shows a four-sided polygon and its four angles measures, thus we sum them all and equate the sum to 360:

x + x + 2x + 3 + 2x + 3 = 360

Simplifying:

6x + 6 = 360

Subtracting 6:

6x = 354

Dividing by 6:

x = 354/6

x = 59

Answer:

59

Step-by-step explanation:

i go to k-12 and the answer is correct!

Answer:

lol it's the same answer from the one I worked out before

Step-by-step explanation:

look at pic

If the GCF of the numbers is 12, then both numbers are multiples of 12:

       12, 24, 36, 48, 60, 72, 84, 96
(stop here, since they have to be less than 100).

If the greater number is a multiple of 10, only 60 fits that bill.

      Greater number: 60

If the difference between the two is 36, then the other one must be 36 less than 60:

      60 - 36 = 24

      Other number: 24

Answer:

A

=

w

l

d

=

w

2

+

l

2

Solving for

d

d

=

l

2

+

(

A

l

)

2

=

11

2

+

(

110

11

)

2

≈

14.86607

The length of the diagonal of the rectangle is 14.9 units.

A diagonal is the longest line that divides a plane shape into two halves.

To calculate the diagonal of the rectangle, we use Pythagoras theorem.

Formula:

Where:

make w the subject of the equation

From the question,

Given:

Substitute these values into equation 2

Finally, to calculate the diagonal of the rectangle, we use the formula below

Given:

Substitute these values into equation 3

Hence, the length of the diagonal of the rectangle is 14.9 units.

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Therefore , the solution of the given problem of unitary method comes out to be Daisy cream and Kremlin cream both have less cream per bulk 1 gallon and 4.5 gallons, respectively than Marble cream.

The objective can be accomplished by utilising what has already been discovered, taking advantage of this worldwide access, and including all essential components from earlier changeable study who employed a certain technique. If the anticipated claim outcome actually occurs, it will either be possible to contact the variable again or both important processes will undoubtedly miss the statement.

Here,

We must convert cups to gallons because daisy cream is sold in bulks of cups. Since a gallon of Daisy cream comprises 16 cups, one quantity of Daisy cream contains:

=> 16 cups per bulk = 1 gallon 16 cups per bulk = 1 gallon

Moscow cream is offered in bulk quantities of 4 1/2 gallons, which is one gallon.

Thus, we must convert pints to gallons. A gallon of Marble cream comprises eight pints, hence one quantity of Marble cream contains:

=> 40 pints in a bulk equal 1 gallon, 8 pints, or 5 gallons.

As a result, we can see that Marble cream, with 5 gallons per bulk, has the most cream.

Daisy cream and Kremlin cream both have less cream per bulk (1 gallon and 4.5 gallons, respectively) than Marble cream.

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Answer:

Where is the rest of the question

Step-by-step explanation:

The complete square form of - 3x² + 33 = 48x is [x + 8]² = 75

To do this, we add and subtract a constant term to the quadratic expression to make it a perfect square.

In this case, we use the formula x² + 2bx + b² = (x + b)² to rewrite the quadratic expression as a perfect square trinomial, and then we solved for the variable by isolating the squared term and taking the square root.

Here we have

- 3x² + 33 = 48x

Keep 'x' terms on one side and constant terms sides on another side

=> - 3x² - 48x = - 33

Divide by - 3 on both sides

=> -3(x² + 4x)/3 = - 33/3  

=> x² + 16x = 11      

Take half of the 'x' term and square it and add on both sides

=> x² + 2(8x) (x) + (8)² = 11 + (8)²  

Which is in the form of x² + 2bx + b² = (x + b)²

=> [x + 8]² = 75

Therefore,

The complete square form of - 3x² + 33 = 48x is [x + 8]² = 75

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During the exponential phase, e.coli bacteria in a culture increase in number at a rate proportional to the current population. If growth rate is 1.9% per minute and the current population is 172.0 million, the population 7.2 minutes from now can be calculated using the following formula:

P(t) = P ₀e^(rt)where ,P₀ = initial population r = growth rate (as a decimal) andt = time (in minutes)Substituting the given values, P₀ = 172.0 million r = 1.9% per minute = 0.019 per minute (as a decimal)t = 7.2 minutes

The population after 7.2 minutes will be:P(7.2) = 172.0 million * e^(0.019*7.2)≈ 234.0 million (rounded to the nearest tenth)Therefore, the population of e.coli bacteria 7.2 minutes from now will be approximately 234.0 million.

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