Fiona is serving iced tea and lemonade at a picnic. She has only 44 cups in which to serve the drinks. If x represents the number of glasses of iced tea and y represents the number of glasses of lemonade, which equation represents the number of glasses of iced tea she can serve?

Final answer:

The midpoint of the line segment with endpoints (3,5) and (7,-3) is calculated using the midpoint formula and is (5,1).

Explanation:

To calculate the midpoint of a line segment with the endpoints (3,5) and (7,-3), you use the midpoint formula, which is given by the average of the x-coordinates and the average of the y-coordinates of the endpoints. The formula looks like this: M = ((x1 + x2) / 2, (y1 + y2) / 2).

For the given points (3,5) and (7,-3), the calculations are as follows:

Therefore, the midpoint of the line segment is (5,1).

The partial product of 452 x 12 is 5,424 which is circled in the image attached.

In multiplication, a partial product is the result of multiplying one digit of a factor by a digit in the other factor.

In the given problem of 452 x 12, the partial product would be the product of 452 and 12.

452 x 12

=   4  5  2

  x    1   2

  ------------------

+    9  0  4

 4 5  2  0

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

5, 4 2 4

Thus, the in this problem,  the partial product is 5,424

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The value of x is 34°, resulting in the measures of angles S and T being 38° and 111° respectively, in triangle RST.

The sum of the angles in a triangle is always 180 degrees. Given that angle R is 31°, we can set up an equation with the other two angles expressed in terms of x. This equation is:

31° + (x + 4)° + (3x + 9)° = 180°

Combining like terms yields:
4x + 44° = 180°
Subtracting 44 from both sides gives:
4x = 136°
Dividing both sides by 4 gives the value of x:
x = 34°

Now, we can find the measures of the other two angles:

​m°S = x + 4 = 34° + 4° = 38°
​m°T = 3x + 9 = 3(34°) + 9° = 102° + 9° = 111°

Therefore, the value of x is 34°, angle S measures 38°, and angle T measures 111°.

Answer:

[tex]h=\frac{25}{b+r}[/tex]

Step-by-step explanation:

We have been given an equation [tex]bh+hr=25[/tex]. We are asked to solve our equation for h.

First of all let us factor out h.

[tex]h(b+r)=25[/tex]

Now let us divide both sides of equation by b+r.

[tex]\frac{h(b+r)}{b+r}=\frac{25}{b+r}[/tex]

Upon simplifying our equation we will get,

[tex]h=\frac{25}{b+r}[/tex]

Hence, our answer will be: [tex]h=\frac{25}{b+r}[/tex].

To solve for 'x' in the equation 'abx-cdx=15m', rewrite the equation, factor out the 'x', and solve for 'x'. The solution is 'x = 15m / (ab - cd)', provided that 'ab' does not equal 'cd'.

To solve for x in the equation abx-cdx=15m, we need to firstly isolate the terms containing x. Let's start by rewriting the equation:

abx = cdx + 15m

Then, factoring out the x, we get:

x(ab - cd) = 15m

Finally, we can solve for x by dividing both sides of the equation by (ab - cd):

x = 15m / (ab - cd)

Note: this solution works provided that ab≠cd since division by zero is undefined in mathematics.

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Final answer:

The properties of integer exponents like multiplication (adding exponents), division (subtracting exponents), raising a power to another power (multiplying exponents), and fractional powers (representing roots) are used to simplify algebraic and numeric expressions.

Explanation:

To simplify algebraic and numeric expressions using the properties of integer exponents, you can apply several different rules. The first step is often to write out the expression in an extended format, like how 34 can be written as 3·3·3·3. When we deal with multiplication of exponentials, we multiply the digit terms and add the exponents of the exponential terms. For example, (23)(24) equals 23+4 which simplifies to 27. When we encounter division of exponentials, we divide the digit terms and subtract the smaller exponent from the larger exponent. For instance, 57 divided by 53 would give us 57-3 which is 54.

For powers raised to another power, like (53)4, you multiply the exponents (3×4) to get 512. Remember to be cautious with examples and ensure clarity in the operations when combining exponents. Lastly, fractional powers, such as 51/2, can be interpreted as square roots. The general rule here is that xa/b represents the b-th root of x, raised to the power of a.

The statement that best represents the information that should be in the box labeled 1 is; AB = BC. Hence, the correct option is A.

The reflexive property of congruence says that the considered geometric quantity, whether it be angle, line segment, or shape etc, is congruent to itself.

It is Given that A conjecture and a portion of the flowchart proof used to prove the conjecture are shown. AB is similar to BC.

Thus, By the segment congruence postulate, AB = BC

Therefore, the statement that best represents the information that should be in the box labeled 1 is; AB = BC.

Hence, the correct option is A.

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Michael's answer is incorrect. He seems to have forgotten to differentiate between tenths and hundredths. The correct subtraction of 5 tenths and 3 hundredths is 0.47 (or 47 hundredths), not 2 tenths.

No, Michael is not correct. He seems to have confused decimal subtraction with simple integer subtraction. When subtracting decimals, we should treat tenths and hundredths differently as they represent different place values in a decimal number. So, when Mrs. Fan wrote 5 tenths minus 3 hundredths on the board, she meant 0.5 (5 tenths) minus 0.03 (3 hundredths), not 0.5 minus 0.3.

Thus, the correct answer should be 0.47 (or 47 hundredths), not 2 tenths.

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The top half of a fraction is called numerator.

Fractions are type of real numbers which are defined as a portion or a part of a whole.

There are many types of fractions like Proper fractions, Improper fractions, Like fractions, Unlike fractions, Mixed fractions and so on.

Fractions are of the form [tex]\frac{a}{b}[/tex] where the number on the top 'a' is called the numerator and the number on the bottom 'b' is called the denominator.

For example take a fraction, 3/10.

Here 3 is the numerator and 10 is the denominator.

For fractions of type 3 [tex]\frac{1}{10}[/tex], it is called mixed fraction.

Here 3 is a whole number part and 1/10 is the fractional part.

We can convert first mixed fraction into improper fraction where the numerator is found by multiplying 3 to 10 and then adding 1 and the denominator equals the denominator of the fractional part.

3 [tex]\frac{1}{10}[/tex] = (3 × 10 + 1) / 10 = [tex]\frac{31}{10}[/tex]

Here numerator is 31 and the denominator is 10.

Hence the top part of the fraction is called numerator.

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There will be no overall adjustment to Audrey's account balance.

Algebra is the study of graphic formulas, while logic is the manipulation of those metaphors.

Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction is referred to as the PEMDAS rule. To answer the problem properly and accurately, this rule is applied.

$27 is deposited into Audrey's account. She then withdraws two amounts totaling $15 and $12.

The entire adjustment to Audrey's account balance will then be shown as,

⇒ $27 - $15 - $12

⇒ $27 - $27

⇒ $0

There will be no overall adjustment to Audrey's account balance.

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The answer is stretch.

The two partial products of 513 x 46 are:

500 x 46 and 13 x 46.

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division. 

We have,

513 x 46 = 23598

We need to find two partial products.

513 can be written as:

513 = 500 + 13

So,

= (500 + 13) x 46

= 500 x 46 + 13 x 46

= 23000 + 598

= 23598

The two partial products are 500 x 46 and 13 x 46.

Thus,

The two partial products of 513 x 46 are 500 x 46 and 13 x 46.

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Final answer:

To calculate 513 multiplied by 46, you should add the first partial product (3078) and the second partial product (20520) to get the total product of 23598.

Explanation:

To find the product of 513 multiplied by 46 using the partial products method, you'll need to break down the equation into parts based on place value and then add those parts together. The process is as follows:

Multiply the ones place of the second number by the entire first number. So, 6 (from the 46) times 513.

Multiply the tens place of the second number by the entire first number. That means 40 (from the 46, which is 4 tens) times 513.

To complete this calculation:

6 * 513 = 3078 (this is the first partial product).

40 * 513 = 20520 (this is the second partial product).

Now, we add both partial products together:

3078 + 20520 = 23598

So, 513 multiplied by 46 equals 23598.

0.0001 can be represented as [tex]\(1 \times 10^{-4}\)[/tex] in scientific notation, showing its value with a coefficient of 1 and an exponent of -4. This notation simplifies large or small numbers, making them easier to work with in calculations and comparisons.

When converting a number to scientific notation, like 0.0001, we aim to express it as a coefficient multiplied by a power of 10. The coefficient is a number greater than or equal to 1 and less than 10, and the power of 10 indicates how many places the decimal point must be shifted to obtain the original number.

In the case of 0.0001, there are four decimal places. Each decimal place corresponds to a division by 10. So, to get from 0.0001 to 1, we need to multiply by 10 four times, which gives us [tex]\(10^{-4}\)[/tex]. This signifies that the decimal point needs to be moved four places to the right to reach 1.

So, 0.0001 can be written as [tex]\(1 \times 10^{-4}\)[/tex], where 1 is the coefficient (because it's between 1 and 10) and -4 is the exponent of 10.

Is the mapping, or movement, of all the points of a figure in a plane according to a common operation *

10 points

Reflection

Translation

Transformation

Rotation

is a transformation that "slides" each point of a figure the same distance and direction. *

10 points

Reflection

Translation

Transformation

Rotation

a transformation that flips a figure over a reflection line *

10 points

Reflection

Translation

Transformation

Rotation

is a transformation that turns a figure about a fixed point for a given angle *

10 points

Reflection

Translation

Transformation

Rotation

is generally used to generate more variable names for things which are similar *

10 points

Verticies

Prime

Congruent

Function

Plural of vertex meaning the corner where two lines meet *

10 points

Verticies

Prime

Congruent

Function

Same size same shape *

10 points

Clockwise

Counter Clockwise

Congruent

Prime

maps each input to one and only one output. *

10 points

Function

Clockwise

Congruent

Prime

in a curve corresponding in direction to the typical forward movement of the hands of a clock. *

10 points

Function

Clockwise

Counter Clockwise

Prime

in the opposite direction to the way in which the hands of a clock move around *

10 points

Function

Clockwise

Counter Clockwise

Prime

it should be 84 x 5 x 73 x 9

which = 275940