A(n)___
is a letter used as a placeholder for an unknown value.

first is 86

we know because of the sum of the interior angles of a triangle being 180, and that 5 + 6 =180

Answer:  The correct options are (1) (D) 94°  and (2) (D) 15.81.

Step-by-step explanation:  The calculations are as follows:

(1) In the attached figure, given that m∠2 = 42° and m∠3 = 52°.

We are to find the measure of ∠6.

In a triangle, the sum of the measures of two remote interior angles is equal to the measure of the exterior angle.

In the given triangle,  ∠2 and ∠3 are remote interior angles and ∠6 is the exterior angle.

So, we have

[tex]m\angle 6=m\angle 2+m\angle 3=42^\circ+52^\circ=94^\circ.[/tex]

Thus, (D) 94° is the correct option.

(2) Given that the areas of two similar hexagons are related to each other as 5 : 2 and one side of the first hexagon is 25.

We are to find the corresponding side in the other hexagon.

Let, 'a' and 'b' be the lengths of the corresponding sides of the two similar hexagons.

The, the ratios of the area of the hexagons will be a² : b².

So, we have

[tex]\dfrac{a^2}{b^2}=\dfrac{5}{2}\\\\\\\Rightarrow \dfrac{25^2}{b^2}=\dfrac{5}{2}\\\\\\\Rightarrow b^2=2\times\dfrac{625}{5}\\\\\\\Rightarrow b^2=250\\\\\Rightarrow b=5\sqrt{10}=15.81.[/tex]

Thus, the correct option is (D) 15.81.

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 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°.

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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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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When dividing 7233 by 164 using long division, the quotient is 44 with a remainder of 131.

When dividing 7233 by 164, we can use long division to find the quotient.

Therefore, 7233 divided by 164 is equal to 44 with a remainder of 131.

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To find out the miles on your uncle's car's odometer, you simply add the extra miles that the uncle's car odometer reads compared to your mother's car to the odometer reading of your mother's car. This gives a total of 24066 miles on your uncle's car's odometer.

The subject here is Mathematics, particularly simple addition and subtraction problems. According to the problem, your mother's car has read 22010 miles and her car's odometer reads 2056 miles less than your uncle's car. To find out the miles on your uncle's car's odometer, you will simply add 2056 to the reading on your mother's car's odometer.

So the equation would be: 22010 miles (Mother's car odometer) + 2056 miles = Uncle's car odometer.

When you add these two sums together, the total odometer reading for your uncle's car comes out to be 24066 miles.

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To solve the equation -3x = 15, you divide by -3 to get x = -5. To check, substitute -5 for x in the original equation to verify that the left and right sides are equal.

To solve the equation -3x = 15, we want to isolate x on one side of the equation. The algebraic property we will use here is the Division Property of Equality, which states that if we divide both sides of an equation by the same nonzero number, the two sides remain equal.

Step-by-Step Solution:

Now, let's check the answer to verify it's reasonable. Substitute x = -5 back into the original equation (-3x = 15) and see if the equation holds true:

it should be 84 x 5 x 73 x 9

which = 275940

The constant rate of change of $8 per hour signifies that for each hour that passes, the associated value increases by $8. To find missing values in the table, you add or subtract $8 per hour depending on whether you're looking forward or backward in time.

Since the constant rate of change in your table is $8 per hour, this means that for each hour that passes, the value in your relationship increases by $8. This value is akin to the concept of constant slope in the graph of a linear function, where the 'rise over run' (or change in y-values over change in x-values) remains the same.

To find the missing values in your table, start with the first known value and add $8 for each subsequent hour. If you're moving backwards (i.e., from a time later to an earlier time), you would subtract $8 for each hour.

For example, if you know that the value at 2 hours is $20, then the value at 3 hours would be $20 + $8 = $28. On the other hand, the value at 1 hour would be $20 - $8 = $12.

By applying this step-by-step process, you should be able to fill in the missing values in your table.

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A number is said to be rational if it can be expressed as a fraction of two integers.

0.87 is a rational number

Let the number be x.

So, we have:

[tex]x = 0.87[/tex]

Express as a fraction with a denominator of 1

[tex]x = \frac{0.87}{1}[/tex]

Multiply the fraction by 100/100

[tex]x = \frac{0.87 \times 100}{1 \times 100}[/tex]

[tex]x = \frac{87}{100}[/tex]

The fraction cannot be reduced further.

87 and 100 are integers.

This means that 0.87 is rational.

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To find what needs to be added to 31/4 to make it equal to 8, you subtract 31/4 from 8. This results in 0.25, which is the number to be added to 31/4 to obtain 8.

To solve this question, we first need to understand the problem. We wish to find a number which, when added to 31/4, equals 8. By subtracting 31/4 from both sides of the equation, we can find the missing number.

So, the equation becomes 8 - (31/4) = missing number.

The computation follows: missing number = 8 - (31/4) = 8 - 7.75 = 0.25

Therefore, if you add 0.25 to 31/4, you will get 8. This illustrates the principle of basic equation solving in mathematics.

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To find the total cost of shipping a 7-pound care package, you can use the formula: Total Cost = (Cost per pound * Number of pounds) + Flat fee. When applying this formula to the given scenario, the total cost to ship a 7-pound care package is $17.95.

To find the total cost of shipping a 7-pound care package, consider that it costs $0.85 per pound plus a flat fee of $12. You can create an algebraic expression to find the total cost:

Total Cost = (Cost per pound * Number of pounds) + Flat fee

Substitute in the values: Total Cost = ($0.85 * 7) + $12 = $5.95 + $12 = $17.95

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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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].