what is the simplified form of each expression (3/4)^5

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 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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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.

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 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°.

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.

it should be 84 x 5 x 73 x 9

which = 275940

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 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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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.

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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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).

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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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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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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