The width of the rectangle is a+10 / 3 a+24 . Write an expression for the length of the rectangle in simplest form.

The simplification of the logarithmic expressions log₇7 is 1.

Logarithmic terms represent numbers in logarithmic form. It's also known as a log term.

A quantity can also be defined as the sum of two or much more quantities. As a result, a term may be the product of 2 different or more quantities, one of which must be in log form. Log terms are used in such cases.

A quantity can also be defined as the product of two quantities. As a result, if a term includes a quotient of amount, and at least a single quantities could be articulated in log form, the conditions are referred to mathematically as log terms.

Now, as the e=question stated;

= log₇7

Apply the Base Rule for solving the given expression;

So, the expression can be written as

= ㏒ₓ7/㏒ₓ7

Both terms will get cancelled as both have same value with similar base.

= 1

Therefore, the simplified form of the given logarithmic expressions log₇7 is 1.

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The measure of ∠A = ∠67°.

Complementary angle

The sum of two angles is equal to 90 degrees is called a complementary angle.

Here it is given that ∠A and ∠∠B is a complementary angle

So from this, we have

m ∠A + m ∠B = 90°

m ∠A = (7x + 18)°

m ∠B = ( 5x - 12)°

So we have,

(7x + 18)° + ( 5x - 12)° = 90°

(12x + 6 )° = 90°

12x = 84°

x = 7°

Now we will put the value of x in the mA equation,

mA = (7x + 18)°

     = (7× 7 + 18)°

     = (49 + 18)°

     = 67°

Therefore we get ∠A = 67°.

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Answer:

the part of the male private part that produces sperm is the testicles

Edit:
i just realized i answered the wrong question

Answer:

Exact Form:

1215 / 2

Decimal Form:

607.5

Mixed Number Form:

607  1/2

The total cost of the book including the sales tax is $10.85.

For the given question;

The original price of the book is $9.95.

The sales tax rate is 9%.

Then, 9% of 9.95 is;

= (9×9.95)/100

= 0.8955

The total cost will become;

Selling cost = original cost + sales cost

Selling cost = 9.95 + 0.8955

Selling cost = 10.84555

or rounding off.

Selling cost = $10.85.

The mistake done by the student is, he multiplied the original cost 9.95 by 1.9 which is incorrect.

Thus, the cost of the book is estimated as $10.85.

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Answer:

274.89

Step-by-step explanation:

Answer: 274.89

Step-by-step explanation: You look at the nearest hundredth and which is 2 numbers right of the decimal and see if the number in the hundredths place is higher or lower than 5 if it is 5 or above you round up if not you round down.

Answer:

31 units

Step-by-step explanation:

When you are performing multiple transformations it is called a composite transformation.

A number of transformations or sequence of transformations that can be combined into a single transformation is called as composition. The resulting matrix is known as composite matrix. The process of combining is known as concatenation.

A composite transformation (or a composition of transformations) refers to the two or more transformations performed one after the other. For example: a translation followed by a reflection which is again followed by a rotation. Another example can be: a rotation followed by a translation or a rotation followed by a reflection.

Therefore, when you are performing multiple transformations it is called a composite transformation.

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The solution to the equation based on the description given is: n = -16.

First, we need to translate each given statement into algebraic expressions.

"11 less than 3 times n" can be translated as: 3 × n - 11 = 3n - 11

"75 less than the product of -1 and n" would be translated as: (-1)(n) - 75 = -n - 75.

It is stated that both statements or description are the same. This means, they are equal to each other. Therefore, the equation that would be formed is:

3n - 11 = -n - 75

Solve for n

3n - 11 + n = -n - 75 + n [addition property of equality]

4n - 11 = - 75

4n - 11 + 11 = - 75 + 11 [subtraction property of equality]

4n = -64

Divide both sides by 4

4n/4 = -64/4 [division property of equality]

n = -16

Therefore, the solution to the equation based on the description given is: n = -16.

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The temperature when the plane reaches an altitude of 8,000 feet is 50.7°.

From the information, there is a 1.1 degree drop in temperature for every thousand feet that an airplane climbs into the sky and the temperature on the ground is 59.5 degree

Therefore, the temperature when the plane reaches an altitude of 8,000 feet will be:.

= 59.5 - 1.1(8000/1000)

= 59.5 - 1.1(8)

= 59.5 - 8.8

= 50.7

Therefore, the temperature when the plane reaches an altitude of 8,000 feet is 50.7°.

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The system of equations has exactly one solution.

Based on the information given, the equation is illustrated as:

2x - 3y = -4

-3x - 3y = 3

Add both equations

5x = -1

Divide

x = -1/5

Since 2x - 3y = -4

2(-1/5) - 3y = 4

-2/5 - 3y = 4

3y = -2/5 - 4

3y = - 4 2/5.

Divide

y = -4 2/5 ÷ 3

y = 1 7/15

Therefore, the system of equations has exactly one solution as the value of x and y are gotten.

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Answer:

88.9294

Step-by-step explanation:

So for this problem we need to convert the top 2% into a z-score, which can be done using a calculator. You also first have to convert top 2% into 98% percentile. In doing so you'll approximately get: [tex]z\approx2.054[/tex]

This z-score just represents how many standard deviations away this is from the mean.

So this means that the minimum score would be represented as: [tex]76.4 + 2.054(6.1)\\88.9294[/tex]

This can be rounded as needed, but this would approximately be the minimum score to be in the top 2%

Using proportions, some equivalent measurements are given as follows:

A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using a rule of three, that can be either direct(cross multiplication) or inverse(line multiplication), deriving from proportional relationships. One example of application of proportions is for unit conversion problems, as unit conversion involve rates between the variables.

Each meter has 100 centimeters, hence:

1 centimeter - 0.01 meters.

Each hour has 60 minutes, hence:

Each feet has 12 inches, hence:

3 and 1/3 feet - 40 inches.

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The product using the distributive property is 12z+8y²-8x+16 in the standard form.

The distributive law, which states that a × (b + c)=(a × b)+(a × c), is generalized by the distributive property of binary operations.

In every scenario, the distributive property can be summed up as follows:

Each summand (or minuend and subtrahend) is multiplied by this factor, and the resulting products are added, to multiply a sum (or difference) by a factor (or subtracted).

This concept states that multiplying the sum of two addends by a number will produce the same outcome as multiplying each addend separately by the number and then adding the results.

Given product: 4×(3z+5+2y²-2x-1)

Using the distributive property we can write it as:

= (4×3z)+(4×5)+(4×2y²)-(4×2x)-(4×1)

= 12z+20+8y²-8x-4

= 12z+8y²-8x+16

So the product using the distributive property is 12z+8y²-8x+16 in the standard form.

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Side height is missing, which is a 6[tex]\sqrt{30}[/tex].

For the right angle triangle we have a formula:

[tex]hypotenuse^{2}[/tex] = [tex]height^{2}[/tex] + [tex]base^{2}[/tex]

Here Hypotenuse and the base are given, we have to find the height of the triangle.

Hypotenuse = 37

Base = 17

To find the height of the triangle we have:

[tex]height^{2}[/tex] = [tex]Hypotenuse^{2}[/tex] - [tex]base^{2}[/tex]

           = [tex]37^{2}[/tex] - [tex]17^{2}[/tex]

           = 1369 - 289

           = 1080

Height =[tex]\sqrt{1080}[/tex]

            = 6√30

Therefore the height of the triangle is 6√30.

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The student's error is not checking the solutions by keeping the values in problem equation. The correct solution is 4.

Rewriting the equation to find the solution of expression -

√x+2=x

Shifting 2 to Right Hand Side of the equation

√x = x - 2

Taking square on both sides

(√x)² = (x - 2)²

Solving the bracket on both sides of the equation -

x = x² - 4x + 4

Solving the equation for the value of x by factorizing it

x² - 4x - x + 4 = 0

x² - 5x + 4 = 0

x² - 4x - x + 4 = 0

x(x - 4) -1(x - 4) = 0

(x - 4) (x - 1) = 0

x = 4, 1

Keep the value of x to validate the result and find correct solution -

x = 1

√x+2=x

√1 + 2 = 1

1 + 2 = 1

3 ≠ 1

x = 4

√4+2=4

2 + 2 = 4

4 = 4

Hence, the correct solution is 4.

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The complete question is -

A student said that 4 and 1 are the solutions of the problem shown. Describe and correct the student's error. √x+2=x

Answer:

1884 metres per second

31.4meters x 60 seconds = 1,884 speed

---------

please mark as brainiest

The solution is 9.

To find the solution, firstly rewriting the given equation -

√(5x+4) - √x = 4

Now, shifting √x from Left Hand Side to Right Hand side of the equation. Rewriting the equation -

√(5x+4) = √(x) + 4

Taking square of complete equation

(√(5x+4))² = (√(x) + 4)²

Solving the square of equation

5x + 4 = x + 16 + 8√x

Simplifying the equation

5x - x - 8√x = 16 - 4

4x - 8√x = 12

Rewriting the equation

4x - 12 = 8√x

Again taking square on both sides

(4x - 12)² = (8√x)²

16x² + 144 - 2×4x×12 = 64x

16x² + 144 - 96x = 64x

16x² + 144 - 96x - 64x = 0

16x² + 144 - 160x = 0

Dividing the equation by 16

x² + 9 - 10x = 0

x² - 10x + 9 = 0

x² - 1x -9x + 9 = 0

x(x - 1) -9(x - 1) = 0

(x - 1) (x - 9) = 0

x = 1, 9

Keep the value of x in equation to find the solution

x = 1

√(5×1 + 4) - √1 = 4

√(5 + 4) - 1 = 4

√9 - 1 = 4

3 -1 = 4

2 ≠ 4

x = 9

√(5×9 + 4) - √9 = 4

√(45 + 4) - 3 = 4

√49 - 3 = 4

7 - 3 = 4

4 = 4

Hence, the solution is 9.

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Answer:

10

Step-by-step explanation:

(x + 4)/7=10

The number is -28.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them. Variables are the name given to these symbols because they lack set values. We frequently observe constant change in specific values in our day-to-day situations. But the need to depict these shifting values is ongoing. These values are frequently represented in algebra by symbols such as x, y, z, p, or q, and these symbols are known as variables. In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

quotient of a number and 4 is -7

let the number be x

So, n/4 = -7

n= 4 x (-7)

n= -28

Hence, the number is -28.

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Answer:

41

Step-by-step explanation:

how all work! 1) Find two consecutive odd integers with a sum of 80. Let x= first consecutive integer 39. Let x+2= second. 41. 2x=78 x+x+2= 80. 2x+2=80.

X= 39 & 41

With Equivalent expressions, the value of the p is -14.

According to the statement

We have to find that the value of the p.

So, For this purpose, we know that the

Equivalent expressions are expressions that work the same even though they look different.

From the given information:

The given values is:

(x^19)(x^-33) = (x^p)

Now, use the method of add the terms bcz in this the base will a same then powers will be add.

(x^19-33) = (x^p)

After adding the power of the x become:

(x^-14) = (x^p)

After comparing the both equations,

The values of the p become -14.

Then p = -14.

So, With Equivalent expressions, the value of the p is -14.

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A magnitude 1.0 star is about 2.5 times brighter than a magnitude 2.0.

In, mathematics a logarithmic equation is inverse of exponential equation. That means, we can easily convert the logarithmic equation into exponential equation and vice versa. The basic form of the logarithm function can be written as  .

   [tex]log_ax=N[/tex]

where, a is the base of function or equation

           x = expression or equation

Mathematically, if  [tex]a^N=x[/tex]  is an exponential function then, this can be converted to logarithmic function as  [tex]log_ax=N[/tex].

There are many formulas that are given to us for solving several simple and complex problems based on logarithmic functions and logarithmic equations.

Some important formulas of logarithms are :

We use the given formula:

[tex]m_2 - m_1 = -2.5 log \frac{b_2}{b_1}[/tex]

now m2 = 2.0 and m1 = 1.0

Hence,

[tex]m_2 - m_1 = -2.5 log \frac{b_2}{b_1}\\\\= > 2.0 - 1.0 = -2.5 log \frac{b_2}{b_1}\\\\= > -1.0 = -2.5 log \frac{b_2}{b_1}\\\\= > log \frac{b_2}{b_1} = 0.4\\\\= > \frac{b_2}{b_1} = 10^{0.4} = 2.5 approx.[/tex]

Thus,  magnitude 1.0 star is about 2.5 times brighter than the magnitude 2.0 star.

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she has $520 after 1 year.

Step-by-step explanation:

principal= 500dollars

rate= 4%

time=1 year

simple interest=principal x rate x time

100

simple interest= 500 x 4 x 1 = 2000/100 = 20

100

To find total amount money in the account

= simple interest + principal

= 20 + 500

= 520dollars

The values of the equation will be:

7z(2a³+5) = 14a³z + 35z

2.) 5p(3s-4t) = 15ps - 20pt

It should be noted that an equation is used to express the relationship between the variables.

Therefore, the equation will be solved by simply opening the brackets and multiplying them. This will be:

7z(2a³+5) = 14a³z + 35z

5p(3s-4t) = 15ps - 20pt

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Answer:60 degrees

Step-by-step explanation: hexagon is 360 degrees. has 6 sides. 360 divided by 6= 60 degrees

For the relations in this problem, we have that:

1.

2.

3.

A relation represents a function if each value of the input is mapped to only one value of the output.

For a point in the format (x,y), we have that:

A graph represents a function if it has no vertically aligned points, that is, each value of x is mapped to only one value of y.

In a graph, the domain and the range are found as follows:

For the first relation, we have that input 10 is mapped to outputs 20 and 50, hence:

For the second relation, we have a graph with no vertically aligned points, hence:

For the third relation, we have a graph with vertically aligned points, hence:

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Option 2, (x, y) --> (x + 3, y - 2) is the algebraic expression that shows how the translation affects the coordinates of the preimage.

Here, we are given that a figure is translated 3 units to the right and two units down.

Now, if the original coordinates of the figure are (x, y), as given in all the options, let us look at the effect of the transformation.

3 units right the x coordinate will increase by 3 units

thus x becomes (x + 3)

2 units down = the y coordinate will decrease by 2 units

thus y becomes (y - 2)

Hence, the new coordinates of the figure become {(x + 3), (y - 2)} Therefore, option 2, (x, y) --> (x + 3, y - 2) is the correct answer.

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Your question was incomplete. Check for the full content below

A figure is translated 3 units to the right and down 2 units. Select the algebraic expression that shows how the translation affects the coordinates of the pre image.

1. (x, y) --> (x-3, y + 2)

2. (x, y) --> (x + 3, y - 2)

3. (x, y) --> (x + 3, y - 2)

4.(x, y) --> (9x, 3y)

It should be noted that the product of ✓b × ✓b = b.

From the information, it should be noted that we want to find the product of ✓b × ✓b.

In this case, it's important to multiply the roots

Therefore, ✓b × ✓b = ✓b²

Then, we will rewrite the expression. In this case, it should be noted that the square root will cancel the square.

Therefore, the product of ✓b × ✓b = b.

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Answer:

Step-by-step explanation:

b