Write each expression in simplest form. 4√7-∛7

If the expression is log₄2+log₄8, then it will look like [tex]log_{4}16[/tex] in single logarithm form.

Given that the expression is log₄2+log₄8.

We are required to express the given expression in single logarithm.

Product property of logarithm basically tells that says that the logarithm of a product is equal to a sum of logarithms and because logs are exponents, and we multiply like bases, we can add the exponents.

The expression is log₄2+log₄8.

log₄2+log₄8=[tex]log_{4}[/tex](8*2) (We are not required to write the base separately)

=[tex]log_{4}[/tex]16

Hence if the expression is log₄2+log₄8, then it will look like [tex]log_{4}16[/tex] in single logarithm form.

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Step-by-step explanation:

1)x=10/2=5

x=5

2)x=27/3=9

x=9

a) The explosion does violate the town regulation

b) The values are , I = [tex]1.65 * 10^{2} W/m^{2}[/tex] and [tex]I_{0}[/tex] = [tex]10^{-12} W/m^{2}[/tex]

The values that we have been given are

        L = loudness of the sound = 10log(I/[tex]I_{0}[/tex])

        I = intensity of the sound in watts per square meter = [tex]1.65 * 10^{2} W/m^{2}[/tex]

        [tex]I_{0}[/tex] = intensity of barely audible sound = [tex]10^{-12} W/m^{2}[/tex]

Putting the required value in the equation of the loudness we get

      a)       L =  [tex]10*log (\frac{1.65*10^{2} }{10^{-12} } )[/tex]

             L = 10*14.217 dB = 1142.17 dB

And according to the town regulation the loudness of the construction work should not exceed 100dB.

Thus the explosion is in violation of the town regulation as it exceeds 100dB.

b)  The respective values of I and [tex]I_{0}[/tex] are

        I = intensity of the sound in watts per square meter = [tex]1.65 * 10^{2} W/m^{2}[/tex]

         = intensity of barely audible sound = [tex]10^{-12} W/m^{2}[/tex]

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let's recall that an angle bisector, bisects = cuts into two equal halves.

Check the picture below.

If Reginald Wallace’s gross weekly salary is $515 and the Medicare tax is 1.45 percent of gross pay. The state tax is 1.5 percent of gross pay. The amount that is deducted from Wallace’s weekly wages for state tax and Medicare tax is: $15.19.

State tax=1.5 percent of gross pay

Medicare tax=1.45 percent of gross pay

State tax=$515 ×0.015

State tax= $7.725

Medicare tax=$515× 0.0145

Medicare tax = $7.4675

Hence:

State tax and Medicare tax=$7.725+$7.4675

State tax and Medicare tax=$15.1925

State tax and Medicare tax=$15.19 (Approximately)

Therefore If Reginald Wallace’s gross weekly salary is $515 and the Medicare tax is 1.45 percent of gross pay. The state tax is 1.5 percent of gross pay. The amount that is deducted from Wallace’s weekly wages for state tax and Medicare tax is: $15.19.

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If we have two pairs  (x₁, y₁) and (x₂, y₂) on the table, use the following formula to get the slope:

a = (y₂ - y₁)/(x₂ - x₁)

A general linear equation in the slope-intercept form can be written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

Now, if the linear equation has a table with some values:

X    Y

x₁    y₁

x₂   y₂

x₃   y₃

etc...

Then you can select any two of the pairs on the table, for example (x₁, y₁) and (x₂, y₂), and use the following formula to get the slope:

a = (y₂ - y₁)/(x₂ - x₁)

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awaer

click here

Step-by-step explanation:

Step-by-step explanation:

Adding A Negative Number

Now let's see what adding and subtracting negative numbers looks like:

add subtract +- goes down

We can add weights (we are adding negative values)

the basket gets pulled downwards (negative)

Example: 6 + (−3) = 3

is really saying

"Positive 6 plus Negative 3 equals Positive 3"

We could write it as (+6) + (−3) = (+3)

The output value of f(5) in the given function f(x) = -4x - 5 is -25

A function is simply a set of ordered pairs where each first element is paired with one and only second element and also no element in either pair is without a partner.

Given the data in the question;

To determine the output value of f(5), replace the variable x with 5 and simplify.

f(x) = -4x - 5

f(5) = -4(5) - 5

Perform the multiplication operation to remove the parenthesis.

f(5) = -4(5) - 5

f(5) = -20 - 5

f(5) = -25

Therefore, the output value of f(5) in the given function f(x) = -4x - 5 is -25.

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Answer:

Answer: 57 & 59

Step-by-step explanation:

Let us assume first odd integer is 'x'

Then, next consecutive integer should be 'x+2'. RIGHT?

Now, put in the form of equation:

x + (x+2) = 116

x + x + 2 = 116

2x + 2 = 116

2x = 116 - 2

2x = 114

x = 114 / 2 => 57

Now, put the value of 'x' in second step:

           x + 2 => 57 + 2 = 59

Therefore, answer would be 57 & 59

The equation of the line passing through the given coordinate with the given slope is; y = 2x + 11

The formula for equation of line in point slope form is;

(y - y1) = m(x - x1)

We are given the slope is 2

Now, if the line passes through the coordinate (-4, 3), then the equation of the line is;

(y - 3) = 2(x - (-4))

y - 3 = 2x + 8

y = 2x + 11

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The negation is "antarctica is not in the northern hemisphere" &  the truth value of the original proposition is FALSE and its negation is TRUE.

The sentences that can be classified as true or false , but not both are called as propositions.

For Example , "Shirt is yellow" is a proposition whereas "a is less than 2" is not a proposition as the value of a is not fixed.

Negation of proposition means writing the opposite of the given proposition.

If the proposition is true then it's truth value is "True".

If the proposition is false then it's truth value is "False".

According to the given Question

The negation of the statement "antarctica is in the northern hemisphere" is "antarctica is not in the northern hemisphere"

The truth value of the original proposition is FALSE as Antarctica is in the Southern hemisphere.

The truth value of the negation is TRUE as Antarctica is not in the Northern hemisphere it is in southern Hemisphere.

Therefore , the negation is "antarctica is not in the northern hemisphere" &  the truth value of the original proposition is FALSE and its negation is TRUE.

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The number of gigabytes Bao can use while staying within her budget is 3.9 gigabytes.

From the information, plan, Bao pays a flat cost of $40.50 per month and $5 per gigabyte and she wants to keep her bill under $60 per month.

The inequality will be:

40.50 + 5g < 60

where g = number of gigabytes

40.50 + 5g < 60

5g < 60 - 40.50

5g < 19.50

g < 19.50 / 5

g < 3.9

Therefore, the number of gigabytes will be less than 3.9 g.

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Answer:

a = 10

Step-by-step explanation:

The image is showing a linear pair which equals 180°
104° is shown.

If you take 180° and subtract 104° you should get the answer to what (8a -4)° should equal to.

180° - 104° = 76°

Your equation should look like : 8a - 4 = 76°
-- Add 4 to both sides

8a - 4 = 76°
     +4    +4

= 8a = 80
-- Divide 8 on both sides

8a/8 = 80/8

a = 10

Proof:

8(10) - 4 =
80 - 4 = 76°

104° + 76° = 180°

Hope this helps!
--Blu

Answer:

Step-by-step explanation:

4,536

The expression √3 + 5  cannot be simplified and the expression √2x/3y  cannot be simplified

Expression 1

The expression is given as

√3 + 5

The above expression is a combination of a radical expression and an integer

The radical expression √3 cannot be simplified

This means that the expression √3 + 5 cannot be simplified

Hence, the expression √3 + 5  cannot be simplified

Expression 2

The expression is given as

√2x/3y

The above expression is a combination of radical expressions

However, the radical expressions do not have a common factor

This means that the expression √2x/3y cannot be simplified

Hence, the expression √2x/3y  cannot be simplified

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Complete question

can √3 + 5 be simplified if yes show your work if not explain why

can √2x/3y be simplified if yes show your work if not explain why

When the given non testable questions are made into testable questions, they become:

A testable question is one that requires the answer to be acquired by means of experimentation.

Instead of asking, "Which planet is the most interesting to study?" you could ask about the conditions that a planet has which are considered subjects of interest.

Also, instead of asking, "What happens if you do not eat breakfast?" you could ask about how the body is affected when we skip breakfast. This can be tested in an experiment that checks the body's functions when breakfast isn't eaten.

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well, for the piece-wise function, we'd like to know f(-2), or namely what is f(x) when x = -2?

well, f(x) is 2 for x = -1

f(x) is 4 for x > -1

keeping in mind that in the negative side of the number line, the closer to 0, the larger, thus -1 is much larger than -1,000, so  hmmm -2 is farther from 0 than -1 is, so -1 is larger than -2, so when x = -2, x < -1, and the function that applies when x < -1 is -(x+1)² + 4, so then

[tex]f(x)= \begin{cases} -(x+1)^2 + 4&\stackrel{-2}{x} < -1\\\\ 2&x=-1\\\\ 4&x > -1 \end{cases} \\\\\\ f(-2)\implies -(~~(-2)+1~~)^2 + 4\implies -(-1)^2+4\implies -(-1)(-1)+4 \\\\\\ -(1)+4\implies -1+4\implies \text{\LARGE 3}[/tex]

Answer: f(-2)=3

Step-by-step explanation:

[tex]f(x)=\left\{\begin{array}{ccc}-(x+1)^2+4\ for\ x < -1\\2\ \ \ \ for\ \ x=-1\\4\ \ \ for \ \ \ x > -1\end{array}\right[/tex]

[tex]-2\in(-\infty,-1)\\Hence,[/tex]

[tex]f(-2)=-(-2+1)^2+4\\f(-2)=-(-1)^2+4\\f(-2)=-1+4\\f(-2)=3[/tex]

Answer:

54

Step-by-step explanation:

Solution :  Three consecutive odd integers are 33,35,37

Three consecutive odd integers :

Odd numbers are whole numbers that when divided by 2 give the remainder as one. Odd numbers are written in the form 2x+1,x∈N where N is the natural numbers

the sum of the first and the third is 70.

1 st number is = a

2nd number = b

3rd number = c

Let the required one integer be x. We need three integers so one integer is x next odd integer can be written as x+2 and the third integer can be written as x+4

a+c = 70 ...1

a= x

b=x+2

c= x+4

for equation 1

x+x+4 = 70

2x+4 =70

2x= 70-4

2x= 66

x=66/2

x=33

a=33

b= x+2 =33+2 =35

c= x+4 = 33+4 = 37

Three consecutive odd integers are 33,35,37

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The solution of the given equation by rounding off it to the nearest ten-thousandth is 10.0427.

What is a round-off of the digit?

In mathematics, a round-off is defined as an approximation of the given number to a fewer number of significant digits by taking into consideration some rules.

For eg: 13.58 ~ 13.6

Solving the given equation:  log 4 + 2 log x = 6

We are given a logarithmic expression: log 4 + 2 log x = 6  

We know that e^(log b) = b

a log b = (log b)^a

log a + log b = log (ab)

Using exponential on both sides, we have

e^(log 4 + 2 log x) = e^6

e^(log 4 + log x² ) = 403.428

e^(log 4x² ) = 403.428

4x² = 403.428

x² = 403.428 / 4

x² = 100.857

x = 10.0427

Hence, the solution of the given equation rounded off to the nearest ten-thousandth is 10.0427.

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The Great Wall of China is about 200 times longer then the Panama Canal

Scientific notation is used to compress large numbers into smaller numbers. In order to write a number in scientific notation, the number is written as a decimal number, between 1 and 10 and multiplied by a power of 10. An examples of 100 expressed in scientific notation is 1 x 10².

In order to determine the difference in the length of the great wall of China and the Panama Canal, divide the length of the Great wall of China by the length of the Panama Canal.

(1 x [tex]10^{4}[/tex]) ÷ (5 x [tex]10^{1}[/tex])

(1/5) x [tex]10^{4 - 1}[/tex]

0.2 x [tex]10^{3}[/tex]

2 x [tex]10^{3 - 1}[/tex]

2 x10² = 200

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Answer:

Step-by-step explanation:

The area is 6

because the base is 4 units and the height it 3 units, and base times height will give you 6.

the negations of the hypothesis and conclusion for the given conditional statement are:

not P = "The sum of the interior angle measures of a polygon is not 180°"

not Q = "The polygon is not a triangle"

For two defined propositions P and Q, we define a conditional statement as a sentence of the form:

If P, then Q.

Particularly in this case, P is called the hypothesis and Q is called the conclusion of the conditional statement.

For the given one:

"If the sum of the interior angle measures of a polygon is 180, then the polygon is a triangle."

We will have that the hypothesis is:

The sum of the interior angle measures of a polygon is 180°

The conclusion will be:

The poñyogn is a triangle.

Now we want to negate these two, it is really simple, for the hypothesis we will have that the sum of the interior angles can be any number but 180°, then we can write the negation as:

"The sum of the interior angle measures of a polygon is not 180°

Similar for the conclusion, we just need to state that the polygon is not a triangle, we will get:

"The polygon is not a triangle"

Then the negations of the hypothesis and conclusion for the given conditional statement are:

not P = "The sum of the interior angle measures of a polygon is not 180°"

not Q = "The polygon is not a triangle"

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Answer:

3

Step-by-step explanation:

6=2*3

9=3*3

The only common factor is 3

Answer:

it would be 1 (im not really sure what it would be, let me know if this helps)

Step-by-step explanation:

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{2^{3x} = 10}[/tex]

[tex]\large\textsf{Take the logarithm to both sides:}[/tex]

[tex]\mathsf{log(2^{3x}) = log(10)}[/tex]

[tex]\mathsf{3x \times (log(2)) = log(10)}[/tex]

[tex]\large\textsf{Simplify it:}[/tex]

[tex]\mathsf{3x = \dfrac{log(10)}{log(2)}}[/tex]

[tex]\large\textsf{Simplify this as well:}[/tex]

[tex]\mathsf{3x = 3.321928}[/tex]

[tex]\large\textsf{Divide 3 to both sides of your current equation:}[/tex]

[tex]\mathsf{\dfrac{3x}{3} = \dfrac{3.321928}{3}}[/tex]

[tex]\large\textsf{Lastly, simplify that last bit of the equation:}[/tex]

[tex]\mathsf{x = \dfrac{3.321928}{3}}[/tex]

[tex]\mathsf{x = 1.107309}[/tex]

[tex]\huge\text{Thus, your answer should be: \boxed{\mathsf{x = 1.107309}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

The time taken for Mel to finish mowing the yard if they have 80 minutes is 53 minutes.

It should be noted that this represents the number of pieces removed from the whole. The denominator of a fraction is the numerical value that comes before the brings together various.

Given that,

Michael mows = 1/3 of the yards

Mel will cut: 1 - 1/3 = 2/3

Therefore, the time taken for Mel to mow the yard will be:

= 80 × 2/3

= 53 minutes

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After Michael mows ⅓ of the yard, Write a fraction division problem that you can use to find out how long it will take Mel to finish mowing the yard if they have 80 minutes.