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The expression log 7 +log 2 can be written as log 14 in a single logarithm form.

Given that the expression is log 7 +log 2.

We are required to write the expression is a single logarithm.

The Power Property basically states that if an exponent is being raised to another exponent, we can multiply the exponents.

The expression is  log 7 +log 2.

We know that log mn= log m +log n.So,

log 7 +log 2=log (7*2)

=log 14

Hence the expression log 7 +log 2 can be written as log 14 in a single logarithm form.

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Answer:

The absolute value of -5 is 5, it's positive opposite.

Have a fantabulous day <3

Answer:

5

Step-by-step explanation:

the only real math to absolute value is if it negative make it not.

After the solving equation ln (x-7)=2, the value of x is equal to [tex]e^{2}[/tex] + 7

We have been asked to find x in ln (x-7)=2

⇒ ln (x-7)=2

⇒ x - 7 = [tex]e^{2}[/tex]

⇒ x = [tex]e^{2}[/tex] + 7

To solve linear equations, utilize the steps that are provided below.

Lets take an example of solve z for 7z – (3z – 4) = 12

Here is no multiplication or division, so this will be easy to solve

⇒ 7z – (3z – 4) = 12

⇒ 7z – 3z + 4 = 12

⇒ 4z = 12 – 4

⇒ 4z = 8

⇒ z = 8/4

⇒ z = 2

See, that was so simple, using the mentioned methods, every linear equation can be solved easily.

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The equivalent expression of the statement is as follows:

[tex](\frac{y^{-3} X z^{5} }{z^{-4} X y^{6} }) ^{2}[/tex]

The expression is as follows:

Quantity y raised to the negative third power times z raised to the fifth power end quantity over quantity z raised to the negative fourth power times y raised to the sixth power end quantity all raised to the negative second power

The equivalent expression of the statement is as follows:

[tex](\frac{y^{-3} X z^{5} }{z^{-4} X y^{6} }) ^{2}[/tex]

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Product rule of logarithms is used in the single logarithm.

A single logarithm can be expanded into many logarithms or compressed into many logarithms by using the features of log. Just another approach to write exponents is with a logarithm. As a result, the characteristics of exponents are used to infer the characteristics of logarithms.

There are 7 properties of logarithms: Product Rule, Quotient Rule, Power Rule, Zero Rule, Identity Rule, Inverse Property of Logarithm, Inverse Property of Exponent, Change of base formula.

In the equation here, only the product rule is applied.

Product rule of logarithms states that the log of a product is equal to the sum of the logs of its factors. Example: logₐ (xy) = logₐ x + logₐ y

Therefore, in this question,log₄5 + log₄5 = log₄ 25

Therefore, in the equation log₄5 + log₄5, the property of the product rule of logarithms is used.

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The coordinate of G' if triangle E'F'G' is created by dilating EFG with a scale factor of 4 about the origin is (8, -8).

In Mathematics, there are different types of transformation and these include the following:

Dilation can be defined as a type of transformation which changes the size of a geometric object, but not its shape. This ultimately implies that, the size of the geometric object would be increased or decreased based on the scale factor used.

Since the dilatation was centered around the origin, then we would multiply the coordinate of G by a scale factor of 4 as follows:

G = (2, -2) → G'[(4 × 2), (4 × -2)]

G = (2, -2) → G'(8, -8)

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Answer:

$780

Step-by-step explanation:

Simple Interest Formula

[tex]\boxed{\sf A = P(1 + rt)}[/tex]

where:

Given:

Substitute the given values into the formula and solve for A:

[tex]\implies \sf A=650(1+0.05(4))[/tex]

[tex]\implies \sf A=650(1+0.2)[/tex]

[tex]\implies \sf A=650(1.2)[/tex]

[tex]\implies \sf A=780[/tex]

Therefore, the amount in the account now is $780.

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The number of bleacher seats that the stadium will include will be 8000 seats.

In this situation, the The team's policy is to have a 3:2 ratio of premium seats to bleacher seats.

Therefore, the total number of premium seats are:

= 4500 + 7500

= 12000

The number of bleachers will be:

= 2/3 ×12000

= 8000

Therefore, the number of bleacher seats that the stadium will include will be 8000 seats.

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Answer:

The anwser is A

Step-by-step explanation:

A is the best anwser choice given

The function that models each variation is : [tex]z = \frac{5 x}{y}[/tex]

value of z = 20/9

The inverse variation property states that , whenever the product of values of two quantities is a constant value then there is opposite variation between them . Or we can also say that if the productive nature of two corresponding values is constant, then one quantity is inversely varies with second quantity. whereas, The direct variation state that the both values will show same pattern i.e. if one value will increase then another will also increase with the same amount or if one decrease another will also decrease.

In the question given,

First of all find the value of K in the model by putting in the values of x, y, and z so that to find the function model.

z = k (x) / (y)

put value of x=6, y=2 and z=15

15 = k (6) /2

k= 5

Thus we can write the equation as,

z=5x / y

put x=4, y=9

z = 20 / 9

Thus, z = 20/9

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The inequality that would represent the possible values for the number of hours babysitting, bb, and the number of hours walking dogs, dd, that Ryan can work in a given week is b + d >= 9.

From the information, Ryan is working two summer jobs, babysitting and walking dogs. He must work at least 9 hours altogether between both jobs in a given week.

Therefore, the inequality that would represent the possible values for the number of hours babysitting, b, and the number of hours walking dogs, d, that Ryan can work in a given week will be:

Babysitting + Walking dogs >= 9

b + d >= 9

Therefore, the inequality is b + d >= 9.

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Answer:

The age of the person who entered the room is 27

Step-by-step explanation:

If there are 6 people and the mean is 19 you would need to multiply 19 by 6. You will get 114 and now you just subtract the age of the others. 114-23-20-15-12-17=27.

All denominators are =[tex]6\sqrt{7xz}[/tex].

The phrase simplifies manner to make something simpler to do or recognize. So, by decreasing or simplifying the fractions method we make the fraction as simple as feasible. We do this by dividing the numerator and the denominator with the aid of the most important range that could divide into both numbers precisely.

The only form is likewise known as the decreased form of a fraction. for instance, ¾ is the most effective shape of a fraction that has a not unusual thing equal to 1. but 2/4 is not the most effective form, because 2/four can in addition be simplified and written as ½.

Step one is to perceive a common issue between the denominator and numerator. The denominator and numerator are each divided by the commonplace thing. The department operation is repeated until there are not any extra elements. The fraction is said to be simplified if no greater factors go out.

[tex]4\sqrt{7xz} +2 \sqrt{7xz}[/tex]

Add similar elements :

[tex]4\sqrt{7xz} + 2\sqrt{7xz}[/tex]

[tex]= 6\sqrt{7xz}[/tex]

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The sum in scientific notation is 6.358 * 10^5

The summation expression is given as

(1.568 × 10^5) + (4.79 × 10^5)

Factor out 10^5 in the above expression

So, we have

10^5 * (1.568 + 4.79)

Evaluate the sum

10^5 * 6.358

Rewrite the expression as

6.358 * 10^5

Hence, the sum in scientific notation is 6.358 * 10^5

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Correct answer is A. The cost of meal in the caffeteria is 24.39.

A percentage is a figure or ratio that represents a portion of 100. In addition to the percent symbol "%," the abbreviations "pct," "pct," and occasionally "pc" are also used to denote it. A% does not have any dimensions or a corresponding unit of measurement.

Your $20.20 bill is made up of the full amount (100%) plus the 15% tip, for a total of 115%. Decimal equivalent is 1.15.

Simply divide the entire charge by 1.15 to determine the price before the tip.

20.20/1.15 = 17.56

Consequently, the final amount due before the 15% tip was $17,56.

The total cost after tax and tip = 24.39

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Answer:

4

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

distance/time=speed

335/5=67

536/t=67

t=8

Eva bought 18 chicken wings with $18

Eva bought 20 chicken wings for $20

The first step is to calculate the cost of one chicken wing

= 20/20

= 1

1 chicken wings cost $1, if Eva spent $18 then the number of chicken wings bought can be calculated as follows

= 18 × 1

= 18

Hence Eva bought 18 chicken wings with $18

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The value of a is 2/√7.

The given quadratic equation is x² ₋ 3ax ₊ a² = 0

sum of the roots of the equation  = 4

here, A = 1

B = 3a

C = a²

Let α and β be the roots of the equation.

α ₊ β = ₋B/A

= ₋3a/1

= ₋3a

⇒ α×β = C/A

= a²/1

= a²

⇒α² ₊ β² = (α ₊ β )²  ₋ 2αβ

= (₋3a)² ₋ 2(a²)

= 9a² ₋ 2a²

therefore, 7a² = 4

a² = 4/7

a = √4/7

a = 2/√7

Hence we found the value of a as 2/√7.

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According to the question, to graph the linear inequality expressions then the given expressions should be equal to the respective number.

In the first equation that is: x<-2 or x = -2

The given expression can be drawn in the second quadrant when the value of the x-axis is negative and it is a straight line which tends to infinity.

In the second equation that is: y ≤ x+2 or y = x+2

The given expression can be drawn in the first as well as in the second quadrant when the value of the x-axis is negative as well as positive  and it is a straight line which tends to infinity.

Similarly, in the third equation that is: y ≤ x-3 or y = x-3

The given expression can be drawn in the first as well as in the second quadrant when the value of the x-axis is negative as well as positive  and it is a straight line which tends to infinity.

What is linear inequality?

Linear inequalities are those expressions in which comparison between the variables is performed. And the comparison can be done between two values or between the two expressions. It uses the symbols of the inequality like greater than, equal to, etc.

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Answer:

1 3/4

Step-by-step explanation:

Answer: Option D

Step-by-step explanation: Explanation:

7/4 is an improper fraction. Let's take the numerator and divide it by the denominator.

Divide 7 by 4. The quotient digit is 1.

Multiply the quotient digit 1 by the divisor 4.

Subtract 4 from 7.

The result of 7 divided by 4 is 1 with a remainder of 3.

Thus, 7/4 as a mixed number can be written as 1 3/4.

Answer:

4.

Step-by-step explanation:

28 = 2*2*7

32 = 2*2*2*2*2

Picking out the common factors:

GCF = 2 * 2 = 4.

Answer:28

Step-by-step explanation:

ask random person the explanation, sorry, I don't know how to explain

The width of the rectangle as an exponential factor whose length is 2^(-1) m and Area is 2^(-4) m^2 is 2^(-3) meter.

As per the question statement, we are given a triangle whose length is 2^(-1) m and Area is 2^(-4) m^2 is 2^(-3) meter. We are supposed to find out the width of the rectangle as an exponential factor.

Before solving the question, we should know the formula for calculating the area of the rectangle

Area = Length * Width

Given Area = 2^(-4) m^2

Given Length =  2^(-1) m

Let Width = "x" m

2^(-4) =  2^(-1) * x

2^(-4)/2^(-1) = x

2^(-4+1) = x

2^(-3) = x

Hence width of the given rectangle as an exponential factor is

x = 2^(-3)  meter

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Step-by-step explanation:

In this question , the 20 year policy is just for fun the probability is 53 / 73

If a man rode his personal transporter 3/10 mi to the library, then 3/4 mi to class, and then 7/2 mi to his part-time job, then he rode his personal transporter for 4.55 miles.

To determine how far the man rode his personal transporter we use addition.

total miles the man rode = miles to the library + miles to the class + miles to the part-time job

total miles = 3/10 + 3/4 + 7/2  

As these fractions have an unlike denominator, we find a common denominator by determining the least common multiple.

As the least common multiple is equal to 20

Therefore,

total miles = 3(2)/10(2) + 3(5)/4(5) +7(10)/2(10)

total miles = 6/20 + 15/20 +70/20

total miles = 6+15+70/20

total miles = 91/20

total miles = 4.55

Hence, the man rode his personal transporter for 4.55 miles.

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The distance between two given points (3, −4) and (−2, 5) is √106 units.

Given that, two points are (3, −4) and (−2, 5).

Distance between two points is the length of the line segment that connects the two given points. Distance between two points in coordinate geometry can be calculated by finding the length of the line segment joining the given coordinates.

The formula for the distance, d, between two points whose coordinates are d=√(x2-x1)²+(y2-y1)²

Now, put two points (3, −4) and (−2, 5) in the distance formula and simplify.

That is, distance = √[(-2-3)²+(5-(-4))²]

=√(25+81)

=√106 units

Therefore, the distance between two given points (3, −4) and (−2, 5) is √106 units.

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Answer:

Step-by-step explanation:

55+18x=175

-55+18x=-55

       18x= 120

Divide by 18

X=6,666666

So it will take 7 months

The value of f(-6) is 72, that is, option A.

In mathematics, a function from a given set X to a given set Y allots to each element of X one and only one element of Y. The set Y is called the range of the function and the set X is called the domain of the function.

Here, we are given a function f(x) = 2x²

f(-6) means that x = -6

Substituting x = -6 in the function, we get-

f(-6) =  2(-6)²

= 2 × -6 × -6

= 2 × 36

= 72

Thus, the value of f(-6) is 72.

From the given options, hence, option A becomes the correct answer.

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The average rate at which Mr. Blade types is 30 words per minute.

Average or mean is a measure of central tendency where it defines the central number of a data set.

Average is calculated by dividing the total sum of the values of the dat set divided by the frequency or the number of data in the set.

Mr. Adi takes 9 minutes.

The average rate of Mr. Adi is 40 words per minute.

So in 9 minutes he writes 40 × 9 = 360 words in total.

Mr. Blade typed the same number of words.

he took 12 minutes to type it.

So average rate = total words typed ÷ time taken (in minutes)

Average rate= 360 ÷ 12 =30 words per minute.

Hence Mr. Blade writes at the average rate of 30 words per minute.

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