Use the properties of logarithms to evaluate each expression. 2 log 5+ log 40

10 order of small popcorn Should be made to keep  the cost same at both the theaters

The theater P charges Admission fee of $10 and small popcorn order of $4.55

The theater Q charges Admission fee of $8 and small popcorn order of $4.75

We need to find the number of order of small popcorn so that the cost remain same

Let the number of small popcorn order be x

Then we can form the algebraic equation as

10 + 4.55x = 8 + 4.75x

now we should simplify the equation

10- 8 = 4.75x-4.55x

2= .2x

x = 2/0.2

x = 10

Hence , 10 order of small popcorn Should be made to keep  the cost same at both the theaters

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It can be proved using the method of inverse variation.

What is inverse variation?

In mathematics, inverse variation refers to the relationships between variables expressed as y = k/x, where x and y are two variables and k is a constant. According to this statement, if the value of one item rises, the value of the other quantity falls.

Given,

(x₁, y₁) and (x₂, y₂) are values from an inverse variation.

inverse function of x and y will be -

y1 = k. 1 / x1  

k = y1 / x1                                                ....(1)

y2 = k. 1 / x2  

k = y2 / x2                                              ....(2)

from (1) , (2)

we can say that,

y1 / x1    = y2 / x2

⇒ y2 / y1 = x1 / x2

Hence proved.

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Answer: t=15

Step-by-step explanation:

ST=9. BC=3

ST/BC=

9/3=3 ==> with this information, we can conclude that triangle ABC needs to be stretched by a scale factor of 3 in order to become triangle RST.

t=RS

RS=AB*3

RS=5*3

RS=15

t=15

Answer:

G' (8, - 8 )

Step-by-step explanation:

since the dilatation is centred at the origin then multiply each of the coordinates by the scale factor of 4

G (2, - 2 ) → G' (4(2), 4(- 2)) → G' (8, - 8 )

The value of the expression 3√70 to the nearest integer will be 25.10.

When the relevant factors and natural laws of a mathematical model are given values, the outcome of the calculation it describes is the expression's outcome.

PEMDAS rule means the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.

The expression is given below.

⇒ 3√70

We know that the value of √70 will be 8.3666. Then the value of the expression will be given as,

⇒ 3√70

⇒ 3 x 8.3666

⇒ 25.0998 ≈ 25.10

The value of the expression 3√70 to the nearest integer will be 25.10.

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The dimensions of the rectangular photo frame, rounded to the nearest whole number of centimeters are: D. 13cm x 9cm.

Whole numbers are numbers that do not have any fractional part and represents a whole quantity.

A mixed number consist of an whole number and a proper fraction or fractional part.

Given the dimensions of the rectangular photo as, 12 11/16 cm by 8 3/4cm, convert each dimension to improper fractions:

12 11/16 would be converted to 203/16

8 3/4 would be converted to 35/4

203/16 = 12.6875 ≈ 13 [nearest whole number of cm]

35/4 = 8.75 ≈ 9 [nearest whole number of cm]

Therefore, the dimensions of the rectangular photo frame, rounded to the nearest whole number of centimeters are: D. 13cm x 9cm.

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Answer:

12a + 3b = no solution

Step-by-step explanation:

You have to add like terms here!

7a + 5a = 12a

12a + 4b - b

4b - b = 3b

And now you're left with 12a and 3b, you can't go any further because 12 a and 3b are not like terms, you cannot add, or subtract them. Which means there is no solution.

I hope this helped :)

Answer:

(1, 7 )

Step-by-step explanation:

- 2x - 4y = - 30 → (1)

- x + y = 6 → (2)

multiplying (2) by 4 and adding to (1) will eliminate y

- 4x + 4y = 24 → (3)

add (1) and (3) term by term to eliminate y

- 6x + 0 = - 6

- 6x = - 6 ( divide both sides by - 6 )

x = 1

substitute x = 1 into either of the 2 equations and solve for y

substituting into (1)

- 2(1) - 4y = - 30

- 2 - 4y = - 30 ( add 2 to both sides )

- 4y = - 28 ( divide both sides by - 4 )

y = 7

solution is (1, 7 )

The simplified form of the given logarithmic expression ln (x+1)+ln (x-1)= 4 is x = 0.67 (to the nearest thousandth).

A logarithmic term represents a number in log form. A log term is another name for it.

A quantity can also be the sum of two or so more quantities. As a result, a term can be the product of 2 or more quantities, one of which must be in logarithmic form. In those kind of instances, the terms are recognized as log terms.

A quantity can also be defined as the quotient of two quantities. So, if a term includes a quotient of quantities, or at least each of the quantities could be expressed in log form, this same terms are known as log terms.

Now, according to the stated condition in question;

ln (x+1)+ln (x-1) = 4

Applying the Product Rule on the left side of the equation;

ln (x+1)/ (x-1) = 4

Convert the obtained expression in the exponent form.

Thus,

e∧[ln (x+1)/ (x-1)] = e⁴

Now, apply the exponent rule.

(x+1)/ (x-1) = 4

Now, simplifying the equation.

(x+1) = 4 (x-1)

x+1 = 4x - 1

4x - x = 1 + 1

3x = 2

x = 2/3

x = 0.666...

x = 0.67 (to the nearest thousandth).

Therefore, the solution for the stated logarithmic expression ln (x+1)+ln (x-1)= 4 is x = 0.67 (to the nearest thousandth).

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The value corresponding to |f(i)| is √2.

The given function is f(x)=1-x.

Given f(x) = 1 - x

To find the value of |f(i)| we have to substitute x=i.

After substituting this, we get

f(i) = 1 - i

As we all know that, this is an imaginary even function in the form a + ib

The modulus of the imaginary function can be represented as √(a²+b²)

Here a = 1 and b = -1

Now, we will substitute this value in the above formula, we get

|f(i)| = √(1² + (-1)²)

|f(i)| = √(1+1)

|f(i)| = √2

Hence, the value of the given function f(x)=1-x which is equivalent to |f(i)| corresponding value is √2.

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Answer:

here to try to help!

Step-by-step explanation:

346.96 why? Kerry was not payed at the overtime for extra hours hope it helped!

The answer is 190m.

The faster train is 160 m long and crosses a lamp post in 12 seconds.

The speed of the faster train = 16012 = 403 m/s

Given that, the speed of the other train is 6 km/hr (53 m/s) less than the faster one. [we can convert speeds from km/h to m/s by multiplying with 5/18]

The speed of the slower train = 353 m/s.

Given that, the two trains cross each other in 14 seconds when running in opposite directions along parallel tracks.

tracks.

Relative speed =  total length of two trains  time taken to cross each other

25m/s = 160+ length of second train 14

Length of the second train = 190m.

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The linear equation y = (5 / 2) · x exhibits the steepest graph in comparison with the other three lines. (Correct choice: D)

Linear equations are equations of the form y = m · x + b, where m, b are the slope and the intercept of the equation, respectively. As slopes may be positive, null or negative, then we should use absolute values to determine the grade of steepness of a linear equation, where |m| ≥ 0. A line is steeper than other line when the absolute value of the former is greater than the absolute value of the latter.

According to this criterion, the linear equation y = (5 / 2) · x exhibits the steepest graph in comparison with the other three lines.

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Descriptive statistics is the correct answer.

Descriptive statistics are numbers that are used to summarize and describe data. The word "data" refers to the information that has been collected from an experiment, a survey, a historical record, etc. (By the way, "data" is plural. One piece of information is called a "datum.") If we are analyzing birth certificates, for example, a descriptive statistic might be the percentage of certificates issued in New York State or the average age of the mother. Any other number we choose to compute also counts as a descriptive statistic for the data from which the statistic is computed. Several descriptive statistics are often used at one time to give a full picture of the data.

Descriptive statistics are just descriptive. They do not involve generalizing beyond the data at hand. Generalizing from our data to another set of cases is the business of inferential statistics, which you'll be studying in another section. Here we focus on (mere) descriptive statistics.

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During the cooking class, the instructor put 1/8 of the salt in each serving

The instructor divided 1/2 of an ounce of salt evenly

The instructor needs to 4 servings in a dish

Therefore the number of salt in each serving can be calculated as follows

= 1/2 ÷ 4

change the expression to multiplication

1/2 × 1/4

= 1/8

Hence 1/8 of the salt was placed in each serving of the dish

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Answer:

d)decreases

Step-by-step explanation:

The inverse of the function y=4 x²+5  is y = √((x-5)/4).

Inverse functions are those that cancel one another out. In other words, if g(x) is f's inverse, then f(g(x)) = g(f(x)) = x. (x). Given an equation for which we want the inverse, we have a fantastic method we can utilize to do this.

Not every function has a counterpart. If f(x) has an inverse, it is clear to see that it will never again have the same value. We give this resource a special name.

A function (f(x)) is said to be one-to-one if each member of the range corresponds to exactly one element of the domain.

Given,

We have a function,

y=4 x²+5

subtracting 5 from each side.

⇒ y - 5 = 4 x²

Divide by 4 and then either

⇒ x² = (y - 5) / 4

⇒ x = √((y-5)/4)

Just change the labels now, x to y.

⇒ y = √((x-5)/4)

So, the inverse of given function is y = √((x-5)/4)

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Answer:North west, the roads should have stopped this answer but north alone wasn’t an option so just pretend Jenna is a lawless maniac ig‍♂️

Step-by-step explanation:

They spent 1/70 of their monthly income on other things.

The family spent GH¢60,000 on clothing.

The monthly income of the family is GH¢168,000.

What is Fraction?

The number is expressed as a quotient in which the numerator is divided by the denominator is called fraction.

Since, The family spend;

On food = (3/7)*x

On clothing = (5/14)*x

On rent = (1/5)*x

Let the family's monthly income = x

Now, To find the fraction of the family's income is spent on other things, we can assume that y is spent on other things, then we should have;

(3/7)*x + (5/14)*x + (1/5)*x + y*x = x

We can divide both sides by x, we get:

(3/7) + (5/14) + (1/5) + y = 1

Now, we can solve this for y as;

3/7 + 5/14 + 1/5 + y = 1

6/14 + 5/14 + 1/5 + y = 1

(6 + 5)/14 + 1/5 + y = 1

11/14 + 1/5 + y = 1

The smallest common factor of 14 and 5 =  14*5 = 70

So, we can multiply in the first fraction by 5/5 and the second by 14/14,

(5/5)*(11/14) + (14/14)*(1/5) + y = 1

55/70 + 14/70 + y = 1

69/70 + y = 1

y = 1 - 69/70

y = 1/70

Hence, They spent 1/70 of their monthly income on other things.

And, On a particular month, the family spends  GH¢2,400 on other things, then if the monthly income is x, we have:

(1/70)*x = GH¢2,400

x = 70* GH¢2,400

x = GH¢168,000

So, The monthly income of the family is GH¢168,000

And, we know that they spend (5/14)*x on clothing,

Then this month they spent on clothing,

⇒ (5/14)*GH¢168,000 = GH¢60,000

So, They spent 1/70 of their monthly income on other things.

The family spent GH¢60,000 on clothing.

The monthly income of the family is GH¢168,000.

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The complete question is this,

A family spends 3/7 of their monthly income on food,5/14 on clothing and 1/5 on rent. What fraction of the family's income is spent on other things? If in a particular month, the family spends GH&2,400 on other things, how much did the family spend on clothing? What was the family's income for the month.

The components of PQ are given by {5; 2}

The components of a vector in a two-dimensional coordinate system are usually thought of as the x and y components. This can be expressed as V = (vx, vy), where V is a vector. These are part of the vectors generated along the axis.

Suppose an angle θ is formed between the vector V and the x component of the vector. A vector V and its x component (vx) form a right triangle if you draw a line parallel to the y component (vy).

Due to the trigonometric relationship:

cos θ = adjacent side/hypotenuse = vx/V

sin θ = opposite side/hypotenuse = vy/V

where V is the magnitude of vector V.

So, the Component of PQ is Given by

PQ = {Bx - Ax; By - Ay} = {3 - (-2); 4 - 2} = {5; 2}

PQ= {5; 2}

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Solution of this polynomial equation is x = 3

In mathematics, polynomial equation can be defined as the equation which consist of coefficient, variables and exponents. A polynomial equation has positive numbers as their exponent which is also known as its degree. All the equations such as quadratic equation, cubic equation which has non  negative number as their powers are part of polynomial equation.

Types of polynomial equations :

Some examples of polynomial equation are :

According to question,

3x = 9

=> 3x / 3 = 9 /3

=> x = 3

Thus solution for given equation is x = 3.

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From the given scatter plot with x and y variables, we can say that the correlation is; Negative Correlation.

We are told that you kept the balance in your "discretionary spending" envelope.

Now, we are further told that a scatter plot shows the number of days that have passed since you were paid and the amount left in your discretionary spending envelope.

Now, In this case, the day of the salary increases the money spent, that is, the amount of money in the envelope decreases. Thus, as the variable increases and the other decreases, it is a negative correlation.

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The simplified form of the expression is 6^(-3)

From the question, we are to simplify the given expression

The given expression is

6^2/6 • 6^12 / 6^8

Simplifying

6^2/6 • 6^12 / 6^8

Applying the division law of indices

6^(2 -1 ) • 6^(12 - 8)

6^(1) • 6^(4)

Applying the multiplication law of indices

6^(1 - 4)

6^(-3)

Hence, the simplified form of the expression is 6^(-3)

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The constraints of the equation will be x > 13 y and 340 x + 670 y < 5650.

Let the number of new bicycles be x

Let the number of new treadmills be y.

Cost of 1 new bicycle = $ 340

Cost of 1 new treadmill = $ 670

Also, he must spend less than $ 56,50

Now, the constraints for this will be:

x > 13 y

x greater than 13 y

340 x + 670 y < 5650

340 x plus 670 y less than or equal to 5650

Therefore, the constraints of the equation will be x > 13 y and 340 x + 670 y < 5650 .

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Answer:

-207

Step-by-step explanation:

38x - 17

38(-5) - 17

-190 - 17

-207

*Please mark brainliest answer

Answer:-173

Step-by-step explanation:

38x - -17

38 multiplied by -5 equals -190

-190 - -17 equals -173

Answer:

Step-by-step explanation:

25/3