Write log6 5 as a logarithm of base 4.

1) (log4)5/(log4)6
2) (log4)6/(log4)5
3) (log5)4/(log6)4
4) (log6)4/(log5)4 ...?

Answer

2x^2+4x-30

Step-by-step explanation:

Foil

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Outside

Inside

Last

Answer is provided in the image attached.

Answer:

3/5

Step-by-step explanation:

i am doing the same thing right now and got it right

When a vertical line passes through the graph of a function, it will intersect the graph at only one point. More than one point on any given vertical line means that the same x is being paired with 2 different y's and that make the graph not a function.

Please rate and thank : )

And btw copying and pasting is plagiarism

The correct option is option C that is the solution of the inequality is 2.

What are inequalities ?

When two values are compared , an inequality represents whether one is greater than, less than, or not equal to the other.

It is given that an inequality is given y > 1.9. Here , y is a number which can be anything greater than 1.9.

Let's check which of the given options is a solution for the given inequality.

A)

-9 is a negative number whereas 1.9 is a positive number , so - 9 is not a solution to given inequality.

B)

-2 is also less than 1.9 , so this also not a solution to given inequality.

C)

2 is greater than 1.9 and it is a suitable solution to the given inequality. So , 2 is a solution of given inequality.

D)

As per the question value of y should be greater than 1.9 and not equal to 1.9 . So , this is also not a solution to given inequality.

Therefore , the correct option is option C that is the solution of the inequality is 2.

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The set of natural numbers is closed under addition but not under subtraction.

The statement that is true for the set of natural numbers is B. The set is closed under addition and not closed under subtraction.

In mathematics, a set is considered closed under an operation if applying that operation to any two elements in the set always produces an element that is also in the set.

For the set of natural numbers, adding two natural numbers will always result in another natural number, so it is closed under addition. However, subtracting two natural numbers may result in a negative number, which is not a natural number, so it is not closed under subtraction.

Robbin needs a GPA of at least 2.5 to be unconditionally accepted into the graduate program.

To determine the undergraduate grade point average (GPA) Robbin must have to be unconditionally accepted into the program, we can set up an equation based on the information given. The criterion for acceptance is that the GMAT score plus 400 times the GPA must be at least 1800. Robbin's GMAT score is 800, so we can use the following equation:

800 + 400(GPA) ≥ 1800

We can then isolate the GPA:

400(GPA) ≥ 1800 - 800
400(GPA) ≥ 1000
GPA ≥ 1000 / 400
GPA ≥ 2.5

Answer:

A rectangle has a width that is 7 centimeters less than its length, and its area is 330 square centimeters. What are the dimensions of the rectangle?

length =  

22

centimeters

width =  

15

centimeters

The dimensions of the box for minimal surface area when volume is 12 are both the cube root of 3. When surface area is 20 for minimal volume, the dimensions are sqrt(5) for the base and (15 / (4*sqrt(5))) for the height.

The concept in this problem is about minimizing surface area and volume with relation to the dimensions of a box.

Let's consider a box with a square base of side 'x' and height 'h'. For part (a), the volume V of a box is given by V = x^2 * h which implies h = V / (x^2).

Substituting V = 12, we get h = 12/x^2. The surface area S of a box is given by S = x^2 + 4xh.

Substituting the value of h in the surface area equation, we have S = x^2 + 48/x.

To find the minimum surface area, we differentiate the above with respect to 'x' and set it equal to 0, which gives the dimensions of the box to be x = h = cube root of 3.

For part (b), the surface area S is given to be 20. So, S = x^2 + 4xh implies 4xh = 20 - x^2. The volume of the box is V = x^2 * h = (20 - x^2) / 4.

To minimize the volume, we differentiate V with respect to 'x' and set it to 0. That gives us the value of 'x' to be sqrt(5), and 'h' to be (20 - 5) / (4*sqrt(5))

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If no students attend the play, then 8 adults can see the play for $80.

The subject of this question is Mathematics, specifically linear equations. The scenario presented involves ticket sales for a school play with different ticket prices for students and adults. $7 is the price for a student ticket and $10 is for an adult ticket. The given equation 7x+10y=80 represents the total sum of $80 that needs to be reached with a combination of student tickets (x) and adult tickets (y).

If no students attend, x in the equation is 0, so we have 10y = 80. To find the number of adults (y) that can attend the play for $80, we need to solve this equation for y. So, y = 80 / 10. Therefore, y = 8, meaning 8 adults can attend the play for $80 when no students attend.

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To find out how many 15-window coverings are needed for 50 windows, divide 50 by 15, which gives approximately 3.33. Rounding up because we can't have partial window coverings, we will need 4 coverings.

The question asks: How many window coverings are necessary to span 50 windows if each window covering is 15 windows long?

To answer this question, we can do a simple division. We divide the total number of windows (50) by the length of each window covering (15).

So, we have 50 ÷ 15 which equals approximately 3.33. However, since we cannot have a fraction of a window covering, we need to round this number up. Therefore, we would need 4 window coverings to span 50 windows.

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The limit does not exist for this expression.

To evaluate the limit as h approaches 0 of (sin(pi/6 + h) - sin(pi/6))/h, we can use the limit definition of the derivative of sin(x).

The derivative of sin(x) is cos(x), so we can rewrite the expression as:

lim h->0 (cos(pi/6 + h) - cos(pi/6))/h

Now, we can use the limit definition of the derivative to evaluate this limit. The derivative of cos(x) is -sin(x), so we have:

lim h->0 (-sin(pi/6 + h))/h

Now, let's substitute h = 0 into the expression:

(-sin(pi/6 + 0))/0

Since sin(pi/6) = 1/2, we have:

(-1/2)/0

However, division by zero is undefined. Therefore, the limit does not exist for this expression.

Answer:

[tex]\frac{2}{5}[/tex]

Step-by-step explanation:

The ratio is hot dogs to chicken the chicken isten tho to find the hot dogs first you do

10+6=16

So it says 20 members so then you needa see how much would equal the amont 20 obviously 4 so the hot dogs equal to 4 so the ratio is 4:10

Answer:

2/5

Step-by-step explanation:

just did it and it is correct

The probability of selecting a card greater than 5 or an odd number from a bag of cards numbered 1 to 10 is 0.8 or 80%.

The question asks for the probability of choosing a number greater than 5 or an odd number from a bag containing numbered cards from 1 to 10. To solve this, we should consider that numbers greater than 5 are 6, 7, 8, 9, and 10. There are 5 odd numbers in the set: 1, 3, 5, 7, and 9. The number 7 and 9 are both greater than 5 and odd, so they are counted only once when combining the two groups.

First, let's count the total unique outcomes that either meet the criterion of being greater than 5 or being odd: 6, 7, 8, 9, 10, 1, 3, 5 (7 and 9 are already counted). There are 8 such numbers.

The total number of possible outcomes is 10, as there are 10 cards. The probability is the number of favorable outcomes divided by the total number of possible outcomes: P = favorable outcomes / total outcomes = 8/10 = 0.8 or 80%.

Answer:

P(x)=  x³ - 3 x² - 46 x +168

Step-by-step explanation:

given roots of the polynomial are given as    (4,6, -7)

hence the polynomial will be equal to

P(x) = (x-4) (x-6) (x+7)

P(x) = (x-4) (x²+7 x -6 x -42)

P(x) = (x-4) (x²+x -42)

P(x) = x³ + x²-42 x -4 x² -4 x +168

P(x) =  x³ - 3 x² - 46 x +168

hence, the required polynomial is P(x) =  x³ - 3 x² - 46 x +168

Answer:

18.4 ft

Step-by-step explanation:

Use Pythagorean Theorem: a^2+b^2=c^2

17^2+7^2=c^2

sqrt 338=sqrt c^2

(sqrt and power 2 cancel)

sqrt 338=c

sqrt 338= 18.4 ft

The three Cs of credit are character, capacity, and capital, which represent the creditworthiness of an individual or business as assessed by lenders based on reputation, ability to repay, and assets for collateral respectively.

The three Cs of credit refer to character, capacity, and capital. These are the main criteria that lenders consider when assessing the creditworthiness of an individual or business. Character refers to the borrower's reputation and track record for repaying debts. Capacity is the borrower's ability to repay the loan, determined by their income and existing debt levels. And capital relates to the wealth or assets the borrower can offer as collateral. When banks conduct credit checks or require a co-signer, they are evaluating these aspects to decide on lending money.

Answer:

(C) Triangles BPA and DPC are congruent.

Step-by-step explanation:

It is given that In quadrilateral ABCD, diagonals AC and BD bisect one another.

We have to prove that quadrilateral ABCD is a parallelogram.

(A) The given statement is:

Angles ABC and BCD are congruent

The above statement is not correct because these angles forms the corresponding angle pair and thus are not congruent.

Hence, this option is not correct.

(B) The given statement is:

Sides AB and BC are congruent.

The above statement is not correct because the given sides are formed by the same vertex and thus cannot be equal.

Hence, this option is not correct.

(C) The given statement is:

Triangles BPA and DPC are congruent.

The above statement is correct because the given triangles are congruent by the SAS rule of congruency.

Hence, this option is correct.

(D) The given statement is:

Triangles BCP and CDP are congruent.

the above statement is  not correct because the given triangles cannot be congruent using any rule of congruency,

Hence, this option is not correct.

Final answer:

To reach a height of 8 feet on the wall, Benton would need to use a ladder length of approximately 4.8 feet.

Explanation:

To determine which ladder length Benton would need to use to reach the desired height of 8 feet on the wall, we can use the concept of similar triangles. The distance from the base of the ladder to the wall is 6 feet and the height Benton wants to reach on the wall is 8 feet. Let x represent the length of the ladder needed. Using the properties of similar triangles, we can set up the following proportion:

(x)/(6) = (8)/(10)

Cross multiplying gives us:

x = (6 * 8) / 10 = 4.8

Therefore, Benton would need to use a ladder length of approximately 4.8 feet to reach a height of 8 feet on the wall. Since this length is not among the options provided, the correct answer is C. None of these ladder lengths would reach this height.