Name the postulate or theorem you can use to prove AKS E ATL

Answer:

35 books

Step-by-step explanation:

56/8 = 7

7 x 5 = 35

5/8 of 56 = 35

J.K. Rowling will autograph 35 of the 56 books sold, which is calculated by multiplying the total number of books by 5/8.

To find out how many books J.K. Rowling will autograph, we need to calculate 5/8 of the 56 books sold. Here's the step-by-step calculation:

Find out what 5/8 of the total amount is by multiplying the total number of books (56) by 5/8.

To do this, first multiply 56 by 5, which equals 280.

Then divide that number by 8, which equals 35.

Therefore, J.K. Rowling will autograph 35 books.

Answer:

8/5

Step-by-step explanation:

[tex](g\circ h)(-3)[/tex] means [tex]g(h(-3))[/tex].

Start with the inside first: h(-3).

h(-3) means use the function called h and replace the x with -3.  The expression that is called h is 4-x.

4-x evaluated at x=-3 gives us 4-(-3)=4+3=7.

So the value for h(-3) is 7, or h(-3)=7.

Now this is what we thus far:

[tex](g\circ h)(-3)=g(h(-3))=g(7)[/tex].

g(7) means use the function called g and replace x with 7.   The expression that is called g is (x+1)/(x-2).

(x+1)/(x-2) evaluated at x=7 gives us (7+1)/(7-2)=(8)/(5)=8/5.

This is our final answer:

[tex](g\circ h)(-3)=g(h(-3))=g(7)=\frac{8}{5}[/tex].

Answer:

28.71

Step-by-step explanation:

The easiest way I do this is by taking the smaller number (33) changing it to a decimal form of .33, and then multiplying it by 87 to get 28.71

Answer:

{ (1,1),(2,9),(4,8) } is the right answer. Mentioned relation has all the ordered pairs of x and y in the form of set, shown in the table.

Step-by-step explanation:

Answer details  

Grade: Middle

Subject: Mathematics

Chapter: Representing Functions and relations

Keywords: relations, ordered pairs, tables and functions, set etc  

Check the picture below.

well, √180 is about 13.4, and √72 is about 8.5, clearly 2*8.5 ≠ 13.4.

Answer:

m<SYD = 106.02°. Reason: alternate exterior angles are equal.

Step-by-step explanation:

Answer:

m<SYD = 106.02°. Reason: alternate exterior angles are equal.

Step-by-step explanation:

Answer:

[tex]a_n=-7+4(n-1)[/tex]

or

[tex]a_n=-7+(n-1)(4)[/tex]

Step-by-step explanation:

-7,-3,1,5,... is a arithmetic sequence.

Arithmetic sequences have a common difference. That is, it is going up by 4 each time.

When you see arithmetic sequence, you should think linear equation.

The point-slope form of a line is [tex]y-y_1=m(x-x_1)[/tex].

m is the common difference, the slope.

Any they are using the point at x=1 in the point slope form.  So they are using (1,-7).

So let's put this into our point-slope form:

[tex]y-(-7)=4(x-1)[/tex]

[tex]y+7=4(x-1)[/tex]

Subtract 7 on both sides:

[tex]y=-7+4(x-1)[/tex]

So your answer is

[tex]a_n=-7+4(n-1)[/tex]

The explicit formula for the sequence -7, -3, 1, 5,... is an = -7 + (n - 1)(4), which corresponds to an arithmetic sequence with a common difference of 4.

The student is looking for the explicit formula for the sequence -7, -3, 1, 5,.... To find the explicit formula for a linear sequence, we look for a pattern in the increments between successive terms. In this sequence, each term increases by 4 from the previous term (-7 + 4 = -3, -3 + 4 = 1, etc.), so the common difference is 4. Using the formula for an arithmetic sequence, which is an = a1 + (n - 1)d, where an is the nth term, a1 is the first term, n is the term number, and d is the common difference, we can find the explicit formula:

an = -7 + (n - 1)(4)

Since the common difference in the question is positive and we are adding it to the first term which is negative, it is clear that choice A is the correct formula representing the given sequence:

an = -7 + (n - 1)(4)

Answer:

PQ must bisect AB

Step-by-step explanation:

Answer:

Joshua had $25 on Monday.

Step-by-step explanation:

We are given the following information:

Money spend on each day for lunch = $3

Number of days he attend school in a week = 5

Total money spent on lunch = [tex]3\times 5 = \$15[/tex]

Money spent on Tuesday for ticket = $5

Money spent on Friday = $2

Money left on Friday = $3

Total money in the start of week =

[tex]15 + 5 + 2 + 3 = 25[/tex]

Thus, Joshua had $25 on Monday.

Answer:

20/45 & 21/45

Step-by-step explanation:

Find a common denominator. What you do to the denominator, you do to the numerator. In this case, the smallest denominator is 45.

(4/9)(5/5) = 20/45

(7/15)(3/3) = 21/45

The two fractions you have is:

20/45 for 4/9

21/45 for 7/15

~

Answer:

20/45 for 4/9  and 21/45 for 7/15

Step-by-step explanation:

The least common denominator of 4/9 is 20/45.

The least common denominator of 7/15 is 21/45.

Answer:

It's the first set.

Step-by-step explanation:

X ≤ 18 or x > 22.

The first set is included in the solution.

Its not the second because 22 is not included.

Nor the third also because of the 22.

Nor the third because of the 19, 20, 21  and the 22.

A set is a mathematical model for a collection of items; it contains elements or members, which can be any mathematical object.

A compound inequality is created when two simple inequalities are combined. This article explains how to graph and solve compound equations.

Compound inequality includes number not included in selected region given in graph  hence including numbers 18,19,20,21,22

Which is option D

Hence correct option is {18,19,20,21,22}

Learn more about compound inequality

https://brainly.com/question/234674

#SPJ2

Answer:

g(3)=82

g(-6)=-6632

Step-by-step explanation:

To find g(3) we are going to use synthetic division for dividing the polynomial x^5-5x^3-10x+4 by x-3.

So this means 3 goes on the outside.

Also since we are missing x^4 and x^2 term, we will need to put a 0 placeholders there.

3  |  1   0    -5    0   -10     4

   |       3     9   12    36    78

   |_____________________

      1    3     4   12    26     82

So g(3)=82

To find g(-6) we will put -6 on the outside:

-6 |  1   0    -5    0       -10     4

   |       -6   36  -186    1116  -6636

    --------------------------------------

      1    -6   31   -186    1106   -6632

So g(-6)=-6632

Answer:

sin(B)=cos(90-B)

Step-by-step explanation:

sin(B)=cos(90-B) is a co-function identity.

We can also prove it using the difference identity for cosine.

Let's do that:

cos(90-B)

equals

cos(90)cos(B)+sin(90)sin(B)

0cos(B)+1sin(B)

0+sin(B)

sin(B)

Therefore cos(90-B)=sin(B).

Answer:

The correct answer option is: infinitely many solutions.

Step-by-step explanation:

We are given the following system of equations:

[tex] 3 x - 2 y = 6 [/tex] --- (1)

[tex] 6 x - 4 y = 1 2 [/tex] --- (2)

Dividing equation (2) by 2 to get:

[tex] 3 x - 2 y = 6 [/tex] --- (3)

As the equation (3) is same as the equation (1), therefore the system will have infinitely many solutions.

Answer:

infinitely many solutions

Step-by-step explanation:

Note that if you multiply the first equation by 2, you get 6x - 4y = 12, which is exactly the same as the second equation.  These two lines coincide, and so there are infinitely many solutions.

Answer:

So the multiplicative rate of change is increased by a factor of 5 per 1 unit increase in x.

Step-by-step explanation:

I think your function is off... but I can look at your ordered pairs.

(1,10)

(2,50)

(3,250),..

As the x increases by 1 the y is being multiply by a factor of 5 each time.

So the multiplicative rate of change is increased by a factor of 5 per 1 unit increase in x.

Answer:

7

Step-by-step explanation:

You can use the distance formula, but since both points have the same y-coordinate, they lie on a horizontal line. Just find the difference between the x-coordinates and take the absolute value.

distance = |-3 - 4| = |-7| = 7

Answer:

The distance is:

[tex]d=7[/tex]

Step-by-step explanation:

The distance d between two points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] is calculated using the following formula:

[tex]d=\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}[/tex]

In this case the points are:

A (4,2), B (-3,2).

Then the distance is:

[tex]d=\sqrt{((-3)-4)^2 + (2-2)^2}[/tex]

[tex]d=\sqrt{((-7)^2 + (0)^2}[/tex]

[tex]d=\sqrt{49}[/tex]

[tex]d=7[/tex]

Step-by-step answer:

APY (annual percentage yield) is the amount of interest in percent one would actually earn by investing a sum of money in a year.

It takes into account the interest rate expressed in any particular form, and the compounding period.

In the current market, most interest rates (for example, credit cards) are expressed in APR (Annual percentage rate) which is an underestimate of the actual amount to be paid, by NOT taking into account the compounding period, monthly (instead of annually) most of the time.  The shorter compounding period increases the APY.

Here the APR is 4.4%.  to take into account the compounding period, we divide the interest rate by 12 to give the monthly rate, 4.4%/12=0.044/12.

This rate will then be compounded 12 times to give the APY, or the future value after 12 months.

Future value = (1+0.044/12)^12 = 1.044898

Therefore the APY is 1.044898 less initial deposit, or

1.044898-1 = 0.044898, or 4.4898%, or 4.49% (rounded to 2 decimal places)

Answer:

78

Step-by-step explanation:

The given functions are:

[tex]f(x) = - 2x - 7[/tex]

and

[tex]g(x) = - 4x + 6[/tex]

[tex](f \times g)(x) = f(x) \times g(x)[/tex]

[tex](f \times g)(x) = ( - 2x - 7)( - 4x + 6)[/tex]

When we plug in x=-5, we get:

[tex](f \times g)( - 5) = ( - 4 \times - 5 + 6)( - 2 \times - 5 - 7)[/tex]

[tex](f \times g)( - 5) = ( 20 + 6)( 10 - 7)[/tex]

[tex](f \times g)(5) = ( 26)( 3) =7 8[/tex]

Answer:

Option C (-0.922107932)

Step-by-step explanation:

Correlation is a concept which explains a linear relationship between two variables. The correlation constant lies between -1 and 1. 0 lies in the center of the interval. A negative correlation means an inverse relationship, and a positive correlation means a direct relationship. 0 technically means no linear relation between the variables. Further the correlation constant lies from 0, more the strength of the relationship. This means that closer the correlation to 1, stronger the positive relationship, and closer the correlation to -1, stronger the negative relationship. It can be seen that Option C (-0.922107932) is the correlation coefficient which is the largest in terms of the magnitude. Therefore, Option C is the correct choice!!!

Answer: Second Option

[tex]f(x)=0.25(5.25)^x[/tex]

Step-by-step explanation:

The exponential growth functions have the following form:

[tex]f(x) = a(b)^x[/tex]

Where a is the main coefficient, b is the base and x is the exponent.

For this type of functions the base b must always be greater than 1. Otherwise it would be an exponential decay function

Among the options given, the only function whose base is greater than 1 is the second option:

[tex]f(x)=0.25(5.25)^x[/tex]

Answer:

The correct answer option is B. [tex] f ( x ) = 0 . 2 5 ( 5 . 2 5 ) ^ x [/tex].

Step-by-step explanation:

If the numbers are positive along with the base of the exponent which must be greater than 1, then it an exponential growth function.

1. [tex]f(x)=6(0.25)^x[/tex]:

Here the numbers are positive but the base of the exponent is 0.25 which is less than 1 so it is not an exponential growth function.

2. [tex] f ( x ) = 0 . 2 5 ( 5 . 2 5 ) ^ x [/tex]:

Positive numbers with base of the exponent greater than 1, therefore it is an exponential growth function.

Answer:

Step-by-step explanation:

x^2-9 = 0

x^2 = 0+9

x^2=9

Take square root  at both sides:

√x^2 =+/-√9

x =+/- 3

This equation has 2 real solutions, x=3 , x=-3....

Answer:

11

Step-by-step explanation:

The distance that a is to b is b-a=17-2=15.

The line segment from a=2 to b=17 has length 15.

We need to know what is 3/5 of 15.

3/5 of 15 means what is 3/5 times 15?

(3/5)(15)=3(3)=9

So this means we are looking to make a line segment that is 9 units from 2 which is 2 to 11.

So 11 is 3/5 the way from a=2 to b=17.

Let's check from 2 to 11 that is a length of 9 and from 2 to 17 that is a length of 15.

Is 9/15 equal to 3/5?

Yes, 9/15 can be reduced to 3/5.

Answer:

covalent bond and low melting point- 3.

Answer:

C)

Step-by-step explanation:

egdenuity 2020

Answer:

the answer to your question is the fourth one listed on your multiple choice, where it shows it curving at the lowest point out of all the others , in the 4th quadrant

Answer:

The correct option is C.

Step-by-step explanation:

Lets solve each option one by one

A) 16a^2-72a+81

According to whole square formula:

a²-2ab+b² =(a-b)²

We have to take the square root of first and third term of each equation.

a² shows the first term = 16a^2

The square root of 16a^2 is 4a.. because 4 is the number which can be multiplied two times to give 16 and when we multiply a two times it gives us a².

b²  shows the third term = 81

The perfect square of 81 is 9.

2ab shows the middle term.

2ab = 2(4a)(9) = 72a

Thus we can factor it as a perfect square trinomial:

a²-2ab+b² =(a-b)²

16a²-72a+81 =(4a-9)²

B) 169x^2+26xy+y^2

a²+2ab+b² =(a+b)²

The square root of 169x² is 13x

Square root of y² is y

The middle term 26xy =2ab= 2(13x)(y)= 26xy

Thus we can factor it as a perfect square trinomial:

a²+2ab+b² =(a+b)²

169x^2+26xy+y^2 = (13x+y)²

C) x^2-18x-81

We can not factor it as a perfect square trinomial because the third term is negative.

D) 4x^2+4x+1

a²+2ab+b² =(a+b)²

The square root of 4x² is 2x

Square root of 1 is 1

The middle term 4x=2ab=2(2x)(1)= 4x

Thus we can factor it as a perfect square trinomial:

a²+2ab+b² =(a+b)²

4x^2+4x+1 = (2x+1)²

Thus the correct option is C....

Answer:

see explanation

Step-by-step explanation:

Given a quadratic equation in standard form

ax² + bx + c = 0 : a ≠ 0, then

The nature of it's roots can be determined by the discriminant

Δ = b² - 4ac

• If b² - 4ac > 0 then roots are real and distinct

• If b² - 4ac = 0 then roots are real and equal

• If b² - 4ac < 0 then roots are not real

For x² - 4x + 4 = 0 ← in standard form

with a = 1, b = - 4, c = 4, then

b² - 4ac = (- 4)² - (4 × 1 × 4) = 16 - 16 = 0

Hence roots are real and equal

This can be shown by solving the equation

x² - 4x + 4 = 0

(x - 2)² = 0

(x - 2)(x - 2) = 0, hence

x - 2 = 0 or x - 2 = 0

x = 2 or x = 2 ← roots are real and equal

The graph's y intercept would be shifted up.

The intercept of the original point is determined as follows;

y = 12x - 7, when compared to , y = mx + c

where;

c is the intercept = -7

The intercept of the second graph is determined as follows;

y = 12x + 1

New intercept = 1

The graph's y intercept will move from -7 to +1, thus, It would be shifted up.

Learn more about intercept here: https://brainly.com/question/1884491

Final answer:

The graph of the new function y = 12x + 1 would not be steeper or less steep than the original but would be shifted up compared to the graph of y = 12x - 7.(Option C)

Explanation:

Changing the equation from y = 12x - 7 to y = 12x + 1 does not alter the slope of the line, which remains 12 in both cases. The slope of a line represents the steepness and direction of the line, and since the slope (the coefficient of x) has not changed, the steepness and direction of the line will remain the same.

The change that does occur involves the y-intercept. The original line has a y-intercept at -7, while the new equation has a y-intercept at +1. This means the entire line is shifted vertically upwards by 8 units (from -7 to +1). Therefore, the correct answer to how the graph of the new function would compare with the original is that it would be shifted up.

Answer:

Eq.

y = -6(x-3.7)^2 + 82.14

the value t = 3.7 represents the maximum amplitude of the rocket in-flight.

Step-by-step explanation:

The standard equation of the parabola is written as

ax^2 +bx +c = 0

But we can rewrite it in vertex form. (See attached picture.)

y = a(x-h)^2 + k

If we look at the question, we can see that the vertex is

(h,k) = (3.7 , 82.14)

y = -6(x-3.7)^2 + 82.14

the value t = 3.7 represents the maximum amplitude of the rocket in-flight.

Answer:

t = 3.7 represents the time at which the rocket will reach at the maximum height.

Step-by-step explanation:

In the diagram,

We have a downward parabola having vertex (3.7, 82.14),

Since, a downward parabola is maximum at its vertex,

That is, the maximum value of the graph is 82.14 at 3.7,

Here, the graph shows the path of a rocket,

That is, it shows the distance covered by the rocket in different time,

Hence, the maximum distance covered is 82.14 unit at 3.7 time.