Write the explicit formula for the sequence below:

Matching a logarithmic function with its graph can be done by understanding the key characteristics of logarithmic functions and how they are represented on a graph.

A logarithmic function is of the form y = log base b (x), where b is the base of the logarithm (usually 10 or e).

The graph of a logarithmic function is a reflection of the exponential function of the same base b, across the line y=x.

Here are some key characteristics of logarithmic functions and their corresponding graphs:

1) Asymptote: The graph of a logarithmic function has a vertical asymptote at x=0, since the logarithm of a non-positive number is undefined.

2) Domain: The domain of a logarithmic function is x>0, since the logarithm of a negative number is undefined.

3)Range: The range of a logarithmic function is all real numbers

4) Increasing or decreasing: A logarithmic function is increasing over its domain

5) Shape: The graph of a logarithmic function is concave down.

6) x-intercept: The x-intercept of the graph is (1,0), since the logarithm of 1 is always 0.

By keeping these characteristics in mind, you can match a logarithmic function with its graph by observing the shape, asymptote, domain and range of the graph.

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Square bases is not an attribute of a right rectangular prism. Option D

A right rectangular prism can be described as a three-dimensional solid shape with 6 faces, 12 edges, and 8 vertices.

It is sometimes called a cuboid.

All the faces of the right rectangular prism are rectangular in shape.

Examples of  right rectangular prisms are books, bricks and aquarium.

Some properties of a right rectangular prism include;

These prisms have no square base(s)

Hence, the right option is square bases.

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Answer:

Step-by-step explanation:

We will check if 5/15 and 1/3 are in proportion or not by cross-multiplication.

5/15 = 1/3

5*3 = 15*1

15 = 15

as the left-hand side is equal to the right side. So, these fractions are in proportion.

The margin of error and the sample mean of the confidence interval are given as follows:

The confidence interval is defined as follows:

(12.7, 19.5).

The definition of a confidence interval is that it is obtained as the sample mean plus/minus the margin of error.

Hence the sample mean is calculated as the mean of the bounds of the interval, hence:

(12.7 + 19.5)/2 = 16.1.

The margin of error is calculated as the absolute value of the difference of each bound from the sample mean, hence:

|19.5 - 16.1| = |12.7 - 16.1| = 3.4.

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Stefan spend price $110 and made price $60 by selling bicycle and helmet to Jin.

A percentage is a number or ratio that can be expressed as a fraction of 100.

Here, given that,

Selling price of bicycle = $146

Selling price of helmet = $19

Total = 146+19= $165

Let,

x represents the original cost Stefan to buy the bike and helmet.

150% of x = $165

1.5x=$165

Dividing both sides by 1.5

we get ,

x=$110

Stefan bought bicycle and helmet for $110.

Profit made by Stefan = Selling price - buying price

Profit made by Stefan = 165-110= 55

Hence, Stefan spend price $110 and,  made $55 by selling bicycle and helmet to Jin.

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The complate table is,

Statement                                                 Reasons

1) K is the midpoint of segments                      Given

  RM and JL.

2) RJ ≅ ML                                                  SSS Congruence Postulate

3) RK ≅ MK ,  JK ≅ LK                                 Definition of Midpoint

4) RK = MK , JK = KL                                    Definition of Congruence

                                                                   Segments

5) Δ EGF ≅ Δ EGH                                      CPCTC

A line segment is a part of line having two endpoints and it is bounded by two distinct end points and contain every point on the line that is between its endpoint.

Given that;

K is the midpoint of segments RM and JL.

Now,

Since, K is the midpoint of segments RM and JL.

Hence, We get;

   Statement                                                 Reasons

1) K is the midpoint of segments                      Given

  RM and JL.

2) RJ ≅ ML                                                  SSS Congruence Postulate

3) RK ≅ MK ,  JK ≅ LK                                 Definition of Midpoint

4) RK = MK , JK = KL                                    Definition of Congruence

                                                                   Segments

5) Δ EGF ≅ Δ EGH                                       CPCTC

Thus, The complete table is shown above.

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The two angles that have the sum of angles as 90° are called as Complementary Angles .

What are Complementary Angles ?

The two angles are said to be complimentary Angles when the sum of two angles is 90° .

In other words, we can say that if the measure of two angles add up to form a right angle, then these angles are called as Complementary Angles.  We can also say that  the two angles complement each other.

For Example : the angles having the measure of 30 degree and 60 degree can be called as Complimentary as their sum adds up to 90 degree .

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Given the function p(x)=6x+2, p(-2) is -10 while p(4) is 26, this shows that value of p(-2) is smaller than the value of p(4). The correct option is B.

A function is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable). It is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. Let A & B be any two non-empty sets; mapping from A to B will be a function only when every element in set A has one end, only one image in set B.

p(x)=6x+2

for p(-2)

p(-2) = 6(-2) + 2

p(-2) = -12 + 2

p(-2) = -10

for p(4)

p(4) = 6(4) + 2

p(4) = 24 + 2

p(4) = 26

p(-2) < p(4)

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Answer:

(B) "The value of p(-2) is smaller then the value of p(4)" is True

Step-by-step explanation:

p(x)=6x+2

p(-2) = 6*(-2)+2

p(-2) = -12+2

p(-2) = -10

p(4) = 6*(4)+2

p(4) = 26

====

p(-2) = -10

p(4) = 26

===

(A) The value of p(-2) is larger then the value of p(4).   False

(B) The value of p(-2) is smaller then the value of p(4).  True

(C) The value of p(-2) is the same as the value of p(4).  False

(D) The values of p(-2) and p(4) cannot be compared.   False

(a) x² + 2xy - y² must be added to x² + xy + y² to get 2x² + 3xy. (b)  5a + b -6 must be subtracted from 2a + 8b + 10 to get -3a + 7b + 16.

a)

Here we are given the expression x² + xy + y²

Now we need to add something so that this expression becomes x² + 3xy

Let the expression to be added be p.

Hence we get

x² + xy + y² + p = 2x² + 3xy

or, p = 2x² + 3xy - (x² + xy + y²)

or, p = 2x² + 3xy - x² - xy - y²

or, p = x² + 2xy - y²

Hence, x² + 2xy - y² must be added.

b)

Here we are given the expression 2a + 8b + 10

We need to subtract another expression to get -3a + 7b + 16

Let the expression be t. Hence we get

2a + 8b + 10 - t = -3a + 7b + 16

or, t = 2a + 8b + 10 - (-3a + 7b + 16)

or, t = 2a + 8b + 10 + 3a - 7b - 16

or, t = 5a + b - 6

Hence 5a + b - 6 must be subtracted,

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Correct Question

(a) What should be added to x² + xy + y² to obtain 2x² + 3xy?

(b) What should be subtracted from 2a + 8b + 10 to get -3a + 7b + 16?

The average rate of driving from Newyork to Boston is d. 54 mph.

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

Given, The distance you drive is proportional to the time.

We know, The arithmetic mean or average can be obtained by adding all the given values and then dividing the total sum by the number of values.

Therefore,

The average rate of driving is,

= (216/4) mph.

= 54 mph.

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The explicit formula for the sequence -28, -31, -34, -37, ..., is aₙ= -28 -3d.

A series of integers called an arithmetic progression or arithmetic sequence (AP) has a constant difference between the terms.

Given:

-28, -31, -34, -37, ...

The general formula of an arithmetic sequence:

aₙ= a₁ + (n)d,

where a₁ is the first term and d is the common difference.

First, we will find the common difference between consecutive terms.

Here,

a₁ = -28

To find the common difference:

a₂ - a₁ = -31 + 28 = -3

a₃ - a₂ = -34 + 31 = 3

a₄ - a₃ = -37 + 34 = 3

Hence, d = -3.

Substitute the values to the formula,

aₙ= a₁ + (n)d,

aₙ= -28 + (-3)d,

aₙ= -28 -3d

Therefore, aₙ= -28 -3d is the required sequence.

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The statement whether each data set is likely to be distributed nor not:

Number of minutes required to complete a marathon - Yes.

Number of miles in a marathon: - No.

Average age of a person who runs a marathon: No.

The distribution of values in a field is described by a statistical distribution, often known as a probability distribution. In other words, the statistical distribution identifies the typical and unusual values. The bell-shaped normal distribution is one of many varieties of statistical distributions.

Let n miles in marathon.

To normally distribute, number of minutes required to complete a marathon:

The number of minutes required to complete a marathon is likely to be normally distributed with small amounts in tails (very slow, very fast) and large amount in middle.

So, yes.

To normally distribute,  number of miles in a marathon:

The number of miles is a fixed number, not normally distributed.

So, no.

To normally distribute, average age of a person who runs a marathon:

The average age is a fixed number

Average age is not likely to be normally distributed.

So, no.

Therefore, the first one is yes, and the other two are no.

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When the root of x²-bx+c = 0 is decreased by 2, the resulting equation is x²-2x+1, then b = 2 and c = 1

The values of variables satisfying the given quadratic equation are called its roots.

if the roots of a quadratic equation ax²+bx+c = 0 are alpha and beta

alpha + beta = -b/a and

alpha × beta = c/a

when the roots are reduced by 2

alpha-2+ beta-2 = -b/a

(alpha+beta)-4 = -b/a

alpha+ Bata = -b/a + 4

the resulting equation is x²-2x+1 = 0

a = 1, b = -2 and c = 1

therefore alpha +beta = -b/a = -(-2)/1 = 2

therefore 2 = -b/a+4

a = 1

2 = -b+4

b = 4-2 = 2

alpha×beta = c/a = 1/1

(alpha -2)× ( beta -2) = (alpha)( beta) -2(alpha+beta) + 4 = 1-2(2)+4 = 1

therefore b = 2 , c = 1

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The solution for given question of algebra are 10, -42, -38 for question 1st, 2nd and 3rd.

There are several sub-branches of algebra, including commutative algebra, abstract algebra, linear algebra, and elementary algebra.

x + 6/x + 3 = 4/7

7x + 42 = 4x + 12

7x - 4x = 42-12

3x = 30

x = 10

2/x+8 = 3/x+9

2x - 18 = 3x + 24

x = -42

x+2/6 = x-4/7

7x+14 = 6x-24

x = -38

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The answer is D) If one angle is a right angle, then the frame must be rectangular,

An angle is a measure of the amount of rotation between two lines or planes. It is measured in degrees or radians. Angles are formed by the intersection of two lines, called the sides of the angle, and a point, called the vertex of the angle. There are different types of angles such as acute angle, right angle, obtuse angle, and straight angle.

A rectangle is a four-sided polygon with four right angles. It has opposite sides that are parallel and congruent, and the opposite angles are also congruent. A rectangle can be defined by its length and width or by the coordinates of its vertices. Rectangles are a special case of parallelograms, which have opposite sides parallel but not necessarily congruent. The special properties of rectangles make them a popular shape in design and construction, such as in building and engineering.

A rectangle is defined as a four-sided polygon with four right angles. Opposite sides of a rectangle are congruent, but adjacent sides may or may not be congruent. Therefore, A and B are not sufficient to prove that the frame is a rectangle. Also, two adjacent angles being supplementary does not guarantee that the frame is a rectangle. The only way to be sure that the frame is a rectangle is if it has one right angle, this is the only way to ensure that all angles are right angles. Therefore, D) is the correct answer.

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Answer:

sry i dont no

The sum of Annie's, Bobby's, Ciro's, and Denise's answers is $ 1140.1.

A number is simplified when it is rounded off, preserving its value while moving it closer to the next number. It is done for whole numbers as well as decimals at various places of hundreds, tens, tenths, etc.

If the number following the decimal is between 0 and 4, a number may be rounded off to its lowest value. If the number after it is between 5 and 9, the number will be rounded off to a greater value.

Annie rounds $ 280.05 to the nearest hundred

$ 280.05 will be equal to $ 300

Bobby rounds $ 280.05 to the nearest ten

$ 280.05 will be equal to = $ 280

Ciro rounds $ 280.05 to the nearest integer

$ 280.05 will be equal to = $ 280

Denise rounds $ 280.05 to the nearest tenth

$ 280.05 will be equal to = $ 280.1

Then, the sum of Annie's answer, Bobby's answer, Ciro's answer, and Denise's answer = $ 300 + $ 280 + $ 280  + $ 280.1 = $ 1140.1

Therefore,

The sum of Annie's, Bobby's, Ciro's, and Denise's answers is $ 1140.1.

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largest possible value of $m$ is  x=5, y =3, 10*5+3=53: 3 x 5 x 53 =795

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Answer:

9978

Step-by-step explanation:

10000 - 22 = 9978

9978 is the answer

Answer: 9978

Step-by-step explanation:

Stack the numbers up like this 10000

                                                          22

     borrow from the one make the zero a ten, and then borrow from that to make the next one and make it a nine and then do it to the last one and subtract. Hope this makes sense

Answer:

y = -x + 5

Step-by-step explanation:

The equation is y= mx + b

m = the slope or rise/run or (y2 - y1) / (x2 - x1)

b = y-intercept

The slope here is -1, and the y-intercept is 5, so our equation is

y = -x + 5

The value of x is 7 and value of y is 8

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

Given data set is {4, 6, x, y, 10}

The mean and the median are the same value.

The median is the middle value, which is x, and the mean is:

M = (4 + 6 + x + y + 10)/5

Then we have that:

(4 + 6 + x + y + 10)/5 = x

Now let's solve this:

(4 + 6 + x + y + 10) = 5x

20 + x + y = 5x

20 + y = 4x

And x and y are whole numbers. Then we can take x = 7 to get:

20 + y = 4*7

y = 28 - 20 = 8

Then we have x = 7 and y = 8.

Hence, the value of x is 7 and value of y is 8 in the data set 4 6 x y 10

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Read the link attached.

I have written it down on the word doc

Radical expression can be defined as the expression containing square root and rational exponent , which is in the form of p/q form.

What is an Algebraic expression ?

Algebraic expression can be defined as combination of variables , constants and exponents.

Radical expression, in which if the expression contains square root than it called as the radical expression.

Examples are  : - [tex]\sqrt{7}[/tex] , [tex]\sqrt{x}[/tex] and etc .

Rational exponent , in which it is in the form of p/q is called as the rational exponent .

Examples are :- 5/8 , 6/9,8/7 and etc .

Hence, Radical expression can be defined as the expression containing square root and rational exponent , which is in the form of p/q form.

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Answer:

D

Step-by-step explanation:

I think it would be D hope this helps!

The best definition of a decimal is decimals are whole counting numbers.

Suppose that the number is abcdefg and belongs to the decimal numerical system.

Remember one thing that the place on the left of decimal point is called ones. Move one-one places to right, and divide by 10 and 10 more and more.

Move one-one places to left, and multiply (un-divide) by 10 and 10 more and more.

Thus, we write abcd.efg as:

[tex]a \times 10^3 + b \times 10^2 + c \times 10^1 + d \times 10^{0} + e \times 10^{-1} + f \times 10^{-2} + g \times 10^{-3}[/tex]

We will call d as ones digit, c as tens digit (it get multiplied by 10), b as hundreds digit etc.

We call e as digit at 10th place (division by 10), f as digit at hundredth place and so on.

Therefore, the definition will be Decimals are whole counting numbers,

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The linear equation f(x) is  4x - 10 and the quadratic equation f(k) is -5/2k^2 + 4k - 1 for the two given points.

The linear equation can be found using the slope-intercept form (y = mx + b), where m is the slope of the line and b is the y-intercept. To find the slope (m) we can use the two points given:

m = (y2 - y1) / (x2 - x1) = (18 - 2) / (7 - 3) = 16/4 = 4

The y-intercept (b) can be found using one of the points and the slope:

b = y - mx = 2 - 4(3) = -10

So the linear equation in standard form is:

f(x) = 4x - 10

For the quadratic equation, we know that it's in the form of y = ax^2 + bx + c. We have 2 points, so we have 2 equations with 2 unknowns. We can use this information to solve for a, b and c.

Let's (3,2) point 1 and (7,18) point 2.

f(k) = ak^2 + bk + c....(1)

point 1: f(3) = 2 = 9a + 3b + c...(2)

point 2: f(7) = 18 = 49a + 7b + c...(3)

Now we have 2 equations and 3 unknowns.

using theirs first equation and substitute it in the second and third equation

18 = 49a + 7b + c

2 = 9a + 3b + c

c = 2 - 9a - 3b

18 = 49a + 7b + (2 - 9a - 3b)

18 = 49a + 7b + 2 - 9a - 3b

18 = 40a + 4b + 2

16 = 40a + 4b

now this equation is used to solve for a and b

b = (16 - 40a) / 4

so a,b and c are

a = -5/2

b = 4

c = -1

so the quadratic equation in standard form is:

f(k) = -5/2k^2 + 4k - 1

4x - 10 is the linear equation f(x)  and -5/2k^2 + 4k - 1 is the quadratic equation f(k) for the two given points.

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The given expression {8.5x + 0.5 + 3.5x - 2x} is equivalent to

10x + 0.5.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign "=".

Given is the expression as follows -

8.5x + 0.5 + 3.5x - 2x

The given expression is -

8.5x + 0.5 + 3.5x - 2x

(8.5x + 3.5x - 2x) + 0.5

12x - 2x + 0.5

10x + 0.5

Therefore, the given expression {8.5x + 0.5 + 3.5x - 2x} is equivalent to

10x + 0.5.

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Answer:

Step-by-step explanation: Two quarters, 50 pennies: N = 52 (N+1 = 53) One quarter, 75 pennies: N = 76 (N+1 = 77) 100 pennies, N = 100 (N+1 = 101) 6 nickels, 70 pennies: N = 76 (N+1 = 77)

Answer:

2 quarters, 2 dime's, 1 Nickel, 2 penny's

Step-by-step explanation:

Well u well need to quarters because 2 quarters are $25 cent then u well need 2 dimes because when your counting dime's that 10 20 30 40 50 so to dime's and 1 Nickel that makes $75 cents so u need 2 penny's and that makes 77

The correct option regarding the surface area of the solid is given as follows:

d. 45 square inches.

The surface area of a solid is composed by the sum of the areas of all the pars of the figure.

The composition of the figure in this problem is given as follows:

Thea area of a triangle is given by half the multiplication of the base by the height, hence the area of the four triangles in this problem is given as follows:

At = 4 x 1/2 x 3 x 6

At = 36 square inches.

The area of a square is given by the square of the side length, hence:

As = 3³

As = 9 square inches.

Thus the surface area of the solid in this problem is given as follows:

S = At + As

S = 36 + 9

S = 45 square inches.

Meaning that option d is correct.

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