Question 2 (Essay Worth 2 points)

(05.06 HC)

Using f(x) = log x, what is the x-intercept of g(x) = log (x + 4)? Explain your reasoning.

Answers

Answer 1

In accordance with comparative comparative, the x-intercept of function g(x) = ㏒ (x + 4) is equal to x = - 4.

How to determine the x-intercept of a logarithmic function

According to function theory, a function f(x) has an x-intercept when f(x) exists for x = 0. Besides, logarithms of 1 for any base is equal to zero, that is:

Logarithm of 1 at any base.

㏒ₐ 1 = 0

If ㏒ x = 0, then x = 1. And if ㏒ (x + 4) = 0, then x + 4 = 0, that is, x = - 4.

Then, by direct comparison between the two logarithmic expression, the logarithmic function g(x) = ㏒ (x + 4) has x = - 4 as its x-intercept.

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Related Questions

How do you factor with 4 parts?

Answers

When a polynomial has four or more terms, the easiest way to factor it is to use grouping.

Grouping can be understand more better with an example:

for eg: factor x^3 + x^2 – x – 1 by using grouping. Just follow these steps:

Break up the polynomial into sets of two. You can go with (x^3 + x^2) + (–x – 1). Put the plus sign between the sets, just like when you factor trinomials. The square x2 is the GCF of the first set, and –1 is the GCF of the second set. Factoring out both of them, you get x^2(x + 1) – 1(x + 1).one can Factor again as many times as you can. The two terms you’ve created have a GCF of (x + 1). When factored out, you get (x + 1)(x^2 – 1).

However, x^2 – 1 is a difference of squares and factors again as (x+1)(x-1). This gives you a final factorization of: (x + 1)(x + 1)(x – 1), or (x + 1)2(x – 1).

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A bag of sugar weighs 3.45 kg What is the weight of three such bags (in kilograms)?

Answers

Answer:
10.35kg

Explained:
The question already gives the weight in kilograms so there is no changing to be done, just the simple multiplication of 3 times 3.45kg which is equal to 10.35kg

3.45 is multiplied by 3 as 3.45 is the price of one bag and to get the price of 3 bagels you need 3 lots of 3.45

Answer:

10.35 kg

Step-by-step explanation:

Given a bag of sugar weighs 3.45 kg, you want the weight of 3 bags.

Weight

The weight of 3 bags will be three times as much as the weight of one bag:

3 × 3.45 kg = 10.35 kg

Three such bags weigh 10.35 kg.

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Is P 3 2 and Q 2 3 represent the same point justify?

Answers

It is Justified that P and Q are different point.

What is cartesian coordinate plane?

The coordinate plane where a location of a point is represented in the form of X and Y coordinate pair, is termed as cartesian plane. In this plane two reference axes are used which are perpendicular to each other.

What is the location of two point stated above?

In the question, two-point P (3, 2) and Q (2, 3) are given. As per the cartesian coordinate system a location of a point is represented by a pair of numerical terms. The first numerical terms denote the X coordinate of the point, and the next terms refers the Y coordinate of that point.

Therefore, P and Q are two different points on the cartesian plane. The point p (3, 2) where 3 is the X coordinate and the distance from Y axis is 3 and 2 is the Y coordinate and distance from X axis is 2.

Similarly for the point Q (2, 3), 2 denotes the X coordinate of the point Q and 3 is the Y coordinate.

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Hello can someone please help me with this please What is the best possible geometric model for a set of rail tracks?

Ray ----Point ---- Line --- Plane

Fine the measure of an angle that is supplement to ABC if m < ABC is 82?

100 ---- 8---------278------

Fine the measure of an angle that is complementary to ABC is 32?

328------148------58------32

The intersection of two lines is a ?
Quadrilateral--------Point--------Line--------Plane

Answers

The best possible geometric model for a set of rail tracks is given as follows: Plane.The measure of the angle that is the supplement to ABC = 82º is given as follows: 98º.The measure of the angle that is the complementary to ABC is given as follows: 32º.The intersection of two lines is a point.

How to model the rail tracks?

A rail track is composed by multiple lines, however all the lines are in the same plane, hence a plane is the best geometric model for the rail track.

How to obtain the supplement of an angle?

Two angles are supplementary if the sum of their measures is of 180º, hence the supplement of an angle is obtained subtracting 180º by the angle measure.

This means that the supplement of ABC = 82º is given as follows:

180º - 82º = 98º.

How to obtain the complement of an angle?

Two angles are complementary if the sum of their measures is of 90º, hence the complement of an angle is obtained subtracting 90º by the angle measure.

This means that the supplement of ABC = 90º is given as follows:

90º - 32º = 58º.

Where do two lines intersect?

Two lines intersect at a single point, which is the solution to the system of equations involving the two lines.

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find the height of the two pillar with same height

Answers

Answer:

ED = AB = 25√3

Step-by-step explanation:

Let ED = AB = X

DC = 100 - BC

Tan 60 = [tex]\frac{\sqrt{3} }{1} = \frac{ED}{DC}[/tex] = [tex]\frac{X}{100-BC}[/tex]

[tex]\sqrt{3} (100-BC) = X[/tex]

Tan 30 = [tex]\frac{1}{\sqrt{3} } = \frac{AB}{BC} = \frac{X}{BC}[/tex]

[tex]\frac{BC}{\sqrt{3} } = X[/tex]

[tex]\sqrt{3} (100-BC) = \frac{BC}{\sqrt{3} } \\3(100-BC) = BC\\300 - 3BC = BC\\300 = BC + 3BC\\300 = 4BC \\75 = BC[/tex]

X = [tex]\frac{BC}{\sqrt{3} } = \frac{75}{\sqrt{3} }\\[/tex]

X = 25√3

Which of the following equations are equivalent? Select three options. 2 + x = 5 x + 1 = 4 9 + x = 6 x + (negative 4) = 7 Negative 5 + x = negative 2

Answers

The equations that are equivalent to each other will be 2 + x = 5, x + 1 = 4, and - 5 + x = - 2. Then the correct options are A, B, and E.

What is an equivalent expression?

The equivalent is the expression that is in different forms but is equal to the same value.

Simplify all the equations, then we have

A. 2 + x = 5, to simplify the equation, then we have

2 + x = 5

x = 3

B. x + 1 = 4, to simplify the equation, then we have

x + 1 = 4

x = 3

C. 9 + x = 6, to simplify the equation, then we have

9 + x = 6

x = - 3

D. x + (- 4) = 7, to simplify the equation, then we have

x - 4 = 7

x = 11

E. - 5 + x = - 2, to simplify the equation, then we have

- 5 + x = - 2

x = 3

The equations that are equivalent to each other will be 2 + x = 5, x + 1 = 4, and - 5 + x = - 2. Then the correct options are A, B, and E.

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Select the linear function from the following:

Select one:

a.
− 3 / x + y / 7 = 11

b.
− x / 3 + 7 / y = 11

c.
− x / 3 + y / 7 = xy

d.
− x / 3 + y / 7 = 11

Answers

The linear function in the option is − x / 3 + y / 7 = 11.

How to know linear function?

A linear function is a function that represents a straight line on the coordinate plane.

Linear function can be represented in slope intercept form as follows:

y = mx + b

where

m = slope of the lineb = y-intercept

Therefore, let's select the linear function from the options:

− 3 / x + y / 7 = 11

-3x⁻¹ + 1 / 7 y = 11 (Not a linear function)

− x / 3 + 7 / y = 11

- 1 / 3 x + 7y⁻¹ = 11 (Not a linear function)

− x / 3 + y / 7 = xy (Not a linear function)

− x / 3 + y / 7 = 11

- 1 / 3 x + 1 / 7 y = 11 (This is the linear function)

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Find the inverse of the function f(x) = 2÷3x -6

Answers

Answer:

f⁻¹(x) = 3/2x +9

Step-by-step explanation:

You want the inverse of the function f(x) = 2/3x -6.

Inverse function

The inverse function can be found by solving for y:

x = f(y)

Here, that is ...

x = 2/3y -6

x +6 = 2/3y . . . . . . . . . . . . . . add 6

y = 3/2(x +6) = 3/2x +9 . . . . multiply by 3/2

The inverse function is f⁻¹(x) = 3/2x +9.

Additional comment

Sometimes the division symbol ÷ is used to mean "divided by everything after this symbol." If that is the intended meaning, the function should be written as f(x) = 2/(3x -6) or f(x) = 2÷(3x -6).

We have interpreted the symbol according to the order of operations, which tells us that 2÷3x-6 means ((2÷3)·x)-6.

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A tore i having a ale on almond and jelly bean. For 5 pound of almond and 2 pound of jelly bean, the total cot i $12. For 3 pound of almond and 8 pound of jelly bean, the total cot i $31. Find the cot for each pound of almond and each pound of jelly bean

Answers

b = $3.5 the cost of each pound of jelly beans.

a = $1, the cost of each pound of almonds

What is the elimination method?

The elimination approach involves taking one variable out of the system of linear equations by utilizing addition or subtraction together with multiplication or division of the variable coefficients.

Here,

We let a be the almond and b be the jelly bean.

5a + 2b = $12....(1)

3a + 8b = $31....(2)

...Solving by elimination method.

5a = 12 - 2b

a = (12 - 2b)/5

Now, we put the value of a in equation(2)

3a + 8b = $31

3(12 - 2b)/5 + 8b = 31

(36 - 6b)/5 + 8b = 31

36 - 6b + 40b = 155

34b = 155 - 36

34b = 119

b = $3.5 the cost of each pound of jelly beans.

a = $1, the cost of each pound of almonds.

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Kyle earns 11.2% commission on his sales at the electrical retail store. He made sales worth $8571 this month. how much commission has he earned? Give your answer to the nearest dollar.

Answers

Answer:

Sales=8571$

Commission=11.2% of Sales

=11.2/100 × 8571$

=(11.2×8571)/100 $

=959.952$ Which is nearly equal to 960$.

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In a circle, an angle measuring 5. 5 radians intercepts an arc of length 8. 4. Find the

radius of the circle to the nearest 10th.

Answers

The circle's radius is equal to 3.659 or 3.7.

What is Radius?

A circle's or a sphere's radius is the length of the line between the center and the edge.

From the center of the circle or sphere to any point on its perimeter, the radius' length is constant.

Its diameter is halved by its length.

A line segment from a circle's or sphere's center to its perimeter or boundary is known as the radius in geometry. I

t is a crucial component of spheres and circles and is frequently abbreviated as "r."

When discussing multiple radiuses at once, the plural form of radius is "radii." the longest line connecting any points on the opposite side of a circle or sphere.

Hence, The circle's radius is equal to 3.659 or 3.7.

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What is a polynomial of degree 4 called?

Answers

A polynomial of degree 4 is called bi-quadratic polynomial.

Bi-quadratic polynomial

A biquadratic equation is a polynomial equation with degree 4, and it strictly does not consist of any term with degrees 3 and 1.

Polynomial

A polynomial is defined as an expression which is composed of variables, constants and exponents, that are combined using mathematical operations such as addition, subtraction, multiplication and division

Degree of polynomial

The degree of a polynomial is defined as the highest exponent of a monomial within a polynomial. Thus, a polynomial equation having one variable which has the largest exponent is called a degree of the polynomial.

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Can a polynomial have no real roots?

Answers

Odd degree polynomials can have no real roots.

A polynomial of even degree can have any number from 0 to n distinct real roots. A polynomial of odd degree can have any number from 1 to n distinct real roots.

polynomials

A polynomial is defined as an expression which is composed of variables, constants and exponents, that are combined using mathematical operations such as addition, subtraction, multiplication and division.

Real root

A real root is a solution to an equation which is also a real number.

Real number

Real numbers are numbers that include both rational and irrational numbers. Rational numbers such as integers (-2, 0, 1), fractions(1/2, 2.5) and irrational numbers such as √3, π(22/7), etc., are all real numbers.

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What is the 3 triangular number?

Answers

A triangular number succession is the representation of numbers as just an ordered set of equilateral triangles. The order of these numbers is 1, 3, and 6.

What exactly is meant by triangular numbers?

A triangular number is one that may be written as the sum of a initial n positive integers.

A good example of a triangular number is 6, which may be written as 1+2+3 when the first three positive integers are added together.Triangular numbers make up a sequence if one considers the sum of the first positive integer as the initial element, the sum of the first two positive integers as the second element, and so on.If a number equals that sum of such initial n positive integers, then n denotes the position of that particular triangular number with in the series.Triangular numbers can be used to create equilateral triangles.

The first 3 triangular numbers are therefore 1, 3, and 6.

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If a scuba diver swam from the surface at −12 1/2 feet per minute, for 4 1/2 minutes, what would be the diver’s change in elevation?

Answers

The change in elevation would be -225/4 feet

What is a mixed fraction?

A fraction represented with its quotient and remainder is a mixed fraction. For example, 2 1/3 is a mixed fraction, where 2 is the quotient, and 1 is the remainder. So, a mixed fraction is a combination of a whole number and a proper fraction.

Given here, Speed of scuba diver as -12¹/₂=-25/2 and time in minutes 4¹/2=9/2

Thus distance traversed -25/2 × 9/2 = -225/4

Hence, the change in elevation is -225/4 feet

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Mattie is twice as old as Pat. Jon is twice as old as Mattie. In 4 years the sum of their ages will be 61. How old is each person?

Answers

Answer:

Let's mark Pat's age is x. Then Mattie's age is 2x and Jon's age is 4x.

So (x + 4) + (2x + 4) + (4x + 4) = 61.

7x + 12 = 61 => 7x = 49 => x = 7.

So the answer is

Pat = 7

Mattie = 14

Jon = 28

The ages of Pat, Mattie, and Jon are as follows: 7 years, 14 years & 28 years.

If we take Pat's age as = 'x' years,

so, Mattie's age will be = '2x' years.

and then, Jon would be = 2(2x)

= '4x' years.

Now, the sum of their ages after 4 years =

=> (x+4) + (2x+4) + (4x+4) = 61

=> 7x+12 = 61

=> 7x= 61-12

=> 7x= 49

=> x= 49/7

=> x = 7

Therefore, Pat's age is = 7 years.

Mattie's age is = 14 years (2×7).

Jon's age is = 28 years (4×7).

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Christopher has set up a lemonade stand outside his house and sells small cups and large cups of lemonade. Each small cup holds 10 ounces of lemonade and each large cup hold 20 ounces of lemonade. Christopher used 800 ounces of lemonade and sold twice as many small cups as large cups. Graphically solve a system of equations in order to determine the number of small cups sold, x , x, and the number of large cups sold, y y.

Answers

Christopher sold 20 cups of large 20-ounce cups of lemonade

outside his house.

What are linear and non-linear functions?

A straight line on the coordinate plane is represented by a linear function. As an illustration, the equation y = 3x – 2 depicts a linear function because it is a straight line in the coordinate plane.

Any function whose graph is not a straight line is said to be nonlinear. Any curve other than a straight line can be a graph of it.

An example of a non-linear function is a quadratic function.

Given, Christopher has set up a lemonade stand outside his house and sells small cups and large cups of lemonade.

Small cups sold is x and the number of large cups sold is y.

Each small cup holds 10 ounces of lemonade and each large cup holds 20 ounces of lemonade and he sold 800 ounces.

Therefore,

10x + 20y = 800...(i)

He also sold twice as many small cups as large cups.

Therefore,

2y = x...(ii)

10(2y) + 20y = 800.

20y + 20y = 800.

40y = 800.

y = 20.

So, He sold 20 cups of large lemonade.

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The population of Smallville in the year 1890 was 6250. Assume the population increased at a rate of 2.75% each year. a) Estimate the population in 1915 and 1940. b) Predict when the population reached 50,000

Answers

If the population grew 2.75% each year then each year the population was multiplied by 1+2.75%=1+0.0275=1.0275

What is the population of Smallville in 1890 was 6250?Population in the year 1890 = 6250. Population increased at the rate of 2.75% per year or increased by 11400 , which will become 411400 after the increaseif you were to do it a step at a time it would mean multiplying 6250 by 0.0275(2.75%), and adding the result to 6250, then repeating the operation with the new number for each year until you reached the amount of years required (25 and 50 years).Now an easier way to do that first step would be multiplying by 1.0275, which already takes care of adding the original number. Now just do that for each of the intervals (25 and 50) required.

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What are directed segments?

Answers

Answer:

A directed segment is a segment that has distance (length) and direction. Hope this helps.

You have four sweaters, five pairs of pants, and three pairs of shoes. How many different combinations can you make, wearing one of each

Answers

Therefore, 60 different combinations can be made wearing one of each type

What is Fundamental Counting Principle? If an event can occur in m different ways, and another event can occur in n different ways, then the total number of occurrences of the events is m × n.This video uses manipulatives to review the five counting principles including stable order, correspondence, cardinality, abstraction, and order irrelevance. When students master the verbal counting sequence they display an understanding of the stable order of numbers.Fundamental Principle of Counting helps to determine how selection is done on the basis of available choices. Fundamental Principle of Counting simplifies the approach of selection considering all the possible choices and their combinations for calculating the ProbabilityThe fundamental counting principle states that if there are p ways to do one thing, and q ways to do another thing, then there are p×q ways to do both things. Example 1: Suppose you have 3 shirts (call them A , B , and C ), and 4 pairs of pants (call them w , x , y , and z ). Then you have. 3×4=12.

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how many solutions does y = 5x - 8 and y = 9x - 8 have

Answers

The equation y = 5x - 8 and y = 9x - 8 have one solution at

(0, -8)

How to find the solution of the equation

The equation is solved simultaneously by elimination method as follows

y = 5x - 8

y = 9x - 8

subtraction the equations

0 = -4x - 0

-4x = 0

x = 0

substituting x = 0 into y = 5x - 8

y = 5x - 8

y = 5 * 0 - 8

y =0 - 8

y = -8

The solution of the equation is at the point (0, -8)

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which shapes have 2 obtuse angles

Answers

Answer: Trapezoid

Step-by-step explanation:

Answer:

Step-by-step explanation:

Trapezoid square and the down right all the way

Miguel has three times as many dimes as he has quarters. He has as many nickels.as he has dimes and quarters.combined. The total amount of money he has is $3.00. How many of each coin does Miguel have?

Answers

Answer:

Step-by-step explanation:

fter solving the algebraic equation, Miguel has 4 quarters, 12 dimes and 16 nickels.

What is algebra?

One of the earliest areas of mathematics that deals with number theory, geometry, and analysis is algebra. Algebra is also defined as the study of mathematical rules and symbols through the manipulation of those mathematical symbols.

The number of quarters is taken to be x, then the number of dimes will be 3x, and the number of nickels will be 3x + x = 4x

$3.00 when converted to cents is 300 cents.

The value of nickels is 5 x 4x=20x.

The value of dimes is 10 x 3x=30x.

The value of quarters is 25x.

As the total value of money Miguel has is 300 cents, then the algebraic equation will be -

20x + 30x + 25x = 300

Solve to get the value of x -

75x = 300

x = 4

Therefore, the amount of quarters is x = 4 quarters.

The amount of dimes is x = 3x = 3 x 4 = 12 dimes.

The amount of nickels is 4x = 4 x 4 = 16 nickels.

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(a+b+c)(a-b+c)=a2+b2+c2 prove

Answers

Answer:

There might be an error in the question, the result below should be the correct answer. It is not possible for a^2+b^2+c^2 to be the answer.

(a+b+c)(a-b+c) = a^2 +2ac - b^2 + c^2

Step-by-step explanation:

(a+b+c)(a-b+c) = a^2 - ab +ac + ba - b^2 +bc + ca - cb + c^2 (expanding the two terms in brackets first)

Since ab = ba, ac = ca and bc = cb,

-ab and ba can be cancelled out

bc and -cb can be cancelled out

Hence, (a+b+c)(a-b+c) = a^2 +2ac - b^2 + c^2

This is what I have obtained through expansion, then simplification by cancelling out the common terms.

Could you help check the question again?

In three complete sentences, describe how i should find the solution to the system of equations below.

-6x + 3y = -12
x - y = 14

Answers

Multiply the second equation by 3 so you get 3x-3y=42. Then using cancellation you can get the equation -3x=30. By solving for x you can get x=-10 and plug it into both equations.

1/4(12x-20)+3(3x+5) I'm extremally confused I'm supposed to simplify

Answers

Answer:

12X+10

Step-by-step explanation:

THAT IS THE SIMPLFY 1-4 x (12x-20)+3(3x+5) Facout our 4 from the expression 1-4 x4 (3x-5)+3(3x+5) Simply the expression cancel out the greatest common factor 4 remove unncessary parntheses if so collect the terms 3x 9x 12x and the solutin is 12x+10

help! thanks !!! asap tho-

Answers

The unit rate of change of the proportional relationship is given as follows:

2.25.

The graph of the proportional relationship is given by the image presented at the end of the answer.

What is a proportional relationship?

A proportional relationship is a linear function with an intercept of zero modeled as follows:

y = kx.

In which k is the constant of proportionality.

The input and output variables for this problem are given as follows:

Input variable x: cups of sugar.Output variable y: cups of flour.

The constant k, representing the unit rate, is obtained by the division of the output of the input from the table, hence:

k = 4.5/2 = 6.73/3 = 9/4 = 2.25.

Meaning that the function is defined as follows:

y = 2.25x.

The function is graphed for a domain of x ≥ 0, as the number of cups of sugar must be a countable, non-negative amount.

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Determine if each infinite geometric series is convergent or divergent.

Answers

The solution to the geometric progression are

a) The geometric progression converges , r = 0.1

b) The geometric progression converges , r = 0.2

c) The geometric progression diverges , r = 5

d) The geometric progression converges , r = 0.2

e) The geometric progression diverges , r = 5

f) The geometric progression converges , r = 0.2

What is Geometric Progression?

A geometric progression is a sequence in which each term is derived by multiplying or dividing the preceding term by a fixed number called the common ratio.

The nth term of a GP is aₙ = arⁿ⁻¹

The general form of a GP is a, ar, ar2, ar3 and so on

Sum of first n terms of a GP is Sₙ = a(rⁿ-1) / ( r - 1 )

Given data ,

Let the geometric progression be represented as A

Now , the value of A is

A geometric progression is said to converge if the common ratio r lies between -1 < r < 1

So , If -1 < r < 1, the geometric sequence converges

The geometric progression is A = 0.3 + 0.03 + 0.003 + ...