Why is the quotient of three divided by one-fifth different from the quotient of one-fifth divided by three?

Answers

Answer 1

Final answer:

The quotients are different because the order matters in division. When 3 is divided by 1/5 it becomes a multiplication problem with reciprocal of 1/5, yielding 15. However, when 1/5 is divided by 3, it becomes multiplication with reciprocal of 3 and yields 1/15.

Explanation:

The reason that the quotient of three divided by one-fifth is different from the quotient of one-fifth divided by three is due to how division works in mathematics. To put it simply, the order of numbers in a division operation matters; it is not commutative like addition or multiplication.

When you divide 3 by 1/5, you're essentially asking, 'how many times does 1/5 fit into 3?'. Here, you're dealing with fractions and whole numbers. To perform the division, we multiply 3 by the reciprocal of 1/5, which is 5. The answer is 3 * 5 = 15.

But, when you divide 1/5 by 3, you're asking 'how many times does 3 fit into 1/5?'. Here, you need to multiply 1/5 by the reciprocal of 3, which is 1/3. The calculation is (1/5) * (1/3) = 1/15.

Learn more about Division Operations here:

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Related Questions

according to the tree diagram below what is the probability that someone buys a book that is paperback and fiction

Answers

Let us check out the diagram. The probability that a person buys a paperback is 0.65. The next leafs of the diagram (to the right of choosing paperback) show two events: the event that the buyer who has bought a paperback buys fiction and the probability he buys non-fiction. So 65% of the buyers buy paperback and 0.45 (=45%) of them buy fiction. Hence the probability that they buy both fiction and paperback is 0.65*0.45=0.2925. This is always a helpful thought procedure with such exercises; we can solve the same way for hardcover non-fiction etc.

see the attached figure to better understand the problem

we know that

[tex]0.65\ (65\%)[/tex] of the buyers buy paperback and [tex]0.45\ (45\%)[/tex] of them buy fiction.

Hence

The probability that they buy both fiction and paperback is equal to

[tex]0.65*0.45=0.2925[/tex]

the answer is

[tex]0.2925[/tex]

Can anyone answer this for me?

Answers

For 24, the answer is 24.

For 19 to 21:

All you need to do is count the spaces between each line of the numerator and then the same with the denominator.

19. You can see that there are 4 spaces between Point A and Point B. There are 6 spaces between point A and Point C. So if you will get ratio you will get:

[tex] \frac{4}{6} [/tex] Then you simplify the expression.
[tex] \frac{2}{3} [/tex]

20. There are 2 spaces from points B to C. There are 3 spaces from points C to D. So the ration then will be:
[tex] \frac{2}{3} [/tex]

This is already in its simplest form. You may be wondering why we did not count from 0. This is because the reference point for the two lines are given. For the first it is B and for the second is C.

21. Moving on to number 21. The distance from point B to D is 5 spaces, and the distance from point A to E is 12 spaces. So you can say that the ratio would be:

[tex] \frac{5}{12} [/tex] Again, this is already in its simplest form.

22. To get the geometric mean between two numbers you first need to multiply them and then get the square root:

STEP 1: Multiply 7 and 28
7 x 28 = 196
STEP 2: Get the square root of the product
√196 = 14

14 is the geometric mean.

23. Simplifying ratios is relatively easy. When you simplify the ratio between two values that are of different units, you first need to make both units the same.
In your case, we need to either convert 10ft to inches or convert 30 inches to feet. So we will not come up with a decimal, let us just convert 10 ft into inches.

[tex] 10 ft [/tex] x [tex] \frac{12in}{1ft} [/tex] = 120 inches

So our new ratio is:
[tex] \frac{120in}{30in} [/tex]
Now we simplify it to its simplest form:
[tex] \frac{4in}{1in} [/tex]

24. The two figures are what we call similar figures. This means that the lengths of each side are proportional to their corresponding sides.

AB is proportional to line FG.
AB = 4 and FG =8
This means that the sides of ABCDE is half the lengths of the sides of FGHJK. Thus we can say that the perimeter of ABCDE is half the perimeter of FGHJK
To get the perimeter of a polygon, all you have to do is add all the sides.
Let's get the perimeter of FGHJK
8 + 8 + 10 + 12 + 10 = 48
Half of 48 =24
So the perimeter of ABCDE is 24

If you want to double check your answer you can get the sides of polygon of ABCDE by getting half of each corresponding side.
AB = 4
BC = 4
CD = 5
DE = 6
EA = 5

If you get the sum of all sides, you can get the perimeter:
4 +4 +5 + 6 + 5 = 24

what is the sum of the arithmetic series 18 t=1 (3t-4)

a. 234
b. 441
c. 25.5
d. 49

Answers

The given arithmetic series is

[tex] \sum_{t=1}^{18} (3t-4) [/tex]

When t =1, we will get the first term,a, which is

[tex] 3(1)-4 =3-4=-1 [/tex]

When t =18, we will get the last term,l , which is

[tex] 3(18)-4 = 50 [/tex]

Now we use the formula of sum of n terms which is

[tex] S = \frac{t}{2} (a+l) [/tex]

Substituting the values of t,a and l, we will get

[tex] S = \frac{18}{2} (-1+50) = 9*49 =441 [/tex]

Consider the arithmetic series [tex] _{t=1}\Sigma^{t=18} (3t-4) [/tex]

Let t=1 in the given series, we get

first term = [tex] a_{1} [/tex] = 3-4 = -1.

Let t=2 in the given series, we get

second term = [tex] a_{2} [/tex] = [tex] (3 \times 2)-4 = 2 [/tex]

Let t=3 in the given series, we get

third term = [tex] a_{3} = (3 \times 3)-4=5 [/tex]

Now, let t=18 in the given series, we get

last term = l = [tex] l = (3 \times 18)-4 = 50 [/tex]

We get the series as

-1, 2, 5,..... 50

Sum = [tex] \frac{n}{2}(a+l) [/tex]

= [tex] \frac{18}{2}(-1+50) [/tex]

= [tex] = 9 \times 49 [/tex]

= 441

Therefore, the sum of the given arithmetic series is 441.

Help Help Help!!! :)
solve the system of equations y=2x^2-3 y=3x-1

Answers

Solution:
y = 2x^2 - 3 ---- equation 1
y = 3x - 1 ------equation 2
Then we get,
2x^2 - 3 = 3x - 1
Now, simplifying the equation, we get
2x^2 - 3x - 3 + 1 = 0
2x^2 - 3x - 2 = 0
After factoring the equation, we get
(2x+1)(x-2) = 0
So, this means
(2x+1) = 0 and (x-2) = 0
From this, we get
x = -1/2 and x = 2
Putting values of x = -1/2 in equation 2
y = 3(-1/2) - 1
y = -2.5
Now, putting value of x = 2 in equation 2
y = 3(2) -1
y = 5

HELP ASAP WILL MARK AS BRAINILEST TO WHOEVER GETS IT RIGHT

Answers

The correct answer is B. For sure it is. It took a while to solve in my head

How far does a ball that is hit from a height of 3 feet at a speed of 120 feet per second travel before it hits the ground if it is hit at an angle of 45 degrees? Round your answer to the nearest integer.

A) 376 Feet
B) 395 Feet
C) 426 Feet
D) 453 Feet

Answers

Selection D is appropriate.

It is convenient to solve for the time of flight, then compute the distance traveled in that time. The ball is in the air about 5.338 seconds.

Jalen traded $4100 for Mexican pesos, immediately changed his mind, and then promptly traded his Mexican pesos back into dollars. Which of these amounts is he most likely to have?

A. More than $0 but less than $4100
B. $0
C. $4100
D. More than $4100

Answers

the answer is the option A.) More than $0 but less than $4100

Because, when currency is exchanged for another currency, the bank or trader usually charges commission for changing it.

APEX APEX APEX APEX APEX APEX APEX APEX APEX APEX

More than $0 but less than $4100

Please help me out :)

Answers

Lets cut it diagonally into 2 triangles.
The diagonal length will be 7 x 2 = 14yd

Area of one triangle = 1/2 x 14 x 7 = 49 yd²

Area of the polygon = 2 x triangles
Area of the polygon = 2 x 49
Area of the polygon = 98 yd²

Answer: The regular polygon is 98 yd²

help plsss need this for tomorrow

Answers

Hello there! I can help you! So there is one blue counter added to two green counters. To solve this problem, we can write and solve an equation. Set it up like this:

12 + 1x = 8 + 2x

We do this, because there are already some of each color in the bag. 1x makes one counter each and 2x is two counters for every blue counter in the bag. Let's solve it. Subtract 1x from each side. 1x - 1x cancels out. 2x - 1x is 1x or just simply x. That simplifies to 12 = 8 + x. Subtract 8 from each side to get the variable by itself. 8 - 8 cancels out. 12 - 8 is 4. That leaves 4 = x. Nothing else needs to be done. Let's plug the value in and see if it works. 1 * 4 is 4. 12 + 4 is 16. 2 * 4 is 8. 8 + 8 is 16. 16 = 16. There. x = 4. 4 blue counters and 8 green counters were added to the bag.

What is the equation, in slope-intercept form, of the line that is perpendicular to the line Y-4=-2/3(X-6) and passes through the point (-2,-2)

Answers

That line is in point-slope form:

[tex]\sf y-y_1=m(x-x_1)[/tex]

Where 'm' is the slope and (x1, y1) is a point on the line.

Perpendicular lines have opposite slopes. To get the opposite, we take the reciprocal and multiply it by -1.

[tex]\sf -\dfrac{2}{3}[/tex]

Reciprocal:

[tex]\sf -\dfrac{3}{2}[/tex]

Multiply by -1:

[tex]\sf\dfrac{3}{2}[/tex]

We can plug this slope and the point into point-slope form, and then convert it to slope-intercept form.

[tex]\sf y-y_1=m(x-x_1)[/tex]

[tex]\sf y-(-2)=\dfrac{3}{2}(x-(-2))[/tex]

Negatives cancel out:

[tex]\sf y+2=\dfrac{3}{2}(x+2)[/tex]

Distribute 3/2 into the parenthesis:

[tex]\sf y+2=\dfrac{3}{2}x+\dfrac{6}{2}[/tex]

Simplify the fraction:

[tex]\sf y+2=\dfrac{3}{2}x+3[/tex]

Subtract 2 to both sides:

[tex]\boxed{\sf y=\dfrac{3}{2}x+1}[/tex]

Answer:

Step-by-step explanation:

helppppppppppppppppppppp

Answers

Answer:
1/4

Explanation:
Assume that:
log base 625 of 5 = y
We will rewrite this in exponent form as follows:
log base (b) of x = y is equivalent to b^y = x
For the given, the exponent will be:
625^y = 5

Now, we know that 5^4 = 625
Therefore, to convert 625 to 5, we will take 4th root.

This means that:
625^y = 5
y = 1/4

Hope this helps :)

Answer:

1/4

Step-by-step explanation:

Please help!! Which of the following could represent the scale factor of the smaller figure to the larger figure?
Smaller figures volume is 216in.^3
Larger figures volume is 343in.^3

Answers

Final answer:

The scale factor from the smaller figure to the larger figure is found by taking the cube root of the ratio of their volumes, which is the cube root of 216/343.

Explanation:

The student asked: Which of the following could represent the scale factor of the smaller figure to the larger figure? When comparing the volumes of two geometric figures, we can determine the scale factor of their linear dimensions by understanding the relationship between volume and linear scale factor.

Given that the smaller figure's volume is 216 cubic inches and the larger figure's volume is 343 cubic inches, we are looking for the cube root of the ratio of these volumes to find the linear scale factor.

To find the scale factor from the smaller figure to the larger figure, divide the volume of the smaller figure by the volume of the larger figure and then calculate the cube root: Scale factor = ∛(216/343). This calculation will give you the scale factor of the linear dimensions from the smaller figure to the larger figure.

What is the value of x?

Answers

x/10 = 10/4x
4x^2 = 100
x^2 = 25
x = 5

answer
5 units

Can someone please help? In the circle at right, AZB is a(n): (A) minor arc, (B) central angle, (C) major arc, (D) arcezoid, or (E). None of these? Thanks

Answers

In this question it has been clearly indicated that AZB is to be taken as an arc. This is because there is the arc symbol on top of AZB. Thus, we have [tex] \overarc{AZB} [/tex] and we need to answer what does the arc [tex] \overarc{AZB} [/tex] represent.

As we can see from the diagram, by visual inspection, that AZ is the chord which is lesser than the diameter and AZB is the segment on that lesser side of the circle. Therefore, the arc [tex] \overarc{AZB} [/tex] must be the minor arc.

Therefore, Option A, minor arc is the correct answer.

For what values of b will F(x) = logb x be an increasing function?

A. b < 0
B. b > 0
C. b < 1
D. b > 1,

Answers

In order to answer you need to keep in mind what is a logarithm:
logb x = n is the equivalent of asking "you should raise the base b to what number n in order to get x?": bⁿ = x

From this follows that b must be positive, otherwise the function is not defined everywhere in R: for example, take log(-2) x = 0.5 ? This means: [tex] (-2)^{1/2} [/tex] =√(-2) which is impossible in R.
Therefore, both answers A and C are not correct because they take in consideration negative values.

If we take the base between 0 and 1 excluded, we have a fraction whose denominator is bigger than the numerator. Such a fraction, elevated to increasing exponents get smaller, for example:
(1/2)² = 1/4
(1/2)³ = 1/8
(1/2)⁴ = 1/16
Therefore the function is dereasing and answer B is incorrect.

The right answer is, therefore, D) b > 1.

Final answer:

The logarithmic function F(x) = logb x is an increasing function when the base b is greater than 1, because the value of logb x increases as x increases for b > 1.(Option D)

Explanation:

The question asks for what values of b will F(x) = logb x be an increasing function. To determine this, we need to understand the behavior of logarithmic functions based on their base value (b). A logarithmic function is increasing if the base of the logarithm is greater than 1. This is because as x increases, the value of logb x increases when b>1. Conversely, if b<1 (but b>0), the function is decreasing because the power to which b must be raised to produce x decreases as x increases. We also know that the base of a logarithm cannot be negative or zero, as this would not produce a valid logarithmic function.

Therefore, the correct answer is D. b > 1, where the logarithmic function F(x) = logb x is an increasing function.

What is the slope-intercept form for each equation in this system? Compare the slopes and y-intercepts to describe the graph of the system. 3x - 4y = 28 4x + 10y = 20 A) y = 3 4 x − 7; y = −2 5 x + 2; one line B) y = - 3 4 x − 7; y = −2 5 x + 2; parallel lines Eliminate C) y = 3 4 x − 7; y = 2 5 x + 2; intersecting lines D) y = 3 4 x − 7; y = −2 5 x + 2; intersecting lines

Answers

3x - 4y = 28
4x + 10y = 20
First we rewrite the system of equations:
Equation 1:
3x - 4y = 28
3x - 28 = 4y
(3/4) x - 7 = y
Equation 2:
4x + 10y = 20
10y = 20 - 4x
y = 2 - (2/5) x
We have then:
y = (3/4) x - 7
y = - (2/5) x + 2
One line has a positive slope and the other line has a negative slope.
Thus, both lines are connected.

Answer:
D) y = 3/4 x - 7; y = -2/5 x + 2; intersecting lines

The slope - intercept form of the equations are : [tex]y = \frac{3}{4} x - 7 [/tex] and [tex]y = - \frac{2}{5} x + 2[/tex]

Given the standard form of the equations :

3x - 4y = 28 - - - - (1)

4x + 10y = 20 - - - - - (2)

The General form of a slope - intercept equation :

y = bx + c

For equation (1) :

3x - 4y = 28

Make y the subject

-4y = 28 - 3x

Divide both sides by - 4 to isolate y

y = -7 + 3/4x

[tex]y = \frac{3}{4} x - 7 [/tex]

For equation (2) :

4x + 10y = 20

Make y the subject

10y = 20 - 4x

Divide through by 10 to isolate y

y = 2 - 2/5x

[tex]y =- \frac{2}{5} x + 2[/tex]

Hence, the slope - intercept equations are : [tex]y = \frac{3}{4} x - 7 [/tex] and [tex]y = - \frac{2}{5} x + 2[/tex]

Learn more :

Cassandra lives in Oklahoma and makes $60,000 a year. If the median annual income in Oklahoma is $64,105 and the median annual income in the United States as a whole is $50,233, is Cassandra likely to qualify for Chapter 7 bankruptcy?

Answers

Yes, Cassandra is likely to qualify, since her yearly income is below the median annual income of Oklahoma.

Answer:

Cassandra is likely to qualify for Chapter 7 bankruptcy.

Step-by-step explanation:

Given scenario is : Cassandra lives in Oklahoma and makes $60,000 a year. The median annual income in Oklahoma is $64,105.

A person qualifies for chapter 7 bankruptcy, if his annual median income is below the median income of his state. So, here the annual median income of Cassandra is below the median income of her state, Oklahoma.

So, she will qualify for chapter 7 bankruptcy.

Which polynomial correctly combines the like terms and expresses the given polynomial in standard form? 8mn5 – 2m6 + 5m2n4 – m3n3 + n6 – 4m6 + 9m2n4 – mn5 – 4m3n3 n6 + 7mn5 + 14m2n4 – 5m3n3 – 6m6 –2m6 – 5m3n3 + 14m2n4 + 7mn5 + n6 14m2n4 + 7mn5 – 6m6 – 5m3n3 + n6 n6 – 6m6 + 7mn5 + 14m2n4 – 5m3n3

Answers

The correct combining of like term is

f(m, n) = [tex]n^{6}[/tex] + 7m[tex]n^{5}[/tex] + 14m²[tex]n^{4}[/tex] - 5m³n³ -6[tex]m^{6}[/tex] - 2[tex]m^{6}[/tex]

What is polynomial equation?

A polynomial equation is the equation in which the unknown variable is one and the highest power of the unknown variable is n.

Given:

8m[tex]n^{5}[/tex] - 2[tex]m^{6}[/tex] +5m²[tex]n^{4}[/tex] - m³n³ + [tex]n^{6}[/tex] - 4[tex]m^{6}[/tex] + 9m²[tex]n^{4}[/tex] - m[tex]n^{5}[/tex] - 4m³n³

Now, Combining the like terms

(8m[tex]n^{5}[/tex] - m[tex]n^{5}[/tex]) + 5m²[tex]n^{4}[/tex] + 9m²[tex]n^{4}[/tex] - m³n³ - 4m³n³ + [tex]n^{6}[/tex] - 4[tex]m^{6}[/tex] - 2[tex]m^{6}[/tex]

=7m[tex]n^{5}[/tex] + 14m²[tex]n^{4}[/tex] - 5m³n³ - 6 [tex]m^{6}[/tex] + [tex]n^{6}[/tex]

now, arranging according to their powers

[tex]n^{6}[/tex] + 7m[tex]n^{5}[/tex] + 14m²[tex]n^{4}[/tex] - 5m³n³ -6[tex]m^{6}[/tex] - 2[tex]m^{6}[/tex]

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Line r passes through points (2, 11) and (10, 4). Line s is perpendicular to r. What is the slope of line s?

Answers

Answer: 8/7

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

Work Shown:

Use the slope formula to find the slope of line r
m = (y2-y1)/(x2-x1)
m = (4-11)/(10-2)
m = -7/8

The slope of line r is -7/8

Now we take the negative reciprocal. In other words, we flip the fraction and flip the sign from negative to positive.

Flip the fraction: -7/8 ---> -8/7
Flip the sign: -8/7 ----> +8/7

The slope of line s is 8/7

Note how multiplying the slope of line r (-7/8) and the slope of line s (8/7) yields -1. Multiplying any two perpendicular slopes leads to a product of -1. This is excluding vertical lines as the slope is undefined.

If a circle has an diameter of 14, what would the area be?
Use 3.14 for Ï€

Answers

A = π r^2
A = 3.14 x 7^2
A = 3.14 x 49
A = 153.86

answer
153.86

Find the perimeter of the rectangle.

If the rectangle has vertices M(−2,4), N(1,5), O(3,−1), and P(0,−2), what is the perimeter of the rectangle?

Round each side length to the nearest tenth, if necessary.

Answers

All you have to do is find the length of the sides using the distance formula and then add the lengths together to find the perimeter

Find the probability that when a couple has four four children, at least one of them is a girl girl. (assume that boys and girls are equally likely.)

Answers

Knowing that each gender has a 50/50 chance there are four in five chance that at least one is a girl. The sequences are BBBB,GGGG,BBGG,BBBG, and GGGB.

One number is one less than five times another. if their sum is decreased by three, the result is eight. find the numbers.

Answers

One number is one less than five times another ....
Let one number be x
The other number is 5x - 1

Their sum ...
x + 5x - 1 = 6x - 1

Their sum is decreased by 3
6x - 1 - 3 = 6x - 4

The result is eight
6x - 4 = 8
6x = 8 + 4
6x = 12
x = 2

x = 2
5x - 1 = 5(2) - 1 = 9
One number is 2 and the other is 9.

3. A prop for the theater club’s play is constructed as a cone topped with a half-sphere. What is the volume of the prop? Round your answer to the nearest tenth of a cubic inch. Use 3.14 to approximate pi.

Answers

we know that
[Volume of a cone]=pi*r²*h/3
and
[Volume of a half-sphere]=(4/6)*pi*r³
then
h=14 in
r=9 in
[Volume of a cone]=pi*r²*h/3-------------> pi*9²*14/3------------> 1186.92 in³
[Volume of a half-sphere]=(4/6)*pi*r³--------->(4/6)*pi*9³------> 1526.04 in³

the volume of the prop=1186.92+1526.04--------> 2712.96 -----------> 2713 in³

the answer is 2713 in³

I have the same problem but with 14 being 15 in and 9 being 7 in, can someone help?

Select ALL the correct answers.
The square of the sum of a number and 6 plus twice the number is equal to 189.

Which equations could be used to represent this relationship?

(3x + 6)2 = 189
(x + 6)2 + 2x = 189
(x + 6)2 = 189 + 2x
x2 + 10x + 36 = 189
x2 + 14x + 36 = 189
x2 + 2x + 6 = 189

Answers

Answer:

[tex](x+6)^{2}+2x=189[/tex]

and

[tex]x^{2}+14x+36=189[/tex]

Step-by-step explanation:

Let

x -----> the number

we know that

The equation that represent the situation is

[tex](x+6)^{2}+2x=189\\ \\x^{2} +12x+36+2x=189\\ \\x^{2}+14x+36=189[/tex]

therefore

The equations that could be used are

[tex](x+6)^{2}+2x=189[/tex] and [tex]x^{2}+14x+36=189[/tex]

Answer:

(x+6)^{2}+2x=189

and

x^{2}+14x+36=189

Step-by-step explanation:

Solve by factoring write the steps.
x2−7x+10=0
Please help show me all the steps and the answers

Answers

x^2−7x+10=0

Step 1: Factor left side of equation.
(x−2)(x−5)=0
Step 2: Set factors equal to 0.
x−2=0 or x−5=0
x=2 or x=5
Answer: x=2 or x=5

[tex] x^{2} - 7x +10 = 0 [/tex]

The middle term should be factored in such a way that the sum of two numbers is -7x and their product is 10x2. These two factors are -5x and -2x. So re-writing the equation, we get:

[tex] x^{2} - 5x - 2x +10 = 0[/tex]

Taking common, we get:

[tex]x( x - 5) -2 (x-5)=0 \\ \\ (x-5)(x-2)=0[/tex]

This means:
x - 5 = 0
⇒ x = 5

or

x - 2 = 0
⇒ x = 2

Therefore, the solution to the given equation are x = 2 and x = 5

MATH HELP PLEASE LOOK AT THE PICTURES BELOW!!!
5 QUESTIONS

Answers

the answer is A, gonna let you know Desmos is your best friend. I use it all the time.

1)

The equation is in form y=mx+b

m is the slope and b is the y-intercept

Slope: -6 and y-intercept: 2

2)

The equation is in form y=mx+b

m is the slope and b is the y-intercept

Slope: 1 and y intercept: -3

3)

C = 14d + 3

4)

8x + 6y = 12
6y = -8x + 12
y = -4/3 + 2

5)

First change the equation to y=mx+b form.

4x + 6y = 12
6y = -4x + 12
y = -2/3x + 2

Slope: -2/3

Hope that helps :)

K - 263.48 = 381.09 solve this equation

Answers

k-263.48=381.09
we add 263.48 on both sides
k=644.57

K=644.57. This is easily found with the addition property of equality, aka adding 263.48 to both sides.

The asymptote of the function f(x) = 3x + 1 – 2 is_________ . Its y-intercept is_____ .

Options for the first blank is
y= -2
y= -1
y= 1
y= 2
Options for the second is
(0,-2)
(0,-3)
(0,1)
(0,-1)

Answers

Answer:

In first blank : y = - 2,

In second blank : ( 0, 1 )

Step-by-step explanation:

Given function is,

[tex]f(x)=3^{x+1}-2[/tex]

The horizontal asymptote of the function f(x),

[tex]y=lim_{x\rightarrow \infty} f(x)[/tex]

[tex]y=lim_{x\rightarrow \infty} 3^{x+1}-2[/tex]

[tex]y=3^{\infty+1}-2[/tex]

[tex]y=3^\infty - 2[/tex]

[tex]y=0-2[/tex]

⇒ y = -2

First option is correct.

Also, the function has no vertical asymptote,

2. For finding the y-intercept, x = 0,

[tex]f(0)=3^{0+1}-2=3-2=1[/tex]

Hence, the y-intercept = (0,1)

Third option is correct.

Final answer:

The function f(x) = 3x + 1 – 2 is a linear function and does not have an asymptote, contrary to the options provided. The y-intercept is found by setting x to 0, which results in the point (0, – 1).

Explanation:

The function in question is f(x) = 3x + 1 – 2. To determine its asymptote and y-intercept, we analyze its structure.

Since this is a linear function and not a rational function, it does not have an asymptote like those found with rational functions, whose denominators can become zero. Instead, the original function is a modification of the function f(x) = 3x, with vertical shifts up by 1 and down by 2, effectively canceling each other out. Therefore, the asymptote is essentially the x-axis, which can be represented by the equation y = 0. However, since none of the provided options include y = 0, and the function we are analyzing is, in fact, linear without any asymptotes, there must be an error in the question regarding this part.

To find the y-intercept, we set x equal to 0 and solve for f(0):

f(0) = 3(0) + 1 – 2 = 1 – 2 = – 1.

Therefore, the y-intercept of the function is the point (0, – 1).

Can anyone help me!?!?!?!?! Here is my question:
Compare the functions shown below:
f(x) = 4 sin (2x − π) - 1
g(x)

x y
-1 6
0 1
1 -2
2 -3
3 -2
4 1
5 6
h(x) = (x − 2)2 + 4

Which function has the smallest minimum y-value?,

Answers

The sine function has a minimum value of -1, so f(x) = 4sin( ) -1 will have a minimum value of -5.

g(x) obviously has a minimum value of -3.

h(x) has a squared term that cannot be negative, so its minimum value is +4.

f(x) has the smallest minimum value.

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