Mathematics College

The graph of f(x) = log x + 3 is the graph of
g(x) = log x translated 3 units a)up b)down c)left D) right

Answers

Answer 1

Correct  ansver:  a) translated 3 units up



Answer 2

Answer:

A)up

Step-by-step explanation:

Given : f(x)=log x +3

            g(x)= log x

To Find :

The graph of f(x) = log x + 3 is the graph of  g(x) = log x translated 3 units

a)up

b)down

c)left

d) right

Solution:

Rule: f(x)→f(x)+b

So, the graph f(x) is translated up by b units

So, on comparing given f(x) with rule , we can say that the graph g(x) is translated up by 3 units

Thus option A is correct.

Hence The graph of f(x) = log x + 3 is the graph of  g(x) = log x translated 3 units up

Related Questions

Compute

$(\sqrt{3755}+\sqrt{3752})(-\sqrt{3755}-\sqrt{3752})(\sqrt{3755}-\sqrt{3752})(\sqrt{3752}-\sqrt{3755})$.
Thanks!

Answers

We could use:

[tex](a-b)(a+b)=a^2-b^2[/tex]

For the first and third factors there will be:

[tex](\sqrt{3755}+\sqrt{3752})(\sqrt{3755}-\sqrt{3752})=(\sqrt{3755})^2-(\sqrt{3752})^2=\\\\3755-3752=3[/tex]

and for the second and fourth:

[tex](-\sqrt{3755}-\sqrt{3752})(\sqrt{3752}-\sqrt{3755})=\\\\= (-\sqrt{3755}-\sqrt{3752})(-\sqrt{3755}+\sqrt{3752})=\\\\= (-\sqrt{3755})^2-(\sqrt{3752})^2=3755-3752=3[/tex]

So the answer is:

[tex]3\cdot 3=\boxed{9}[/tex]

Solve the trigonometric equation on the interval 0 ≤ θ < 2π. (enter your answers as a comma-separated list.) 2 sin(θ) − 2 = 0

Answers

Final answer:

The solution to the trigonometric equation 2 sin(θ) − 2 = 0 on the interval 0 ≤ θ < 2π is θ = π/2.

Explanation:

The given trigonometric equation is 2 sin(θ) − 2 = 0. To solve this equation, we can isolate the sine function by adding 2 to both sides, resulting in 2 sin(θ) = 2. Then, dividing both sides by 2 gives us sin(θ) = 1. Since we are looking for solutions on the interval 0 ≤ θ < 2π, we know that the sine function is equal to 1 at π/2. Therefore, the solution to the equation is θ = π/2.

The sum of three numbers is 104. The first number is 6 less than the second. The third number is 3 times the second. What are the numbers

Answers

We can write this in math as x+y+z=104, x=y-6, and z=3y

Because we already know what x and z are in terms of y, we can substitute our values for x and z into the first equation. This now looks like (y-6) + y + (3y) = 104. Now we can simplify our equation to find our value for y.

y-6 + y + 3y = 104 simplifies to 5y - 6 = 104, then 5y=110, and finally y=22.

Now that we know our value for y we can find our values for x and z by substituting our value for y into the other two equations.

The second equation x = y-6 can be simplified as x = 22 - 6 and further simplified as x = 16.

The third equation z = 3y can be written as z = 3(22) or z = 66.

Our three numbers are 16, 22, and 66. Hope this helps you!

State the ratio of 700 participants to 28 judges

Answers

700 : 28 are both divisible by 7 AND 4, so it would be (25 : 1)

Which graph represents the function f(x)=8 1/3x

Answers

The second one. Try plotting the points by plugging in a few values for x. 

f(x=0) = 8^0 = 1
f(x=2) = 8^(1/3)*2 = 4
f(x=4) = 8^(1/3)*4 = 16

Answer:

The correct option is 2.

Step-by-step explanation:

The given function is

[tex]f(x)=8^{\frac{1}{3}x}[/tex]

At x=0,

[tex]f(0)=8^{\frac{1}{3}(0)}=8^0=1[/tex]

At x=1,

[tex]f(1)=8^{\frac{1}{3}(1)}=8^{\frac{1}{3}}=2[/tex]

At x=2,

[tex]f(2)=8^{\frac{1}{3}(2)}=8^{\frac{2}{3}}=4[/tex]

At x=3,

[tex]f(3)=8^{\frac{1}{3}(3)}=8^{1}=8[/tex]

The graph of f(x) passing through the points (0,1), (1,2), (2,4),(3,8).

According to these coordinates we can say that the graph of f(x) is represented by option 2.

Therefore correct option is 2.

Add 1/7+7/10 as a fraction in simplest form

Answers

1/7 = 10/70 ; 7/10 = 49/70

10/70 + 49/70 = 59/70

59/70 is your answer.

First, we need to find the least common denominator in order to add these fractions together. The lowest common denominator is 70.

[tex]\frac{10}{70}[/tex] + [tex]\frac{49}{70}[/tex] = [tex]\frac{59}{70}[/tex]

Charissa is eating out with friends, and it is her turn to pay the gratuity. The bill for the food is $26.50. If she plans to tip at 20%, what should she pay if she doesn’t want to leave pennies on the table?

Answers

The Tip will be $5.30
So the total she’ll pay is $31.80

Problem Page Round 84,548 to the nearest thousand.

Answers

85,000 will be your answer

hope this helps
if you round it to the nearest thousand it becomes 85000

What is the area of a square deck, if one side is 10 feet long?

Answers

Since we know the length of one side, and it's a square, we simply multiply 10 by 10 to get 100. The final answer is 100 square feet.

Answer:100 square feet

Step-by-step explanation: since we know that a square has all equal sides, and we know one length of one side is 10, we know all sides are ten then. We then multiply 10 x 10 which will equal, 100

What number is greater 87 or 13.688?

Answers

87 is greater of course
87, if it's easier to see, you can round 13.688 and get 14. 87 > 14

q(a+y)=67y+93 help me answer this

Answers

The answer your looking for is q-67

What multiplies to 14 and adds to -15?

Answers

This would be -14 and -1 (I'm assuming you're trying to factor a quadratic equation).

Check:
-14*-1=14
-14-1=-15

Whats 12 divided by 3 1/2

Answers

3 1/2 = 7/2

12 / 7/2 = 12*2 =24/7 = 3 3/7

If (x)=x/2-2 and g(x)=2x2+x-3, find (f+g)(x)

Answers

(f+g)(x)=f(x)+g(x)=
[tex]\frac{x}{2}-2+2x^2+x-3=2x^2+\frac{2}{2}x+\frac{1}{2}x-2-3=[/tex]
[tex]2x^2+\frac{3}{2}x-5[/tex]


[tex](f+g)(x)=2x^2+\frac{3}{2}x-5[/tex]

how to solve -x+4=-2x-6

Answers

Regroup terms

Add 2x to both sides 

Simplify 4 - x + 2x to 4 + x

subtract 4 from both sides

subtract -6 - 4.

Answer: x = -10

-x+4 = -2x-6

add 6 to each side:

-x+10 = -2x

add 1x to each side

10 = -x

divide each side by -1

x = -10

Alisa says it is easier to compare the numbers in Set A (45,760 and 1,025,680) than the numbers in Set B (492,111 and 409,867). What is one way you could construct an argument justifying whether Alisa's conjecture is true?

Answers

To construct the argument, one could look at the value of the largest digit. In Set A, the largest-valued digit (1) has a value of one million, while the 4 in the other value is only valued at 40,000. Set B has two 4 values that are both worth 400,000, which will end up requiring a second comparison to tease out the larger value.

The ratio of a number and 6 written as an algebraic expression is

Answers

The answer to your question is:
x/6

The required algebraic expression is x / 6.

Given that,
In the question, was asked to determine the ratio of the number 6 in the form of algebraic expression.

What is an algebraic expression?

The algebraic expression consists of constant and variable. eg x, y, z, etc.

What is a polynomial function?

A polynomial function is a function that applies only integer dominions or only positive integer powers of a value in an equation such as the quadratic equation, cubic equation, etc. ax+b is a polynomial.

Let the number be x,
The ratio of numbers x and 6,
= x / 6
Here above expression is an algebraic expression, because the x is a variable in the equation.

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In your own words explain how to round 9660 to the nearest thousand

Answers

9660 rounded to the nearest thousand.

first, find the number in the thousands place. It is the 9. Now look to the number directly to the right of it. 
** if that number is 5 or above, u round the 9 up to 10.
** if that number is 4 or below, that 9 stays the same.

that number directly to the right of 9 is 6. It is above 5, therefore, u round the 9 up to a 10.

so 9660 rounded to the nearest thousand is 10,000. Because , after all, 9660 is closer to 10,000 then it is to 9000.

How many pair of socks a person has to take out from the drawer to be sure to have at least 4 pairs of blue socks?

Answers

I suspect you have more info than you have shared here.  How many pair of socks, total, are in that drawer, and of what colors are they?

Frederick is working on a number puzzle and discovers that the product of the two base numbers is exactly twice as large as the sum of those same base numbers.
Help on this, please?

Answers

To solve this problem, we are going to use trial and error.

If the 2 numbers are 3 and 4 then 3 and 4 is 12 and 3 + 4 = 7 which cannot be divided equally, so this is not the answer.


3 and 5 = 15 but this is not divisible by 2.


6 and 3 = 18 and 6 + 3 = 9 which is 1/2 of 18


therefore, one set is 6 and 3.

What is the value of 0 in 601,199

Answers

The value of 0 in 601,199 would either be 00,000 or since its in the ten thousandths place it would be
10,000.

Find the value of $ 15,000 at the end of one year if it is invested in an account that has an interest rate of 4.95 % and is compounded in accordance with the rules below. a. compounded monthly b. compounded daily​ (assuming a​ 365-day year) c. compounded quarterly

Answers

a)

[tex]\bf \qquad \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\to &\$15000\\ r=rate\to 4.95\%\to \frac{4.95}{100}\to &0.0495\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{twelve months, thus} \end{array}\to &12\\ t=years\to &1 \end{cases} \\\\\\ A=15000\left(1+\frac{0.0495}{12}\right)^{12\cdot 1}[/tex]

b)

[tex]\bf \qquad \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\to &\$15000\\ r=rate\to 4.95\%\to \frac{4.95}{100}\to &0.0495\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{365 days, thus} \end{array}\to &365\\ t=years\to &1 \end{cases} \\\\\\ A=15000\left(1+\frac{0.0495}{365}\right)^{365\cdot 1}[/tex]

c)

[tex]\bf \qquad \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\to &\$15000\\ r=rate\to 4.95\%\to \frac{4.95}{100}\to &0.0495\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{four quarters, thus} \end{array}\to &4\\ t=years\to &1 \end{cases} \\\\\\ A=15000\left(1+\frac{0.0495}{4}\right)^{4\cdot 1}[/tex]

A) compounded monthly; A = $15,759.579

B)  compounded quarterly; A = $15,756.396

What is Compound interest?

Compound interest, also known as interest on principle and interest, is the practise of adding interest to the principal amount of a loan or deposit.

We have,

P = $15,000

R= 4.95%

a) Using A = P(1+ r/n[tex])^{nt[/tex]

A = 15,000 (1 + 0.0495 /12[tex])^{12[/tex]

A= 15,000 x 1.0506386172

A = $15,759.579

b) Again, A = P(1+ r/n[tex])^{nt[/tex]

A = 15,000 (1 + 0.0495 /365[tex])^{365[/tex]

c) Again, A = P(1+ r/n[tex])^{nt[/tex]

A = 15,000 (1 + 0.0495 /4.1[tex])^{4.1[/tex]

A = 15, 000 x 1.05042644766

A = $15,756.396

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A school party visit the gift shop. They all want to buy a badge. Your friend needs to get 37 badges from the stock room. The badges come in packs of 10. How many packs does she need?

Answers

She needs 4 packs and she will then have a spare 3

Answer:

She will need 4 packs.

Step-by-step explanation:

The badges come in packs of 10 but this person only needs 37 badges.

If she buys two packs, she will get 20 badges.

If she buys three packs, she will get 30 badges.

Is she buys four packs, she will get 40 badges.

She will need four packs so she can have 37 badges and there will be 3 remaining badges.

3. You are looking into two long distance telephone plans offered by GT&T. The “One Rate 5 cents” plan has a monthly fee of $7.95 and all calls are 5 cents per minute. The “One Rate 7 cents” plan has a monthly fee of $4.95 and all calls are 7 cents per minute. Under what circumstances is one plan less expensive than the other?

a. The "One Rate 5 cents" plan is less expensive for calls lasting less than 1.5 minutes. The "One Rate 7 cents" plan is less expensive for calls lasting more than 1.5 minutes.

b. The "One Rate 7 cents" plan is less expensive for calls lasting less than 1.5 minutes. The "One Rate 5 cents" plan is less expensive for calls lasting more than 1.5 minutes.

c. The "One Rate 5 cents" plan is less expensive for calls lasting less than 150 minutes. The "One Rate 7 cents" plan is less expensive for calls lasting more than 150 minutes.

d. The "One Rate 7 cents" plan is less expensive for calls lasting less than 150 minutes. The "One Rate 5 cents" plan is less expensive for calls lasting more than 150 minutes.

Answers

 D. After 150 minutes, the 5 cent one is more.

Hope this helps!

Answer:

D.The "One Rate 7 cents" plan is less expensive for calls lasting less than 150 minutes. The "One Rate 5 cents" plan is less expensive for calls lasting more than 150 minutes.

Step-by-step explanation:

let the total number of minutes of calls be x minutes.

Now let us find the total cost incurred in both plan for x mins.

Plan 5 cent : 7.95+0.05x

Plan 7 cent : 4.95+0.07x

Let us find the time at which both the plans will give you same Bill.

Hence

7.95+0.05x=4.95+0.07x

7.95-4.95=0.07x-0.05x

3=0.02x

x=150

Hence at 150th min, both the plan will charge you same cost. Hence the plan giving you less Bill for 100 mins will give you high Bill in 200 mins. Let us calculate the bill incurred by both plan at 100th min.

Plan 5 cent : 7.95+0.05×100=12.95

Plan 7 cent: 4.95+0.07×100=11.95

Hence plan 7 cent is lesser than 5 cent for calls more than 150 mins

Let find which plan cost you cheaper

please help with below question
find the smallest possible constant C such that x,y,z are all integers

2x+y=C
3y+z=C
x-4z=C

Answers

Hello,

C=23
[tex]\ \left \lbrace \begin{array} {r @{ = } l} 2x+y & C \\ 3y+z & C \\ x-4z & C \end{array}\right\\\\ \ \left \lbrace \begin{array} {r @{ = }l} x & \frac{7}{23}*C \\ y & \frac{9}{23} *C \\ z & \frac{7}{23}* C \end{array}\right\\\\ [/tex]
2x + y = C [1]
3y + z = C [2]
x - 4z = C [3]

PART 1:
Rearrange [3] like so, to get an expression for x:
x = 4z + C
Sub' expression equivalent to x into [1] and rearrange to get an expression for C:
2(4z + C) + y = C
8z + 2C + y = C
8z + C + y = 0
C = -8z - y [4]
This equation will be useful later on so I will let it be [4]

PART 2:
We will also need this rearrangement (can be found by rearranging [4]):
8z + C = -y
We need to take out x from the left side like so:
x = 4z + C
So:
8z + C = x + 4z
And so:
-y = 4z + x
y = -4z - x [5]
This one is also essential so I will let it be [5]

PART 3:
Sub' expression for C from [4] into [2] and rearrange to get an expression for z like so:
-8z - y = 3y + z
9z = -4y
z = -4y/9 [6]

PART 4:
Sub' expression for y from [5] into [2] and simplify like so:
3(-4z - x) + z = C
-12z - 3x + z = C
-11z - 3x = C

PART 5:
Now, sub' in expression for C from [3] into the equation just above and rearrange to express in terms of z:
-11z - 3x = x - 4z
7z = -4x
z = -4/7x [7]

PART 6:
Sub' in expression for z from [6] into [7] and simplify:
-4/7x = -4/9y
-36x = -28y
-9x = -7y
9x = 7y

From the equation just above; we know 9 and 7 must both multiply by two integers to give the same number;
In order to find the two integers (x and y), we first need to find the LCM (lowest common multiple) of the two so:
Multiples of 9: 9, 18, 27, 36, 45, 54, 63, ...
63 is a the LCM, none of the multiples of 9 are also multiples of 7;
All we have to do know is set 9x and 7y equal to 63 and solve for x and y:

9x = 63
x = 7

7y = 63
y = 9

PART 7:
Now, to get z, we just sub' y = 9 or x = 7 into equations [6] and [7] respectively;
It is good practice to double check answers when you can so I would sub' both y = 9 and x = 7 into their respective equations to see if I get the same value (you should get the same value as equations [6] and [7] are both equivalent to z) and hence confirm whether my working is correct;
So:
z = -4/9y
z = -4/9(9)
z = -4

z =-4/7x
z = -4/7(7)
z = -4

As you can, see z = -4 regardless of whether I used the x in the x equation or the y in the y equation.

So, the values of x, y and z are:
x = 7
y = 9
z = -4
And the value of C, therefore, is 23

PART 8:
You should always check your values as I mentioned before so lets do that:
For [1]:
2(7) + 9 = 23
For [2]:
3(9) - 4 = 23
For [3]:
7 - 4(-4) = 23

As you can see, the integer values of x, y and z that I have found can all be subbed in to any of the equations in their respective variables and you will get the same number, 23.
I am quite sure this is the smallest value of C you would find as I did use the lowest common multiple and so I would expect I did get the smallest possible C value.

In 448,244, how is the relationship between the first pair of 4's the same as the relationship between the second pair of 4's?

Answers

They are all whole numbers , Judy in different spaces and positions
Final answer:

The similar relationship between the two pairs of '4's in the number 448,244 is based on their order of magnitude or place value each pair differing by one order of magnitude.

Explanation:

In the number 448,244, the relationship between the first pair of 4's is the same as the relationship between the second pair of 4's in terms of their place value or order of magnitude.

The first '4' is in the hundred thousands place and the second '4' is in the ten thousands place, a difference of one order of magnitude (105 vs 104). Similarly, the third '4' is in the hundreds place and the second '4' is in the units place, also a difference of one order of magnitude (102 vs 100). So, despite the fact they are located in different parts of the number, the relationship between each pair of '4's is consistent based on their order of magnitude.

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Jimmy’s new cell phone cost him $49.99 when he signed a 2 year plan, which was 75% off the original place. What was the original price?

Answers

If Jimmy's new cell cost him $49.99 with a 75% discount, then $49.99 is 100%−75%=25% of the original price.

The original price of the cell phone was $199.96.

Item 10 A restaurant earns $1240 on Friday and $921 on Saturday. Write and solve an equation to find the amount xx (in dollars) the restaurant needs to earn on Sunday to average $1000 per day over the three-day period. Write your equation so that the units on each side of the equation are dollars per day.

Answers

Let the restaurant need to earn x dollars on Sunday, to average 1000$/day .

The average earning over the 3 days is [tex] \frac{1240+921+x}{3}= \frac{2161+x}{3} [/tex] dollars.

we equalize this expression to $1000:

[tex]\frac{2161+x}{3} =1000\\\\ 2161+x=3000\\\\x=3000-2161\\\\x=839[/tex] dollars


Thus the equation is : [tex]\frac{1240+921+x}{3}(\$/day)=1000(\$/day) [/tex]

If R is the midpoint of QS, QR= 8x-51 and RS=3x-6, find QS.

Answers

QS = 11x - 57 

since r is the midpoint, QR + RS = QS

Answer:  The required length of QS is 42 units.

Step-by-step explanation:  Given that R is the midpoint of QS, where

[tex]QS=8x-51,~~RS=3x-6.[/tex]

We are to find the length of QS.

Since R is the midpoint of the segment QS, so we must have

[tex]QR=RS\\\\\Rightarrow 8x-51=3x-6\\\\\Rightarrow 8x-3x=51-6\\\\\Rightarrow 5x=45\\\\\Rightarrow x=\dfrac{45}{5}\\\\\Rightarrow x=9.[/tex]

Therefore, the length of QS is given by

[tex]QS\\\\=QR+RS\\\\=8x-51+3x-6\\\\=11x-57\\\\=11\times9-57\\\\=99-57\\\\=42.[/tex]

Thus, the required length of QS is 42 units.

The difference between 29 and a number

Answers

The word "difference" means subtract (-)

29 equals 29

A number equals w

So, your answer would be: 29 - w
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