Mathematics College

The function f(x)=log[7]x is increasing. True or false

Answers

Answer 1
I would say that the answer is true
Answer 2

The given function increases as x increases, so the statement is true.

Is the function increasing?

Here we have the function:

[tex]f(x) = log_7(x)[/tex]

To see if it is increasing, we can evaluate in two values, 10 and 15, this will serve to see if the function is increasing or not:

[tex]f(10) = log_7(10) = 1.18\\\\f(15) = log_7(15) = 1.39[/tex]

As you can see, when x increases also does f(x), so the function is increasing.

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Related Questions

Devaughn is 13 years older than Sydney. The sum of their ages is 77 . What is Sydney's age?

Answers

77-13=64....64÷2=32 the age should be 32

how to solve this linear equation step by step please

Answers

[tex]\bf \cfrac{3}{c^2-4c}-\cfrac{9}{2c^2+3c}=\cfrac{2}{2c^2-5c-12}\\\\\\ \begin{cases} c^2-4c=&c(c-4)\\ 2c^2+3c=&c(2c+3)\\\\ 2c^2-5c-12= &(2c+3)(c-4) \end{cases}\\\\ -------------------------------\\\\ \textit{therefore, our LCD for the \underline{left-side} will have to be }\underline{c(c-4)(2c+3)}\\\\ -------------------------------\\\\[/tex]

[tex]\bf \cfrac{3}{c(c-4)}-\cfrac{9}{c(2c+3)}=\cfrac{2}{(2c+3)(c-4)} \\\\\\ \cfrac{3(2c+3)-9(c-4)}{c(c-4)(2c+3)}=\cfrac{2}{(2c+3)(c-4)} \\\\\\ \cfrac{6c+9-(9c-36)}{c(c-4)(2c+3)}=\cfrac{2}{(2c+3)(c-4)} \\\\\\ \cfrac{6c+9-9c+36}{1}=\cfrac{2[c(c-4)(2c+3)]}{(2c+3)(c-4)} \\\\\\ -3c+45=2c\implies 45=5c\implies \cfrac{45}{5}=c\implies 9=c[/tex]

Two linear equations are shown.
What is the solution to the system of equations?

Answers

1/3x + 2 = 4/3x - 5
2 + 5 = 4/3x - 1/3x
7 = x

y = 1/3(7) + 2
y = 7/3 + 2
y = 7/3 + 6/3
y = 13/3

solution is : (7,13/3) <=

Answer:

B.

Step-by-step explanation:

What's the correct answer for this?

Answers

[tex]\bf \qquad \qquad \textit{inverse proportional variation}\\\\ \textit{\underline{y} varies inversely with \underline{x}}\qquad \qquad y=\cfrac{k}{x}\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array}\\\\ -------------------------------\\\\[/tex]

[tex]\bf \textit{\underline{N} is inversely proportional to \underline{A}}\qquad N=\cfrac{k}{A} \\\\\\ \textit{we also know that } \begin{cases} A=3\\ N=16 \end{cases}\implies 16=\cfrac{k}{3}\implies 16\cdot 3=k \\\\\\ 48=k\qquad thus\qquad \boxed{N=\cfrac{48}{A}}\\\\ -------------------------------\\\\ \textit{if \underline{A} is 4, what is \underline{N}?}\qquad N=\cfrac{48}{4}[/tex]

(APEX) If a product is equal to zero, we know at least one of the factors must be zero. And the constant factor cannot be zero. So set each binomial factor equal to 0 and solve for x, the width of your project (-2x^-6x-4)

Answers

The rule described above is called the Zero Product Property. To illustrate it more clearly, suppose there is a quadratic equation with a general form of ax²+bx+c=0. Because it's degree is 2, then there are two possible roots. When you factor the quadratic equation, that would be

(x-q)(x-r) = 0

where q and r are the roots of the equation. Because their product is zero, the Zero Product Property states that x-q - 0 and x-r = 0

Thus, for the given equation above, a = -2, b = -6 and c=-4. Then, we find the roots using the quadratic formula.

[tex]x= \frac{-b+/- \sqrt{ b^{2}-4ac } }{2a} [/tex]
[tex]x= \frac{-(-6)+/- \sqrt{ (-6)^{2}-(-2)(-4) } }{2(-2)} [/tex]

x = -1 and -2. That means q=-1 and r=-2. Hence, the two binomials are (x+1) and (x+2).

What is 1/4 of 268 ?

Answers

The answer to your question is not very complicated, you just had to divide 268 by 4 and you'd get 67
Answer: 67
Final answer:

To find 1/4 of 268, you divide 268 by 4. The result of this operation is 67.

Explanation:

Calculating 1/4 of a number involves a simple mathematical operation known as division. In this case, we want to find out what is 1/4 of 268. To do this, you simply divide 268 by 4.

The calculation is as follows:

Divide the number 268 by 4.268 ÷ 4 equals 67.

This means that 1/4 of 268 is 67.

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other form to write 600,000+80,000+10

Answers

six hundred eighty thousand and ten

hope this helps


or 680,010

The building of Jim's Hardware is assessed at $109,000. The tax rate is $86.95 per $1,000 of assessed valuation. The tax due is A. $8,695.45. B. $947.75. C. $9,477.55. D. $8,659.54. E. 94,698.23.

Answers

The answer is C, $9,477.55

109,000 / 1,000 = 109

109 x 86.95 = 9,477.55

53 ℃ below zero degrees

Answers

I don't really understand this...
your answer is -53 degrees celsius

hope this helps

a class voted for either kayaking, fishing, or hiking as their favorite summer activity. if hiking got 17% percent of the vote and fishing got 33%, what percentage of the class voted kayaking?

Answers

50%
100-17-33
Just the difference after subtraction

The percentage of the class that voted for kayaking is 50%.

Given data:

To find the percentage of the class that voted for kayaking, use the fact that the total percentage of votes adds up to 100%.

Hiking got 17% of the vote.

Fishing got 33% of the vote.

Let x be the percentage of the class that voted for kayaking.

Since the total percentage of votes is 100%:

17% + 33% + x = 100%

On solving for x:

x = 100% - (17% + 33%)

x = 100% - 50%

x = 50%

Hence, 50% of the class voted for kayaking.

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A set of equations is given below:

Equation A: y = x + 1
Equation B: y = 4x + 5

Which of the following steps can be used to find the solution to the set of equations?

x + 1 = 4x + 5
x = 4x + 5
x + 1 = 4x
x + 5 = 4x + 1

Answers

The correct answer is A, or x + 1 = 4x + 5.  We used the substitution method to replace y with x + 1.

Answer:

x + 1 = 4x + 5

Step-by-step explanation:

To solve this set of equation you can just equalize them ot one another, as you can see they are already in Y form, which means that they have already been solved for Y, so that makes things easier for us, we just insert the second equation in the place of Y in the first one, and we can solve for "x".

There are two aircraft carriers, A and B, and the carrier A is longer in length the carrier B. The total length of these two carriers is 4178 feet, while the difference of their lengths is only 14 feet.

Answers

Answer:

Length of carrier A = 2096 feet Length of carrier B=2082 feet.

Step-by-step explanation:

Given , two air craft carriers are A and B . The carrier A is longer than the carrier B in length.

Total length of two carriers =4178 feet

Difference of two carriers = 14 feet

Let

Length of carrier A =x  feet

And

Legth of carrier B =y feet

According to question  

The I equation is

x+y=4178

The II equation is

x-y= 14

Substitution method:  In this method step I :  we  find value of x or y from the equation I

Step II:  put the value of x or y in II equation then we get the value of another  varaiable x or y  

Step : Again put the obatined value of variable x or y  from  step II   in equation I then we get value of other variable x or y .

By  using substitution method ,

we find value of x from equation I

x= 4178-y

Now, put the value of x in equation II then we get

4178-y-y=14

4178-2y=14

4178-14=2y

4164=2y

[tex]y=\frac{4164}{2}[/tex]

y= 2082

Again , put the value of y in equation I

2082 +x=4178

x= 4178-2082

x=2096

Hence, the length of carrier A = 2096 feet

The length of carrier B= 2082 feet

Final answer:

To solve the problem, we set up two equations based on the given total length and the length difference of the two aircraft carriers. By solving these equations, we find that carrier A is 2096 feet long and carrier B is 2082 feet long.

Explanation:

The student's question involves solving a system of linear equations to find the lengths of two aircraft carriers, A and B. Given that the total length is 4178 feet and the length difference is 14 feet, we can set up the following equations:

Equation 1: A + B = 4178

Equation 2: A - B = 14

To solve for A and B, we can add the two equations together to eliminate B.

This gives us 2A = 4192, hence A = 2096 feet.

Substituting A back into one of the equations, we find B = 2082 feet.

Therefore, carrier A is 2096 feet long and carrier B is 2082 feet long.

A rectangular yard measuring 26ft by 40ft is bordered (and surrounded) by a fence. Inside, a walk that is 2ft wide goes all the way along the fence. Find the area of this walk. Be sure to include the correct unit in your answer.

Answers

In order to find the area of the walk, first you must find the area of the yard, then the area of the walk and yard combined. 

The area of the yard (minus the walk) is simple to find. Just multiply 26 and 40, and you'd get 1,040 ft squared. 

The area of the yard including the walk is a bit more complicated. You have to include add measurement of the walk to the measurements of the length and width of the yard. However, you must add it twice, considering it goes all the way around the yard. So, since the walk is 2 feet wide, you add it (twice) to 26 (26 + 4 = 30) and twice to 40 (40 + 4 = 44). Now, multiply the two new measurements. You now have 1,320 feet squared.

So now you have the combined area of the walk and yard, and the area of the yard without the walk. To find the area of the walk, you just subtract the area of the yard from the entire measurement of both. 1,320 square feet - 1,040 square feet is 280 square feet.

A parallelogram has an area of 48 m². If the base is 12 m long, what is the height?

Answers

The area of a parallelogram is its base times the height. So the height is 48/12 which is 4.

48/12=4 so the height is 4

Manuel is choosing a 3 -letter password from the letters A, B, C, D, and E. The password cannot have the same letter repeated in it. How many such passwords are possible?

Answers

Here they are... ABC ABD ABE ACB ACD ACE ADB ADC ADE.. Just do the same thing with the others... Ex. BCD BDE BCE BCA BDA BDC BDE etc. 

A rubber ball has a radius of about 2.86 in. Can the ball be packaged in a box shaped like a cube with a volume of 125 in3?

Answers

volume of the ball = 4/3 * PI *r^3 =

4/3 * 3.14 * 2.86^3 = 97.99 cubic inches

 this is less than the volume of the box, so yes it will fit

A and B are mutually exclusive events. P(A) = 1/3 and P(B) = 1/2. What is the P(A or B)?

Answers

When you have mutually exclusive events and what to find the probability of one or another, add the probabilities.
1/3+1/2=5/6
Final answer: 5/6
P(A or B) = 1/2 + 1/3 = 3/6 + 2/6 = 5/6

answer
P(A or B) = 5/6

A class tossed coins and recorded 165 heads and 172 tails. What is the experimental probability of tails?

Answers

165+172=337

172/337 is the experimental probability of tails.

Hope this helps!

Answer:

Probability of tails = 0.51

Step-by-step explanation:

Probability is the ratio of number of favorable outcome to the total number of outcomes.

Total number of outcomes = Total number of heads + Total number of tails

                                              = 165 + 172 = 337

Number of favorable outcome = Total number of tails = 172

[tex]\texttt{Probability}=\frac{172}{337}=0.51[/tex]  

Express the ratio of A's to N's in the word SAVANNAH, in simplest form

Answers

[tex]\dfrac{3}{2}[/tex]
there are 3 a's, and there are 2 n's so the ration is 3:2 or 3/2 or 3 to 2

A school graduation class wants to hire buses and vans for a trip to Jasper National Park. Each bus
holds 40 students and 3 teachers and cost $1200 to rent. Each van holds 8 students and 1 teacher
and costs $100 to rent. The school has at least 400 students wanting to go, but at most 36 teachers.
What is the minimum transportation cost?

Answers

Let the school hire x buses and y vans.

A bus can hold 40 students and 3 teachers.
A van can hold 8 students and 1 teacher.

The number of students riding in  buses and vans is at least 400, therefore
40x + 8y ≥ 400          (1)

The number of teachers riding in buses and vans is at most 36, therefore
3x + y ≤ 36                (2)

Write (1) and (2) as
y ≥ 50 - 5x                 (3)
y ≤ 36 - 3x                 (4)

The equality portion of the solution of (3) and (4) is
36 - 3x = 50 - 5x
2x = 14
x = 7   =>  y = 36 - 3*7 = 15

A graph of the inequalities indicates the acceptable solution in shaded color, as shown below.

The minimum cost of renting buses and vans is
7*$1200 + 15*$100 =  $9900

Answer: The minimum cost is $9,900

Malia is observing the velocity of a cyclist at different times. After two hours, the velocity of the cyclist is 15 km/h. After five hours, the velocity of the cyclist is 12 km/h.
Part A: Write an equation in two variables in the standard form that can be used to describe the velocity of the cyclist at different times. Show your work and define the variables used. (5 points)
Part B: How can you graph the equations obtained in Part A for the first 12 hours? (5 points)

Answers

We must to remember what is the standard form of equation of straight line. It looks like that:
Ax+By+C=0.  A,B and C it's coefcients; x and y - it's variables.A and B must not be equal to zero at same time.This condition can be writen like this: (A^2+B^2) not equal to zero.
We know that x=2 ("after two hours") and y=15 ("velocity of the cyclist is 15 km/h")
AND
x=5 ("after five hours") and y=12 ("velocity of the cyclist is 12 km/h").
Lets look at standart form and give the values on variables.1. 2A+15B+C=0

2. 5A+12B+C=0and it is system.let's subtract the bottom equation from the top  -3A+3B=03A=3BA=B.So we can choose any value for A and B, just A=B.I choose for A=B=1.Our equation takes the formx+y+C=0
x+y=-C
and if we giving the value to variables, we can find coefficients "C".
5+12=-CC=-17.
Standart form is:x+y-17=0. ---- answer for Part A.
and the graph of this function is a straight line.For find the answer to Part B, we need to prolong our straight line into the perpendicular vertical line wich contain x=12.
In the point of the intersection of the lines, you must to turn at right angle to axis OY and to come at the value in the axis OY, it's will be the velocity after 12 hours.  

Which statement is true?

Answers

hello : 
f(x) = 9x-6
g(x) =√(x-4)
(f0g)(x) = f(g(x)) exist if  g(x) exist  and    f(g(x)) exist.
g(1) no exist because :  √(1-4) =√(-3) ... no real
conclusion : 1 is not in the domain of : f0g

What is the step by step process of solving for the GCF from a list of terms.
Ex. (see picture)

Answers

[tex]\bf 18a^5b^8c^4\quad \begin{cases} 18=\underline{2\cdot 3}\cdot 3\\ a^5=\underline{aaaaa}\\ b^8=\underline{b} bbbbbbb\\ c^4=cccc \end{cases}\qquad 12a^6b\quad \begin{cases} 12=2\cdot \underline{2\cdot 3}\\ a^6=\underline{aaaaa} a\\ b=\underline{b} \end{cases} \\\\\\ \textit{notice the underlined factors, those are common to both terms} \\\\\\ 2\cdot 3\cdot aaaaa\cdot b\implies 6a^5b\impliedby GCF[/tex]

write 103,727,495 in word form and expanded

Answers

one hundred three million seven hundred twenty seven thousand four hundred ninety five. 100,000,000+3,000,000+700,000+20,000+ 7,000+400+90+5
Word Form:
One hundred three million, seven hundred twenty seven thousand, four hundred ninety five

Expanded Form:
100,000,000 + 3,000,000 + 700,000 + 20,000 + 7,000 + 400 + 90 + 5

Hope this helped

What is the equation of the line that passes through (4,3) and (2,2)

Answers

The Equation of (4,3) and (2,2) is y=1/2x+1

Answer:

The equation of line is [tex]y=\frac{1}{2}(x)+1[/tex].

Step-by-step explanation:

Given information: The line passes through the point (4,3) and (2,2).

If a line passes through the points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex], then the equation of line is

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

The line passes through the point (4,3) and (2,2), so the equation of line is

[tex]y-3=\frac{2-3}{2-4}(x-4)[/tex]

[tex]y-3=\frac{-1}{-2}(x-4)[/tex]

[tex]y-3=\frac{1}{2}(x-4)[/tex]

Using distributive property, we get

[tex]y-3=\frac{1}{2}(x)+\frac{1}{2}(-4)[/tex]

[tex]y-3=\frac{1}{2}(x)-2[/tex]

Add 3 on both sides.

[tex]y=\frac{1}{2}(x)-2+3[/tex]

[tex]y=\frac{1}{2}(x)+1[/tex]

Therefore the equation of line is [tex]y=\frac{1}{2}(x)+1[/tex].

In the rhombus, m<1=8y-6. Find the value of y. Please help!!

Answers

i think the answer is A.

Answer: 12

The value of y= 12.

Step-by-step explanation:

We know that the diagonal of rhombus are perpendicular bisector of each other.

i.e. the angle made at the intersection of diagonal is 90 degrees.

Thus , for the given figure m∠1 = 90°

Since it is given that  m∠1 = 8y-6

Thus , 8y-6= 90

⇒8y=96   [Adding 6 both sides]

⇒ y = 12  [Dividing both sides by 8]

Hence, the value of y= 12.

You have taken over an abandoned drilling project. After drilling for 2 hours, the depth is 110 feet. After 5 hours, the depth has increased to 114.5 feet. Write an equation in the form y = mx + b to describe the relationship between x, the hours of drilling, and y, the depth of the well.

Answers

(2,110)(5,114.5)
slope = (114.5 - 110) / (5 - 2) = 4.5 / 3 = 1.5

y = mx + b
slope(m) = 1.5
use either of ur points..(2,110)...x = 2 and y = 110
now we sub and find b, the y int
110 = 1.5(2) + b
110 = 3 + b
110 - 3 = b
107 = b

so ur equation is : y = 1.5x + 107 <==

From 1980 to 1990, the consumer price index (CPI) increased from 82.4 to 130.7. If a bottle of dish soap cost $0.74 in 1980 and the price of dish soap increased at the same rate as the CPI from 1980 to 1990, by approximately how much did the price of a bottle of dish soap increase from 1980 to 1990?

Answers

Using proportions, it is found that the price of a bottle of dish soap increased $0.43 from 1980 to 1990.

What is a proportion?

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

The percent increase, as a proportion, of the CPI is given by:

P = 130.7/82.4 = 1.5862.

Hence, for the price of the bottle:

Pb = $0.74 x 1.5862 = $1.17.

The difference is:

1.17 - 0.74 = $0.43.

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Answer: $0.43

Step-by-step explanation:

The cool dude above me already explained it

Explain the place value relationship when the same two digits are next to each other in a multi-digit number.

Answers

Take one value as an example, 5664 where there are two digits of '6' next to each other

Partitioning this value, 
5664 = 5000 + 600 + 60 + 4

Notice that one digit of 6 worth 100 and the other worth 10

Take another example, 78869 where there are two digits of '8'

Partitioning this value, we have
78869 = 70000 + 8000 + 800 + 60 + 9

Notice that one digit of '8' worth 8000 and the other worth 800

One other characteristic that we can tell from both example, is that when two same digits are placed next to each other in a value, one digit's value is always worth ten times than the other digit.

for example, the value 600 and 60 from the first example, 600 = 10 × 60

What is the value of b2 - 4ac for the following equation? x(x + 8) = 9 28 64 100

Answers

Answer:

C) 100

Step-by-step explanation:

The given equation is x(x + 8) = 9

Distributing x insides, we get

x^2 + 8x = 9

Now set the equation equal to zero.

x^2 + 8x - 9 =0

Here a = 1, b = 8, and c = -9

b^2 - 4ac = (8)^2 - 4*1*-9

= 64 + 36

= 100

Therefore, b^2 - 4ac = 100.

Answer: C) 100

Hope this will helpful.

Thank you.

Answer:

C. 100

Step-by-step explanation:

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