Which function is equivalent to f(x) = lnx?

f(x) = log3x
f(x) = log10x
f(x) = logbx
f(x) = logex

Answer:

y-1/3x=17/3

Step-by-step explanation:

ax+by=c is standard form

first I'll start with slope interecept form and then we can change it to standard

y=mx+b

y=1/3x+b

4=1/3(-5)+b

4=-5/3+b

12/3+5/3=b

17/3=b

y=1/3x+17/3

to change to standard

y-1/3x=17/3

Answer:

C) 4ft3

Step-by-step explanation:

volume is measured in cubes and cubes are to the 3rd power

The answer is 67.6

You have to find the angle that has cos=8/21=0.381.

Answer:

67.6 degrees

Step-by-step explanation:

You need to use cosine to solve this.

so, cosine is adjacent leg over hypotenuse. which is 8/21. and it is 0.381.

and when you do cos^-1 (0.381), then it is 67.6.

I believe the answer will be (9,9)

Answer:

-1/3

Step-by-step explanation:

To find the slope you have to find the rise over run. Start at the first point then  go down 3 and over to the right 1. Your slope is -1/3.

Answer:

A

Step-by-step explanation:

Calculate the slope m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (1, 4) and (x₂, y₂ ) = (2, 1) ← 2 points on the line

m = [tex]\frac{1-4}{2-1}[/tex] = [tex]\frac{-3}{1}[/tex] = - 3 → A

The answer is 0.6 . 3 divide 5 is 0.6

.6 is correct . To get that u just divide the 3 by the 5

Answer:

General equation of line : [tex]y = mx+c[/tex]   --1

Where m is the slope or unit rate

Table 1)

p    d

1      3

2     6

4     12

d = Number of dollars (i.e.y axis)

p = number of pound(i.e. x axis)

First find the slope

First calculate the slope of given points

[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]   ---A

[tex](x_1,y_1)=(1,3)[/tex]

[tex](x_2,y_2)=(2,6)[/tex]

Substitute values in A

[tex]m = \frac{6-3}{2-1}[/tex]

[tex]m = 3[/tex]

Thus the unit rate is 3 dollars per pound.

So, It matches the box 1 (Refer the attached figure)

Equation 1 : [tex]p=3d[/tex]

[tex]\frac{p}{3}=d[/tex]

Since p is the x coordinate and d is the y coordinate

On Comparing with 1

[tex]m = \frac{1}{3}[/tex]

Thus the unit rate is [tex]\frac{1}{3}[/tex] dollars per pound

So, It matches the box 2 (Refer the attached figure)

Equation 2 : [tex]\frac{1}{3}d=3p[/tex]

[tex]d=9p[/tex]

Since p is the x coordinate and d is the y coordinate

On Comparing with 1

[tex]m =9[/tex]

Thus the unit rate is 9 dollars per pound

So, It matches the box 3 (Refer the attached figure)

Table 2)

p        d

1/9      1

1         9

2        18

d = Number of dollars (i.e.y axis)

p = number of pound(i.e. x axis)

[tex](x_1,y_1)=(\frac{1}{9},1)[/tex]

[tex](x_2,y_2)=(1,9)[/tex]

Substitute values in A

[tex]m = \frac{9-1}{1-\frac{1}{9}}[/tex]

[tex]m = \frac{8}{frac{8}{9}}[/tex]

[tex]m = 9[/tex]

Thus the unit rate is 9 dollars per pound

So, It matches the box 3 (Refer the attached figure)

Answer: See image attached

Step-by-step explanation:

Answer:

2/6

Step-by-step explanation:

There are 6 sides, and two are green. That makes it 2/6

Answer:

2/6

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

A cube has 6 sides

Only one side of the cube has 2 on it

The probability of getting 2 would be 1/6

Only one side of the cube has 6 on it

The probability of getting 6 would be 1/6

For both events to happen together

1/6 x 1/6 = 1/36

To find the probability of rolling a 2 on the first die and a 6 on the second, multiply the independent probabilities of each event (1/6 for each die) to get 1/36, making the correct answer A) 1/36.

The question asks for the probability of rolling two number cubes and getting a 2 on the first number cube and a 6 on the second number cube. When rolling two dice, the outcome of one die does not affect the other, so the probabilities of each outcome are independent. Since a die has six faces, the probability of rolling any specific number on a single die is 1/6.

Therefore, the probability of rolling a 2 on the first die is 1/6 and the probability of rolling a 6 on the second die is also 1/6. To find the combined probability of both events happening together, you multiply the probabilities of each event by each other, which is (1/6) × (1/6) = 1/36. So, the correct answer is A) 1/36.

Answer:

A

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 5x + 2 ← is in slope- intercept form

with slope m = 5

• Parallel lines have equal slopes, hence

y = 5x + c ← is the partial equation of the parallel line

To find c substitute (- 6, - 1) into the partial equation

- 1 = - 30 + c ⇒ c = - 1 + 30 = 29

y = 5x + 29 → A

Luke's square mosaic increased in area by 3.25 square meters after he added a border, turning the side length from 3 meters to 3.5 meters.

Luke originally made a square mosaic with side lengths of three meters. The area of this original square is calculated by squaring the side length: 3 meters × 3 meters = 9 square meters. When Luke added a border to his mosaic, the side length became 3.5 meters. Calculating the new area, we square the new side length: 3.5 meters × 3.5 meters = 12.25 square meters.

The increase in the area of the mosaic is the difference between the new area and the original area, which is 12.25 square meters - 9 square meters = 3.25 square meters. Therefore, the area of Luke's mosaic has increased by 3.25 square meters after adding the border.

Answer:

1.

Step-by-step explanation:

( 1 - sin^2 O ) / cos^2 O

Now 1 - sin^2 O = cos^2 O

So the function becomes cos^2 O / cos^2 O

= 1.

Answer:

It's 0.90.

Step-by-step explanation:

Answer:

the answer is B

Step-by-step explanation:

Answer:

a = 0

b = 2

Step-by-step explanation:

Synthetic division gives rise to two equations:

b -2a = 2

b +2a = 2

The solution to these equations is (a, b) = (0, 2).

___

The remainder from the division is the lower-right sum shown in the attached tables. For the factor x+2, the remainder from dividing your cubic by x+2 is (4b-8a-8). Setting this to zero and putting it into standard form gives the first equation shown above.

The remainder from division by (x-2) is (4b+8a-4). Setting this to 4 and putting the result into standard form gives the second equation above.

___

Pen skips and chocolate smudges make the first attachment less "professional" than it might otherwise be. Please forgive. The graph in the second attachment verifies this result.

Answer:

72 mm^3

Step-by-step explanation:

To find the volume of the combined object, we can find the volume of each cube and add it together

Volume of the 4 mm cube

V = s^3

V = 4^3 = 64 mm^3

Volume of the 2 mm cube

V = s^3

V = 2^3 = 8 mm^3

Add the volumes together

64+8 = 72 mm^3

Answer:

72 mm^3

Step-by-step explanation:

To find the volume of this irregular figure, first find each of the cubes.

Part I. Finding the bottom cube

Since the volume of a cube is s^3 where s is the side, we can plug 4 in and we get 64 mm^3.

Part II. Finding the top cube

Using the formula for volume of a cube, we get the volume of the upper cube to be 8 mm^3.

Part II. The total volume of the irregular figure

To find the total volume we simply add the two volumes together. In doing so, we get 64+8 = 72 mm^3 as our volume.

Answer:

30

Step-by-step explanation:

If P is the number of peach trees and T is the total number of trees, then:

P = 2/5 T

P + 18 = T

If we substitute the first equation into the second:

2/5 T + 18 = T

18 = 3/5 T

T = 30

The gardener has 30 trees.

Answer:

D

Step-by-step explanation:

Given

11x = 11 - 55xz²

Collect the terms in x together by adding 55xz² to both sides

11x + 55xz² = 11 ← factor out x on the left side

x(11 + 55z²) == 11 ← divide both sides by 11 + 55z²

x = [tex]\frac{11}{11+55z^2}[/tex] ← factor out 11 on the denominator

x = [tex]\frac{11}{11(1+5z^2)}[/tex] ← cancel 11 on numerator/denominator

x = [tex]\frac{1}{1+5z^2}[/tex] → D

Answer:

If 10 minutes block, then it can be rented for 20 minutes. If no blocks, then 27.27 minutes

Step-by-step explanation:

Initial setup cost is $6.

Every 10 minutes, $5.5 is charges, so each minute  [tex]\frac{5.5}{10}=0.55[/tex] is charged.

Let time used be t, so we can set up an equation as:

21 = 6 + 0.55t

Where t is in minutes

we solve for t to find out how many minutes we can rent for $21:

[tex]21 = 6 + 0.55t\\21-6=0.55t\\15=0.55t\\t=\frac{15}{0.55}=27.27[/tex]

since it is charged PER 10 MINUTES, so we can rent it for 10, 20 , 30 minutes etc.

WE CANNOT RENT FOR 30 minutes as we dont have enough money (only for fractional amount of a little over 27 minutes). Thus, we will have to have some money left over and rent for 20 minutes.

For $21, you can rent approximately 20 minutes of time at the local copy center when there's a $6 setup charge and each 10-minute period costs an additional $5.50.

The question is asking how much time can be rented for $21 at a local copy center, where there's a $6 setup charge and an additional $5.50 for every 10 minutes. To figure this out, we first need to subtract the setup charge from the total amount of money that can be spent. So, $21 - $6 = $15. Next, we need to see how many 10 minute increments can be rented with $15. Since each 10 minute increment costs $5.50, we divide $15 by $5.50 to get approximately 2.72. Since we can't rent time in fractions of a minute, we round this down to 2. Therefore, we can rent about 20 minutes of time for $21.

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Vehicle A travels 750 feet and Vehicle B travels 600 feet in 15 seconds. Adding these distances together, we find they are 1350 feet apart after 15 seconds.

The subject of your question falls under the realm of Mathematics, specifically in the area of vector addition or relative velocity. Let's imagine the two vehicles are moving away from each other in a straight line at an angle. We mainly need to consider the relative velocity of vehicle B to vehicle A.

After 15 seconds, vehicle A will have traveled (50 feet/second * 15 seconds) = 750 feet. Similarly, vehicle B will have traveled (40 feet/second * 15 seconds) = 600 feet. In this situation, the total distance separating vehicle A and vehicle B is the sum of their individual distances traveled, which equals 750 feet + 600 feet = 1350 feet.

Therefore, the two vehicles are 1350 feet apart after 15 seconds.

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To simplify the expression (6.15x+0.24y)">">1.5 + 5.9x - 1.6y, divide the terms in the parenthesis by 1.5 and then combine like terms to yield the simplified expression 10.0x - 1.44y.

To simplify the expression (6.15x+0.24y)">">1.5 + 5.9x - 1.6y, first, divide the terms within the parenthesis by 1.5. This action distributes the division across each term:

This simplifies to:

Now, combine like terms with those outside the parenthesis:

Therefore, the simplified expression is:

10.0x - 1.44y

y = –4x + 33

y-33 = –4x

y-33/4 = x

X=y-33/4.

Answer: The answer to your question is (8.25, 0)

Step-by-step explanation:

Answer:

[tex]48\ pieces[/tex]

Step-by-step explanation:

we know that

To find how many pieces can be made from the pipe, divide the total length of the pipe by 3/4 feet

so

[tex]\frac{36}{(3/4)} =\frac{36*4}{3}=48\ pieces[/tex]

Answer:

11.2 feet

Step-by-step explanation:

The width of the actual train car, to the nearest foot, is 11 feet.

To find the width of the actual train car, we need to use the scale factor provided.

Given:

- Width of the model train's car = 2.4 inches

- Scale = 1:56

To find the actual width, we'll use the scale factor:

[tex]\[ \text{Actual width} = \text{Model width} \times \text{Scale factor} \][/tex]

First, we need to convert the width of the model train's car from inches to feet because the scale factor is given as a ratio. There are 12 inches in a foot.

[tex]\[ \text{Model width} = \frac{2.4 \text{ inches}}{12 \text{ inches/foot}} = 0.2 \text{ feet} \][/tex]

Now, we can find the actual width:

[tex]\[ \text{Actual width} = 0.2 \text{ feet} \times 56 = 11.2 \text{ feet} \][/tex]

Answer:

450pi

Step-by-step explanation:

The volume of this figure is just the sum of the volumes of two cones. They both have radius of 5 and one has a height of 7 and the other has a height of 11.

The easiest way (for me) to calculate the volume is to find the average of the heights (9) and multiply the volume of a cone with the same radius as the other two and the other height by two.

The volume for a cone is just (pi*r^2*h)/3, so the 'average' cone's volume is 25pi * 9/3 or 75pi.

Double this to get 150pi.

Alternatively, you could calculate the volumes of the two cones using separate heights, but here you will end up with non-whole numbers (times pi) for both cones if you use that method.

Answer:

471.24 in³

Step-by-step explanation:

Volume of the left cone

= 1/3 π (5)²(7)

= 175π/3 in³

Volume of the right cone

= 1/3 π(5)²(11)

= 275π/3 in³

Total volume

= 175π/3 + 275π/3  

= 150π

= 471.24 in³

Answer:

120°

Step-by-step explanation:

Answer:

the costs of the career is low

Step-by-step explanation:

Answer:

819

Step-by-step explanation:

Givens

Formula

Sum = a(1 - r^n) / ( 1 - r)

Sum = -1(1 - (-4)^6 / (1 - -4)

Sum = -1 (1 - 4096) / 5

Sum = -1 (- 4095 ) / 5

Sum = 819

Answer:

Step-by-step explanation:

We know: If a quadrilateral is inscribed in a circle, then the sum of measures of opposite angles is equal to 180°.

Therefore we have the equations:

[tex](1)\qquad2x+(2x+4)=180\\\\(2)\qquad y+(3y+8)=180[/tex]

Solve:

[tex](1)\\2x+2x+4=180\qquad\text{subtract 4 from both sides}\\\\4x=176\qquad\text{divide both sides by 4}\\\\x=44\\\\(2)\\y+3y+8=180\qquad\text{subtract 8 from both sides}\\\\4y=172\qquad\text{divide both sides by 4}\\\\y=43[/tex]

Answer:

A. x=44 y=43

Step-by-step explanation:

i just did the test yrdlf

Answer: The smallest angle x is 75.5

Step-by-step explanation:

3x+x+58=360

4x=360-58

4x=302

x=302/4

x=75.5

Well that’s it for today I just wanna was a really good day I wanna

To find the actual speed and direction of the canoe, we can add the velocity of the canoe relative to the water to the velocity of the current. Using vector addition, the approximate resultant velocity of the canoe is 2.19 miles per hour at an angle of 51.3° relative to the shore.

To find the approximate actual speed and direction of the canoe, we can use vector addition. The canoe's velocity relative to the water is 2 miles per hour in the direction of 55°. The velocity of the current is 1 mile per hour due east. We can add these two vectors to find the resultant vector, which represents the total velocity of the canoe relative to the shore.

Using the formula for vector addition, we can find the magnitude and direction of the resultant velocity. The magnitude can be found using the Pythagorean theorem: Vtotal = √(Vcanoe)2 + (Vcurrent)2. The direction can be found using the tangent function: θ = tan-1(y/x), where y is the vertical component of the resultant vector and x is the horizontal component.

In this case, the resultant velocity of the canoe will be approximately 2.19 miles per hour (rounded to two decimal places) and the canoe will move in a direction of 51.3° (rounded to one decimal place) relative to the shore.

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