the function f (x) = 1n ( x ) has been transformed so that there is a vertical asymptote at x= -3 what is the equation of the resulting function g ( x) ?
A: g (x) = 1n (x)-3
B: g (x) = 1n (x) + 3
C: g (x) = 1n ( x-3)
D: g = 1n ( x +3)

Answer:

67.5

Step-by-step explanation:

Okay so I spent way to long overthinking this problem but in the end, I just used common sense to figure this one out. *it still may be wrong though...

A way to check if this is correct is dividing 67.5 by 5 and it equals to 13.5 which should make that answer correct?

Answer:

67.5

Step-by-step explanation:

Okay so I spent way to long overthinking this problem but in the end, I just used common sense to figure this one out. *it still may be wrong though...

A way to check if this is correct is dividing 67.5 by 5 and it equals to 13.5 which should make that answer correct?

The population density of Hawaii is 109.09 with an area of [tex]1.1 \times 10^4[/tex]square miles and a population of [tex]1.2 \times 10^6[/tex] people.

Given that:

The area of Hawaii is 1.1 × 10^4 square miles

The population  of Hawaii is  1.2 × 10^6 square miles

The population density of Hawaii can be calculated as:

[tex]Population \ density = \dfrac{Number \ of \ people} {land\ area}[/tex]

Substitute the values in the given formula:

[tex]Population \ density = \dfrac{ 1.2 \times 10^6} {1.1 \times 10^4}[/tex]

This can be further solved as:

[tex]Population \ density = \dfrac{ 1.2 \times 10^{(6 -4)}} {1.1}[/tex]

The laws of exponent are used here,

Where,  [tex]\dfrac{x^m}{x^n} = x^{(m-n)[/tex]

This can be solved as:

Population  density = [tex]1.0909 \times10^2[/tex]

                                   = [tex]1.0909 \times 100[/tex]

                                    = 109.09

The population density of Hawaii is 109.09.

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The complete question is :

Hawaii has an area of [tex]1.1 \times 10^4[/tex] square miles and a population of [tex]1.2 \times 10^6[/tex] people. Which keystrokes on a calculator will give the population density of Hawaii?

Final answer:

To find the population density of Hawaii, divide the population by the area. The key strokes on a calculator would be 1.2 divided by 1.1 equals 1.09. The population density of Hawaii is approximately 1.09 people per square mile.

Explanation:

To calculate the population density of Hawaii, you will need to divide the population by the area. The formula for population density is: Population Density = Population / Area. Using the provided information, the key strokes on a calculator to find the population density of Hawaii would be: 1.2 / 1.1 = 1.09. Therefore, the population density of Hawaii is approximately 1.09 people per square mile.

Answer:

4 and 8

Step-by-step explanation:

corresponding angles are two angles that have the same angle degree and are on the same side of the graph if you were to take the bottom part and move it up to the top part

Answer:

64! For those of you that really need help!

Step-by-step explanation:

Answer:64

Step-by-step explanation:64

Answer:

5

Step-by-step explanation:

We gonna multiply the 36 inches long, 8 inches wide and 10 inches tall and divide it by no of bag (576)

To rewrite the equation 4^5 = 1024 as a logarithmic equation, we use the definition of a logarithm to get log4(1024) = 5, which indicates that 4 raised to the power of 5 equals 1024.

To rewrite the exponential equation 4^5 = 1024 as a logarithmic equation, we need to apply the definition of a logarithm which states that if b^y = x, then logb(x) = y. In this case, our base (b) is 4, the exponent (y) is 5, and the result (x) is 1024. Therefore, the equivalent logarithmic equation is log4(1024) = 5.

Remember that a logarithm essentially answers the question: To what exponent must the base be raised to produce a given number? Here, we are saying that 4 must be raised to the power of 5 to get 1024. This transformation from an exponential to a logarithmic form is a fundamental concept in mathematics, particularly when dealing with logarithmic scales and operations.

Answer:

yes 7 grams is greater than 60mg

Step-by-step explanation:

as 1gram is 1000 milligrams

The equation of the line is [tex]5x+y-38=0[/tex]

Step-by-step explanation:

The slope is [tex]m=-5[/tex]

Also, the line passes through the points [tex](7,3)[/tex]

To find a line with slope [tex]m=-5[/tex] that passes through the points [tex](7,3)[/tex], let us use the equation of a line with slope that passes through the point is given by [tex](y-y_{1} )=m(x-x_{1} )[/tex] where m is the slope and [tex](x_{1} ,y_{1} )[/tex] are the points [tex](7,3)[/tex].

Thus, substituting the values in the equation of a line, we get,

[tex](y-3)=-5(x-7)[/tex]

Multiplying the term [tex](x-7)[/tex] by -5, we get,

[tex]y-3=-5 x+35[/tex]

Adding both sides by 5x,

[tex]5x+y-3=35[/tex]

Subtracting 35 from both sides of the equation,

[tex]5x+y-38=0[/tex]

Thus, the equation of the line is [tex]5x+y-38=0[/tex]

Answer:

83 yards

Step-by-step explanation:

We are given;

We are required to determine the length;

That is;

P = 2 (L + W)

P = 2L + 2W

Rearranging the formula;

2L = P - 2W

Therefore;

2L = 294 yards - 2 (64 yards)

     = 294 - 128

     = 166

L = 166 ÷ 2

  = 83 yards

Thus, the length of the rectangle is 83 yards.

Answer: Rational "yes"

Step-by-step explanation: The square root of 25 is indeed a rational number. Rational numbers are numbers. The square root of 25 is a perfect square which means that it has a number that can be multiplied by itself which gives us 25.

In this case, the number is 5 so yes, it's rational.

Answer:

Step-by-step explanation:

-(-(-65))

a neg times a neg times a neg = negative

ur answer is -65

Answer:

- 65

Step-by-step explanation:

–(–(–65))?

Note: - × - = +

- × + = -

So, +(-65) = -65

Answer:

The original price of the skirt is $24

Step-by-step explanation:

The complete question is

Jade buys a blouse and a skirt for 3/4 of their original price. Jade pays a total of $31.50 for the two items. If the original price of the blouse is $18, what is the original price of the skirt?

Let

x ----> the original price of the blouse

y ---> the original price of the skirt

we know that

Three fourth of the sum of the original price of the blouse and the original price of the skirt, must be equal to the total paid for the two items

so

The linear equation that represent this situation is

[tex]\frac{3}{4}(x+y)=31.50[/tex]

we have

[tex]x=18[/tex] ----> given problem

substitute the value of x in the expression above and solve for y

[tex]\frac{3}{4}(18+y)=31.50\\[/tex]

Multiply by 4 both sides

[tex]3(18+y)=4(31.50)\\54+3y=126\\3y=126-54\\3y=72\\y=24[/tex]

therefore

The original price of the skirt is $24

Answer:

Step-by-step explanation:

Answer:

Nein, du schlauer Penner

Step-by-step explanation:

Answer:

infinite

Step-by-step explanation:

if you graph the  equation it would overlap.

overlap = infinite

parallel = no solution

intersect = one solution

Answer:

The slope of g(x) is: [tex]m=0[/tex]

The slope of f(x) is: [tex]m-1[/tex]

Step-by-step explanation:

For this exercise you need to know that:

1. By definition the slope of any horizontal line is zero ([tex]m=0[/tex])

2. The slope of a line can be calculated using the following formula:

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

In this case, you can observe in the graph of the function g(x) given in the exercise that it is an horizontal line.  Then, based on the explanation given before, you can conclude that its slope is:

[tex]m=0[/tex]

To find the slope of the function f(x) shown in the table attached, you need to follow these steps:

- Choose two points  from the table:

[tex](0,3)[/tex] and [tex](4,-1)[/tex]

- You can say that:

[tex]y_2=-1\\y_1=3\\\\x_2=4\\x_1=0[/tex]

- Substitute values into the formula [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]:

[tex]m=\frac{-1-3}{4-0}[/tex]

- Finally, evaluating, you get:

[tex]m=\frac{-4}{4}\\\\m=-1[/tex]

Answer:

0

Step-by-step explanation:

replace x with 3 and you will get the answer

Answer: [tex]k=\frac{M^t(v-P)}{P}[/tex]

Step-by-step explanation:

Given the following equation provided in the exercise:

[tex]P=\frac{v}{1+kM^{-t}}[/tex]

You can follow these steps in order to solve for "k":

1. You must multiply both sides of the equation by [tex]1+kM^{-t}[/tex]:

[tex](P)(1+kM^{-t})=(\frac{v}{1+kM^{-t}})(1+kM^{-t})\\\\P+PkM^{-t}=v[/tex]

2. The next step is to subtract "P" from both sides of the equation:

[tex]P+PkM^{-t}-(P)=v-(P)\\\\PkM^{-t}=v-P[/tex]

3. Now apply the Negative Exponent Rule, which states that:

[tex]a^{-n}=\frac{1}{a^n}[/tex]

Then:

[tex]\frac{Pk}{M^{t}}=v-P[/tex]

4. Multiply both sides of the equation by [tex]M^t[/tex]:

[tex](M^t)(\frac{Pk}{M^{t}})=(M^t)(v-P)\\\\Pk=M^t(v-P)[/tex]

5. And finally, you must divide both sides of the equation by "P":

[tex]\frac{Pk}P=\frac{M^t(v-P)}{P}\\\\k=\frac{M^t(v-P)}{P}[/tex]

Answer:

Box plot

Step-by-step explanation:

Box plot because it’s comparing the median and I guessed it, and got it right so...

Answer:

Parallelograms

Step-by-step explanation:

Opposite sides are parallel by definition. Opposite sides are congruent. Opposite angles are congruent.

Answer:

Parallelegrams :)

Step-by-step explanation:

all of them have at least 2 parallel sides

Answer:

68°, 82°, and 30°

Step-by-step explanation:

x+x+14+x-38=180

combine like terms

3x-24=180

put variables on one side

3x=204

divide

x=68

substitute

x=68

x+14=82

x-38=30

By using the triangle angle sum theorem, we find that the measures of the angles of the triangle in question are 68 degrees, 82 degrees, and 30 degrees.

This question involves using the fact that the sum of internal angles in any triangle totals 180 degrees. In this triangle, the three angles are given as x, x+14, and x-38. To find the measures of these angles, we set up the below equation:

x + (x+14) + (x−38) = 180

The step above incorporates the triangle angle sum theorem. Now we simplify and solve for 'x':

3x - 24 = 180
3x = 204
x = 68

So the measure of the angles in the triangle are 68 degrees, 82 degrees, and 30 degrees.

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Answer:

[tex]x+2y=-11[/tex]

Step-by-step explanation:

Slope intercept form of a line is given by:

[tex]y=mx+b[/tex]

Where

m is the slope and b is the y-intercept

Given slope is  [tex]-\frac{1}{2}[/tex]

We can write:

[tex]y=-\frac{1}{2}x+b[/tex]

Now to find b, we replace x with -3 and y with -4, given, so we have:

[tex]y=-\frac{1}{2}x+b\\-4=-\frac{1}{2}(-3)+b\\-4=\frac{3}{2}+b\\b=-5.5[/tex]

So, the equation is:

[tex]y=-\frac{1}{2}x-\frac{11}{2}[/tex]

Now,

The standard form is given by:

[tex]Ax+By=C[/tex]

So, we take x and y to left side and the constant to right side. Rearranging, we get:

[tex]y=-\frac{1}{2}x-\frac{11}{2}\\2y=-x-11\\x+2y=-11[/tex]

The first answer choice is right.

Final answer:

The equation of line b that passes through the point (-3, -4) and has a slope of -1/2 in standard form is x + 2y = -11.

Explanation:

To find the equation of line b that passes through the point (-3, -4) and has a slope of -1/2, we will start with the slope-intercept form of a line equation y = mx + b, where m is the slope and b is the y-intercept. While we know the slope (-1/2), we do not yet have the y-intercept. We can use the given point to solve for b. Plugging the point into the equation gives -4 = (-1/2)(-3) + b, which simplifies to -4 = 3/2 + b. Solving for b yields b = -11/2.

Now we have the slope-intercept form of the line: y = (-1/2)x - 11/2. To convert this to standard form, which is Ax + By = C, we multiply through by 2 to clear the fractions, which gives us 2y = -x - 11. Rearranging this, we add x to both sides to get x + 2y = -11. Therefore the correct equation in standard form is x + 2y = -11.

Area of Square = 3² = 9 in²

Area of Rectangle = 3x10 = 30 in²

Area of Circle = 3.14(4.5)² = 63.585 in²

Add them all up and you get... 102.585.

answer: second choice

Answer:

13,200 feet

Step-by-step explanation:

So, the rocket starts descending at a given rate and time, so we first need to find the length it passed during that descent.

Length equals to speed multiplied with time:

s = v • t

since speed is given in feet per second, we need to convert minutes to seconds; if one minute has 60 seconds, then two minutes have 120 seconds.

s = 15 feet/s • 120 s

s = 1800 feet

So, the rocket descended 1800 feet, but it still has 11,400 feet to the Moon's surface. That means that the rocket was on 11,400 + 1,800 = 13,200 feet elevation when it started to drop.

Answer:

I think 28. Sorry if its wrong

Step-by-step explanation

The kite is a quadrilateral with 4 sides and angles. The length of line segment CD from the given kite is 28 units

The kite is a quadrilateral with 4 sides and angles.

From the given diagram,

AB = 3x + 1

BC = 22

Since AB = BC, hence;

3x + 1 = 22

3x = 22 - 1

3x = 21

x = 7

Since AD = CD = 4x, hence;

CD = 4x

CD = 4(7)

CD = 28 units

Hence the length of line segment CD from the given kite is 28 units

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Answer:

5n

Step-by-step explanation:

Answer:

total cost of the candy bars = 5 x n

Step-by-step explanation:

Answer:

Nathan use scale of 5 inches : 2 feet.

Step-by-step explanation:

Given:

Nathan drew a scale drawing of a hotel.

A room in the hotel is 55 inches long in the drawing.

The actual room is 22 feet long.

Now, to find the scale Nathan use.

The scale drawing of room = 55 inches.

The actual room = 22 feet.

Now, to get the scale Nathan use we set the ratio:

The scale drawing of room : The actual room.

= [tex]55\ inches:22\ feet[/tex]

[tex]=\frac{55}{22}[/tex]

[tex]=\frac{5}{2}[/tex]

[tex]=5\ inches:2\ feet.[/tex]

Therefore, Nathan use scale of 5 inches : 2 feet.

The scale factor Nathan used is 2/5.

To find the scale factor, we can set up a proportion using the length in the drawing and the actual length. Let x represent the scale factor. The proportion can be set up as follows:

55 inches / 1 = 22 feet / x

Cross multiplying, we get:

55 * x = 1 * 22

Simplifying, we have:

x = 22 / 55 = 2 / 5

Therefore, the scale factor Nathan used is 2/5.

Answer:

$remaining=86-6m

Step-by-step explanation:

$remaining = 80 - (m + 2m) - (3m-6)

$remaining = 80 - 3m - 3m +6

$remaining = 86 - 6m

80 -> total amount she brings into the store

m -> money spent on milk

2m -> money spent on fruit (two x m)

3m-6 -> bread (six dollars less than three times the milk value)

Simplify and the result is 86-6m

Answer:

No, primes cannot be divided by anything else then the number itself and one. Therefor you cannot divide it by any other prime.

Final answer:

A fraction with a numerator and denominator that are both prime numbers and different from each other cannot be simplified because there are no common factors to remove, as prime numbers only have 1 and themselves as factors.

Explanation:

If the numerator and denominator of a fraction are both prime numbers and are not equal to each other, the fraction cannot be simplified further. This is because prime numbers have only two factors: 1 and themselves. To simplify a fraction, you would prime factorize both the numerator and the denominator and then remove any common factors found in both.

However, since prime numbers have no other factors besides 1 and the number itself, and the two primes in our fraction are not equal, there are no common factors to remove. For example, in the fraction ⅓, both 3 and 5 are prime and there is no number other than 1 that can divide both. Hence, ⅓ is already in its simplest form.