how to tell if a function has a vertical asymptote

The average temperature change per hour was -2.708 degrees Fahrenheit.

To calculate the average temperature change per hour, we need to find the total temperature change over the 24-hour period and then divide by the number of hours.

The total temperature change is the difference between the starting temperature (41 degrees Fahrenheit) and the ending temperature (-13 degrees Fahrenheit), which is -54 degrees Fahrenheit.

Dividing the total temperature change by the number of hours, we get:

-54 degrees Fahrenheit / 24 hours = -2.25 degrees Fahrenheit per hour.

Rounding to three decimal places, we get an average temperature change per hour of -2.708 degrees Fahrenheit per hour.

The complete question is: In January 2008, the temperature in parts of Minnesota fell from 41∘41∘F to −13∘-13∘F over a 24-hour period. What was the average temperature change per hour?

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To help Tim get the refrigerator into the truck, we need to calculate the force he should apply on the ramp. The fridge weighs 250N, and the ramp is 40m long while the truck bed is 3m high. First, find the incline angle of the ramp by using the right triangle with a 3m rise and 40m hypotenuse.

To get the refrigerator into the truck bed, Tim will need to use a force that is greater than the weight of the fridge. This force will need to overcome the force of gravity, which is pulling the fridge down towards the ground. Since the ramp is 40 meters long, Tim will have a longer distance to work with, which means he can use less force to get the fridge up the ramp.

However, the ramp will also increase the distance that Tim will need to move the fridge, which will require more force. Ultimately, the force that Tim needs to use will depend on the angle of the ramp and the friction between the fridge and the ramp.

Step 1: Calculate the angle using the sine function:
sin(angle) = opposite side (3m) / hypotenuse (40m)
angle = arcsin(3/40) ≈ 4.29 degrees

Step 2: Calculate the force required along the ramp:
Force_required = weight * sin(angle)
Force_required = 250N * sin(4.29 degrees) ≈ 18.87N

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Answer:

∠JKP = 35°

Step-by-step explanation:

since P is the incenter, then lines to incenter bisect the corner angles:

7x - 6 = 5x + 4

subtract 5 x from both sides of the equation:

2x - 6 = 4

add 6 to each side:

2x = 10

divide both sides by 2:

x = 5

∠KJP = 7(5) - 6 = 29°

∠LJP = 5(5) + 4 = 29°

then ∠KJL = 29° + 29° = 58°

∠KLJ = 26° + 26° = 52°

∠JKL = 180° - 58° - 52° = 70°

∠JKP = 1/2 ∠JKL = 1/2(70°) = 35°

there might be a more direct way about it but this was the least confusing way I know to explain it.

Answer:

Cheetah A ran at a faster speed than Cheetah B, as it ran 18 miles in 16 minutes while Cheetah B ran 54 miles in 50 minutes.

Step-by-step explanation:

Answer: its A

Step-by-step explanation:

Answer: -2, 3

Step-by-step explanation:

so E is correct

Answer:

C

Step-by-step explanation:

m=rise/run

rise is 1

run is 4

1/4=0.25

hope this helps :3

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Answer:

The answer is going to be A. DX = YZ

Step-by-step explanation:

Answer:

\(\sf \boxed{\bold{x=1}}\)

Explanation:

\(\rightarrow \sf 7 log_9 (x + 8) = 7\)

divide both sides by 7

\(\rightarrow \sf \dfrac{7\log _9\left(x+8\right)}{7}=\dfrac{7}{7}\)

simplify the following

\(\sf \rightarrow \log _9\left(x+8\right)=1\)

apply log rules                   \(\underline{The \ rule}: \ \bold{log_{b} (a)= c} \ \ \Longrightarrow \sf a = b^c\)

\(\sf \rightarrow x+8 = 9^1\)

simplify

\(\sf \rightarrow x+8=9\)

subtract both sides by 8

\(\sf \rightarrow x=1\)

\(\\ \rm\Rrightarrow 7log_9(x+8)=7\)

\(\\ \rm\Rrightarrow log_9(x+8)=1\)

\(\\ \rm\Rrightarrow x+8=9^1\)

\(\\ \rm\Rrightarrow x+8=9\)

\(\\ \rm\Rrightarrow x=9-8\)

\(\\ \rm\Rrightarrow x=1\)

Answer:

£164.50

Step-by-step explanation:

If the discount is 6%, then the discounted price is 94% of the original price.

95% of £175 = 0.94 × £175 = £164.50

Answer:

52

Step-by-step explanation:

f(n) is purely based on the previous value of f(n), or f(n-1), so we can start with f(1) and work our way up. We know f(1) = 2, so to find f(2), we plug f(1) into

f(n-1)²+3 to get

f(1)²+3 = 2²+3 = 4+3=7

Thus, f(2) =7. Similarly,

f(3) = f(3-1)²+3 = f(2)² + 3 -= 7² + 3= 52

Polynomials are algebraic expressions consisting of terms that include real numbers, variables, and positive integer exponents. Each term in a polynomial has a variable raised to a non-negative integer power, and the coefficient of each term is a real number. Polynomials are classified by the degree of their highest power. If two or more terms in a polynomial have the same variable raised to the same power, they can be combined into a single term.

1. -x² + x - x² + 1

Combine like terms: -x² + x - x² + 1 = -2x² + x + 1

This polynomial has degree 2 because the highest power of the variable is 2.

2. x² + x + 2x³ - x

Rearrange terms: 2x³ + x² + x - x = 2x³ + x²

This polynomial has degree 3 because the highest power of the variable is 3.

3. 4x + x + x - 2

Combine like terms: 4x + x + x - 2 = 6x - 2

This polynomial has degree 1 because the highest power of the variable is 1.

4. 3x² + 4 - 3x² - 1

Combine like terms: 3x² - 3x² + 4 - 1 = 3

This polynomial has degree 0 because there is no variable term.

Therefore, the four given polynomials have degrees 2, 3, 1, and 0, respectively.

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Answer:

32%

Step-by-step explanation:

100 - 68

Answer:

32%

Step-by-step explanation:

subtract 68 from 100 to get your answer

Answer:

option 3

Step-by-step explanation:

Answer:

A = 8^2 mm = 64 mm^2   area of square

Radius of circle = 4 mm

a = area of circle = pi R^2 = 3.14 (4 mm)^2 = 3.14 * 16mm^2

A - a =  (64 - 50.3) mm^2 = 13.7 mm^2

The reflection in the line y = x, followed by a reflection in the x-axis transformation that maps the preimage to the image.

What is the transformation?

Transformations are changes done in the shapes on a coordinate plane by rotation, reflection, or translation. A function, f, that maps to itself are called the transformation, i.e., f: X → X. The pre-image X becomes the image X after the transformation. This transformation can be any or combination of operations like translation, rotation, reflection, and dilation.

In geometry, transformation involves changing the position and/or size of a shape.

The transformation that maps the pre-image to the image is dilation

From the given diagram

We can see that the size of and are not the same.

When the No change in size or shape or orientation and Flips the pre-image and produces the mirror-image, then the transformation type is Reflection.

Hence, the reflection in the line y = x, followed by a reflection in the x-axis transformation that maps the preimage to the image.

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Percentage increase= $768÷32000=0.024

=0.024×100=2.4%

Therefore , the solution of the given problem of speed comes out to be the average distance travelled is  225 meters.

We can determine how fast that anything is traveling by looking at it from a distance. The amount of distance an object can go in a given length of time depends on its speed. Velocity is calculated using the formula velocity = distance/time. The three most used units of speed are meters per second (m/s), kilometers per hour (km/h), and miles per hour (mph) (mph).

Here,

Given :

Time =  40 seconds.

To find the distance:

We use speed and time formula

=> distance = speed * time

=> distance = 15 * 30

=> distance =  225 meters.

Therefore , the solution of the given problem of speed comes out to be the average distance travelled is  225 meters.

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Answer:

Step-by-step explanation:

Answer:

cevap =560...........

the solution of the given differential equation is:y = [16 ln |x| + 8x2 + C1]1/16

The given differential equation is y15 x dy/dx = 1 + x. Now, we will solve the given differential equation.

The given differential equation is y15 x dy/dx = 1 + x. Let's bring all y terms to the left and all x terms to the right. We will then have:

y15 dy = (1 + x) dx/x

Integrating both sides, we get:(1/16)y16 = ln |x| + (x/2)2 + C

where C is the arbitrary constant. Multiplying both sides by 16, we get:y16 = 16 ln |x| + 8x2 + C1where C1 = 16C.

Hence, the solution of the given differential equation is:y = [16 ln |x| + 8x2 + C1]1/16

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Answer:

\(\boxed{\sf n= \dfrac{2}{5} ,\: n=1}\)

Step-by-step explanation:

\(\rightarrow 5n^2 = 7n -2\)

\(\rightarrow 5n^2 - 7n +2=0\)

\(\rightarrow 5n^2 - 5n -2n+2=0\)

\(\rightarrow 5n(n - 1) -2(n-1)=0\)

\(\rightarrow (5n-2)(n-1)=0\)

\(\rightarrow 5n-2= 0,\: n-1=0\)

\(\rightarrow 5n= 2,\: n=1\)

\(\rightarrow n= \dfrac{2}{5} ,\: n=1\)

Step-by-step explanation:

\(\hookrightarrow\sf{5n^2 = 7n -2}\\\\\hookrightarrow\sf{5n^2 - 7n +2=0}\\\\\hookrightarrow\sf{5n^2 - (5+2)n +2=0}\\\\\hookrightarrow\sf{5n^2 - 5n -2n+2=0}\\\\\hookrightarrow\sf{ 5n(n - 1) -2(n-1)=0}\\\\\hookrightarrow\sf{ (5n-2)(n-1)=0}\\\\\hookrightarrow\sf{ 5n-2= 0\:or~ n-1=0}\\\\\hookrightarrow\sf{ 5n= 2\:or~n=1}\\\\\hookrightarrow\bold{ n= \dfrac{2}{5} \:or~ n=1}\)

$12.25

                                                                   you welcome that the answer

Answer:

11.25$

Step-by-step explanation:

19.00 - 7.75 = 11.25

Answer:

13x + 16

Step-by-step explanation:

Add the like terms together, like terms are terms that have the same variable or power. Ex. x and 4x are like terms, 4x and 4 are not. x^2 and x^3 are not like terms, x^2 and 2x^2 are like terms.

3+9+5x+4+8x

5x+8x+3+9+4

13x + 16

The probability of picking a blue and then a red is  12%.

To find the probability of picking a sample we need to know about the probability formula. Probability can be determined by

P = (number of groups) / total

From the question above, we know that :

red = 4

blue = 3

green = 2

yellow = 1

so the total cubes = 10

Before calculating the probability of picking a blue and then a red, we should know first the probability of each

P blue = number of blue / total

P blue = 3 / 10

Then the probability of red is

P red = number of red / total

P red = 4 / 10

By multiplying P blue and P red we can determine the probability of picking a blue and then a red

P = P blue x P red

P = 3/10 x 4/10

P = 12/100

P = 12%

Hence, the probability of picking a blue and then a red is  12%.

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Answer:

Given the point-slope form of a line, y = mx + b, to get the y-intercept of a line, you first have to solve for b by setting x = 0. This gives you the b-value of y = 0 + b = b. We see that b is the y-intercept.

Step-by-step explanation:

Answer:

See below

Step-by-step explanation:

The point-slope form of a line looks like
y - \(y_{1}\)  = m( x - \(x_{1}\))

The number that is the place of the 'm' is the slope.

For example:

If we had the equation

y - 3 = 12(x +4)

The slope would be 12.

The ratios that could be the lengths of the two legs in a 30-60-90 triangle are √3:3 (option E) and 12√3 (option D).

In a 30-60-90 triangle, the angles are in the ratio of 1:2:3. The sides of this triangle are in a specific ratio that is consistent for all triangles with these angles. Let's analyze the given options to determine which ones could be the ratio between the lengths of the two legs.

A. √2:√2

The ratio √2:√2 simplifies to 1:1, which is not the correct ratio for a 30-60-90 triangle. Therefore, option A is not applicable.

B. 15

This is a specific value and not a ratio. Therefore, option B is not applicable.

C. √√√√5

The expression √√√√5 is not a well-defined mathematical operation. Therefore, option C is not applicable.

D. 12√3

This is the correct ratio for a 30-60-90 triangle. The ratio of the longer leg to the shorter leg is √3:1, which simplifies to √3:3. Therefore, option D is applicable.

E. √3:3

This is the correct ratio for a 30-60-90 triangle. The ratio of the longer leg to the shorter leg is √3:1, which is equivalent to √3:3. Therefore, option E is applicable.

F. √2:√5

This ratio does not match the ratio of the sides in a 30-60-90 triangle. Therefore, option F is not applicable. So, the correct option is D. 1 √2.

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The diver collected water samples at every 3 meters, starting from 5 meters below the water surface, up to a final depth of 35 meters.

We can find the number of samples collected by dividing the total depth range by the distance between each sample and then adding 1 to include the first sample.

The total depth range is:

35 m - 5 m = 30 m

The distance between each sample is 3 m, so the number of samples is:

(30 m) / (3 m/sample) + 1 = 10 + 1 = 11

Therefore, the diver collected a total of 11 water samples.