Write each fraction as an expression with negative exponents.

v/w raised to the second power ...?

When a trail branches off from a path with a 10° slope at a 45° angle, the angle of ascent of the branch trail is still 10° if the steepness remains constant.

If you are climbing a mountain by the steepest route at a slope of 10° and then encounter a trail that branches off at a 45° angle from your current path, we can calculate the angle of ascent of the branch trail using geometric relationships. To do this, we must comprehend that slopes can also be represented in percentages and are related to angles. For instance, a 100% slope corresponds to a 45° angle.

The steepest route you are initially taking has a 10° slope. When the branch trail diverts at a 45° angle from your path, this is not the angle of ascent but rather the angle between the two paths. If we consider a straight climb as a slope of 90°, your ascent angle would not change as it is still 10°. The branch trail effectively shifts direction but not necessarily the steepness of the path. Hence, the angle of ascent for the branch trail would also be 10°, assuming it maintains the same steepness as your original path.

Answer:

200 texts = same costs

Step-by-step explanation:

Plan A:   20 + (.05 x 200)

              20 +  10 =30

Plan B  10 + (.10 x 200)

            10 + 20 = 30

Answer:

f(x) = (x - 3)²

Step-by-step explanation:

If the function given below is g(x) = x²

Then we have to find the function f(x) which is same as g(x) but shifted 3 units left.

As we know in the given equation f(x) = (a + x)²+ k, x defines the shift of the function and and k defines the shift of a graph on y-axis upwards or downwards.

Here the graph is shifted left so the value of x will be (-3) which defines the shifting of 3 left on x-axis.

Therefore the new function will be f(x) = (x - 3)²

Answer:

F(x)=(x+3)^2

Step-by-step explanation:

The inequality that represents the situation is 1*R + 4*D <= 64 which indicates that the total amount of ribbon used to make regular and deluxe barrettes should not exceed 64 yards.

Let's denote the number of regular barrettes as R and that of deluxe barrettes as D. Each regular barrette requires 1 yard of ribbon and each deluxe barrette requires 4 yards of ribbon. We know that Capricia has a total of 64 yards of ribbon. Therefore, we can create the inequality as follows:

1*R + 4*D <= 64

This inequality states that the total amount of ribbon used for both the regular and the deluxe barrettes should not exceed 64 yards.

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Answer: y (x)= 125 x

input :  number of visits "x"

output  :total cost "y"

Step-by-step explanation:

Hi, to answer this question we have to write an equation with the information given:

So, to obtain the total cost (y) we have to multiply the cost per visit by the number of visits (x)

y (x)= 125 x

Where the input is the number of visits "x" and the output is the total cost "y"

Feel free to ask for more if needed or if you did not understand something.

We used the tangent difference identity to rewrite the LHS in terms of [tex]\( \tan x \) and \( \tan \frac{\pi}{4} \)[/tex], then simplified to match the RHS, confirming the identity.

To prove the identity [tex]\( \tan(x-\frac{\pi}{4}) = \frac{\tan x - 1}{\tan x + 1} \),[/tex] we'll start with the left-hand side (LHS) and manipulate it to match the right-hand side (RHS).

LHS: [tex]\( \tan(x-\frac{\pi}{4}) \)[/tex]

Using the tangent difference identity, [tex]\( \tan(a - b) = \frac{\tan a - \tan b}{1 + \tan a \cdot \tan b} \)[/tex], we have:

[tex]\[ \tan(x-\frac{\pi}{4}) = \frac{\tan x - \tan \frac{\pi}{4}}{1 + \tan x \cdot \tan \frac{\pi}{4}} \][/tex]

Since [tex]\( \tan \frac{\pi}{4} = 1 \)[/tex], we can substitute:

[tex]\[ \tan(x-\frac{\pi}{4}) = \frac{\tan x - 1}{1 + \tan x \cdot 1} \][/tex]

[tex]\[ = \frac{\tan x - 1}{\tan x + 1} \][/tex]

This matches the RHS of the identity. Therefore, we have successfully proved the identity.

In this mathematical problem involving weight reduction over time, Keith's dog has to lose 15 pounds to reach a healthy weight. If the dog can lose an average of 1.25 pounds per week, it would take the dog 12 weeks to achieve the desired weight.

The subject of the question is Mathematics, specifically a problem concerning weight loss over time, which is a real-world application of arithmetic and rate problems. In the given scenario, Keith's dog weighs 90 pounds, and the desired healthy weight is less than 75 pounds. Therefore, the dog needs to lose a total of 15 pounds. Given the dog can lose an average of 1.25 pounds per week, we can calculate the number of weeks it would take for the dog to reach a healthy weight.

Step 1: Identify the total amount of weight to be lost, which is the difference between the current weight and desired weight. This is calculated as 90 pounds - 75 pounds = 15 pounds.

Step 2: Divide the total weight to be lost by the average weight loss per week. This is calculated as 15 pounds ÷ 1.25 pounds per week = 12 weeks.

Therefore, it would take the dog 12 weeks to reach a healthy weight if he loses an average of 1.25 pounds per week.

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Answer:

Average velocity is 32 miles/hr.

Step-by-step explanation:

Given that a particle moves on a line away from its initial position so that after t hours it is  [tex]s=6t^2+2t[/tex] miles from its initial position.

We have to find the average velocity of the particle over the interval [1, 4].

As, average velocity is the change is position over the change in time.

[tex]s(4)=6(4)^2+2(4)=104[/tex]

[tex]s(1)=6(1)^2+2(1)=8[/tex]

∴ [tex]\text{Average Velocity=}\frac{s(4)-s(1)}{4-1}[/tex]

                            =[tex]\frac{104-8}{3}=\frac{96}{3}=32miles/hr[/tex]

Hence, average velocity is 32 miles/hr.

The average velocity of the particle is [tex]\boxed{{\mathbf{21 units}}}[/tex] .

Further explanation:  

Velocity is the speed of an object in a given direction. Velocity is the vector quantity.

The average velocity can be calculated as,

[tex]{\text{average velocity}}=\frac{{{\text{distance travelled}}}}{{{\text{time taken}}}}[/tex]

Given:

The position of the particle after [tex]t[/tex]  hours is [tex]s\left(t\right)=4{t^2}+t[/tex] . The given interval is [tex]\left[{1,4}\right][/tex] .

Step by step explanation:

Step 1:  

The position of the particle after [tex]t[/tex]  hours is [tex]s\left(t\right)=4{t^2}+t[/tex]  

First we need to find the distance travelled in the interval of [tex]\left[{1,4}\right][/tex] .

The distance travelled by the particle at [tex]t=1[/tex]  is as follows,

[tex]\begin{gathered}s\left(t\right)=4{\left(t\right)^2}+t\hfill\\s\left(1\right)=4{\left(1\right)^2}+1\hfill\\s\left( 1 \right)=5\hfill\\\end{gathered}[/tex]

The distance travelled by the particle at [tex]t=4[/tex]  is as follows,

[tex]\begin{gathered}s\left(t\right)=4{\left(t\right)^2}+t\hfill\\s\left(4\right)=4{\left(4\right)^2}+1\hfill\\s\left( 1 \right)=68\hfill\\\end{gathered}[/tex]

Now find the distance travelled by the particle in the interval of [tex]\left[{1,4}\right][/tex]  .

[tex]\begin{aligned}{\text{distance travelled}}&=s\left(4\right)-s\left(1\right)\\&=68-5\\&=63\\\end{aligned}[/tex]

Step 2:  

The given interval is [tex]\left[{1,4}\right][/tex] .

Now we need to find the time as,

[tex]\begin{aligned}{\text{time elapsed}}&=4-1\\&=3\\\end{aligned}[/tex]

Step 3:  

Now we find the average velocity of the particle.

The average velocity can be calculated as,

[tex]\begin{aligned}{\text{average velocity}}&=\frac{{{\text{distance travelled}}}}{{{\text{time taken}}}}\\&=\frac{{63}}{3}\\&=21{\text{units}}\\\end{aligned}[/tex]

Therefore, the average velocity of the particle is [tex]21{\text{ units}}[/tex] .

Learn more:  

Answer details:

Grade: High school

Subject: Mathematics

Chapter: Speed, distance and time

Keywords: velocity, initial position, particle, moves, interval, distance travelled, time elapsed, position, average velocity, units, vector quantity, speed, direction, hours.

The problem involves finding the time and the rung at which Bob and Rob meet. They both meet on the 10th rung after 10 seconds of Bob's descent and Rob's ascend on their ladders, moving at their respective rates.

In this problem, we are asked to find the rung at which both Bob and Rob meet. Each ladder has 30 rungs. Bob is descending from 30 rungs, moving down 2 rungs every second. Rob is ascending from 0 rungs, moving up 1 rung every second. To determine where they meet, we need to find the time at which the rungs they're on coincide.

Bob goes down 2 rungs per second, so in 't' seconds Bob will be on the 30 - 2t rung. Similarly, Rob goes up 1 rung per second, so in 't' seconds Rob will be on the t rung. They meet when 30 - 2t equals t. Solving this equation gives us that t equals 10 seconds.

So at 10 seconds, they meet & the rung they're on is t = 10. Hence, Bob and Rob meet on the 10th rung.

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To find out what number 125% is equal to 264, one should set up the equation 1.25x = 264 and solve for x, which gives x = 211.2.

The question asks to find a number such that 125% of it equals 264. To solve for the original number, we set up the equation 1.25x = 264, where 1.25 represents 125% in decimal form, and x is the unknown number we are solving for. We divide both sides of the equation by 1.25 to isolate x, giving us x = 264 / 1.25.

By performing this division, we get:

x = 211.2

Therefore, 125% of 211.2 is 264.

Answer: red sus tbh

Step-by-step explanation: