When a line of symmetry divides an image, every point on one side of the line has a corresponding point on the other side.

The value of a rare baseball card A appreciated by 20 percent over a five year period; over the next five years, the value plumm

lbvjy [14]

<h2>Answer:</h2>

<em><u>Percent value of A with respect to Percent value of B is,</u></em>

$30\%$

<h2>Step-by-step explanation:</h2>

In the question,

Let us say the value of the Baseball card A and B initially is = 100x

So, for Baseball card A in first 5 years percent increase = 20%

So,

Value after 5 years = 100x + 20% of 100x = 120x

<u>After 5 more years,</u>

Percent decrease = 50%

So,

<u>Value at the end of 10 years = 120x - 50% of 120x = 60x</u>

Now,

For Baseball card B, Percent increase in 10 years = 100%

So,

<u>Value of card B = 100x + 100% of 100x = 200x</u>

So,

<em><u>Percent value of A with respect to Percent value of B is,</u></em>

$\frac{60x}{200x}\times 100=30\%$

7 0

3 years ago

Solve the given initial-value problem. the de is of the form dy dx = f(ax + by + c), which is given in (5) of section 2.5. dy dx

shutvik [7]

$\dfrac{\mathrm dy}{\mathrm dx}=\cos(x+y)$

Let $v=x+y$ , so that $\dfrac{\mathrm dv}{\mathrm dx}-1=\dfrac{\mathrm dy}{\mathrm dx}$ :

$\dfrac{\mathrm dv}{\mathrm dx}=\cos v+1$

Now the ODE is separable, and we have

$\dfrac{\mathrm dv}{1+\cos v}=\mathrm dx$

Integrating both sides gives

$\displaystyle\int\frac{\mathrm dv}{1+\cos v}=\int\mathrm dx$

For the integral on the left, rewrite the integrand as

$\dfrac1{1+\cos v}\cdot\dfrac{1-\cos v}{1-\cos v}=\dfrac{1-\cos v}{1-\cos^2v}=\csc^2v-\csc v\cot v$

Then

$\displaystyle\int\frac{\mathrm dv}{1+\cos v}=-\cot v+\csc v+C$

and so

$\csc v-\cot v=x+C$

$\csc(x+y)-\cot(x+y)=x+C$

Given that $y(0)=\dfrac\pi2$ , we find

$\csc\left(0+\dfrac\pi2\right)-\cot\left(0+\dfrac\pi2\right)=0+C\implies C=1$

so that the particular solution to this IVP is

$\csc(x+y)-\cot(x+y)=x+1$

5 0

3 years ago

The dot plots show rainfall total for several spring storms in highlands areas an lowlands areas what is the median rainfall for

tankabanditka [31]

*See attached picture showing the dot plots referred to

Answer:

16mm

Step-by-step Explanation:

Given the dot plot showing rainfall for Highlands storms, we can find out the median rainfall for Highlands storms by mere observing the dot plot and locating where the middle value falls within the data set that is represented on the dot plot.

Thus, we have 44 data sets that is being represented on the plot, with one dot representing one data set for rainfall. This means, since the total number of data set is even, our median lies between the 22nd and the 23rd dot or data set that is being plotted.

From the dot plot for Highlands, the 22nd and 23rd dots are 16 and 16 respectively.

Therefore, median rainfall for Highland storms = (16 + 16) ÷ 2 = 16.

8 0

3 years ago

Read 2 more answers

Represent the following expressions as a power of the number (a≠0):

Vsevolod [243]

The answer should be a^7

3 0

3 years ago

Solve the following quadratic by factoring.

Lina20 [59]

Answer:

4, -1

Step-by-step explanation:

We can reverse the FOIL (First, outside, inside, last) method to break down the equation. The question is asking to solve by factoring so you want to find the right combination of numbers this equation can be broken down into:

x^2 - 3x - 4 = 0

Because we want x squared, x needs to be multiplied by itself, so we can put x in the first slot for each.

(x + or - ?) ( x + or - ?) = 0

Then we need to find numbers that could be added to get -3 and multiplied to get -4. The only set of numbers that works for this is -4 and 1. Note that the sign you put in front of each number has an impact on your answers. With this we get:

(x - 4) (x + 1) = 0

To test that this is equal to the original equation, simply multiply it out using FOIL.

x * x = x^2

x * 1 = x

x * -4 = -4x

-4 * 1 = -4

Putting each component into an equation:

x^2 + x - 4x - 4 = 0

Simplifying:

x^2 - 3x - 4 = 0

Once we are sure it is still the same equation, we find the solutions. We know 0 multiplied by anything equals 0, so to get 0 as the answer, one of the sets in the parentheses must equal 0. (It doesn't matter what the other one is as long is one equals 0)

Therefore, we have 2 solutions, 4, and -1 because if x is 4, 4-4 is 0 which solves the equation, and if x is -1, then -1 + 1 is 0 which also solves the equation.

You can also check your answers by plugging them back into the original equation.

5 0

3 years ago