The value of a DS depreciates by 30% per year. Work out the current value of a DS brought 4 years ago for £99

The solution of the system of equations are;

⇒ x = - 1 and y = - 1

What is substitution method?

To find the value of any one of the variables from one equation in terms of the other variable is called the substitution method.

Given that;

The system of equation is,

⇒ 2x + 5y = - 7

⇒ 7x + y = - 8

Now,

Solve the system of equation as;

⇒ 2x + 5y = - 7     ... (i)

⇒ 7x + y = - 8       .. (ii)

Multiply by 5 in equation (ii) and subtract from (i), we get;

⇒ 2x + 5y - 35x - 5y = - 7 + 40

⇒ - 33x = 33

⇒ x = - 1

And, 2x + 5y = -7

⇒ 2 × -1 + 5y = -7

⇒ - 2 + 5y = - 7

⇒ 5y = - 7 + 2

⇒ 5y = - 5

⇒ y = - 1

Thus, The solution of the system of equations are;

⇒ x = - 1 and y = - 1

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Answer:

41

Step-by-step explanation:

Answer:

41

Step-by-step explanation:

angle 7 and angle 4 are corresponding angles.

corresponding angles are equal

∠7 = ∠4

∠7 = 41

41 = ∠4

Answer:

25

Step-by-step explanation:

They are relevant

3x=75

x=75/3

x=25

Answer:

Red Line:  y = \(\frac{5}{2} x\) - 9

Blue Line: y = -2x + 6

Yellow Line: y = \(\frac{-1}{3}x\) + 9

Step-by-step explanation:

y=mx+b is the slope-intercept formula for a line. This means that this equation tells you the y-intercept of a line as well as the slope of a line. In this formula, m is equal to the slope, and b is equal to the y-intercept.

The Y-intercept of a line is where the line crosses the y-axis.

The slope of a line is how much the line is increasing or decreasing by. You can calculate this number by dividing how much the line increases by the y-axis by how much the line increases on the x-axis. Essentially, you divide the line's rise over its run, or the change in y over the change in x.

Slope formula: \(\frac{x_{1}-x_{2}}{y_{1}-y_{2}}\)

\(x_{1}\) and \(y_{1}\) make up one coordinate, and \(x_{2}\) and \(y_{2}\) make up another. Both of these points must land on the same line--the line you are trying to find the slope of.

Red Line:

In this photo, we can clearly see what the y-intercept is. The slope intercept is -9, so b = -9.

To find the slope, you take two points and find the difference of their y-values and divide that by the difference of their x-values.

On the red line, we can see that the line crosses points (2, -4) and (0, -9). Let's find the slope by subtracting the y-values first:

-4 - (-9) = 5

5 is your change in y values, or your rise!

Now, let's subtract the x-values:

2 - 0 = 2

2 is your change in x values, or your run!

In order to finally find the slope of this line, you divide your change in y by your change in x. Therefore, you divide 5 by 2.

Your slope is \(\frac{5}{2}\). It's okay to leave slopes in fraction form!

So, now you plug in your slope and y-intercept that we found before into your formula! Remember:

b = y-intercept

m = slope

So, y = \(\frac{5}{2} x\) - 9 is the formula for your line!

Red line:  y = \(\frac{5}{2} x\) - 9

Now, we repeat the process with the other lines. Let's do the blue line:

We can see that the y-intercept is 6. So, b = 6.

Now, let's calculate the slope. Let's find points on the blue line that we can use!

Point 1: (0, 6)

Point 2: (1, 4)

Let's subtract the y values:

6 - 4 = 2

Let's subtract the x values:

0 - 1 = -1

When we divide 2 (our change in y) by -1 (our change in x), we are left with -2 as our slope!

Slope = -2

So, when we plug everything into our equation, we get:

y = -2x + 6

Blue Line: y = -2x + 6

Now, for the last one!

We can see that the y-intercept is 9, so b = 9.

Let's calculate the slope:

Point 1: (0, 9)

Point 2: (3, 8)

Subtract the y-values:

9 - 8 = 1

Subtract the x-values:

0 - 3 = -3

Divide the change in y by the change in x:

1  ÷ -3 = \(\frac{-1}{3}\)

Slope = \(\frac{-1}{3}\)

Plug everything in!

y = \(\frac{-1}{3}x\) + 9

Yellow Line: y = \(\frac{-1}{3}x\) + 9

Answer:

did you use google.if not use it it is good to use.

Answer:

it took her 54 mins to finish her walk.

Step-by-step explanation:

Given;

total distance walked by Katie, d = ⁵/₆

time taken to walk ¹/₆ mile = 10 mins

break time = 1 min

There are five ¹/₆ mile in the total distance which is ⁵/₆ miles.

Time for the first  ¹/₆ mile  = 10 mins +

                    break time = 1 min

Time for the second  ¹/₆ mile  = 10 mins +

                     break time = 1 min  

Time for the third  ¹/₆ mile  = 10 mins +

                     break time = 1 min  

Time for the fourth  ¹/₆ mile  = 10 mins +

                     break time = 1 min  

Time for the fifth  ¹/₆ mile  = 10 mins

Total time = 5 (10 mins)  + 4 (1 min)

                 = 50 mins + 4mins

                = 54 mins

Therefore, it took her 54 mins to finish her walk.

Answer:

Slope = 3

Step-by-step explanation:

A secant is a straight line cutting a curve at two or more points.

Given function:

\(f(x)=x^2-8\)

Find the values of y for the given x-values:

\(\begin{aligned}\implies f(-3)&=(-3)^2-8\\&=9-8\\&=1\end{aligned}\)

\(\begin{aligned}\implies f(6)&=(6)^2-8\\&=36-8\\&=28\end{aligned}\)

Therefore, the endpoints of the secant line are:

\(\boxed{\begin{minipage}{8cm}\underline{Slope Formula}\\\\Slope $(m)=\dfrac{y_2-y_1}{x_2-x_1}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are two points on the line.\\\end{minipage}}\)

To find the slope of the secant line, substitute the found endpoints into the slope formula:

\(\implies \textsf{Slope}=\dfrac{28-1}{6-(-3)}=\dfrac{27}{9}=3\)

The budgets of Hong Kong, the United States of America, and Korea differ in contents, formats, advantages, and disadvantages. While each budget has its strengths and weaknesses, they all aim to provide a clear and transparent financial plan for their respective countries.

A budget is a financial plan that estimates expected income and expenditure for a specific period. It may include income, expenses, debts, and savings. Budgets may vary from country to country and can be analyzed by comparing their contents, formats, advantages, and disadvantages. Here are the budgets of Hong Kong, the United States of America, and Korea:

United States Budget:

Korean Budget:

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The number of tiles with a length of 0.15 meters that would be needed by Hassan to place along the edge of the counter is: 20 tiles.

The tile's length is the longer side of a tile depending on the shape of the tile.

The length of the given tile is, 0.15 meter.

Length of the edge of he counter = 3 meters.

Number of tiles Hassan needs = 3/0.15

Number of tiles Hassan needs = 20 tiles.

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Answer: 20 tiles.

Step-by-step explanation:

The number of tiles with a length of 0.15 meters that would be needed by Hassan to place along the edge of the counter is: 20 tiles.

What is a Tile's Length?

The tile's length is the longer side of a tile depending on the shape of the tile.

The length of the given tile is, 0.15 meter.

Length of the edge of he counter = 3 meters.

Number of tiles Hassan needs = 3/0.15

Number of tiles Hassan needs = 20 tiles.

the area of a circle with a rectangle will be [π w²2]/4.

What is the area of a circle?

The measurement of the circle's boundaries is called as the circumference or perimeter of the circle. whereas the circumference of a circle determines the space it occupies. The circumference of a circle is its length when it is opened up and drawn as a straight line. Units like cm or unit m are typically used to measure it. The circle's radius is considered while calculating the circumference of the circle using the formula. As a result, in order to calculate the circle's perimeter, we must know the radius or diameter value.

area of the circle will be πr².

The area of a circle inscribed in a rectangle if the length of the rectangle is l and the width is w

= [π w²2]/4.

Hence the area of a circle with a rectangle will be [π w²2]/4.

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Answer:

They are 12, 13, 14 and 15.

Step-by-step explanation:

If the least integer is x, then:

x + x + 1 + x + 2 + x + 3 = 54

4x + 6 = 54

4x = 48

x = 12.

The distresses experienced by asphalt mixture due to high and low temperatures can be mitigated by using new materials as modifiers of the asphalt binder or mixture.

Distresses caused by high temperatures:

1. Rutting: This is the permanent deformation of the asphalt mixture due to the excessive pressure exerted by heavy traffic. It leads to the formation of ruts or grooves on the road surface.

2. Fatigue cracking: This is the formation of cracks in the asphalt pavement due to repeated loading and unloading of the pavement under high temperatures. It reduces the overall strength and life of the pavement.

Distresses caused by low temperatures:

1. Thermal cracking: This is the formation of cracks in the asphalt pavement due to the contraction and expansion of the asphalt binder under low temperatures. It occurs primarily in areas with significant temperature variations.

2. Cold temperature stiffness: This is the reduced flexibility of the asphalt binder at low temperatures, leading to decreased performance and increased susceptibility to cracking.

Modifiers and their significant effects:

1. Polymer modifiers: These are materials added to the asphalt binder or mixture to improve its performance at high and low temperatures. Polymers enhance the elasticity and flexibility of the binder, making it more resistant to rutting and cracking.

2. Fiber modifiers: These are fibers added to the asphalt mixture to increase its tensile strength and resistance to cracking. They help in reducing the formation of cracks, especially under low-temperature conditions.

3. Warm mix asphalt (WMA) additives: These additives allow the asphalt mixture to be produced and compacted at lower temperatures compared to traditional hot mix asphalt. WMA reduces the energy consumption during production and offers improved workability and compaction.

By using polymer modifiers, fiber modifiers, and warm mix asphalt additives, the distresses caused by high and low temperatures in the asphalt binder or mixture can be mitigated. These modifiers enhance the performance of the asphalt pavement by improving its resistance to rutting, fatigue cracking, thermal cracking, and cold temperature stiffness.

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Answer:

1000

Step-by-step explanation!

The formula for the amount accrued [ƒ(x)] on an investment earning compound interest is f(t) = P(1 + r)^t where:

P = the amount of money invested (the principal)

r = the interest rate per payment period expressed as a decimal fraction

t = the number of periods

Your formula is

f(x) = 1000(1 + 0.05)^x

In comparison, we can see that the term that represents the amount of money originally invested is 1000.

Answer:

(A) 1,000

Step-by-step explanation:

i just took the test

(-5, 0 ) and (0, 5) are the ordered pair satisfies the inequality y < x+5

a relationship between two expressions or values that are not equal to each other is called 'inequality.

The given inequality is y < x+5

First, we have to find the x-intercept which occurs at y = 0

0 < x + 5

x<-5

For y-intercept,

y <  0+ 5

y <5

As a result, the obtained ordered pair is  (-5, 0 ) and (0, 5).

Hence, (-5, 0 ) and (0, 5) are the ordered pair satisfies the inequality y < x+5

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Answer:

the answer is 7/12..

thank u

Answer:

p=0.78837351631052428187102047390789

n=5

The solution of the given differential equation u'x^4 4ux^3 u''x^4 8u'x^3 12ux^2 be,

u''x^6 u'x^5

Given, a differential equation

u'x^4 4ux^3 u''x^4 8u'x^3 12ux^2

we have to find the solution of the given differential equation

on integrating both the sides, we get

u''x^6 u'x^5

So, we get u''x^6 u'x^5 as a solution of the given differential equation on solving by the reduction method.

Hence, the solution of the given differential equation u'x^4 4ux^3 u''x^4 8u'x^3 12ux^2 be,

u''x^6 u'x^5

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There are 217 bacteria there now.

A percentage is defined as the ratio that can be expressed as a fraction of 100.

We have:

initial count (P) = 155

growth rate (r) = 40% = 0.4 (from the image)

current count = P(1 + r)

current count = 155(1 + 0.4)

current count = 155(1 .4)

current count = 217

Therefore, 217 bacteria are there now.

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Complete Question

Check attached image

Answer:

x>-3

Step-by-step explanation:

−x+7<10

Step 1: Subtract 7 from both sides.

−x+7−7<10−7

−x<3

Step 2: Divide both sides by -1.

−x−1<3-1

x>−3

Answer:

slope = 2 , y- intercept = -8

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 )

given

- 4x + 2y = - 16 ( add 4x to both sides )

2y = 4x - 16 ( divide both sides by 2 )

y = 2x - 8 ← in slope- intercept form

with slope m = 2 and y- intercept c = - 8

Answer:

the slope is 2 and y-intercept is (0,-8)

Step-by-step explanation:

Step 1: is to subtract 2y from both sides, -4x+2y-2y=-16-2y

Step 2: Simplify, -4= -16-2y

Step 3: Divide both sides by -4, -4x/4=-16/-4-2y/-4

4x/4=x=1

Answer: Commutative property of multiplication: Changing the order of factors does not change the product.

Step-by-step explanation: For example, 4 × 3 = 3 × 4 4 \times 3 = 3 \times 4 4×3=3×44, times, 3, equals, 3, times, 4.

A primary difference between how B cells recognize antigens and how T cells recognize antigens is that B cells directly bind to the antigen, whereas T cells recognize antigens only when they are presented on the surface of antigen-presenting cells (APCs) in the context of major histocompatibility complex (MHC) molecules.

Here's a step-by-step explanation of this difference:

1. B cells have B cell receptors (BCRs) on their surface that can directly bind to the specific antigen. This binding leads to B cell activation, proliferation, and differentiation into plasma cells that produce antibodies specific to that antigen.

2. T cells, on the other hand, have T cell receptors (TCRs) on their surface that do not directly recognize free antigens. Instead, they recognize small fragments of antigens (peptides) that are presented on the surface of APCs, such as dendritic cells, macrophages, and B cells.

3. The antigens are processed inside the APCs into smaller peptides, which then bind to MHC molecules. There are two types of MHC molecules:

MHC class I and MHC class II. MHC class I molecules present antigens to CD8+ T cells (also called cytotoxic T cells), while MHC class II molecules present antigens to CD4+ T cells (also called helper T cells).

4. The TCR of a T cell recognizes the specific peptide-MHC complex on the surface of an APC, leading to T cell activation, proliferation, and differentiation into effector T cells that help in eliminating the pathogen or infected cells.

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Answer:

1/2= 5/10

5/10 - 3/10 = 2/10 or 1/5

so planet X is 1/5 of a light-year closer

Step-by-step explanation:

Answer:

5/10

Step-by-step explanation:

Simplified

Answer:

Ella got the highest marks.

Step-by-step explanation:

Given that:

Camilla got 4/5 of the 200 marks.

Marks of Camilla = \(\frac{4}{5}*200\)

Marks of Camilla = 160 marks

Lincoln got 44% of the 200 marks.

Marks of Lincoln = \(\frac{44}{100}*200\)

Marks of Lincoln = 88 marks

Ella got 198 out of 200.

On comparing,

198 is the highest out of 200.

Hence,

Ella got the highest marks.

Mean = 3550

SD = 870

Find P(1810 <x<4420)

z = x -mean / sd

= (1810 - 3550 / 870) < z< (4420 - 3550 / 870)

= -2 <z< 1

Using the -z table -2 = 0.0228 and 1 = 0.8413

Subtract: 0.8413 - 0.0228 = 0.8185 x 100 = 81.85%

Rounding everything may change answer slightly so

The closest one is B 81.5%

Answer:

E

Step-by-step explanation:

a. To solve the ODE y" + 4y = 10cos(5t) using Laplace transforms, we follow these steps:

Applying the Laplace transform to the equation, we get:

\(s^2Y(s) - sy(0) - y'(0) + 4Y(s) = 10/(s^2 + 25)\)

Using the initial conditions y(0) = 0 and y'(0) = 0, we simplify the equation to:

\(s^2Y(s) + 4Y(s) = 10/(s^2 + 25)\)

Combining the terms and factoring out Y(s), we have:

\(Y(s) = 10/(s^2 + 25) / (s^2 + 4)\)

We can rewrite Y(s) as:

\(Y(s) = A/(s^2 + 25) + B/(s^2 + 4)\)

Multiplying through by the common denominator\((s^2 + 25)(s^2 + 4)\), we get:

\(10 = A(s^2 + 4) + B(s^2 + 25)\)

Equating coefficients of the like terms, we have:

\(0s^3: 0 = Bs^2: 0 = 4A + 25B\)

0s: 0 = 4B

constant: 10 = 4A

From these equations, we find that A = 10/4 = 5/2 and B = 0

Taking the inverse Laplace transform of Y(s), we obtain the solution in the time domain:

y(t) = (5/2)cos(5t)

Therefore, the solution to the given ODE with the initial conditions is y(t) = (5/2)cos(5t).

b. To solve the ODE y^(4) - y = 0 using Laplace transforms, we follow these steps:

Applying the Laplace transform to the equation, we get:

\(s^4Y(s) - s^3y(0) - s^2y'(0) - sy''(0) - y'''(0) - Y(s) = 0\)

Using the initial conditions y(0) = 0, y'(0) = 1, y''(0) = 0, and y'''(0) = 0, we simplify the equation to:

\(s^4Y(s) - s^2 = s^3\)

Combining like terms and rearranging the equation, we have:

\(s^4Y(s) - Y(s) = s^3 + s^2\)

Factoring out Y(s), we get:

\(Y(s) = (s^3 + s^2) / (s^4 - 1)\)

We can rewrite Y(s) as:

\(Y(s) = (s^3 + s^2) / [(s^2 + 1)(s^2 - 1)]\)

Using partial fraction decomposition, we have:

\(Y(s) = (s + 1) / (s^2 + 1) + (s - 1) / (s^2 - 1)\)

Taking the inverse Laplace transform of Y(s), we obtain the solution in

the time domain:

y(t) = cos(t) + sinh(t)

Therefore, the solution to the given ODE with the initial conditions is y(t) = cos(t) + sinh(t).

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By taking quotients between the prices and the numbers of boxes, we can see that the pack of 16 boxes is the better buy.

To identify which one is the better buy, we need to see which pack gives a smaller price per juice box.

To get that, we need to take the quotient between the price and the number of boxes for each case.

The pack of 14 boxes costs $11.34, then the price per box is:

P = $11.34/14  =$0.81

For the pack of 16 boxes the price is $12.64, in this case we will have:

P' = $12.64/16 = $0.79

We can see that the second option is cheaper, so that is the better buy.

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Answer:

C

Step-by-step explanation:

Split up the polygon into three parts. The first rectangle will be 264 and the two small squares are 16, but since there is two we multiply them by 2, making it 32.

Answer:

the answer would be C

Step-by-step explanation:

you can split it up into different parts