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Answer:

Missing term [tex]\dfrac{1}{4}[/tex]

Factored term on RHS:   [tex]$(x+\dfrac{1}{2})^{2}$[/tex]

Step-by-step explanation:

The value of y for the linear differential equation is:

y= [5(x³+6x²+12x)/3(16+32x+24x²+8x³+4x⁴)]  + c₁ /(16+32x+24x²+8x³+x⁴)

You should know that a differential equation is in which we find the value of y with respect to x

The given parameter is

(x-2)² dy/dx = 5-8y-4xy

Differentiate y with respect to x to have

y= [5(x³+6x²+12x)]/[3(16+32x+24x²+8x³+x⁴)] + c₁/(16+32x+24x²+8x³+x⁴)]

Recall that the differential equation is (x-2)² dy/dx = 5-8y-4xy

Solving the Ordinary Differential Equation we have

y= y= [5(x³+6x²+12x)]/[3(16+32x+24x²+8x³+x⁴)] + c₁/(16+32x+24x²+8x³+x⁴)]

In conclusion, the value of y is:  y= [5(x³+6x²+12x)]/[3(16+32x+24x²+8x³+x⁴)] + c₁/(16+32x+24x²+8x³+x⁴)]

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The polynomial function, y= (x+4)(x-2)²(x+7) has three different roots

From the question, we have the following parameters that can be used in our computation:

y = (x+4)(x-2)^2(x+7)

Rewrite the equation properly

So, we have the following representation

y= (x+4)(x-2)²(x+7)

Set the factor to 0

So, we have

x + 4 = 0, x - 2 = 0 and x + 7 = 0

When these equations are solved, we have

x = -4 , x = 2 and x = -7

See that the counts of the values of x is 3

Hence, it has three different roots

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36 houses are left to be sold.

We need to convert 1/4 and 2/5 into decimals. We do this by dividing the numerator by the denominator:

1 ÷ 4 = 0.25

2 ÷ 5 = 0.4

Now, we can set up this equation to find out how many were sold in the first month:

0.25 x 80 = 20

Now, 20 isn't the answer, it is 60 houses left, because 80 - 20 = 60.

Let's do the next one:

0.4 x 60 = 24

60 - 24 = 36

36 houses are left to be sold.

I hope my answer helped you! If you need more information or help, comment down below and I will be sure to respond if I am online. Have a wonderful rest of your day!

The confidence interval, expressed as a trilinear inequality, is 71.6%

What does a confidence interval mean?

The range of values we see in our sample and expect to find the value that most accurately represents the population are referred to as a confidence interval.

The lower bound is 71.6% - 8.2% = 63.4% and the upper bound is 71.6% + 8.2% = 79.8%.

Thus the confidence interval, expressed as a trilinear inequality, is 63.4% < p < 79.8%, where p= 71.6%.

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The simplification of complex fraction -⅔/⅚ is - 4/5

A complex fraction is a rational expression that has a fraction in its numerator, denominator or both. In other words, there is at least one small fraction within the overall fraction.

In fraction when the numerator is bigger than the denominator , then it is called improper fraction, when a fraction consist of whole number and proper fraction is called mixed fraction

-2/3 ÷ 5/6

= -2/3×6/5

= -4/5

Therefore -⅔/⅚ can be simplified to -⅘

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Answer:

Your answer is 7 + a - 5b.

Step-by-step explanation:

All you have to do is subtract the numbers.

Hope this helped! :D

Answer: 2^2*3^1*5^2

Step-by-step explanation:

1st step: find the factors

2 x 2 x 3 x 5 x 5

2nd step: simplify

2^2*3^1*5^2

The graph for  |x| + 3 > 3 is attached below.

It is unknown if a mathematical sentence is true or false since it uses variables, which is known as a "open sentence" in mathematics. On the other hand, a closed sentence is a mathematical statement that is known to be either true or untrue.

Given:

|x| + 3 > 3

|x| > 3- 3

|x| > 0

Now, The open sentence is an absolute inequality, so we start by analyzing the inequality sign > 0 means that, the x-values of the inequality is not less than 0.

So, the shaded area of the graph are: x >0 then right side of the graph is shaded.

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Answer:

n < –1

Step-by-step explanation:

8n + 4n < –4 + 8n

12n < –4 + 8n

12n – 8n < –4

4n < –4

divide both sides by (4) to obtain

n < –1

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The ratio y/x is not constant (k) for all the data points, then y does not vary directly with x.

What is the constant of variation?

The constant of variation is the number that relates two variables that are directly proportional or inversely proportional to one another.

We have,

         x         y

         2         10

         4         24

         6         36

To determine whether y varies directly with x, you need to see if the ratio of y to x is constant for all the data points.

If y varies directly with x, then the ratio y/x will be constant for all the data points. In this case, you can write an equation for the direct variation in the form y = kx, where k is the constant of variation, which is equal to the ratio y/x.

If the ratio y/x is not constant for all the data points, then y does not vary directly with x.

so, let's see the k constant of variation,

k =  y/x

k = 2/10 =1/5

k = 4/24 = 1/6

k = 6/36 = 1/6

so,  k = 1/5, k=1/6, k=1/6.

Hence, the ratio y/x is not constant (k) for all the data points, then y does not vary directly with x.

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Answer: 0.25 or 1/4

Hope this helps :)

Step-by-step explanation:

Answer:

0.25 or 1/4

Step-by-step explanation:

1/2 as a decimal is 0.50 and that squared is 0.25, which as a fraction is 1/4.

Answer: The function F(x) = 32 + 1.87x converts Celsius temperatures to Fahrenheit temperatures. To confirm this, you can plug in a few different values for x (the Celsius temperature) and see if the corresponding value of F(x) (the Fahrenheit temperature) is correct.

For example, if x = 0, the function gives us F(0) = 32 + 1.87 * 0 = 32, which is the correct conversion from Celsius to Fahrenheit for 0 degrees Celsius.

If you want to find a formula for the function C that converts Fahrenheit temperatures to Celsius temperatures, you can start by rearranging the formula for F(x). The Fahrenheit temperature is equal to the Celsius temperature plus 32, multiplied by 1.8.

If we solve for the Celsius temperature, we get:

x = (F - 32) / 1.8

This is the formula for the function C that converts Fahrenheit temperatures to Celsius temperatures. To use this function, you would plug the Fahrenheit temperature into the function as the input, and it will give you the corresponding Celsius temperature as the output.

For example, if you want to convert 100 degrees Fahrenheit to Celsius, you would plug 100 into the function as the input:

C(100) = (100 - 32) / 1.8 = 37.78 degrees Celsius.

Answer:

156

Step-by-step explanation:

4x + 3 = 3(2x - 5)

4x + 3 = 6x - 15

3 = 2x - 15

2x = 18

x = 9

4(9) + 3

= 36 + 3

= 39

39 * 4 = 156

Hope it helps!

Answer: 156 inches

Step-by-step explanation:

So we know that all of the sides are equal to each other.

Now we need to know what x equals.

4x + 3 = 3(2x -5)

4x + 3 = 6x - 15

3 = 2x -15

18 = 2x

9 = x

Plug 9 into one of the equations.

4(9) + 3

36 + 3 = 39

39 * 4 = 156

Perimeter = 156 inches

Hope this helps!!! :)

Answer:

B (192 ft^2)

Step-by-step explanation:

The area of the blue shaded region: total area - small rectangle

This is:

(11x20) - (4x7)

= 220 - 28

= 192 ft^2

Hope this helps,

:]

Answer:

A.

Explanation:

20*11=220

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Answer: x+7=1+2x

Step-by-step explanation:

If x represents the number,The sum of a number and 7 is x + 7One more than twice the number is 1 + 2xThe IS in the middle of the sentence means =So, x + 7 = 1 + 2x  Solve this equation,If you need further assistance message me.

The velocity of a shell shot into the air with a velocity of 58 m/s, its height in meters after t seconds is given by y=58t - 20t² is 38 m / s.

When anything is moving, its velocity tells us how quickly that something's location is changing from a certain vantage point and as measured by a particular unit of time.

If a point moves along a path and covers a certain distance in a predetermined amount of time, its average speed over that period of time is equal to the distance covered divided by the travel time. A train traveling 100 kilometers in two hours, for instance, is doing it at an average speed of 50 km/h.

Given:

Height equation, y = 58t - 20t²,

The time, t = 0.5 seconds,

The initial velocity, u = 58 m/s,

Calculate the height at 0.5 sec,

y = 58 × 0.5 - 20 × 0.5²

y = 24 m

Calculate the acceleration at 0.5 sec by using the motion equation given below:

[tex]s = ut+1/2at^2[/tex]

24 = 58 × 0.5 + 1 / 2 × a × 0.5²

-5 = 0.125 × a

a = - 40 m / s²

Calculate the velocity by using the formula given below,

[tex]v = u + at[/tex]

v = 58 + (-40) × 0.5

v = 38 m /s

Therefore, the velocity of a shell shot into the air with a velocity of 58 m/s, its height in meters after t seconds is given by y = 58t - 20t² is 38 m / s.

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The value of y is 21, when x = 6.

What are Inverse variations?

The link between two variables known as "inverse variation" occurs when the value of one variable rises while the value of the other variable falls.

Here, we have

Inverse variations look like this: y = k/x

We need to make our own inverse variation given y = 18  and x = 7. We can plug this into the standard inverse variation with variables.

y = k/x

18 = k/7

k = 126

We've determined that k =126. Now we have what it takes to create an inverse variation. This is our final equation:

y = 126/x

We still need to find what y equals when x is 6. Let's plug in 6 for x

y = 126/6

y = 21

Hence, the value of y is 21, when x = 6.

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The amount of money Dana Jones have after 7 years with an investment of $ 1100 at 5 % interest compounded continuously is $ 1560.97

What is Compound Interest?

Compound interest is interest based on the initial principle plus all prior periods' accumulated interest. The power of compound interest is the ability to generate "interest on interest." Interest can be added at any time, from continuously to daily to annually.

The formula for calculating Compound Interest is

A = P ( 1 + r/n )ⁿᵇ

where A = Final Amount

P = Principal

r = rate of interest

n = number of times interest is applied

b = number of time periods elapsed

When compounded continuously , the Compound Interest Amount is calculated by the formula ,

A = Pe^rt

Given data ,

Let the investment be P

The value of P = $ 1100

The rate of interest r = 5 %

The number of years t = 7 years

The Compound Interest Amount when compounded continuously is calculated by the formula ,

A = Pe^rt

Substituting the values in the equation , we get

A = 1100 x e ^ 0.05 x 7

A = 1100 x e ^ 0.35

A = 1100 x 2.718 ^ 0.35

A = 1100 x 1.419067

A = $ 1560.97

Therefore , the value of the amount is A = $ 1560.97

Hence ,

The amount of money Dana Jones have after 7 years with an investment of $ 1100 at 5 % interest compounded continuously is $ 1560.97

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Answer:

C.

19.5m2+11.7m

Step-by-step explanation:

hope this helps

Answer:

C.

19.5m2+11.7m

Step-by-step explanation:

what i got on the test

If she starts with £400 in her account, her balance for the next three years IS; $608.35

The general formula for exponential equation is;

y = a(b)ˣ

where;

a represents an initial value or amount

b is the constant multiplier, is a growth factor or factor of decay.

We are given;

Initial value; a = £400

constant multiplier; b = an increase of 15% yearly = 1.15

Thus, her balance for the next three years is;

y(3) = 400(1.15)³

y(3) = $608.35

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Answer:

it was decreased by $28

Step-by-step explanation:

$80 – x = $52

–x = $52 – $80

–x = $28

x = $28

i hope this answer helped

The diagonal can be written as -

d = √{(L)² + (B)² + (H)²}

Given is a graph as shown in the figure.

Since the dimensions of a right rectangular prism are not given, assume the length, width and height to be [L], [W] and [H]. Then the diagonal can be written as -

d = √{(L)² + (B)² + (H)²}

Therefore, the diagonal can be written as -

d = √{(L)² + (B)² + (H)²}

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Yes, the equation defines the value of y in terms of x which is ±10x.

A mathematical statement that has an "equal to" symbol between two expressions with equal values is called an equation. Equations come in a variety of forms, including linear, quadratic, cubic, and others.

Given, the equation defines y as a function of x.

100x² = y²

Hence,

Y² = (10x)²

Taking square root on both sides.

y = ±10x

Since the value of the y is in the term of x. Therefore, The value of y is defined in terms of x, which is 10x, in the equation.

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Answer:

Step-by-step explanation:

160/3

The equation of the line that is parallel to the line x + y + 2 = 0 and passing through (2, -2) will be x + y = 0.

Let the equation of the line be ax + by + c = 0. Then the equation of the parallel line that is parallel to the line ax + by + c = 0 is given as,

ax + by + d = 0

The equation of the line is given below.

y = - x - 2

x + y + 2 = 0

Then the equation of the line that is parallel to x + y + 2 = 0 is given as,

x + y + d = 0

The line is passing through (2, -2), then we have

2 + (-2) + d = 0

d = 0

The equation of the line that is parallel to the line x + y + 2 = 0 and passing through (2, -2) will be x + y = 0.

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Answer:

1 gallon of gas is $2.95

9.5 gallons of gas is $28.025

Step-by-step explanation:

[tex]\frac{12.2}{35.99} =\frac{1}{y}[/tex]

Cross Multiply.

12.2 · y = 1 · 35.99

12.2y = 35.99

12.2y ÷ 12.2 = 35.99 ÷ 12.2

y = 2.95

1 gallon of gas is $2.95.

[tex]\frac{1}{2.95} =\frac{9.5}{y}[/tex]

1 · y = 2.95 · 9.5

y = 28.025

9.5 gallons of gas is $28.025.

140 is the same as multiplying by 319 as an equation can be written as 140 = a x 319.

An equation is a mathematical expression that contains an equal symbol. Equations often contain algebra. Algebra is used in mathematics when you do not know the exact number in a calculation.

Hence, the sentence as an equation for 140 is the same as multiplying by 319 is, 140 = a x 319.

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To express the given numbers in equation form it can be written as =

140 is the same as multiplying by 319 as an equation can be written as 140 = a x 319.

What is an equation?

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