Sabina used long division to divide 3x³ + x + 2 by a x+ 2. Her work is shown. which error or error did sabrina make?
I'm not sure if those are the real answers ​

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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110 kilograms is equal to 242.44 pounds.

To convert kilograms to pounds, you can use the conversion factor:

1 kilogram = 2.204 pounds.

Given that you want to convert 110 kilograms to pounds, you can multiply 110 by the conversion factor:

110 kilograms x 2.204 pounds/kilogram = 242.44 pounds

Therefore, 110 kilograms is equal to 242.44 pounds.

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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 inequality will be;

For Hotel A; 80x + 25 < 225

For Hotel B; 105x + 25 < 225

For Hotel C; 75x + 25 < 225

For Hotel D; 90x + 25 < 225

A relation by which we can compare two or more mathematical expression is called an inequality.

Given that;

The coach wants to keep the total cost for each player at $225 with an absolute deviation of at most $25.

Now,

Since, The coach wants to keep the total cost for each player at $225 with an absolute deviation of at most $25.

Hence, We get;

The inequality will be;

For Hotel A;

⇒ 80x + 25 < 225

For Hotel B;

⇒ 105x + 25 < 225

For Hotel C;

⇒ 75x + 25 < 225

For Hotel D;

⇒ 90x + 25 < 225

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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

Answer:

Downward

Step-by-step explanation:

A parabola is a curve that is shaped like a U. The direction in which a parabola opens depends on the sign of the coefficient of the x^2 term in the equation defining the parabola. If the coefficient is positive, the parabola opens upwards. If the coefficient is negative, the parabola opens downward.

In the equation y = -x + 2, the coefficient of the x^2 term is 0, so the direction of the parabola does not depend on it. However, the coefficient of the x term is -1, which is negative. This means that the parabola defined by this equation opens downward.

The type of taxation that this table best represent is B. Progressive

A progressive tax is one in which the tax rate rises (or progresses) as taxable income rises. It imposes a lower tax rate on low-income earners and a higher tax rate on higher-income earners. This is usually accomplished by establishing tax brackets that categorize taxpayers based on their income levels.

A progressive tax is one in which the tax rate rises in proportion to the taxable amount. The term progressive refers to the manner in which the tax rate rises from low to high, resulting in a taxpayer's average tax rate being less than the person's marginal tax rate.

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Answer:

I got c

Step-by-step explanation:

Took the test and that’s what it told me 4nem

The set of all x for which the f(x) graph crosses the x-axis is the solution of f(x) = 0. The set of all x for which the graph of f is strictly above the x-axis is the solution of f(x) > 0

Given data :

f(0) =

The set of all x for which the graph of f is strictly above the x-axis is the solution of f(x) > 0

f (x) = -3

x = − 3 is a vertical line that crosses the -axis at -3. y = 3 is a horizontal line that crosses the -axis at 3. y = − 3 is a horizontal line that crosses the -axis at -3.

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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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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 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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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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By solving 3 (8-x) -6x + 15 , x = -1

Find the attachment answer

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An inequality that uses Alicia's salary as the unit of measurement is x > $124.3.

Data for the stated question-

'x' is the Alicia's Paycheck

Half money is taken for dinner x/2

Total spending on dinner =  $42.15

Cost of home she bought home more than $20.00.

Thus, inequality to represent the situation becomes-

x/2 - $42.15  > $20.00

Add both side by 42.15.

x/2 > $62.15

Divide the number by 2.

x > $124.3

Therefore, an inequality that uses Alicia's salary as the unit of measurement is x > $124.3.

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The complete question is-

Alicia cashed her paycheck and used half her earnings to take three friends to dinner. She spent $42.15 on dinner and she brought home more than $20.00. Write an inequality to represent the situation, using x to represent the amount of Alicia's paycheck.

Statments Two more students prefer blue than purple and Twice as many students prefer green than purple are true.

What is frequency distribution table?

A frequency distribution table is a tool for structuring the provided data in a way that makes sense and facilitates comprehension. Two or three columns make up a frequency distribution table.

All of the results are presented in the first column as individual values or as class intervals.

The table's second column contains the results' totals, which also display the frequency as vertical lines. It's not required.

The frequency of each result is revealed in the third column.

From the given frequency distribution table we will first calculate the numeric value of the number of students with their favourite colour.

Number of students like red colour = 6

Number of students like yellow colour = 2

Number of students like blue colour = 5

Number of students like purple colour = 3

Number of students like green colour = 6

Now according to above data we find that number of students prefer red colour is equal to number of students prefer green colour.

Twice as many students prefer green than purple.

More students prefer blue than yellow.

Two more students prefer blue than purple.

Therefore, statments Two more students prefer blue than purple and Twice as many students prefer green than purple are true.

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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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The time needed for the investment to triple is approximately 32.59 years.

The compound interest formula can be expressed as;

A = P(1 + r/n)^(n*t)

Where A is accrued amount, P is principal, r is interest rate, t is time elapsed.

Given the data in the question;

Plug the given values into the above formula and solve for t.

A = P(1 + r/n)^(n*t)

t = In( A/P) / n[In( 1 + r/n ) ]

t = In( 7500 / 2500) / (2[In( 1 + 3.4%/2 ) ])

t = In( 7500/2500 ) / ( 2[In( 1 + 0.017 ) ]

t = 32.59 years

Therefore, the required time for the investment to $7,500 is is 32.59 years.

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a) The numeric value at t = 4 is of H(4) = 7.

b) The meaning of the numeric value H(2) = 10 is given as follows:

The height of the plant was 10 cm after 2 weeks.

The function in this problem has the definition presented as follows:

H(t) = 5 + 0.5t.

The variables of the function are given as follows:

The numeric value at t = 4 is calculated replacing the lone instance of t in the function by 4, as follows:

H(4) = 5 + 0.5(4) = 5 + 2 = 7 cm.

H(2) = 10 means that when t = 2, H(t) = 10, that is, after 2 weeks, the height is of 10 cm, and thus the last option is correct.

(considering the interpretation of each variable).

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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:

50 liters

Step-by-step explanation:

2.5 liters drained per minute x 2 minutes = 5 liters drained total

(2.5 x 2 = 5)

55 liters at the start - the 5 liters drained = 50 liters remaining

(55 - 5)

whole equation would be

55 - (2.5 x 2) = 50

Answer:

Step-by-step explanation:

y = 4×[tex]5^{0}[/tex] y=4
y=4×[tex]5^{2}[/tex] y=100
y=4×[tex]5^{4}[/tex] y=2500
y=4×[tex]5^{6}[/tex] y=62500
y=4×[tex]5^{7}[/tex] y=312500

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.

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!

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:

K = 17

Step-by-step explanation:

x = 8

Measures of Central Tendency

A central tendency in statistics is a typical or centralised value for a probability distribution. Measures of central tendency are commonly referred to as averages in everyday speech. In the late 1920s, the phrase "central tendency" first appeared. The arithmetic mean, the median, and the mode are the three most used measurements of A central tendency in statistics is a typical or centralised value for a probability distribution. Measures of central tendency are commonly referred to as averages in everyday speech. In the late 1920s, the phrase "central tendency" first appeared. The arithmetic mean, the median, and the mode are the three most used measurements of central tendency.

[tex]\text { Mean }=\frac{\text { sum of all the numbers }}{\text { how many numbers there are }}[/tex]

There are 6 numbers and their sum is 525

Therefore, their mean is

[tex]\text { Mean }=\frac{\text { sum of all the numbers }}{\text { how many numbers there are }}[/tex]

Mode is the number with the highest frequency i .e which number appears the most in the sequence

In this case, there is NO mode because each number there appears only once

Median is the middle number when you place the numbers in ascending order

79,85,86,90,92,93

The middle number is between 86 and 90 . So your middle number can be found by  [tex]\frac{86+90}{2}=88[/tex]

So your median is 88

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