PLEASE I will be your best friend lol just please help me !!! 10 points

factor the polynomial: -x^3-2x^2-3x

The total differential of the function \(\(Z = (2x_1 + 3)(x_2 + 9)\)\) is given by:

\(\[\mathrm{d}Z = \frac{\partial Z}{\partial x_1}\mathrm{d}x_1 + \frac{\partial Z}{\partial x_2}\mathrm{d}x_2\]\)

To calculate the total differential, we need to find the partial derivatives of Z with respect to \(\(x_1\)\) and \(\(x_2\)\). Taking the partial derivative of Z with respect to \(\(x_1\)\) while treating \(\(x_2\)\) as a constant, we get:

\(\[\frac{\partial Z}{\partial x_1} = 2(x_2 + 9)\]\)

Next, taking the partial derivative of Z with respect to \(\(x_2\)\) while treating \(\(x_1\)\) as a constant, we have:

\(\[\frac{\partial Z}{\partial x_2} = 2x_1 + 3\]\)

Substituting these partial derivatives into the total differential equation, we get:

\(\[\mathrm{d}Z = (2(x_2 + 9))\mathrm{d}x_1 + (2x_1 + 3)\mathrm{d}x_2\]\)

Therefore, the total differential of the function Z is:

\(\[\mathrm{d}Z = (2(x_2 + 9))\mathrm{d}x_1 + (2x_1 + 3)\mathrm{d}x_2\]\)

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Answer:

4x+8y=16

8y=4x+16

4/8. 16/8

y=1/2x+2

The population proportion who participated in voting (63%) is higher than the sample proportion from this survey (58.91%).

To determine whether the population proportion who participated in voting or the sample proportion from the survey is higher, we need to compare the percentages.

The population proportion who participated in voting is given as 63% of all registered voters.

This means that out of every 100 registered voters, 63 participated in voting.

In the survey of retired voters, 162 out of 275 participants voted. To calculate the sample proportion, we divide the number of retired voters who participated (162) by the total number of retired voters in the sample (275) and multiply by 100 to get a percentage.

Sample proportion = (162 / 275) \(\times\) 100 ≈ 58.91%, .

Comparing the population proportion (63%) with the sample proportion (58.91%), we can see that the population proportion who participated in voting (63%) is higher than the sample proportion from this survey (58.91%).

Therefore, based on the given data, the population proportion who participated in voting is higher than the sample proportion from this survey.

It's important to note that the sample proportion is an estimate based on the surveyed retired voters and may not perfectly represent the entire population of registered voters.

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Answers:

Length = 270 feet

Width = 45 feet

========================================================

Work Shown:

x = width

6x = length, since it is 6 times the width

P = perimeter of rectangle

P = 2*(Length + Width)

P = 2*(6x + x)

P = 2*(7x)

P = 14x

Plug in the given perimeter P = 630 and solve for x.

P = 14x

14x = P

14x = 630

x = 630/14

x = 45

The width is 45 feet.

The length must be 6x = 6*45 = 270 feet.

The required length and width of the lawn is given as Length = 270 feet and Width = 45 feet.

Given that,
A landscaper buried a water line around a rectangular lawn to serve as a supply line for a sprinkler system. The length of the lawn is 6 times its width. If 630 feet of pipe was used to do the job, what is the length and the width of the lawn is to be determined.

Perimeter is the measure of the figure on its circumference.

Here,
let the length be l and the width be w,
According to the question,
l = 6w
and
Perimeter of the lawn = 630
2 [l + w] = 630
2 [6w + w] = 630
14w = 630
w = 45
Now,
l = 45[6] = 270

Thus, the required length and width of the lawn is given as Length = 270 feet and Width = 45 feet.

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The true statement is that D. On average, Rosalie scored higher on her maths test that Marvin.

Mean = (68+73+76+76+83+83+86)/7 = 77.14%

Therefore, this claim is untrue.

Rosaline's test results fall within a range of scores that is 11.

Q3 - Q1 = 16% is the interquartile range (IQR).

Therefore, this claim is untrue.

C) Marvin and Rosalie both had a wider range of test results.

The gap between the greatest and lowest scores is known as the range.

Range = 86 - 68 = 18% for Marvin.

Range = 97 - 70 = 27% for Rosalie

Therefore, this claim is untrue.

Rosalie performed better than Marvin on math exams on average.

Rosalie's test results' average were calculated as follows: Mean = (70+84+86+89+93+95+97)/7 = 87.14%

So, this assertion is accurate.

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Answer:

C.) AFD measures 30°

Step-by-step explanation:

it is 150 degrees

Answer:

the answer is C

Step-by-step explanation:

A)  angle EFC is 80 degrees so a is a true statement

B) angle BFC is 60 degrees and angle DFE is 30 degrees 60+30=90 so that's a true statement

D) angle AFB is 40 degrees and angle CFD is 50 degrees  40+50=90 so that a true statement

that leaves C and angle AFD is more than 30 degrees its 150 degrees

Answer:

641654654

Step-by-step explanation:

Answer:

1) r=9 v=972

2) r=6 v=288

3) r=12 v=2,304

Step-by-step explanation:

Sample Answer on edmentum

After answering the given query, we can state that  the solutions to the simultaneous equations are (x, y) ≈ (3.1, 10.2) and (x, y) ≈ (-1.9, 0.2).

In mathematics, a linear equation has become one that takes the form y=mx+b. The inclination is B, and the y-intercept is m. Since y and x are variables, the preceding clause is frequently referred by the term a "linear equation involving two variables."

Bivariate linear equations are linear equations with two variables. Linear equations can be found in many places, including 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. When the formula has the structure y=mx+b, where m denotes the slope and b the y-intercept, it is often referred to because of being quadratic.A mathematical equation is said to be linear if its solution has the form y=mx+b, where m stands for the slope and b for the y-intercept.

To show that 3y² - 10y - 24y¯47 = O, we need to find constants C and k such that |3y² - 10y - 24y¯47| ≤ C|y| for all y > k.

3y² - 10y - 24y¯47 ≤ 3y² + 10|y| + 24

3y² + 10|y| + 24 ≥ 3y² - 10y - 24y¯47 for y ≥ 5

C = 6:

|3y² - 10y - 24y¯47| ≤ 6|y| for y ≥ 5

3y² - 10y - 24y¯47 = O.

b) Using the result from part a), we can rewrite the simultaneous equations as:

3y² - 10y - 24y¯47 = O

y - 2x = 4

y = 2x + 4

3(2x + 4)² - 10(2x + 4) - 24y¯47 = O

12x² - 8x - 79 = O

x = (8 ± √(8² + 41279))/24

x ≈ 3.1 or x ≈ -1.9

y ≈ 10.2 or y ≈ 0.2

Therefore, the solutions to the simultaneous equations are (x, y) ≈ (3.1, 10.2) and (x, y) ≈ (-1.9, 0.2).

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The answers for the given differentiable functions are:

- r'(9) = 102

- v'(8) = 5

- h'(5) = 42

- b'(10) = 48.

To answer the questions, we need to differentiate the given functions based on the values provided in the table. Let's go through each question one by one:

1. Find r'(9) if r(x) = c(x) * a(x):

To find r'(9), we need to differentiate the function r(x) = c(x) * a(x) and evaluate it at x = 9.

From the table, we can see that c(9) = 9 and a(9) = 8.

Differentiating c(x) and a(x), we find:

c'(x) = 6 and a'(x) = 6.

Now, we can differentiate r(x) using the product rule:

r'(x) = c'(x) * a(x) + c(x) * a'(x).

Plugging in the values:

r'(9) = c'(9) * a(9) + c(9) * a'(9)

      = 6 * 8 + 9 * 6

      = 48 + 54

      = 102.

Therefore, r'(9) = 102.

2. Find v'(8) if v(x) = c(x):

To find v'(8), we need to differentiate the function v(x) = c(x) and evaluate it at x = 8.

From the table, we can see that c(8) = 7.

Differentiating c(x), we find:

c'(x) = 5.

Now, we can directly evaluate v'(8):

v'(8) = c'(8)

      = 5.

Therefore, v'(8) = 5.

3. Find h'(5) if h(x) = c(a(x)):

To find h'(5), we need to differentiate the function h(x) = c(a(x)) and evaluate it at x = 5.

From the table, we can see that a(5) = 9 and c(9) = 8.

Differentiating a(x) and c(x), we find:

a'(x) = 7 and c'(x) = 6.

Now, we can differentiate h(x) using the chain rule:

h'(x) = c'(a(x)) * a'(x).

Plugging in the values:

h'(5) = c'(a(5)) * a'(5)

      = c'(9) * 7

      = 6 * 7

      = 42.

Therefore, h'(5) = 42.

4. Find b'(10) if b(x) = c(c(x)):

To find b'(10), we need to differentiate the function b(x) = c(c(x)) and evaluate it at x = 10.

From the table, we can see that c(10) = 9.

Differentiating c(x), we find:

c'(x) = 8.

Now, we can differentiate b(x) using the chain rule:

b'(x) = c'(c(x)) * c'(x).

Plugging in the values:

b'(10) = c'(c(10)) * c'(10)

       = c'(9) * 8

       = 6 * 8

       = 48.

Therefore, b'(10) = 48.

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Answer:

x = 3/2 ( Answer in fraction )

x = 1.5 ( Answer in decimal )

Answer:

Step-by-step explanation:

Answer: x = 40

Step-by-step explanation: 72/43.2 =x/27

1,944 =43.2 (round off)

x = 40

(i think!)

Answer:

\( \boxed{ \bold{ \huge{ \boxed{ \sf{ \sqrt{218} \: \: units}}}}}\)

Step-by-step explanation:

Let the points be A and B

Let A ( -4 , 6 ) be ( x₁ , y₁ ) and B ( 3 , -7 ) be ( x₂ , y₂ )

Finding the distance between these two points

\( \boxed{ \sf{distance = \sqrt{ {(x2 - x1)}^{2} + {(y2 - y1)}^{2} } }}\)

\( \dashrightarrow{ \sf{ \sqrt{ {(3 - ( - 4))}^{2} + { (- 7 - 6)}^{2} } }}\)

\( \dashrightarrow{ \sf{ \sqrt{ {(3 + 4)}^{2} + {( - 7 - 6)}^{2} } }}\)

\( \dashrightarrow{ \sf{ \sqrt{ {7}^{2} + {13}^{2} } }}\)

\( \dashrightarrow{ \sf{ \sqrt{49 + 169} }}\)

\( \dashrightarrow{ \sf{ \sqrt{218}}} \) units

Hope I helped!

Best regards! :D

Answer:

--------------------------

Hope it helps...

Answer:

(A) Over the interval [-2.5, 0.5], the local maximum is 2.

Step-by-step explanation:

"Over the interval [-2.5, 0.5], the local maximum is 2."

Correct. The local maximum is the maximum, or highest point, of the graph in a certain area of interval. In [-2.5, 0.5], the highest point is at the y-value of 2.

"As the x-values go to positive infinity, the function's values go to negative infinity."

Wrong. As the x values go to positive infinity (meaning they go to the right, or positive side of the graph), the function goes up, meaning the function's values go to positive infinity.

"The function is decreasing over the interval (-1, 0.75)."

Wrong. Only from [-1, 0] is where that area of the graph decreases. The other half of it, (0, 0.75), is where the graph increases.

"The function is negative for the interval [-2, 0]."

Wrong. Only from [-1, 0] is the function negative. In the interval [-2, -1], the function is positive.

Hope that helps (●'◡'●)

Answer:

\(8.11\)

Step-by-step explanation:

Rounded to nearest hundredth.

After Round to the nearest hundredth value of number is,

⇒ 8.11

We have to given that;

A number is,

⇒ 8.113

And, We an Round to the nearest hundredth.

Since, Rounding numbers refers to changing a number's digits such that it approximates a value.

Here, In number 8.113,

Digit in thousandth place is 3 which is less thn 5.

Hence, After Round to the nearest hundredth value of number is,

⇒ 8.11

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Answer: 1840 pounds

Step-by-step explanation:4x4=16

460 x 4 = 1840

The solution of the Cauchy problem for the given partial differential equation 2xyux + (x² + y²) uy = 0 with the initial condition u = exp(x/(x-y)) on the curve x + y = C, where C is a constant, can be found by solving the equation using the method of characteristics.

To solve the given partial differential equation, we use the method of characteristics. Let's define a parameter s along the characteristic curves. We have the following system of ordinary differential equations:

dx/ds = 2xy,

dy/ds = x² + y²,

du/ds = 0.

From the first equation, we can solve for x: x = x0exp(s²), where x0 is a constant determined by the initial condition. From the second equation, we can solve for y: y = y0exp(s²) + 1/(2s), where y0 is a constant determined by the initial condition.

Differentiating x with respect to s and substituting it into the third equation, we obtain du/ds = 0, which implies that u is constant along the characteristic curves. Therefore, the initial condition u = exp(x/(x-y)) determines the value of u on the characteristic curves.

Now, we can express the solution in terms of x, y, and the constant C as follows:

u = exp(x/(x-y)) = exp((x0exp(s²))/(x0exp(s²) - y0exp(s²) - 1/(2s))) = exp((x0)/(x0 - y0 - 1/(2s))),

where x0 and y0 are determined by the initial condition and s is related to the characteristic curves. The curve x + y = C represents a family of characteristic curves, so C represents a constant.

In conclusion, the solution of the Cauchy problem for the given partial differential equation is u = exp((x0)/(x0 - y0 - 1/(2s))), where x0 and y0 are determined by the initial condition, and the curve x + y = C represents the family of characteristic curves.

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Answer:

a = b + 6

b = 8

Step-by-step explanation:

a = b + 6

b = 8

Answer:

There is actually no solution.

The range of sines are -1 ≤ y ≤ 1. And -29.3 does not fall into the range, making this solution not logically possible to come to.

the [OH⁻] in the solution is approximately 6.281 × \(10^{(-10)}\) M.

To determine the [OH⁻] in a solution with a pH of 4.798, we can use the relationship between pH, [H⁺], and [OH⁻].

pH + pOH = 14

Since we have the pH value, we can calculate the pOH as follows:

pOH = 14 - pH

pOH = 14 - 4.798

pOH = 9.202

Now, we can convert pOH to [OH⁻]:

[OH⁻] = 10^(-pOH)

[OH⁻] = 10^(-9.202)

Using a calculator, we find:

[OH⁻] ≈ 6.281 × 10^(-10) M

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Answer:

$2/ hat

Step-by-step explanation:

Find the unit rate:

$ to hats

8 to 4

Divide by four to get the unit rate; over 1

2 to 1

So, $2 per hat

Hope this helps!

The equation relating A to B is A = 9 + B, and the graph is a line with a slope of 1 passing through the point (0, 9).

To write an equation relating A to B, we need to consider that Karen earns 9 dollars per hour working part-time at the bookstore.

Additionally, she earns one additional dollar for each book she sells.

Therefore, the equation relating A (the amount Karen earns in dollars) to B (the number of books she sells) can be expressed as:

This equation states that Karen's earnings in dollars (A) are equal to the base hourly wage of 9 dollars plus the additional earnings she receives for each book sold (B).

To graph this equation, we can plot the values on a coordinate plane. We'll assume B represents the horizontal axis (x-axis), and A represents the vertical axis (y-axis).

On the graph, the line starts at the point (0, 9) and has a slope of 1, indicating that for each additional book Karen sells, her earnings increase by 1 dollar.

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Answer:

Step-by-step explanation:

Given:

N₀ = 298 pages

N = 20 pages

You can apply the formula:

Number of days

D = [N₀ / N] + 1 = [298 / 20 ] + 1 =

= [14.9] + 1 = 14 + 1 = 15 day,

where the square brackets are the integer part of the number

If a book has 298 pages, and I read 20 pages a day, then it will take 15 days to read the entire book.

Total pages in the book= 298

Total pages that I daily read= 20

Then it will take 15 days to read the entire book.

The formula for this problem:

The solution to this type of problem can be figured out with the help of unitary method.

20 pages of a book can be read in = 1 day

1 page of a book can be read in = 1/20 days

298 pages of a book can be read in = 1/20×298 days = 14.9 days

But days cannot be 14.9, so it will be 15 days which is the nearest value of 14.9.

15 days it will take to read the entire book.

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Answer:

4th option

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 m = \(\frac{1}{2}\) , then

y = \(\frac{1}{2}\) x + c ← is the partial equation

to find c substitute (- 3, 2 ) into the partial equation

2 = - \(\frac{3}{2}\) + c ⇒ 2 + \(\frac{3}{2}\) = \(\frac{7}{2}\) = 3.5

y = \(\frac{1}{2}\) x + 3.5 ← equation of line

Answer:

39 SIR

Step-by-step explanation:

Work Shown:

Use the circumference to determine the radius.

C = 2pi*r

12pi = 2pi*r

12 = 2r

r = 12/2

r = 6

Then find the area.

A = pi*r^2

A = pi*6^2

A = 36pi

The units for the area will be "square feet" which can be abbreviated to "sq ft",  ft^2 or \(\text{ft}^2\)

The probability that a randomly selected point within the circle falls in the red shaded area is 15.9%

The radius is given s:

r = 4 cm

So, the area of the triangle is

A1 = 0.5r^2

Similarly, the area of the circle is

A2 = πr^2

The probability that a randomly selected point within the circle falls in the red shaded area is

P = A1/A2

This gives

P = 0.5r^2/πr^2

Evaluate

P = 15.9%

Hence, the probability that a randomly selected point within the circle falls in the red shaded area is 15.9%

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The width of rectangle is 15 feet and the length of rectangle is 23 feet.

According to the statement

Width of rectangle = x

Length of rectangle = x+10

Area of rectangle = 345 sq-feet.

we know that the area of rectangle is

Area of rectangle = L*W

Substitute the values in it then

345 = (x) (x+8)

345= (x)^2 + 8x

(x)^2 + 8x - 345 = 0

By factorisation

(x-15) (x+23) = 0

So, width of rectangle is 15 feet and the length of rectangle is 23 feet.

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