Solve the following differential equation by using integrating factors. y' = y + 5x2, y(0) = 30 = =

The numeric values for the given functions are given as follows:

a) f(-2) = 11.

b) h(4) = -4.

c) g(7) = 7.

d) j(3) = 27.

The numeric value of a function is found replacing each instance of x by the value that we want to find.

Hence, considering the functions given at each item, the numeric values for the functions are found as follows:

a) f(-2) = |-2 - 7| + 2 = 9 + 2 = 11.

b) h(4) = -2(4) + 4 = -8 + 4 = -4.

c) g(7) = 2(7) - 7 = 14 - 7 = 7.

d) j(3) = 3³ = 27.

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Step-by-step explanation:

Reflecting across the x axis will result in a sign change for. the y component, therefore (-7,-9) becomes (-7,9)

Reflecting across the y axis will result in a sign change for the x component, therefore (-7,-9) becomes (7,-9)

The relationship between the number x of days and the total cost represent as piecewise function.

f(x) = -x < 0

      = x if x ≥ 0

The bike store charges $20 for the first day and $15 for each additional day. The relationship between the number x of days and the total cost represent as:

f(x) = 20 , if 0 < x ≤ 1

      = 35,  if 1 < x ≤ 2

      = 50,  if 2 < x ≤ 3

      = 65,  if 3 < x ≤ 4

The absolute value function f(x) = |x| can be written as a piecewise function.

f(x) = -x < 0

      = x if x ≥ 0

Piecewise functions: A piecewise function is made up of two or more functions, each defined on a specific domain. Piecewise functions follow the following format:

f(x)    ⇒ -x,   x < 0

               ⇒  0,  x = 0

                ⇒ x,  x > 0

The piecewise function above is the absolute value function. As you can see, piecewise functions include:

A curly bracket to indicate that the function is comprised of more than one subfunction

The subfunctions that make up the piecewise function

The subdomains corresponding to each subfunction

The domains of the subfunctions cannot overlap, but one function can end where another starts. If different functions were part of the same domain, the piecewise function would not be a function anymore!

To graph a piecewise function, graph each subfunction at the indicated domain. Be wary of the inequality symbols (< , ≤ , > , ≥) and whether they include or exclude the end of the subdomain. If they include the domain, draw a point and fill it in. If they exclude the domain, draw a point but do not fill it in.

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Answer:

14 and 2 maybe?

Answer:

14, 2

Step-by-step explanation:

a + b = 16

a - b = 12

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

2a  = 16 + 12

2a = 28

a = 14

14 + b = 16

b = 2

This will be complicated work

12:6:3... Total is 21.

We will divide it by 21 to show the percentage of each chemical and times by 27 because 27 kg bag.

(12/21x27):(6/21x27):(3/21x27)

108/7:54/7:27/7

Rounded Decimals (To the hundredth): 15.43:7.71:3.86

108/7 or approx 15.43 kg of nitrogen, 54/7 or approx 7.71 kg of phosphorous, and 27/7 or approx 3.86 kg of potash.

Answer:

x=-1

Step-by-step explanation:

\( \frac{x ^{100} + 1 }{x + 1} \)

\(x + 1 = 0\)

\(x = - 1\)

Answer:

$1.50 per filled donut and $0.72 per regular donut

Step-by-step explanation:

We need to set up a system of equations to find the price of each type of donut:

Since Bill bought 4 regular donuts and 8 filled donuts for $14.88, we can use the equation 4R + 8F = 14.88

Since Mary Ann bought 7 regular donuts and 7 filled donuts for $15.54, we can use the equation 7R + 7F = 15.54

From first glance, it is clear that elimination will be the best method to solve:

\(4R+8F=14.88\\7R+7F=15.54\\\\7(4R+8F=14.88)\\-4(7R+7F=15.54)\\\\28R+56F=104.16\\-28R-28F=-62.16\\28F=42\\F=1.5\\\\4R+8(1.5)=14.88\\4R+12=14.88\\4R=2.88\\R=0.72\)

Step-by-step explanation:

IF  x-4   is a factor, then putting in x = + 4    will make the polynomial = 0

5 ( 4^3) - 20 (4^2) - 5(4)  + 20   =   0    Yes...it is a factor

\(x - 4 = 0 \\ x = 4 \\ \)

substitute value of x in the function to see if it equals to zero , if not it won't be a factor of the function

\(5 {x}^{3} - 20 {x}^{2} - 5x + 20 = 0 \\ 5(4) ^{3} - 20( {4})^{2} - 5(4) + 20 = 0 \\ 5(64) - 20(16) - 20 + 20 = 0 \\ 320 - 320 - 20 + 20 = 0 \\ 0 = 0\)

so (x-4) is a factor for the function

Answer:

-1.2

Step-by-step explanation:

8x2 - 20x + 8 = 0

16 - 20x + 8 = 0

24 - 20x = 0

-20x = 24

x = -1.2

Answer:

y= x2+x-3

Step-by-step explanation: i think this is the answer

The nurse will advise the patient to take 1 ml of medication with each dose.

The physician orders medication at 400 mg po twice daily. The pharmacy supplies medication with a dosage strength of 2 grams per 5 ml.

How many milliliters does the nurse advise the patient to take with each dose?

The nurse should advise the patient to take 1 ml of medication with each dose.

To find the number of milliliters, the following formula will be used.

Dose × Volume/Strength

Given, Dose = 400 mg

Strength = 2 grams per 5 ml

Volume = ?

To convert 400 mg to grams, divide by 1000.

400 mg = 400/1000 = 0.4 g

Now, put the values in the formula,

0.4 g × Volume / 2 g/ 5 ml= 5/2 × 0.4/1= 5/2 × 0.4= 1 ml

Hence, the nurse will advise the patient to take 1 ml of medication with each dose.

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Answer:

18/35= 18.35

= 1.43 - 18/35=?

Answer:

2

4

6

8

1.7412137e+12

Step-by-step explanation:

the first 4 are basic addition and the last one I put into calculator and it came up with that

Answer:

34-6=?

Step-by-step explanation:

34-6=?

Answer:

Ali is 14

Sally is 20

Step-by-step explanation:

let's call Sally S.

let's call Ali A.

using what's given, you can make this equation:

A + 6 = S

(because Ali is 6 years younger than Sally)

you can also make this equation:

A + S = 34

(because the sum of their ages is 34)

now, substitute S for A + 6.

A + A + 6 = 34

2A + 6 = 34

subtract 6 from both sides of the equation

2A + 6 - 6 = 34 - 6

2A = 34 - 6

2A = 28

divide both sides of the equation by 2

2A/2 = 28/2

A = 28/2

A = 14

almost done! now you just need to substitute A for 14 in the first equation.

A + 6 = s

14 + 6 = s

20 = s

Ali is 14

Sally is 20

The quadrilateral ABCD is a parallelogram because angle A and angle C are congruent.

The theorem that states if all sets of opposite angles are congruent, then the quadrilateral is a parallelogram must be applied in order to demonstrate that quadrilateral ABCD is a parallelogram based on the provided facts.

Let's write the quadrilateral ABCD's angles as follows:

Angle C (provided) = Angle A

(Opposite angles) Angle B = Angle D

We must demonstrate that both pairs of opposite sides are parallel in order to demonstrate that ABCD is a parallelogram.

We can infer from the facts provided that Angle A is congruent with Angle C.

We will now use the theorem that says the quadrilateral is a parallelogram if both pairs of opposite angle pairs are congruent.

Angles A and B are congruent with Angles C and D, respectively, hence we can infer that the quadrilateral ABCD is a parallelogram.

Since the opposite sides of a parallelogram are parallel, we have: AB || CD (opposite sides).

(Opposite sides) AD vs. BC

Therefore, we may deduce that quadrilateral ABCD is a parallelogram based on the available data and the theorem.

In conclusion, since Angle A and Angle C are congruent, we can use the theorem saying that if both pairs of opposite angles are congruent, then the quadrilateral is a parallelogram to show that ABCD is a parallelogram.

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Thus, Jakob's function C(n) = C(n-1) + 4 accurately represents the number of circles needed to make the nth figure in the given pattern, while Margaret's function C(n) = 4n - 3 does not .

Jakob's function states that the number of circles needed to make the nth figure is equal to the number of circles needed to make the (n-1)th figure plus 4. This implies that for each subsequent figure, 4 more circles are added to the previous figure.

As given C(1) = 1, then according to Jakob's function,

C(2) = C(1) + 4 = 1 + 4 = 5,

C(3) = C(2) + 4 = 5 + 4 = 9, and so on.

This matches the pattern where each figure requires 4 more circles than the previous figure. Therefore, Jakob's function represents the number of circles needed to make the nth figure in the pattern.

Thus, Jakob's function C(n) = C(n-1) + 4 accurately represents the number of circles needed to make the nth figure in the given pattern with each figure using 4 more circles than previous one

Margaret's function: C(n) = 4n - 3

Margaret's function states that the number of circles needed to make the nth figure is equal to 4 times n minus 3. This function represents a linear relationship where the number of circles increases with n. If we plug in n = 1, we get C(1) = 4(1) - 3 = 1, which matches the first figure in the pattern.

However, for n > 1, the function does not accurately represent the number of circles needed for the subsequent figures in the pattern. Therefore, Margaret's function does not fully represent the number of circles needed to make the nth figure in the pattern.

Margaret's function C(n) = 4n - 3 does not represents the number of circles needed to make the nth figure .

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Complete Question: Two students each write a function, C(n) , that they think can be used to find the number of circles needed to make the nth figure in the pattern shown. Use the drop-down menus to explain why each function does or does not represent the number of circles needed to make the nth figure in the pattern?(refer to the image attached)

orangle marbles = 1

white marbles = 6

yellow marbles = 7

Total marbles = 1 +6 + 7 = 14

Probability of not getting a yellow = orange+ white / total = 1 + 6 / 14 = 7/14 = 1/2

Probability of not getting a orange = white + yellow / total = 6 +7 /14 = 13/14

probability of not getting a yellow and then not getting a

orange = 1/2 * 13/14 = 13/28

Answer:

equal to

Step-by-step:

Again, the mean reflects the slanted the most.

To summarize, generally if the distribution of data is slanted to the left, the mean is less than the median, which is often less than the mode. If the distribution of data is slanted to the right, the mode is often less than the median, which is less than the mean.

Answer:

Equal

Step-by-step explanation:

The median is the midmoint of all points (as many values below as above this value). The mean is the (sum of values) / (count of values). Since every value has the exact same count, the mean and median will be the same.

The range of the values of the third side of the triangle is 10<x<66.

A triangle is a polygon with three sides. The sum of the two sides of the triangle should be always greater than the third side of the triangle.

For a triangle, the sum of the length of the two sides of a triangle should be equal to the third side of the triangle. Therefore, the value of x can be written as,

x < 28 + 38

x < 66

28 < x + 38

-10 < x

38 < x + 28

10 < x

Concluding all the inequalities, the value of x should be between 10 to 66, both not included.

Therefore, the range of the values of the third side of the triangle is 10<x<66.

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The inequality that describes how many movies Parv can buy is: n ≤ 10.025

Let's denote the number of movies Parv wants to buy as n. We are given that each movie costs $3.99. To determine the inequality that describes how many movies Parv can buy, we need to consider the amount of money he has remaining after purchasing the pack of games.

Parv starts with a $50 gift card and spends $9.99 on a pack of games. The remaining amount on the gift card is $50 - $9.99 = $40.01.

Now, let's consider the cost of n movies. Each movie costs $3.99, so the total cost of n movies would be n * $3.99.

Since Parv wants to buy the movies using the remaining amount on his gift card, we can set up the inequality:

n * $3.99 ≤ $40.01

This inequality states that the total cost of n movies, represented by n * $3.99, must be less than or equal to the remaining amount on the gift card, which is $40.01.

Simplifying the inequality further, we have:

3.99n ≤ 40.01

Now, if we want to solve for n, we can divide both sides of the inequality by 3.99:

n ≤ 40.01 / 3.99

Calculating this value, we have:

n ≤ 10.02506265664

Therefore, the inequality that describes how many movies Parv can buy is:

n ≤ 10.025

This means that Parv can buy a maximum of 10 movies, as he cannot purchase a fractional part of a movie.

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Answer: if (1/x) = (3/5) then

x = 5/3.

As far as equivalent ratios to 3:5 go, there are an infinite number

3:5 = 6:10 = 12:20 = 1.5:2.5

Step-by-step explanation:

^

The expressions correctly represents the slope formula for calculating the slope of the line passing through the points (3, 6) and (-7, -4) is  (y₂ - y₁) / (x₂ - x₁) and   (change in y) / (change in x)

The slope formula is used to determine the slope of a line given two points on the line.

The slope (m) is defined as the change in y-coordinates divided by the change in x-coordinates. To find the slope of the line passing through the points (3, 6) and (-7, -4), we can use the formula:

m = (y2 - y1) / (x2 - x1)

Substituting the given values, we have:

m = (-4 - 6) / (-7 - 3)

Simplifying this expression, we get:

m = -10 / -10

The negatives cancel out, resulting in:

m = 1

Therefore, the correct expression for the slope formula is:

m = 1

This indicates that the line has a slope of 1, which means it has a constant upward or positive inclination as we move from left to right.

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Complete question should be:

Which  expressions correctly represents the slope formula for calculating the slope of the line passing through the points (3, 6) and (-7, -4)?

Answer:

Step-by-step explanation:

Graph of the given piecewise function will show the three straight lines,

f(x) = 2  If 2 < x ≤ 4

        x + 3 If 4 < x < 8

        2x If x ≥ 8

1). f(x) = 2 will be a straight line parallel to x-axis for 2 < x ≤ 4

2). f(x) = x + 3 is a straight line with input output points in the interval 4 < x < 8

       x               4                  5          6         7              8      

     f(x)        Not defined      8          9         10    Not defined  

3). f(x) = 2x

      x            8         9          10         11

     f(x)         16        18         20       22

By using these points on a graphing calculator we can graph the piecewise function as attached.