choose the letter of the equation for the graph.

The solution to the given differential equation is y = e⁽ˣ³⁾⁽²⁸ˣ ⁺ ᶜ⁾, where C is a constant.

To solve the first-order linear differential equation of the form y' + p(x)y = q(x), where p(x) and q(x) are functions of x:

Find the integrating factor (IF) = e⁽∫ᵖ⁽ˣ⁾ᵈˣ⁾

Multiply both sides of the equation by the IF.

Apply the product rule to the left side and simplify the right side.

Integrate both sides with respect to x.

Solve for y.

Using this method, for the given equation:

y' - 3x²y = 28e⁽ˣ³⁾

Find the integrating factor (IF):

IF = e⁽∫ᵖ⁽ˣ⁾ᵈˣ⁾ = e⁽⁻³/¹ * ∫ˣ²ᵈˣ⁾ = e⁽⁻ˣ³⁾

Multiply both sides by the IF:

e⁽⁻ˣ³⁾y' - 3x²e⁽⁻ˣ³⁾y = 28

Apply the product rule to the left side and simplify the right side:

d/dx (e⁽⁻ˣ³⁾y) = 28

Integrate both sides with respect to x:

e⁽⁻ˣ³⁾)y = 28x + C, where C is the constant of integration.

Solve for y:

y = e⁽ˣ³⁾(28x + C)

Therefore, the solution to the given differential equation is y = e⁽ˣ³⁾(28x + C), where C is a constant.

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Complete question:

How to solve the first order linear differential equation

Y'- 3x²y=28eˣ³

Let's use the proportion method to solve the problem. We know that \frac{3}{4} pound of nails fills \frac{2}{3} of the container. Let x be the total weight of nails that will fill the container. Then we can set up the proportion:

\frac{3}{4} / \frac{2}{3} = x / 1

To solve for x, we can cross-multiply and simplify:

\frac{3}{4} * \frac{3}{2} = x

x = \frac{9}{8} = 1.125 pounds of nails

Therefore, 1.125 pounds of nails will fill the container.

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Answer:

Step-by-step explanation:

X axis intercept (y=0)

3x+2(0)=5

3x=5

x=5/3

Y axis intercept (x=0)

3(0)+2y=5

2y=5

y=5/2

so, the interception points are: (5/3,0) and (5/2,0)

Theorem 22.8 states several properties of rings with additive identity 0. These properties involve the multiplication and negation of elements in the ring.

Specifically, the theorem asserts that the product of any element with the additive identity is zero, the product of an element with its negative is the negation of the product with the positive element, and the product of two negatives is equal to the product of the corresponding positive elements.

Theorem 22.8 provides three key properties of rings with additive identity 0:

0aa0 = 0:

This property states that the product of any element a with the additive identity 0 is always 0.

In other words, multiplying any element by 0 results in the additive identity.

a(-b) = (-a)b = -(ab):

This property demonstrates the relationship between the negation and multiplication in a ring.

It states that the product of an element a with its negative -b is equal to the negation of the product of a with the positive element b.

This property highlights the distributive property of multiplication over addition in a ring.

(-a)(-b) = ab:

This property shows that the product of two negatives, -a and -b, is equal to the product of the corresponding positive elements a and b. It implies that multiplying two negatives yields a positive result.

These properties are fundamental in ring theory and provide important algebraic relationships within rings.

They help establish the structure and behavior of rings with respect to multiplication and negation.

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Answer:

your slope intercept form is y=-5x+6

Step-by-step explanation:

you distribute the -5 and then you add 5 to your now positive 5 to isolate your y variable

then once you have the equation you start at your y-intercept (0,6) and then you go up and or down 5 then you move to the left one because you have a negative slope

The correct answer is (D) Because the population mean of 118 mph does not fall within the confidence interval around the new mean, we can conclude that the program had an impact. In fact, we can conclude that the program seemed to increase the average speed of women’s serves.

Because the population mean of 118 mph does not fall within the confidence interval around the new mean, we can conclude that the program had an impact. In fact, we can conclude that the program seemed to increase the average speed of women’s serves.

The confidence interval around the group mean of 123 mph suggests that the true population mean lies somewhere within a certain range. Since the lower limit of this range is above the population mean of 118 mph, we can infer that the program had a positive impact on the participants' average serve speed.

This suggests that the program was successful in improving the participants' skills and abilities in tennis, resulting in faster serves.

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Answer:

When we say that an allele is "fixed," it means that a particular allele has reached a frequency of 100% in a population.

Step-by-step explanation:

Alleles are different forms of a gene that occupy the same position on homologous chromosomes. In a population, different alleles can exist for a specific gene. However, through various evolutionary processes such as natural selection, genetic drift, or gene flow, one allele may become predominant and eventually fixate within the population.

The fixation of an allele can occur through different mechanisms. For example, if a beneficial allele provides a selective advantage to individuals carrying it, it is more likely to increase in frequency and eventually become fixed in the population. On the other hand, genetic drift, which is the random change in allele frequencies due to chance events, can also lead to the fixation of an allele, especially in small populations.

Once an allele is fixed in a population, it means that all future generations will inherit that allele, and no alternative alleles will be present at that particular gene locus.

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A radical equation is an equation that contains a variable within a radical expression.

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Using Complete the Square method, we find out that \(x^{2} -5x+8\) can be expressed in the form of \((x-a)^{2}+b\) as \((x-\frac{5}{2}) ^{2} +\frac{7}{4}\) where a and b are top-heavy fractions.

It is given to us that the expression is -

\(x^{2} -5x+8\) ----(1)

We have to express it in the form of\((x-a)^{2}+b\) where a and b are top-heavy fractions.

In order to achieve the required expression in the form of  \((x-a)^{2}+b\) we have to use "Completing the Square" method.

The given expression from (1) is -

\(x^{2} -5x+8\)

This expression is in the form of \(ax^{2} +bx+c\)

Adding and subtracting \((b/2)^{2}\) terms into the expression, we get

\(x^{2} -5x+[\frac{5}{2}] ^{2}-[\frac{5}{2}] ^{2}+8\) -----(2)

Equation (2) can also be represented as -

\((x-\frac{5}{2}) ^{2} -[\frac{5}{2}] ^{2} +8\)

\(= > (x-\frac{5}{2}) ^{2} -\frac{25}{4} +8\\= > (x-\frac{5}{2}) ^{2} +\frac{7}{4}\)------- (3)

We see that equation (3) is in the form of \((x-a)^{2}+b\).

So, we can derive that -

\(a=\frac{5}{2}\)

and, \(b=\frac{7}{4}\).

Thus, \(x^{2} -5x+8\) can be expressed in the form of \((x-a)^{2}+b\) through "Complete the Square" method as \((x-\frac{5}{2}) ^{2} +\frac{7}{4}\) where a and b are top-heavy fractions.

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Answer:

58 hours.

Which can also be 2days 10 hours.

Step-by-step explanation:

3 pizza orders = 1hour

200 deliveries per month= bonus

26 orders so far this month.

X= 200-26= 174

174 divided by 3 = 58 hours.

A truth table is a table used in logic to systematically represent the possible truth values of a logical expression.

To construct truth tables for the provided statement forms, we need to consider all possible combinations of truth values for the individual propositional variables involved.

Let's go through each statement form and build the respective truth tables:

(a) p∧∼q:

p q ∼q p∧∼q

T T     F     F

T F   T     T

F T   F     F

F F   T     F

(b) ∼(p∧q)∨(p∨q):

p q p∧q ∼(p∧q) p∨q ∼(p∧q)∨(p∨q)

T T   T       F    T            T

T F   F       T    T            T

F T   F       T    T              T

F F   F       T    F             T

(c) p∧(q∧r):

p q r q∧r p∧(q∧r)

T T T   T     T

T T F   F     F

T F T   F        F

T F F   F     F

F T T   T     F

F T F   F     F

F F T   F     F

F F F   F     F

(d) p∧(∼q∨r):

p q r ∼q ∼q∨r p∧(∼q∨r)

T T T   F      T               T

T T F   F      F               F

T F T   T      T               T

T F F   T      T               T

F T T   F      T               F

F T F   F      F               F

F F T   T      T               F

F F F   T      T               F

These truth tables display all the possible combinations of truth values for the propositional variables p, q, and r, and the resulting truth values for each statement form based on the logical operations involved.

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\(~~~~~x(x+1)(x-2)^2 =0\\\\\implies x = 0~~ \text{or}~~ x +1 = 0~~ \text{or}~~ (x-2)^2 = 0\\\\\implies x = 0, ~ x = -1 , ~x=2\\\\\text{Hence the roots are}~0,-1 ,~2\)

Answer:

Lashawn used 15, $0.50 stamps, 21, $0.35 stamps, and 8, $0.02 stamps to mail the package

Step-by-step explanation:

The given parameters are;

The number of stamps Lashawn used to mail the small package = 44

The price of the combination of 44 stamp = $15.01

The price categories of the stamps are $0.50, $0.35, and $0.02

The number of $0.35 stamps = 2 × The number of $0.50 stamps - 9

Let, x represent the number of $0.50 stamps Lashawn used to mail the package

We have;

The number of $0.50 stamps Lashawn used to mail the package = x

The number of $0.35 stamps = 2 × x - 9 = 2·x - 9

The number of $0.35 stamps = 2·x - 9

The number of $0.02 stamps = 44 - x - (2·x - 9) = 44 - x - 2·x + 9 = 53 - 3·x

The number of $0.02 stamps = 53 - 3·x

Which gives;

0.5 × x + 0.35 × (2·x - 9) + 0.02 × (53 - 3·x) = 15.01

0.5·x + 0.7·x - 3.15 + 1.06 - 0.06·x = 15.01

1.14·x - 2.09 = 15.01

1.14·x = 15.01 + 2.09 = 17.1

x = 17.1/1.14 = 15

x = 15

The number of $0.50 stamps Lashawn used to mail the package = x = 15 stamps

The number of $0.50 stamps Lashawn used = 15 stamps

The number of $0.35 stamps Lashawn used = 2·x - 9 = 2 × 15 - 9 = 21 stamps

The number of $0.02 stamps Lashawn used = 53 - 3·x = 53 - 3 × 15 = 8 stamps.

The circumference of a circle with a radius of 11 is 68.1

The route or boundary that encircles any shape in mathematics is defined by the shape's circumference. In other terms, the circumference is also known as the perimeter, which aids in determining how long a shape's outline is.

The formula to calculate the circumference of a circle is C=2\(\pi\)r where r is the radius of the circle.

The problem tells us that r= 11, substituting that in the equation and solving:

C=2\(\pi\)r =2\(\pi\)(11) = 22\(\pi\)

The value of \(\pi\) is approximately 3.14, putting the value of  \(\pi\) in the equation:

C= 22(3.14) = 68.08→ 68.1

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The correct option is (C) Isosceles. An Isosceles triangle can be constructed with a 50° angle between two 8-inch sides.

This is because isosceles triangle having two sides that are equal in length, and have 50° angle, which is acute angle, that is less than 90°. This state that the remaining angle in the triangle must also be acute triangle, as the sum of all angles in a triangle must equal 180°.

This means that the remaining angle must be 80° (i.e. 180 - 50 = 80). An isosceles triangle is triangle consisting of  two sides of equal length and two angles of equal measure. The two equal sides that make up the isosceles triangle are referred to as the base and the remaining side is height or altitude.

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Answer:

G: -10 F

Step-by-step explanation: The temparature went down by 10 which means it subtracted 10 so it's -10

Complete question :

A reporter determines a baseball player's batting average, which is a ratio of number of hits to the number of times at bats. The result shown on a calculator as 0.2121....

How many hits would the player be expected to get in 200 at bats? Explain

Answer:

42

Step-by-step explanation:

Given that:

Batting average = number of hits / number of time at bats

Batting average obtained = 0.2121...

If at bats of the player = 200

Hence, number of hits ;

Batting average = number of hits / number of time at bats

0.2121 = number of hits / 200

Number of hits = 0.2121 * 200

Number of hits = 42.42..

= 42 ( approx)

Answer:

10

Step-by-step explanation:

Remark

Technically, we can't. We have no way of knowing what kind of figure we are working with. We can say to you that if this is not at least a parallelogram then no answer is possible.

Opposite sides of a parallelogram are equal.

Equation

2x = x + 5                  

Solution

Subtract x from each side

2x - x = 5

x = 5

HE = 2x

HE = 2*5

HE = 10

Answer:

3 is vertical

1 is same side interior

2 is correspnding

4 is straight angles

Step-by-step explanation:

\(\sqrt{-245}\implies \sqrt{(-1)(245)}\implies \sqrt{-1}\sqrt{245}\implies i\sqrt{49\cdot 5} \\\\\\ i\sqrt{7^2\cdot 5} \implies 7\sqrt{5}~i\)

Step-by-step explanation:

the correct answer is option a 6a-7

Answer: A, B

Step-by-step explanation:

Answer:

5.047 and 5.009

el gato?

Answer:

Question 4 : 10 m

Question 5 : Square root 37

Step-by-step explanation:

QUESTION 4: So for the this one here we need to make a drawing (unfortunately). Lets break down the question because having a math problem with a ton of words is confusing sometimes. So we have a pole that is 8m high, so we can draw that out. So we take some cable and go 6 m from the bottom of the pole. So now we want to know how long the cable is and if we go from the top of the pole to the bottom 6m away it looks like this. (Below I'll put what I have written) Since now it's a 90 degrees angle there is a specific formula we can use in situations like this. Where we know 2 sides and need 1 more. a^2 + b^2 = c^2 should look familiar if it doesn't its all good! :D a^2 + b^2 = c^2 is called 'Pythagorean's theorem' (we don't really need to know that part) but basically we use it whenever we need to figure out a side when we already know the other two. We know that the straight line is 8, and the horizontal line is 6. So we can use that formula to get the last number. just know that whenever we have the right triangle, we can use the a^2 + b^2 = c^2 to get all the sides for it. The a and b in the formula are always the straight lines. The c is always the slanted line (the red line I drew). We don't know what it is, so we'll just put c^2 into our equation but we can solve for it! So 8^2 would equal to 64. 6^2 would equal to 36. 64 + 36 here gets us 100. Here's another trick you might need to memorize. Whenever there is a number squared like c^2, we can take the square root of both sides to get rid of it. So c^2 just becomes c. It's a little weird but very useful to remember.  But if you remember the a^2 + b^2 = c^2 and use that square root technique you can get an A+ every time. :D Now all we need to know is the square root of 100. It's a big one so using a calculator is fine, here its just 10. Therefore our answer is 10.

QUESTION 5:  We'll start off by reading 'distance between points' is a big thing to note here. There is a formula that we can directly use here. (I'll write under the picture in black). So distance between points always uses this formula: (In black). Okay, so the formula in black has more letters in it (which sucks) but we can break it down. When we have numbers like this (3, 0) it means (x, y). So I wrote down what the x1, y1, x2, y2, are here. X1 is just the first number, y1 is the second, x2 is the third, and y2 is the fourth. I just plugged in all the numbers from above in the order we put (x2, x1, y2, y1). Basically we can just solve this now! As of right now we'll need to solve (-3 -3)^2 when we solve that we should get 36. Next we're gonna solve  (-1 - 0)^2 and we should get the answer of 1. Now we need to solve 36 +1 and we should know that it equals 37. Therefore we'd get answer: square root 37.

Answer:

5

Step-by-step explanation:

There are 4 equal sides on a square so 20/4 which is 5.

Answer:

Step-by-step explanation:

We'll look for a line with the form of y = mx + b, where m is the slope and b is the y-intercept (the value of y when x = 0).

A parallel line will have the same slope as the reference line,  For y=3x-8, the slope is 3.  We can write:

y =3x + b for the new line.  We need a value of b that will cause the line to include point (6,-4).  To find a b that will work, simple use the given point in the above equation and solve for b:

y =3x + b

-4 =3(6) + b  for (6,-4)

-4 =18 + b

b = -22

The parallel line that goes through point (6,-4) is y = 3x - 22

See the attached graph.

Answer:

142

Step-by-step explanation:

x+38=180

x=142

Answer is 142

Answer:

very easy x=180-38= 142 is ans

Step-by-step explanation:

itis Because the sum of all side in triangle is 180 so 180-38=x

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

Proof:

We'll break the proof into two cases which I'll label A and B

-----------

Case A: 'a' is even

k = some integer

a = 2k = some even integer

a+1 = 2k+1

a(a+1) = 2k(2k+1) = 2(2k^2+k) = 2*(some integer)

Since 2 is a factor of that last expression, this shows that a(a+1) is even when 'a' is even.

-----------

Case B: 'a' is odd

k = some integer

a = 2k+1 = some odd integer

a+1 = (2k+1)+1 = 2k+2

a(a+1) = (2k+1)(2k+2) = 2(2k+1)(k+1) = 2(some integer)

This shows that a(a+1) is even when 'a' is odd.

-----------

Therefore, for any integer 'a', the expression a(a+1) is always even.

Some examples:

-----------

Here's a slightly different way to interpret why the proof works.

a(a+1) consists of factors 'a' and 'a+1'

Either way, we'll have 2 as a factor somewhere in a(a+1).