how do i work this out i dont understand it

The given lengths of 3 feet, 3 feet, and 7 feet cannot form a triangle because they do not satisfy the Triangle Inequality Theorem, which is the sum of the lengths of any two sides is greater than the length of the third side.

To form a triangle, the sum of the lengths of any two sides of the triangle must be greater than the length of the third side. This is known as the Triangle Inequality Theorem.

Let's apply this theorem to the given lengths of 3 feet, 3 feet, and 7 feet:

The sum of the first two sides is 3 + 3 = 6 feet, which is less than the length of the third side of 7 feet. So, the first two sides cannot form a triangle.

The sum of the first and third sides is 3 + 7 = 10 feet, which is greater than the length of the second side of 3 feet. However, the sum of the second and third sides is 3 + 7 = 10 feet, which is also greater than the length of the first side of 3 feet.

Therefore, neither of the two combinations of sides satisfy the Triangle Inequality Theorem, and so it is impossible to form a triangle with sides of 3 feet, 3 feet, and 7 feet.

To learn more about triangle click on,

https://brainly.com/question/18959763

#SPJ4

It is correct to state that if there is a sample, the standard error is used in the denominator of the z stat or t stat formula.

The t-distribution is used when we have the standard deviation for the sample instead of the population, hence the equation is given as follows:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

In which:

The standard error is modeled as follows:

[tex]s_e = \frac{s}{\sqrt{n}}[/tex]

Which is the denominator of the formula for the test statistic, hence the statement is true.

When we have the standard deviation for the population, we use the z-distribution, however the formula for the standard error is similar.

More can be learned about the z-distribution at https://brainly.com/question/25890103

#SPJ1

In response to the stated question, we may state that As a result, the figure's pairs of congruent angles are: ∠BAC ≅ ∠EDF; ∠ABC ≅ ∠DEF; ∠ACB ≅ ∠DFE

An angle is a form in Euclidean geometry that is constructed from two rays, known as the tone's sides, that connect at a central location known as angle's vertex.

Two beams may combine to generate an inclination in the plane in which they are located. They are known as dihedral angles. In plane geometry, an angle is a potential arrangement of two rays or planes that meet a termination.

The English term “angle” derives from the Latin phrase "angulus," which means "horn." The vertex is the point at where the twin rays, also termed as the angle's sides, converge.

The congruent angles in the illustration are:

BAC and EDF are vertically opposed angles with the same measurement.

ABC and DEF are equivalent angles with the same measure.

ACB and DFE are equivalent angles with the same measure.

Therefore, the figure's pairs of congruent angles are:

∠BAC ≅ ∠EDF

∠ABC ≅ ∠DEF

∠ACB ≅ ∠DFE

Learn more about angle here:

https://brainly.com/question/28451077

#SPJ1

Answer:

a. 6

b. 6

Step-by-step explanation:

A. mean proportion

3:x::x:12

product of mean = product of extreme

3 x 12 = x^2

x^2= 36

now take square root on both sides

x = 6

as sqaure root will cancel the square on x and square root of 36 is 6.

B. the geometric mean is the product of all

the numbers in a set, with the root of how many numbers there are. here, there are two numbers, so a square root is used. the value of the geometric mean of 3 and 12 is 6.

Hope's it helps...

Thus, the total area of composite figure (circle on a rectangle) is found as  29.91 m².

Area of sector of the circle = (Ф/360°) *π*r²

r is the radius = 5.5 m

π = 3.14

Area =  (30/360°) *3.14 * 5.5²

Area = 7.91 m²

Area of rectangle = width × length

Area = 4 × 5.5 = 22 m²

Total area of composite figure = area of the circle's sector + area of the rectangle

Total area of composite figure =  7.91 m² + 22 m² = 29.91 m²

Know more about the sector of the circle

https://brainly.com/question/22972014

#SPJ1

In conclusion  the values of p that satisfy this inequality are p = 11, p = 12, p = 13, etc.  The equation showing that Elena saves exactly $20 is:

5 + (1.5)p = 20

Why it is?

The expression for how much money Elena saves after selling p pens is:

Total money saved = 5 + (1.5)p

The equation showing that Elena saves exactly $20 is:

5 + (1.5)p = 20

Solving the equation:

5 + (1.5)p = 20

(1.5)p = 15

p = 10

We notice that the value of p is a whole number, which makes sense since Elena cannot sell a fractional number of pens.

If Elena wants to have some money left over, we can write the inequality:

5 + (1.5)p > 20

Some values for p where Elena would have money left over are p = 11, p = 12, p = 13, etc.

To describe the values of p where Elena would be able to buy the t-shirt and still have money left over, we can write the inequality:

5 + (1.5)p > 20

(1.5)p > 15

p > 10

Therefore, the values of p that satisfy this inequality are p = 11, p = 12, p = 13, etc.

To know more about Selling related questions, visit:

https://brainly.com/question/30615010

#SPJ1

Answer:

3m

Step-by-step explanation:

red wire = 27

black wire= 12

so, we take HCF (highest common factor)

which would be 3 so all the wires would be cut into 3m long.

I hope it helps.

Answer:2m

Step-by-step explanation:

as the factors of 12 are:1, 2, 3, 4, 6 and 12

and the factors of 26 are:1, 2, 13 and 26

so if you are talking meters 2 would be the longest

i hope you get this right x

Step-by-step explanation:

40 Years is the right answer

Answer:

son is 10 , father is 40

Step-by-step explanation:

let x be the sons age then father is x + 30

in 5 years

son is x + 5 and father is x + 30 + 5 = x + 35

at this time the father is three times as old as his son , then

x + 35 = 3(x + 5)

x + 35 = 3x + 15 ( subtract x from both sides )

35 = x + 15 ( subtract 15 from both sides )

20 = x

then sons age = x = 10 and fathers age = x + 30 = 10 + 30 = 40

The probability that the jury makes the correct decision is approximately 0.7063.

To solve this problem, we need to find the probability that the jury makes the correct decision if the defendant is guilty. Let's break down the problem into smaller steps.

We know that the probability of a single juror making the correct decision is 0.80. If the defendant is guilty, then the probability of a juror making the correct decision is still 0.80. Therefore, the probability that a single juror makes the correct decision if the defendant is guilty is 0.80.

We can use the binomial distribution formula to determine the probability of at least 10 out of 12 jurors making the correct decision. The formula is:

P(X ≥ k) = 1 - Σ(i=0 to k-1) [n!/(i!(n-i)!) x [tex]p^i \times (1-p)^{(n-i)}[/tex] ]

where:

P(X ≥ k) is the probability of at least k successes

n is the total number of trials (in this case, 12 jurors)

p is the probability of success in a single trial (in this case, 0.80)

k is the number of successes we want to find the probability of (in this case, 10)

Plugging in the values, we get:

P(X ≥ 10) = 1 - Σ(i=0 to 9) [12!/(i!(12-i)!) x [tex]0.80^i \times (1-0.80)^{(12-i)}[/tex]]

Using a calculator or software, we can calculate this to be approximately 0.7063.

To know more about probability here

https://brainly.com/question/11234923

#SPJ4

Answer:

D) he did not multiply -3 with -2 to get +6 instead of -6

Step-by-step explanation:

-3(x - 2)

-3x + 6

Compare the two

-3x + 6 ≠ -3x - 6

They are not equal! Looking at the options, D is the answer.

Answer:

The correct answer is D) he did not multiply -3 with -2 to get +6 instead of -6.

To expand -3(x-2), we need to distribute -3 to both terms inside the parentheses, which gives us:

-3(x-2) = -3x + (-3(-2)) = -3x + 6

Therefore, the correct equivalent expression is -3x + 6, not -3x - 6 as Rob wrote. He made a mistake in multiplying -3 and -2, which should have given him +6 instead of -6.

(please mark my answer as brainliest)

The given probability distribution "a teacher monitored the number of people texting during class each day and calculated the corresponding probability distribution." is a type of discrete probability distribution.

The probability distribution is used to describe the probability of each outcome in a series of possible outcomes. It is a mathematical representation of the outcomes of an experiment.

The teacher likely used a discrete probability distribution to calculate the probability of a certain number of people texting during class each day.

A discrete probability distribution is used to analyze data where the outcome is counted in whole numbers, such as the number of people texting in a given class period.

Learn more about Probability distribution here:

https://brainly.com/question/14210034

#SPJ11

The number we are looking for is N = 2 × 2^3 × 3^2 = 72.

Let's first recall some properties of the number of divisors of an integer. If we factorize an integer n as a product of prime powers, say

n = p_1^a_1 × p_2^a_2 × ... × p_k^a_k

then the number of divisors of n is given by

d(n) = (a_1 + 1) × (a_2 + 1) × ... × (a_k + 1).

Using this fact, we can deduce some information about the number we are looking for. Let's call it N. We know that N has 8 divisors, so it must be of the form

N = p_1^2 × p_2^2, or N = p_1^7,

where p_1 and p_2 are distinct prime numbers.

Now, we are told that each of N/2 and N/3 has four divisors. We can use the same fact about the number of divisors to conclude that

N/2 = q_1^3 × q_2, or N/2 = q_1^1 × q_2^3,

and

N/3 = r_1^3 × r_2, or N/3 = r_1^1 × r_2^3,

where q_1, q_2, r_1, and r_2 are distinct prime numbers.

To simplify the notation, let's introduce the variables a, b, c, d, e, and f, defined by

p_1 = q_1^a × q_2^b,

p_2 = r_1^c × r_2^d,

N/2 = q_1^e × q_2^f,

N/3 = r_1^g × r_2^h.

Using the information we have so far, we can write down equations for a, b, c, d, e, f, g, and h in terms of unknown exponents:

a + 1 × (b + 1) = e + 1 × (f + 1) = 4,

c + 1 × (d + 1) = g + 1 × (h + 1) = 4,

2a × 2b = ef,

2c × 2d = gh.

We can solve this system of equations by trial and error. For example, we can start by trying all possible values of a and b such that 2a × 2b = 4. This gives us two possibilities: a = 0, b = 2, or a = 1, b = 1. Using the first possibility, we get e = 3, f = 1, which leads to N/2 = q_1^3 × q_2, and hence N = 2 × q_1^3 × q_2^2. Substituting this into the equation for the sum of divisors, we get

(1 + q_1 + q_1^2 + q_1^3) × (1 + q_2 + q_2^2) = 216.

We can solve this equation by trial and error as well, or by observing that 216 = 2^3 × 3^3, and hence the two factors on the left-hand side must be equal to 2^3 and 3^3, respectively. This gives us the unique solution q_1 = 2 and q_2 = 3, and hence N = 2 × 2^3 × 3^2 = 72.

Learn more about divisor here

brainly.com/question/17879555

#SPJ4

Answer:51

Step-by-step explanation:

Answer: 30

Step-by-step explanation: So what you do is,

1) Add the 25 to the 8

2) Find the sum

3) Subtract 3 from the sum

4) Done!

I hope this helps!

Best,

Abigail H

8th Grade

The absolute maximum value is attained: (0, 0)

The given function is, f(x, y) = xy - 7y - 49x + 343The region is on or above y = x^2 and on or below y = 50. To find the absolute minimum and absolute maximum value of the function, f(x, y), first we will find the critical points of the function.f(x, y) = xy - 7y - 49x + 343 ⇒ ∂f/∂x = y - 49 = 0 ⇒ y = 49 ⇒ ∂f/∂y = x - 7 = 0 ⇒ x = 7Thus, the critical point is (7, 49).Next, we will check for the boundary points. The boundary of the region is y = x^2 and y = 50. The points of intersection are:x^2 = 50 ⇒ x = ±√50 (not in the region)x = ±1.58 ⇒ y = x^2 = 2.50 (not in the region)Also, x = 0 ⇒ y = 0, and x = 0 ⇒ y = 50Thus, the critical points are (7, 49) and (0, 0).f(7, 49) = 7(49) - 7(49) - 49(7) + 343 = -7f(0, 0) = 0 - 7(0) - 49(0) + 343 = 343f(0, 50) = 0 - 7(50) - 49(0) + 343 = -357f(±1.58, 2.50) = ±1.58(2.50) - 7(2.50) - 49(±1.58) + 343 = ∓36.97The absolute minimum value is -7. The points at which the absolute minimum value is attained are (7, 49) and (0, 50).The absolute maximum value is 343. The point at which the absolute maximum value is attained is (0, 0).Hence, the required points are as follows:Points at which the absolute minimum value is attained: (7, 49) and (0, 50)Points at which the absolute maximum value is attained: (0, 0)

Learn more about Absolute

brainly.com/question/28767824

#SPJ11

The combined ratio of x : y : z from x ; y = 4 : 3 and y : z = 5 ; 2 is x:y:z = 20:15:6

Given the following ratios

x ; y = 4 : 3

y : z = 5 ; 2

To find the ratio of x:y:z, we need to combine the two given ratios and simplify:

x:y = 4:3

y:z = 5:2

To combine these ratios, we need to have a common term for y.

We can do this by multiplying the first ratio by 5 and the second ratio by 3:

5(x:y) = 5(4:3) = 20:15

3(y:z) = 3(5:2) = 15:6

Now we have a common term of 15 for y, so we can combine the ratios:

x:y:z = 20:15:6

Therefore, the ratio of x:y:z is 20:15:6

Read more about ratio at

https://brainly.com/question/21003411

#SPJ1

Answer:

28 is the ans of 252÷9here we go

252 divided by 9 equals 28.

To divide 252 by 9, you can use long division, which involves dividing the number in steps until there is no remainder left.

Here's the step-by-step process:

Write down the dividend (252) and the divisor (9), and set up the long division format:

9 | 252

Look at the leftmost digit of the dividend (2) and see if it's divisible by the divisor (9). Since 2 is less than 9, we bring down the next digit (5) to the right of 2, making it 25.

9 | 252

2

Divide the new number (25) by the divisor (9). The result is 2, which is the first digit of the quotient. Multiply this result by the divisor (2 x 9 = 18) and write it below the 25, then subtract it from 25:

9 | 252

25

18

--

7

Bring down the next digit (2) from the dividend to the right of the remainder (7), making it 72. Now, divide 72 by 9, which gives you 8. Multiply this result by the divisor (8 x 9 = 72) and write it below the 72, then subtract it from 72:

9 | 252

25

18

--

72

72

---

0

There is no remainder left, and the dividend has been completely divided. The quotient is the result of the division, which is 28.

Therefore, 252 divided by 9 equals 28.

Learn more about long division click;

https://brainly.com/question/28824872

#SPJ6

Step-by-step explanation:

remember, the sum of all angles in a triangle is always 180°.

the law of sine :

a/sin(A) = b/sin(B) = c/sin(C)

with a, b, c being the sides, and A, B, C being the three corresponding opposite angles.

so, the angle at Q is

180 = 48 + 48 + angle Q = 96 + angle Q

84° = angle Q

5mm/sin(48) = PR/sin(84)

PR = 5×sin(84)/sin(48) = 6.691306064... mm

The length of PR is approximately 10.33 mm.

what is isosceles triangle ?

An isosceles triangle is a triangle with at least two sides that have equal length, and thus two corresponding angles that are also equal in measure. The third side and angle of an isosceles triangle may or may not be of different length or measure. The two sides that are equal in length are called the legs, and the third side is called the base. The angle opposite the base is called the vertex angle, while the angles adjacent to the legs are called the base angles. In an isosceles triangle, the two base angles are equal in measure.

Since the sum of the angles in a triangle is 180 degrees, we can find the measure of angle PQR as follows:

PQR = 180 - QPR - QRP

PQR = 180 - 48 - 48

PQR = 84 degrees

Since angles QRP and QPR have the same measure, we know that sides OP and OR have equal length (they are opposite those angles). Therefore, triangle POR is an isosceles triangle.

To find the length of PR, we can use the Law of Cosines:

PR^2 = OP^2 + OR^2 - 2(OP)(OR)cos(POR)

Since OP and OR are equal in length, we can simplify this equation to:

PR^2 = 2(OP^2) - 2(OP^2)cos(POR)

We know that POR is 180 - PQR = 96 degrees. We also know that OP = OR, and that QP = 5 mm. Using the Law of Cosines, we can find the length of OP:

OP^2 = QP^2 + OR^2 - 2(QP)(OR)cos(QPR)

OP^2 = 5^2 + OR^2 - 2(5)(OR)cos(48)

OP^2 = OR^2 - 5ORcos(48) + 25

Since OP = OR, we can substitute OP for OR in the above equation:

OP^2 = OP^2 - 5OPcos(48) + 25

5OPcos(48) = 25

OP = 25/(5cos(48))

OP ≈ 6.25 mm

Now we can substitute this value into the equation we derived earlier to find PR:

PR^2 = 2(OP^2) - 2(OP^2)cos(POR)

PR^2 = 2(6.25^2) - 2(6.25^2)cos(96)

PR ≈ 10.33 mm

Therefore, the length of PR is approximately 10.33 mm.  

To know more about triangles visit :-

https://brainly.com/question/17335144

#SPJ1

There will be a total of 28 handshakes when the 3 late members arrive.

The first n-1 positive integers are added together using the formula n(n-1)/2, where n is the total number of terms being added together.

The number of combinations or arrangements of a given collection of items may be determined using this formula, which can be obtained using the process of mathematical induction. It is often used in combinatorics and discrete mathematics. For instance, the formula was used to determine how many times a group of individuals shook hands in the scenario above. It might also be used to determine the number of pathways in a network of nodes or vertices or the number of ways to choose a portion of an object set from a bigger set in other settings.

Given that, 3 members arrive late, and 5 members are already present.

The total members are 5 + 3 = 8.

Now, using the sum of positive integer formula:

n(n-1)/2

We can determine the number of handshakes.

8(8-1)/2 = 28

Hence, there will be a total of 28 handshakes when the 3 late members arrive.

Learn more about integers here:

https://brainly.com/question/27908445

#SPJ1

Answer:

-12 is the y intercept while your slope is -4

Step-by-step explanation:

The scale factor of the following pair of similar polygons after the dilation is 0.7

Given

The pair of similar polygons

From the pair of similar polygons, we have the following corresponding side lengths

Pre-image of the polygon = 30

Image of the polygon = 21

The scale factor of the similar polygons is then calculated as

Scale factor = 21/30

Evaluate the quotient

Scale factor = 0.7

Hence, the scale factor is 0.7

Read more about scale factor at

https://brainly.com/question/17031580

#SPJ1

The volume of the rectangular prism is approximately 0.2996 cubic meters.

Six rectangular faces that are congruent and parallel to one another make up the three-dimensional solid known as a rectangular prism. A rectangular cuboid is another name for it.

By multiplying the prism's length, width, and height, one may get the volume of a rectangular prism, which is the volume of the interior space of the prism.

Given that, area of the square base is 7 1/2 sq. m.

The side of the square base is thus,

√(7 1/2) ≈ 2.7386 m

The volume of the rectangular prism is given as:

Volume = length x width x height

Volume ≈ 2.7386 x 2.7386 x 1/5 m

Volume ≈ 0.2996 cubic meters.

Hence, the volume of the rectangular prism is approximately 0.2996 cubic meters.

Learn more about volume of prism here:

https://brainly.com/question/22023329

#SPJ1

The value of x in the right triangle when calculated is approximately 13.8 units

Given the right-angled triangle

The side length x can be calculated using the following sine ratio

So, we have

sin(39) = x/22

To find x, we can use the fact that sin(39 degrees) = x/22 and solve for x.

First, we can use a calculator to find the value of sin(39 degrees), which is approximately 0.6293.

Then, we can set up the equation:

0.6293 = x/22

To solve for x, we can multiply both sides by 22:

0.6293 * 22 = x

13.8446 = x

Rewrite as

x = 13.8446

Approximate the value of x

x = 13.8

Therefore, x is approximately 13.8 in the triangle

Read about right triangle at

https://brainly.com/question/2437195

#SPJ1

The factorizations of these integers above represent their factorizations into their respective prime numbers.

(a) 756 = 2^2.3^3.7, (b) 819 = 3^2.7.11, (c) 9,075 = 3^2.5^2.7The unique factorization theorem refers to an essential theorem in standard algebraic theory that characterizes the unique factorization properties of integers. Standard factored form, on the other hand, refers to an expression in which an integer is factored into its standard, irreducible components.In view of this, the three provided integers, 756, 819, and 9,075 can be factored as follows:756 = 2^2.3^3.7 (in standard factored form)819 = 3^2.7.11 (in standard factored form)9,075 = 3^2.5^2.7 (in standard factored form)Note that the factorizations of these integers above represent their factorizations into their respective prime numbers.

Learn more about Factorizations

brainly.com/question/14067703

#SPJ11

How does cellular respiration help maintain homeostasis in animals?

Answer: Cellular respiration helps animals maintain homeostasis by breaking down glucose to produce ATP, which is the energy currency of the cell. ATP is necessary for many cellular processes that help maintain homeostasis such as active transport and protein synthesis.

Explain why cells separate and expel waste.

Answer: Cells separate and expel waste to prevent the accumulation of toxic substances that can disrupt cellular function and lead to disease. The waste products are transported out of the cell and into the bloodstream where they are filtered and excreted by organs such as the kidneys.

Why do cells in organisms such as animals reproduce?

Answer: Cells in organisms such as animals reproduce to replace damaged or dying cells, and to enable growth and development. Reproduction ensures that the organism maintains the proper balance of cells and that there is enough tissue to perform necessary functions.

Explain how plant cells use photosynthesis to maintain homeostasis?

Answer: Plant cells use photosynthesis to maintain homeostasis by converting light energy into chemical energy in the form of glucose. This glucose is then used to produce ATP, which is necessary for cellular processes such as active transport and protein synthesis. Additionally, plants use photosynthesis to produce oxygen, which is necessary for respiration.

I hope this helps :)

Answer:

30 minutes

Step-by-step explanation:

Use ratios. This is an inverse function, as speeding up makes the time traveling go down. So, when dividing the speed by 3 (done so 15 can get to 5), we multiply the time traveled by 3.

10 minutes * 3 = 30 minutes

We can graph this solution on the number line by placing a point at 7.6.

Graphs are visual representations of data or information. They are used to show relationships between different pieces of data and display numerical data in a more meaningful way. Graphs are made up of individual elements called nodes which are connected by edges. Nodes represent individual data points or pieces of information. Edges represent the relationship between two nodes and can represent either a physical or a logical link. Graphs can be used to represent many different types of data or information, such as social networks, transportation networks, and even biological relationships. Graphs are a powerful tool for understanding complex data sets, making them an essential tool for data analysis.

80∠ 10x + 4 = 20

80 10x + 4 = 20

80 - 4 = 10x

76 = 10x

7.6 = x

To learn more about graph

https://brainly.com/question/19040584

#SPJ1

We can graph this solution on the number line by placing a point at 7.6.

Graphs are visual representations of data or information. They are used to show relationships between different pieces of data and display numerical data in a more meaningful way. Graphs are made up of individual elements called nodes which are connected by edges. Nodes represent individual data points or pieces of information. Edges represent the relationship between two nodes and can represent either a physical or a logical link. Graphs can be used to represent many different types of data or information, such as social networks, transportation networks, and even biological relationships. Graphs are a powerful tool for understanding complex data sets, making them an essential tool for data analysis.

80∠ 10x + 4 = 20
80 10x + 4 = 20
80 - 4 = 10x
76 = 10x
7.6 = x

To learn more about graph
brainly.com/question/19040584
#SPJ1

The number of bacteria in a second study is modeled by the function, the growth rate r for the equation is 0.017, since the equation is [tex]A(t) = 2500e^{(0.017t)}[/tex].

To find the growth rate r of an exponential function, use the following formula:[tex]A = Pe^{(rt)}[/tex] Where:

To determine r, divide both sides by P and take the natural logarithm of both sides. It yields: ln(A/P) = rt Therefore: r = ln(A/P) / tNow, given that the number of bacteria in a second study is modeled by the equation: [tex]A(t) = 2500e^{(0.017t)}[/tex] Compare the given equation with [tex]A = Pe^{(rt)}[/tex]. The initial amount (P) is 2500, since that is the starting amount. The final amount (A) is [tex]2500e^{(0.017t)}[/tex], since that is the amount after a certain period of time (t).Thus, [tex]r = ln(A/P) / t= ln(2500e^{(0.017t)} / 2500) / t= ln(e^{(0.017t))} / t= 0.017[/tex] (rounded to 3 decimal places)Therefore, the growth rate r for the equation is 0.017.

See more about rate r of an exponential function at: https://brainly.com/question/27161222

#SPJ11

The solution to the differential equation y" - 8y' + 16y = 24x + 2 is y = (c1 + c2 x) e^(4x) - 3x + 1 plus any constants determined by initial or boundary conditions.

To solve the given differential equation y" - 8y' + 16y = 24x + 2 using the method of undetermined coefficients, we first find the complementary solution of the homogeneous equation y" - 8y' + 16y = 0:

The characteristic equation is r^2 - 8r + 16 = 0, which has a double root of r = 4. Therefore, the complementary solution is y_c = (c1 + c2 x) e^(4x).

Next, we need to find a particular solution for the non-homogeneous equation. Since the right-hand side has two terms, we can try a particular solution of the form y_p = Ax + B for the homogeneous term and y_p = C for the constant term.

Substituting this form into the differential equation, we get:

y_p" - 8y_p' + 16y_p = 24x + 2

Taking the derivatives and plugging them back into the equation, we get:

-8A + 16B + 16C = 2

0 + 0 + 16C = 24

Solving for A, B, and C, we get A = -3, B = -1/2, and C = 3/2.

Therefore, the particular solution is y_p = -3x - 1/2 + 3/2 = -3x + 1.

The general solution is then y = y_c + y_p = (c1 + c2 x) e^(4x) - 3x + 1.

To learn more about differential equations

https://brainly.com/question/14620493

#SPJ4