show that if a, b, c, and d are integers, where a = 0, such that a | c and b | d, then ab | cd.

The general solution of the given second-order differential equation is

y = [tex]e^{5t}[/tex]([tex]c_{1}[/tex]cost + [tex]c_{2}[/tex]sint).

In the given question we have to find the general solution of the given second-order differential equation.

The given second-order differential equation is:

y'' − 10y' + 26y = 0

We can write this equation as

d^2(y)/dx^2 − 10dy/dx + 26 = 0

Let d/dx = D

then, d^2/dx^2 = D^2

Now the equation is:

(D^2 − 10D + 26)y = 0

Now solving the equation as a quadratic equation.

m^2 − 10m + 26 = 0

m = [tex]\frac{-(-10)\pm\sqrt{(-10)^2-4\times1\times26}}{2\times1}[/tex]

m = [tex]\frac{10\pm\sqrt{100-104}}{2}[/tex]

m = [tex]\frac{10\pm\sqrt{-4}}{2}[/tex]

m = [tex]\frac{10\pm2i}{2}[/tex]

m = 5±1

Now the general equation for quadratic equation is

y = [tex]e^{at}[/tex]([tex]c_{1}[/tex]cosbt + [tex]c_{2}[/tex]sinbt)

As a = 5 and b = 1

Now the general solution of the given second-order differential equation is y = [tex]e^{5t}[/tex]([tex]c_{1}[/tex]cost + [tex]c_{2}[/tex]sint).

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The type of reasoning used to prove the remainder theorem is; Deductive reasoning

Logical reasoning involves using a given set of facts or data to deduce other facts by reasoning logically

There are 4 major types of reasoning here and they are;

1) Deductive reasoning; This is defined as a logical process in which a conclusion is based on the concordance of multiple premises that are generally assumed to be true.

2) Inductive reasoning; This is a method of drawing conclusions by going from the specific to the general.

3) Abductive reasoning; This is defined as a syllogism in which the major premise is evident but the minor premise and therefore the conclusion only probable.

4) Reasoning by analogy; This involves using a well known situation to assert something about a less well understood situation

In this case, we are told that since (x - 5) is a factor of the polynomial x² - 25, if he performs the long division (x² - 25) ÷ (x - 5), the remainder would be zero.

Now, this is an example of deductive reasoning because it has used the initial premise to draw a conclusion on the remainder.

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Answer:i don't know thanks for the brainy money tho

Step-by-step explanation:

Answer: 0.5 Liters

Step-by-step explanation:

1 Liter = 1000 milliliters

500 milliliters = 0.5 Liters

I just need to take 500 divided by 1000 = 0.5 Liters

The choice that correctly names angles 2 and 3 is called the: D. vertical angles.

Two angles are named vertical angles if both angles form a pair of angles that share the same vertex both not the same side, and they are on the opposite sides of two straight lines that intersect each other.

Given the image above, it shows that angle 2 and angle 3 form a pair that shares the same vertex when two straight lines intersect, and both angles are non-adjacent angles, that is they do not share any common side with each other.

Therefore, according to the definition given above, the angles 2 and 3 can be correctly named as: D. vertical angles.

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Answer:

1.

2(2x-5)-7(2x-1)=3

Multiply both sides of the equation by 14, the least common multiple of 7,2.

2(2x−5)−7(2x−1)=42

Use the distributive property to multiply 2 by 2x−5.

4x−10−7(2x−1)=42

Use the distributive property to multiply −7 by 2x−1.

4x−10−14x+7=42

Combine 4x and −14x to get −10x.

−10x−10+7=42

Add −10 and 7 to get −3.

−10x−3=42

Add 3 to both sides.

−10x=42+3

Add 42 and 3 to get 45.

−10x=45

Divide both sides by −10.

x= −10/45

​Reduce the fraction  to lowest terms by extracting and canceling out 5.

x=− 2/9

​

2. I don't know this one. Sorry.

3. is in the file

Answer:

2. ......................

The piece of wood that is needed to build each brace 5√2 feet.

Let  the piece of wood that be  needed to build each brace x feet.

A bookcase is 5 feet high and 5 feet wide, so

By condition we can write (5^2)+(5^2)=x^2

⇒25+25=x^2
⇒ 50=x^2

x=√50
prime factors:

50=2 × 5 × 5  

 50 = 2 × 5^2

√50 = √(25 × 2) = 5√2

The piece of wood that is needed to build each brace 5√2 feet .

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The school district have to  purchase 8 laptops for the cost to be the same for both companies.

What is sequence?

A sequence is an enumerated group of items in mathematics where repetitions are permitted and order is important. It has members, just like a set does. The length of the sequence is the number of elements.

Given that the company 1 offers:

The cost of 1 laptop is $425.

The cost of 3 laptop is $475.

The cost of 5 laptop is $525.

The difference of cost 1 laptop to cost 3 laptop = the difference of cost 3 laptop to cost 5 laptop = $50

The company 2 offers:

The cost of 1 laptop is $250.

The cost of 3 laptop is $350.

The cost of 5 laptop is $450.

The difference of cost 1 laptop to cost 3 laptop = the difference of cost 3 laptop to cost 5 laptop = $100

Take the cost as a sequence:

The common difference of first sequence is 50/2 = 25.

The common difference of second sequence is 100/2 = 50.

Assume that the school district needs to buy n computer.

The nth term of a sequence is a + (n - 1)d, where a is the first term, d is common difference.

The nth term of the first sequence is 425 + (n - 1) 25

The nth term of the second sequence is 250 + (n - 1) 50

According to question,

425 + (n - 1) 25 = 250 + (n - 1) 50

425 + 25n - 25 = 250 + 50n - 50

25n - 50n = 250 - 50 - 425 + 25

- 25n = -200

Divide both sides by 25

n = 8

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Answer:

y > -2/3x + 2, y [tex]\geq[/tex] x

[tex]\left \{ {{y > -2/3x + 2} \atop {y \geq x}} \right.[/tex]

Step-by-step explanation:

Knowledge Needed

A system of linear inequalities is graphing 2 lines.

If the line's y side is less than it's x-side (y </ [tex]\leq[/tex] x), shade below.

If the line's y side is greater than it's x-side (y </ [tex]\leq[/tex] x), shade above.

If the line is dotted, it is < or >.

If the line is filled in, it is [tex]\leq[/tex] or [tex]\geq[/tex].

Where both regions are shaded is the solution.

Question

Examine the dotted line.

1) We know it is < or > because it is dotted.

2) We know it is y > .... because if it was less than, it would be shaded below, which is impossible because the shaded region is above.

3) We know the y-intercept, when x=0, is 2.

4) We know the slope, how much the y-value of a line changed when the x-value changes by 1, is -2/3.

y > -2/3x + 2

Examine the solid line.

1) We know it is [tex]\geq[/tex] or [tex]\leq[/tex] because it is solid.

2) We know it is y [tex]\geq[/tex] .... because if it was less than, it would be shaded below, which is impossible because the shaded region is above.

3) We know the y-intercept, when x=0, is 0.

4) We know the slope, how much the y-value of a line changed when the x-value changes by 1, is 1.

y [tex]\geq[/tex] 1x + 0

y [tex]\geq[/tex] x

The solution to the linear inequality is when both lines are shaded in (true), which means both lines are the solution together.

y > -2/3x + 2, y [tex]\geq[/tex] x

Answer:

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

Find the lines first, then determine inequalities based on the shaded region and types of lines.

One line has positive slope and passes through the origin. Its x and y-coordinates are same, hence it is:

The shaded region is above this line and the line is solid, therefore the inequality is:

The second line has a negative slope and it has y-intercept at (0, 2), x- intercept at (3, 0).

Its slope is m = (0 - 2)/(3 - 0) = - 2/3.

So the line is:

Again, the shaded region is above the line, and the line is dashed, hence the inequality is:

The triangles JKL and XYZ are congruent by Side-Angle-Side Theorem as KL ≅ XV, JK ≅ VZ, ∠ K ≅ ∠V.

Herein we find a case of two triangles that we must prove that they are congruent, this is a congruency problem. Two triangles are congruent if the two triangles share the same sides in the same order. In accordance to the figure, we find the given assumptions:

KL ≅ XV, JK ≅ VZ, ∠ K ≅ ∠V

This assumptions satisfies the Side-Angle-Side Theorem and according to it we conclude that the triangles JKL and XYZ.

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Answer: (A) One solution

The special segment that matches the picture is the Median.

What is the median segment?

A median is a line segment that connects any triangle vertex to the middle of the opposite side. It is also the path that connects an angle's opposite internal side to its midpoint. At the centroid, they coexist.

From the figure, the given triangle in which segment is concurrent at the centroid. It bisects each side of the triangle into two equal parts.

Hence, the special segment that matches the picture is the Median.

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two buses leave towns miles apart at the same time and travel toward each other. then the Rate of first bus = 72 mph and Rate of second bus  = 62 mph

let first bust travels at x mph

then,  2nd but will travel at ( x - 10) mph

distance travelled by first bus in 2 hours = 2x

distance travelled by 2nd but in 2 hours = 2( x- 10) = 2x - 20

distance between the two is 268 miles

so we can write

2x + 2x - 20 = 268

4x = 288

x = 288 / 4 = 72 mph

rate of first bus = 72 mph

and second bus = 72 - 10 = 62 mph

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The height of the object 1 second after it was launched is equals to 243.1 feet.

Let the launching velocity /initial velocity = u ft./s

and final velocity = 0 feet/sec , because at the maximum height, the final velocity of launching is '0'.

Maximum height , s = 3136 feet

time, t = 14 sec

Using the Equation of motion,

v² - u² = -2gs

where, v --> final velocity

u --> initial velocity

g --> acceleration due to gravity and it is a constant with value 9.8 m/sec²

s --> distance ( max. height)

plugging all known values in above formula,

0 - u² = -2 (9.8)(3136) = - 61465.6

=> - u² = - 61465.6

=> u² = 61465.6

=> u = √61465.6 = 247.92 ~ 248

=> u = 248 feet/sec

Now, the height, in feet, of the object 1 second after it was launched is

s = ut + (1/2)(-g)t²

=> s = 248(1) + (1/2)(-9.8)(1)

=> s = 248 - 4.9 = 243.1 feet

So, the required height is 243.1 feet.

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Answer:

Answer is B.

Step-by-step explanation:

Option A seem to look like a rotation of 180°.

Option B is a reflection across the x-axis.

Option C is a translation shift.

To solve this problem, we can set up a system of equations to represent the given information. Let x represent the cost of one steak burger. Then we can set up the following system of equations:

3x + 2(f) = 18

2x + 3(f) = 15.75

Where f represents the cost of one order of fries.

Subtracting the second equation from the first equation gives us:

x = 18 - 2(f) - 15.75 + 3(f)

= 18 - 15.75

= 2.25

Therefore, the cost of one steak burger is $2.25, which is answer choice C.

Answer: root 70

Step-by-step explanation:

starting info:

KL = 2NM

KM = 20

NO = 7

Using the fact the ratio of similar sides must be equal:

KL/NO = KM/NM

Therefore sub in values…

KL/7 = 20/NM

As KL = 2NM

2NM/7 = 20/NM

Rearrange:

2(NM)^2 = 140

(NM)^2 = 70

NM = root(70)

(Obviously take positive as can’t have negative length)

Answer:

16%

Step-by-step explanation:

Let's assume the original price of the item was Rs. 100.

After the price increased by 45%, the new price became:

New price = Original price + (45% of Original price)

New price = 100 + (0.45 x 100)

New price = Rs. 145

Now, the price dropped by 20% from the increased price of Rs. 145:

Final price = New price - (20% of New price)

Final price = 145 - (0.2 x 145)

Final price = Rs. 116

We can calculate the overall change in price by finding the difference between the final price and the original price:

Overall change in price = Final price - Original price

Overall change in price = 116 - 100

Overall change in price = 16

So, the price increased by Rs. 16. To find the percentage increase, we can use the formula:

Percentage increase = (Overall change in price / Original price) x 100%

Plugging in the values, we get:

Percentage increase = (16 / 100) x 100%

Percentage increase = 16%

Therefore, the price of the item increased by 16%.

BRAINLIEST PLEASE

The percentage by which the price increased is; 16%

Percentage Increase

Let the price of an item be denoted as x

Now, we are told that the price of the item increased by 45%. Thus means that the price will be; 1.45x

Now, the price after inflation decreased by 20% or 0.2. Thus;

Final price is now; 1.45x(1 - 0.2)

⇒ 0.8(1.45x)

⇒ 1.16 x

Since the original price is x, then;

Difference in price = 1.16x - x

Difference in price = 0.16x

In percentage, this difference in price represents a 16% increase.

The complete question is;

Due to inflation, the price of an item increased by 45% and then dropped by 20%. By what percent did the price increase?

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Answer: x=23

Step-by-step explanation:

1. First we need to find how much needs to be multiplied by 25, so 525/25=21.

2. Now that we know that x-2=21, we do 21+2.

3. 21+2=23, so x=23

Please give brainliest.

Answer: C -  square root of 74

Step-by-step explanation: took the test and got it right. hope this helps.

have a good day :)

Answer:

[tex]\sqrt{74}[/tex]

Step-by-step explanation:

The first and second numbers are -10 and 10, respectively. because their difference is zero

What is unitary method?

Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape.

On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a shape on paper is the area that it occupies.

Consider your square as being composed of smaller unit squares.

The number of unit squares necessary to completely cover the surface area of a specific 2-D shape is used to calculate the area of a figure. Some typical units for measuring area are square cms, square feet, square inches, square meters, etc.

Draw unit squares with 1-centimeter sides in order to calculate the area of the square figures shown below. The shape will therefore be measured.

According to our question-

Let us consider that first number is x and second number is y.

Hence, The first and second numbers are -10 and 10, respectively.

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Answer:

[tex]2^3 * 3 * 7[/tex]

Step-by-step explanation:

Linked below.

Find two factors and break down individually. Circle prime numbers. If there are more than one of the same prime number, write as an exponent:

i.e. 6 x 6 = [tex]6^{2}[/tex]

P (two red counters) = 1/15

P (two green counters) = 2/15

P (two yellow counters) = 1/145

P (white and then red) = 1/30

P (white or yellow, in either order but not both) = 3/10

P (white or red, in either order but not both) = 2/5

The probability of drawing a white or yellow counter first and then any

color second = 7/30

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

We have,

Number of red counters = 3

Number of green counters = 4

Number of yellow counters = 2

Number of white counters = 1

Total number of counters = 3 + 4 + 2 + 1 = 10

The probability of drawing 2 red counters.

= [tex]^3C_2[/tex] / [tex]^{10}C_2[/tex]

= 3 / 5 x 9

= 1/ 15

The probability of drawing 2 green counters.

= [tex]^4C_2[/tex] / [tex]^{10}C_2[/tex]

= 2 x 3 / 5 x 9

= 2/15

The probability of drawing 2 yellow counters.

= [tex]^2C_2[/tex] / [tex]^{10}C_2[/tex]

= 1 / 45

The probability of drawing one white and then one red counter.

= 1/10 x [tex]^3C_1[/tex]/[tex]^{9}C_1[/tex]

= 1/10 x 3/9

= 1/10 x 1/3

= 1/30

The probability of drawing one white or one yellow counter.

= 1/10 + 2/10

= 3/10

The probability of drawing one white or one red counter.

= 1/10 + 3/10

= 4/10

= 2/5

The probability of drawing one white or one yellow counter and one any counter.

= 3/10 x 7/9

= 7/30

Thus,

The required probabilities are given above.

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Answer:

Step-by-step explanation:

Answer = D Explanation: If some closed walk in a graph contains all the edges then the walk is called Euler. 32) Which of the following is not a type of graph ? Answer = D Explanation:Path is a way from one node no another but not a graph.

Answer:

x = $2351

Step-by-step explanation:

By using normal distribution of probability, it can be calculated that-

a) When x = 142, z = 1.4

b) When x = 130, z = 0.6

c) When x = 103, z = -1.2

What is normal distribution of probability?

Normal distribution of probability is a continuous type probability distribution whose probability density function is given by

f(x) = [tex]\frac{1}{\sigma \sqrt{2\pi}}e^{-\frac{z^2}{2}}[/tex]

Where z = [tex]\frac{x - \mu}{\sigma}[/tex] , [tex]\mu[/tex] is the mean and [tex]\sigma[/tex] is the standard deviation

Here Systolic blood pressure is normally distributed

Mean = 121

Standard deviation = 15

a) x = 142

z = [tex]\frac{142 - 121}{15}[/tex] = 1.4

b) x = 130

z = [tex]\frac{130 - 121}{15}\\[/tex] = 0.6

c) x = 103

z = [tex]\frac{103 - 121}{15}[/tex] = -1.2

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the total number of medium jerseys (20) by the total number of jerseys (50). To express this as a percentage, we must multiply the result by 100. Which results as 40%

In order to calculate the percentage of medium jerseys, we must divide the total number of medium jerseys (20) by the total number of jerseys (50).

To express this as a percentage, we must multiply the result by 100. Therefore, 20 ÷ 50 = 0.4 and 0.4 x 100 = 40%. Thus, 40% of the jerseys are medium size. the total number of medium jerseys (20) by the total number of jerseys (50). To express this as a percentage, we must multiply the result by 100. Which results as 40%

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