Initial value problems dy/dx+2y=3. Y(0)=1

The image of (3, 3) after dilation  by a scale factor of 1/3 centered at the origin will have coordinate (1, 1)

Dilation refers to the transformation that increases or reduces the image formed after the transformation

When the scale factor is greater that 1 the transformation will lead to magnification when the scale factor is less than 1 the image formed is compressed.

The transformation rule fir dilation is (x, y) → (kx, ky)

where k is the scale factor = 1/3

(3, 3)  → (1/3 * 3, 1/3 * 3)  → (1, 1)

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Answer:

8x - 20

Step-by-step explanation:

P.S Can I have brainliest?

Step-by-step explanation:

=4(2x-5)

=8x-20

hope it helps.

Answer:

3x+2x+a=180 degree(being linear pair)

5x+25=180

5x=180-25

x=155/5

x=31

Step-by-step explanation:

The computation of the increased in salary is $500.

Here, we have,

Explanation:

Data provided in the question

Salary for the first year = $50,000

CPI increase during the year = 4%

Overstated inflation = 1% i.e. 5%

The computation of the increased in salary is shown below:

= Salary of the first year × inflation rate - salary of the first year × CPI increase during the year

= $50,000 × 5% - $50,000 × 4%

= $2,500 - $2,000

= $500

Hence, The computation of the increased in salary is $500.

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complete question:

Mark's wage contract specifies a $50,000 salary for the first year, and specifies a salary increase equal to the percentage increase in the CPI during the second year. The increase in the CPI during the year was 4.0%. If the CPI overstates inflation by 1.0% (that is, the actual price increase was 3% and not 4%), at the end of the first year Mark's salary increased by $________ more than it would have without the upward bias.

An odd integer can be expressed as x = 2n+1 where n is an integer. (Therefore making 2n an even number and 2n+1 an odd number).

Three consecutive odd integers can then be expressed as  (2n+1), (2n+3), and (2n+5).

The sum of the first two integers is (2n+1) + (2n+3) = 4n+4 = 4(n+1). It is supposed to be 24 less than 4 times the third integer, or

4(2n+5)-24.

Setting both equal and solving for n:

4(n+1) = 4(2n+5)-24

24 = 4·6, so you can factor out 4 in the right-hand expression.

4(n+1) = 4(2n+5-6)   or   4(n+1) = 4(2n-1)

Cancel out factor 4 and solve for n.

n+1 = 2n-1      this yields   n=2

Now plug in into your three consecutive odd integer expressions:  (2n+1) = 5, (2n+3) = 7, (2n+5) = 9. The sum is therefore 5+7+9 = 21.

Double check your answer:  

Sum of first two integers:  5+7 = 12

24 less than 4 times third integer:  4·9 - 24 = 36-24 = 12.

The triangle is obtuse because 11^2 + 21^2 does not equal 29^2.

The Pythagorean Theorem states that the sum of the squares of the two shorter sides of a triangle must equal the square of the longest side in order for the triangle to be a right triangle.

We can use this theorem to determine the type of triangle by calculating the square of the longest side (29^2), and then comparing it to the sum of the squares of the other two sides (11^2 + 21^2). Since 11^2 + 21^2 does not equal 29^2, the triangle is obtuse.

The Pythagorean Theorem states that the sum of the squares of the two shorter sides of a triangle must equal the square of the longest side in order for the triangle to be a right triangle.

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Answer:

a = 5, b = - 13

Step-by-step explanation:

The Remainder theorem states that the remainder when f(x) is divided by (x - a) is equal to f(a)

Thus the remainder for division by (x + 2) is zero , then by substituting x = - 2 into the expression.

2(- 2)³ + a(- 2)² + b(- 2) - 30 = 0

2(- 8) + 4a - 2b - 30 = 0

- 16 + 4a - 2b - 30 = 0

- 46 + 4a - 2b = 0 ( add 46 to both sides )

4a - 2b = 46 → (1)

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

Similarly when f(x) is divided by (cx - a) the remainder is f(\(\frac{c}{a}\) )

The remainder on dividing by (2x - 1) is - 35, then by substituting x = \(\frac{1}{2}\)

2(\(\frac{1}{2}\) )³ + a(\(\frac{1}{2}\) )² + \(\frac{1}{2}\) b - 30 = - 35

2(\(\frac{1}{8}\) ) + \(\frac{1}{4}\) a + \(\frac{1}{2}\) b - 30 = - 35 ( add 30 to both sides )

\(\frac{1}{4}\) + \(\frac{1}{4}\) a + \(\frac{1}{2}\) b = - 5 ( multiply through by 4 to clear the fractions )

1 + a + 2b = - 20 ( subtract 1 from both sides )

a + 2b = - 21 → (2)

Solve (1) and (2) simultaneously )

Add (1) and (2) term by term to eliminate b

5a = 25 ( divide both sides by 5 )

a = 5

Substitute a = 5 into (2)

5 + 2b = - 21 ( subtract 5 from both sides )

2b = - 26 ( divide both sides by 2 )

b = - 13

According to the remainder theorem, when a polynomial P(x) is divided by (x-t) then the remainder of the division is equal to P(t). The value of a and b are 5 and -13, respectively.

According to the remainder theorem, when a polynomial P(x) is divided by (x-t) then the remainder of the division is equal to P(t). If P(t)=0, then the (x-t) is the factor of the polynomial.

Using the remainder theorem we can write,

f(x) = 2x³+ ax² + bx - 30

f(-2) = 2(-2)³ + a(-2)² + b(-2) - 30 = 0

-16 + 4a - 2b - 30 = 0

4a - 2b = 46   ........ equation 1

f(x) = 2x³+ ax² + bx - 30

f(1/2) = 2(1/2)³ + a(1/2)² + b(1/2) - 30 = -35

(1/4) + a(1/4) + b(1/2) = -35 + 30

(1+a+2b)/4 = -5

1 + a + 2b = -5 × 4

a + 2b = -21   .......... equation 2

Adding the two equations,

4a + 2b + a - 2b = 46 - 21

5a = 25

a = 25/5

a = 5

Substitute the value of a in any one of the equation,

a + 2b = -21

5 + 2b = -21

2b = -21 - 5

2b = -26

b = -26/2

b = -13

Hence, the value of a and b are 5 and -13, respectively.

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Answer:

A. -4 ≤ x ≤ 9

Step-by-step explanation:

Domain is the set of x-values that can be inputted into function f(x).

We see that our x-values span from -4 to 9. Since both are closed dots, they are included in the domain:

[-4, 9] or -4 ≤ x ≤ 9

$2010.458 is her new balance after she makes one new transaction for $51.

What does a credit balance mean?

The amount that the credit card company owes you is shown as a credit balance on your billing statement. Each payment you make results in credits being added to your account.

                                   When you return something you purchased with your credit card, you can receive an additional credit.

Credit balance  = $1,603

   APR = 28.6%

        = 28.6%  * $1,603

         =   458.458

Credit balance  = $1,603 + 458.458

                        = $2061.458

  net balance =  $2061.458 - 51

                      = $2010.458

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There's a rule where the the sum of the lengths of any two sides of a triangle has to be greater than the length of the third side So, add the two smallest numbers of each triangle and see if it is greater than the biggest number:

A: 10+13=23 and the longest side is 22. 23 is more than 22, so 'B' can be a triangle! We know this is an answer, but we should always check to see if any other answers work.

C: 12 + 7 = 19, and the longest side is 19. 19 isn't more than 19, so the answer isn't C.

B: 7 + 11 = 18, and the longest side is 24. 18 isn't more than 24, so the answer isn't B.

D: 6 + 9 = 15, and the longest side is 21. 15 isn't more than 21, so the answer isn't D.

Answer 'A' is the only one that can make a triangle, so it's the right answer!

Hope I helped, let me know if you have any questions :)

The measure of the missing side length from the given figure is 11 feet.

The right angle is created when two straight lines cross at a 90° angle or when they are perpendicular at the intersection.

It is referred to as a right angle if the angle formed by two rays exactly equals 90 degrees, or π/2.

The adjacent angles are right angles if a ray is positioned so that its terminus is on a line and they are equal.

In the given figure, assuming that all the intersecting sides meet at right angles.

So, the opposite sides are parallel to each other.

Let x be the length of missing side.

Thus, The length of missing side = Sum of length of parallel sides

Now, x= 5+6

= 11 feet

Therefore, the length of side missing is 11 feet.

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Answer:

60.3 mph

Step-by-step explanation:

211.05 miles / 3.5 hours = 60.3 miles/hour

The value of the inverse of the equation is this: x³ -3 = y

To find the inverse of the equation follow these steps:

1. Replace H(x) with y.

y = (x + 4)³ - 1

2. Interchange the values of X and Y.

X = (y + 4)³ - 1

3. Find the cube root of both sides

x³ = y + 4  - 1

4. Find the value of y

x³ - 4 + 1 = y

x³ -3 = y

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Answer:

2x^3+x^2-7x+3

Step-by-step explanation:

To do this you have to multiply the first term in the first parenthesis so you would multiply 2x by x^2 x and -3 so you get 2x^3+2x^2-6x  for the first part and then you would multiply -1 by the terms again so you would get -x^2-x+3 so you would get 2x^3+2x^2-6x-x^2-x+3 then you would add add teh like terms together so you get 2x^3+x^2-7x+3 as the final answer

The required expression is (x / 5) + 9

Given that we have to build an equation for the statement "9 more than the quotient of x and 5,

So,

This expression represents the quotient of x divided by 5, and then adding 9 to the result.

Therefore,

"9 more than the quotient of x and 5" can be written mathematically as:

(x / 5) + 9

Hence the required expression is (x / 5) + 9

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Answer:

It is most likely B from the graph

Answer:

b is the correct answer of the question

The measure of the unknown angles in the parallel lines AC and DF with transversal HJ are as follow,

m ∠DEH = 63° , m ∠BEF = 63° ,m ∠CBJ = 63°, m ∠CBE = 117° , m ∠FEH = 117° , m ∠BED = 117° , and m ∠ABJ = 117°.

Two lines AC and DF are parallel to each other  in the attached figure

Transversal HJ cut  lines AC and DF at point B and E respectively.

Measure of ∠ABE = 63°.

Using the result based on corresponding angles, alternate interior angles , and vertically opposite angles of a parallel lines we get,

Measure of ∠ABE ≅ Measure of ∠DEH ( corresponding angles)

⇒Measure of ∠DEH = 63°

Measure of ∠ABE ≅ Measure of ∠BEF ( alternate interior angles)

⇒Measure of ∠BEF = 63°

Measure of ∠ABE ≅ Measure of ∠CBJ ( vertically opposite angles)

⇒Measure of ∠CBJ = 63°

Using the result of linear pair angles,

Measure of ∠ABE + Measure of ∠CBE = 180°

⇒ Measure of ∠CBE = 180° -63°

⇒  Measure of ∠CBE = 117°

Measure of ∠CBE ≅ Measure of ∠FEH ( corresponding angles)

⇒Measure of ∠FEH = 117°

Measure of ∠CBE ≅ Measure of ∠BED ( alternate interior angles)

⇒Measure of ∠BED = 117°

Measure of ∠CBE ≅ Measure of ∠ABJ ( vertically opposite angles)

⇒Measure of ∠ABJ = 117°

Therefore, the measure of the seven unknown angles formed in the parallel line are given by m ∠DEH = 63° , m ∠BEF = 63° ,m ∠CBJ = 63°, m ∠CBE = 117° , m ∠FEH = 117° , m ∠BED = 117° , and m ∠ABJ = 117°.

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The above question is incomplete, the complete question is:

Lines AC and DF are parallel. They are cut by transversal HJ with your partner find the seven unknown angle measures in the diagram explain your reasoning. What do you notice about the angles with vertex B and the angles with vertex E.

In the attached figure.

The appropriate adjusting entry necessary at the end of the fiscal period on a Thursday is:

DR Salaries and Wages Expenses, $24,000

CR Salaries and Wages Payable, $24,000

What amount does the company pay weekly for wages and salaries?

The company pays for a five-day week, the salaries and wages of $30,000, which spans from Monday-Friday, in this case, the fiscal year ended on Thursday when workers have worked from Monday-Thursday but payment would be made the next day, on the 1st of a new year which is a Friday, hence, as at Thursday 31st the workers were owed for 4-day salaries and wages.

In essence, we need to show expense for 4 days and at the same show that the amount is owed by crediting wages and salaries payable.

The amount owed, which is also the expense incurred to date is computed as 4days divided by 5 days in a week multiplied by 1-week salary cost

4-day wages and salaries=4/5*$30,000

4-day wages and salaries=$24,000

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Sebastian's basis in the two assets are: $42,389 and $66,611

The computation of the Sebastian's basis in these two assets is shown below:

= Market value of the first piece of equipment ÷ Total market value of two pieces of equipment × purchase value of two pieces of equipment

= ($76300 ÷ $(76300 + 119900)) × $109,000

= $42,389

= Market value of the second piece of equipment ÷ Total market value of two pieces of equipment × purchase value of two pieces of equipment

= ($119,900 ÷ $(76300 + 119900)) × $109,000

= $66,611

The Total market value of two pieces of equipment

= $(76300 + 119900)

= $196,200

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The circled portion in the confidence interval formula p ± z represents the Margin of Error, which plays a crucial role in interpreting the range of plausible values for the population parameter.

In the confidence interval formula p ± z, the circled portion represents the Margin of Error.

The Margin of Error is a critical component of a confidence interval and quantifies the level of uncertainty in the estimate.

It indicates the range within which the true population parameter is likely to fall based on the sample data.

The Margin of Error is calculated by multiplying the critical value (z) by the standard deviation of the sampling distribution.

The critical value is determined based on the desired level of confidence, often denoted as (1 - α), where α is the significance level or the probability of making a Type I error.

The Margin of Error accounts for the variability in the sample and provides a measure of the precision of the estimate.

It reflects the trade-off between the desired level of confidence and the width of the interval.

A larger Margin of Error indicates a wider confidence interval, implying less precision and more uncertainty in the estimate.

Conversely, a smaller Margin of Error leads to a narrower confidence interval, indicating higher precision and greater certainty in the estimate.

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Answer:

3

Step-by-step explanation:

3/4 divided by 1/4 equals 3

Answer:

3

Step-by-step explanation:

3/4 is currently left

Subtract 1/4 by 3/4 until nothing is left

The number you get is 3 therefore the answer is 3

Answer:

slope represents the steepness of a line and can be found by taking any two points on the line and finding the difference of the y-values divided by the difference of the x-values

Step-by-step explanation:

slope represents the steepness of a line and can be found by taking any two points on the line and finding the difference of the y-values divided by the difference of the x-values

the variable 'm' represents slope

m = \(\frac{y-y}{x-x}\)

The correct statement regarding the transformation is given as follows:

Dilation bu a scale factor of 0.5 about the origin. Then reflect over the x-axis.

The true statements about the dilation are given as follows:

A dilation can be defined as a transformation that multiplies the distance between every point in an object and a fixed point, called the center of dilation, by a constant factor called the scale factor.

For this problem, the coordinates of the dilated line segment are half the coordinates of the original line segment, hence the scale factor is given as follows:

k = 0.5.

The y-coordinate then has the signal exchange, hence the figure is also reflected over the x-axis.

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Answer:

Yes

Step-by-step explanation:

40^2 +45^2 = C^2

1600+2025 = C^2

\(\sqrt3625=\sqrt C^2\)

C = 60.2

Answer:

Yes, 60.2>50

Step-by-step explanation:

Because 60.2 is more than 50, it is possible that the whiteboard fits on the wall.

Your welcome :)

Answer:

90 minutes

Step-by-step explanation:

See attachment for graph.

First, we need to determine the slope.

When y = 900, x = 0

When y = 600, x = 30

The slope is then calculated as:

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

m = (600 - 900)/(30 - 0)

m = -300/30

m = -10

Next, we determine the equation of the line using

y - y1 = m(x - x1)

So, we have:

y - 900 = -10(x - 0)

y - 900 = -10x

y = 900 - 10x

When the container is empty, y = 0.

So, we have:

0 = 900 - 10x

Collect Like Terms

10x = 900

Solve for x

x = 900/10

x = 90