Find the area of the parallelogram

The differential equation

y''' - 5y'' + 7y' - 3y = 0

has characteristic equation

r ³ - 5r ² + 7r - 3 = (r - 3) (r - 1)² = 0

with roots at r = 3 and r = 1 (with multiplicity 2), so that the characteristic solution to the DE is

y = C₁ exp(3x) + C₂ exp(x) + C₃ x exp(x)

Answer:

3/5=12/20 multiply by 4

4/7=16/49 a square of

25/30=5/6 divide with 5

improper fractions

9/5

21/8

10/1

Answer:

a.

1. The rule in this sequence is (+5) every next pattern

2. 22, 27, 32, 37

3. 42

4. 12 term

5. 67

b.

1. The rule in this sequence is (-3) every next pattern

2. -7, -10, -13, -16

3. -16

4. 13 term

5. -37

Step-by-step explanation:

Answer:

I'm not sure about the answer.

a.

1. The rule in this sequence is (+5) every next pattern

2. 22, 27, 32, 37

3. 42

4. 12 term

5. 67

b.

1. The rule in this sequence is (-3) every next pattern

2. -7, -10, -13, -16

3. -16

4. 13 term

5. -37

Hope this helps you ^^

Answer:

Step-by-step explanation:

(1/4 + 1/9 + 1/3)x = 25.

x = 36

Answer:

Let the number be x

(1/4 + 1/9 + 1/3) * x = 25

25/36 * x = 25

25x = 25*36

x = 25*36/25

x = 36

Step-by-step explanation:

Answer:

P+T+t+R=TA

Step-by-step explanation:

this should help

Answer:

17,600

Step-by-step explanation:

16,586 + 1,038 = 17,624 ≈ 17,600

alright I can help!

so to find the two values of x that are roots of the equation we need to put the variables all on one side so that we can set up the quadratic formula.

3x^2+2x-5=0 (the -3x^2 becomes positive when moved across the equal sign)

now we can set up the quadratic formula. the equation is x= (-b+-(sqrt of b^2 -4ac))/ 2a

so now we just plug in our variables.

x= (-2+-(sqrt of 2^2 -4×3×-5))/ 2×3

x= (-2+-8)/6

now we just seperate the equations so that we have the two roots. and then just solve!

x= (-2-8)/6 -> x= -5/3

x= (-2+8)/6 -> x=1

hope this helps! best wishes and best of luck!!

Answer:

127

Step-by-step explanation:

[(-33) + 46 + 68] - (15 - 61)

(114-33)-(-46)

81+46

127

Answer:

[tex]n=\frac{9}{2}[/tex]

Step-by-step explanation:

[tex]\frac{8}{3} =\frac{12}{n}[/tex]

Cross multiply.

8n=12(3)

8n=36

[tex]n=\frac{9}{2}[/tex]

I hope this helps!

pls ❤ and give brainliest pls

Answer: n = 9/2

Step-by-step explanation:

8/3 = 12/n

Now doing cross multiplication

8/3 = 12/n

8(n) = 12(3)

8n = 36

n = 36/8

n = 9/2

Therefore value of n is 9/2

Must click thanks and mark brainliest

Answer:

x = 1, y = −1

x = 5/2, y = 1/2

Step-by-step explanation:

From the question given above, the following data were obtained:

y = 2x² − 6x + 3 ........ (1)

y = x − 2 ...... (2)

We can obtain the solutions to the equation as follow:

y = 2x² − 6x + 3 ........ (1)

y = x − 2 ...... (2)

Substitute the value of y in equation 2 into equation 1

y = 2x² − 6x + 3

y = x − 2

2x² − 6x + 3 = x − 2

Rearrange

2x² − 6x − x + 3 + 2 = 0

2x² − 7x + 5 = 0

Solve by factorization

Obtain the product of 2x² and 5. The result is 10x².

Find two factors of 10x² such that their sum will result to −7x.

The factors are −2x and −5x.

Replace −7x in the equation above with −2x and −5x as shown below:

2x² − 2x − 5x + 5 = 0

2x(x − 1) − 5(x − 1) = 0

(x − 1)(2x − 5) = 0

x − 1 = 0 or 2x − 5 = 0

x = 1 or 2x = 5

x = 1 or x = 5/2

Substitute the value of x into equation 2 to obtain y

y = x − 2

x = 1

y = 1 − 2

y = −1

x = 5/2

y = x − 2

y = 5/2 − 2

y = (5 − 4)/2

y = 1/2

SUMMARY:

x = 1, y = −1

x = 5/2, y = 1/2

Answer:

y-3

Problem:

What is the remainder when the dividend is xy-3, the divisor is y, and the quotient is x-1. ?

Step-by-step explanation:

Dividend=quotient×divisor+remainder

So we have

xy-3=(x-1)×(y)+remainder

xy-3=(xy-y)+remainder *distributive property

Now we just need to figure out what polynomial goes in for the remainder so this will be a true identity.

We need to get rid of minus y so we need plus y in the remainder.

We also need minus 3 in the remainder.

So the remainder is y-3.

Let's try it out:

xy-3=(xy-y)+remainder

xy-3=(xy-y)+(y-3)

xy-3=xy-3 is what we wanted so we are done here.

Answer:

Step-by-step explanation:

Rolling two dice, there are 6*6 = 36 outcomes

The outcomes with the difference of 4:

Required probability:

Correct choice is b

Your Answer Is in this attachment.

Answer:

D-212 Degrees

Step-by-step explanation

i got it right on edge

Answer:

here you go! with step by step so you can do it next time

Answer:

-7/8

Step-by-step explanation:

cross multiply first then expand the equations when you cross multiply it will be

(3x+3)(x+4)=(3x+2)(x-1)

3x(x+4)+3(x+4)=3x(x-1)+2(x-1)

3x²+12x+3x+12=3x²-3x+2x-2

3x²+15x+12=3x²-x-2

3x²-3x²+15x+x=-2-12

16x/16=-14/16

x=-14/16

simplified to

-7/8

I hope this helps

Answer:

9.8 cm

Step-by-step explanation:

Volume of a cylinder can be gotten with this formula

V=πr2h

h = height of the oil.

We were told that 3 litres of oil was removed, then, there is a falling in the level of oil by 10 cm, hence the height of the oil is now

h° =( h) - (0.1)

Then the new volume can be calculated as

V°= V - (3×10^-3)

But

volume= (π r2h°)

Then substitute we have

πr2h - 0.003 = π r2 (h-0.1)

If we open the bracket we have

0.003 = (πr2 ×0.1)

πr2=0.003/0.1

Then r=√ (0.03/0.1π)

=9.8 cm

Note that 1L = 10-3 m3

Answer:

all real numbers

Step-by-step explanation:

The domain is the numbers that the input, x, can take

We can put in any real number for x since there are no restrictions on the input

Answer:

option D is domain

Step-by-step explanation:

because no change is happen in range by keeping any real number

Answer:

-1

Step-by-step explanation:

Vector a=(1,0) if visualized as a line has points (0,0) and (1,0). This means the line is horizontal and has equation y=0.

This means we are looking for a vertical line.

Instead of lambda, I'm going to use u.

So we want a+ub=(1,0)+u(1,1). to vertical. If we visualize this as a line with points (0,0) and (1+u,u). We would need u=-1 so this would be vertical.

So vectors a=(1,0) and a+ub=(1,0)+u(1,1) are perpendicular for u=-1.

So we are saying vectors (1,0) and (0,-1) are perpendicular. If you draw these, you can get a visual confirmation.

The value of λ is -1 and is perpendicular to vector a.

A vector is a number or phenomena with two distinct properties: magnitude and direction. The term can also refer to a quantity's mathematical or geometrical representation. In nature, vectors include velocity, momentum, force, electromagnetic fields, and weight.

We have,

Vector a = (1, 0) and b = (1, 1).

Here the vector is visualized as line is horizontal and has equation y=0.

Now, we have a + λb is perpendicular to vector a.

So, a + λb = (1, 0) + λ(1, 1)

                 = (1 + λ, 1)

Now, to get the vertical component we must have λ= -1.

Then, a(1, 0) and a+λb= (1,0)+ λ(1, ) are perpendicular to λ=-1.

Learn more about Vector here:

https://brainly.com/question/29740341

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5+(-18x+15)5 + (-18x +15)5

5+ (-90x +75) + (-90x + 75)

-180x +155

let's see the alternatives:

a) -2000x - 2018 -> -200x - 201,8

b) -30x - 33 -> -180x -198

c) none of the above

so, c is the right one

hope it helps :)

Answer:

ITS C

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

The area (A) of a rectangle is calculated as

A = length × breadth

   = (2 + [tex]\sqrt{2}[/tex] )(4-2[tex]\sqrt{2}[/tex] ) ← expand using FOIL

   = 8 - 4[tex]\sqrt{2}[/tex] + 4[tex]\sqrt{2}[/tex] - 4 ← collect like terms

   = 4 units²

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

The opposite sides of a rectangle are congruent , so

perimeter = 2(4 - 2 [tex]\sqrt{2}[/tex]) + 2(2 + [tex]\sqrt{2}[/tex] ) ← distribute parenthesis

                 = 8 - 4[tex]\sqrt{2}[/tex] + 4 + 2[tex]\sqrt{2}[/tex] ← collect like terms

                 = 12 - 2[tex]\sqrt{2}[/tex] units

Answer:

heyyy thereee

4) 572 = five hundred seventy two

5) 2.897 = two and eight hundred ninety seven thousandths

6) three hundred twenty five and 10 hundredths  or three hundred twenty five and 1 tenth

glad if brainliest ig ?

Answer: quadrant 1

Step-by-step explanation:

the triangle will make 5 360° rotations and then one 180° rotation. we know this because 1980/360=5.5

Answer:

Option d

Step-by-step explanation:

-5(8x)

= -5×8×x

= -40x

Answered by GAUTHMATH

Answer:

136+(4n-8)=180

136+4n-8=180

4n+128=180

4n=52

n=13

Step-by-step explanation:

please mark me as brainliest

Answer:

x ≈ 13.7

Step-by-step explanation:

Using the cosine ratio in the right triangle

cos70° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{x}{40}[/tex] ( multiply both sides by 40 )

40 × cos70° = x , then

x ≈ 13.7 ( to the nearest tenth )

Answer:

$962.00

Step-by-step explanation:

We can start from the first sentence of the word problem and work from there.

First, the employee is working for 40 hours at $18.50 per hour. This means that for each hour, the employee is gaining $18.50 . This can be represented as $18.50 * 40 = $740 for their base pay.

Next, the employee works 8 hours of overtime at 1.5 * base pay (18.50). For each hour of overtime they work, they earn 1.5 * 18.50 = $27.75 dollars. Their earnings from overtime work for the week can be represented as

8 * 27.75 = $222

Because all the employee's hours are encompassed in overtime and base pay, we can add the two together to get

740 + 222 = $962.00 for their total pay for the week

The first term in the series is 336. The second term is obtained by subtracting 4 from the first term; subtract 4 from that to get the third term; and so on. Then the n-th term in the series is

336 - 4 (n - 1)

or

340 - 4n

The last term in this series is 4, so we solve for n :

340 - 4n = 4

336 = 4n

n = 336/4 = 84

The sum of the series is then

[tex]\displaystyle\sum_{n=1}^{84}(340-4n) = 340\sum_{n=1}^{84}1 - 4 \sum_{n=1}^{84}n[/tex]

Recall that

[tex]\displaystyle \sum_{n=1}^{N} 1 = N[/tex]

[tex]\displaystyle \sum_{n=1}^N n = \frac{N(N+1)}2[/tex]

Then the sum we want is

[tex]\displaystyle\sum_{n=1}^{84}(340-4n) = 340\times84 - 4\times\frac{84\times85}2 = \boxed{14,280}[/tex]