Which statement accurately describes the graph 2y=4x+8?
A
an increasing line that passes through (0, 4)
B
a decreasing line that passes through (0, 0)
C
an increasing line that passes through (0, 8)
D
a decreasing line that passes through (0, 2)

Answer:

AED congruent to FEC

Step-by-step explanation:

If you look closely, BOth of the angles are vertical.

First look for the fundamental solutions by solving the homogeneous version of the ODE:

[tex]y''+3y'=0[/tex]

The characteristic equation is

[tex]r^2+3r=r(r+3)=0[/tex]

with roots [tex]r=0[/tex] and [tex]r=-3[/tex], giving the two solutions [tex]C_1[/tex] and [tex]C_2e^{-3t}[/tex].

For the non-homogeneous version, you can exploit the superposition principle and consider one term from the right side at a time.

[tex]y''+3y'=2t^4[/tex]

Assume the ansatz solution,

[tex]{y_p}=at^5+bt^4+ct^3+dt^2+et[/tex]

[tex]\implies {y_p}'=5at^4+4bt^3+3ct^2+2dt+e[/tex]

[tex]\implies {y_p}''=20at^3+12bt^2+6ct+2d[/tex]

(You could include a constant term f here, but it would get absorbed by the first solution [tex]C_1[/tex] anyway.)

Substitute these into the ODE:

[tex](20at^3+12bt^2+6ct+2d)+3(5at^4+4bt^3+3ct^2+2dt+e)=2t^4[/tex]

[tex]15at^4+(20a+12b)t^3+(12b+9c)t^2+(6c+6d)t+(2d+e)=2t^4[/tex]

[tex]\implies\begin{cases}15a=2\\20a+12b=0\\12b+9c=0\\6c+6d=0\\2d+e=0\end{cases}\implies a=\dfrac2{15},b=-\dfrac29,c=\dfrac8{27},d=-\dfrac8{27},e=\dfrac{16}{81}[/tex]

[tex]y''+3y'=t^2e^{-3t}[/tex]

[tex]e^{-3t}[/tex] is already accounted for, so assume an ansatz of the form

[tex]y_p=(at^3+bt^2+ct)e^{-3t}[/tex]

[tex]\implies {y_p}'=(-3at^3+(3a-3b)t^2+(2b-3c)t+c)e^{-3t}[/tex]

[tex]\implies {y_p}''=(9at^3+(9b-18a)t^2+(9c-12b+6a)t+2b-6c)e^{-3t}[/tex]

Substitute into the ODE:

[tex](9at^3+(9b-18a)t^2+(9c-12b+6a)t+2b-6c)e^{-3t}+3(-3at^3+(3a-3b)t^2+(2b-3c)t+c)e^{-3t}=t^2e^{-3t}[/tex]

[tex]9at^3+(9b-18a)t^2+(9c-12b+6a)t+2b-6c-9at^3+(9a-9b)t^2+(6b-9c)t+3c=t^2[/tex]

[tex]-9at^2+(6a-6b)t+2b-3c=t^2[/tex]

[tex]\implies\begin{cases}-9a=1\\6a-6b=0\\2b-3c=0\end{cases}\implies a=-\dfrac19,b=-\dfrac19,c=-\dfrac2{27}[/tex]

[tex]y''+3y'=\sin(3t)[/tex]

Assume an ansatz solution

[tex]y_p=a\sin(3t)+b\cos(3t)[/tex]

[tex]\implies {y_p}'=3a\cos(3t)-3b\sin(3t)[/tex]

[tex]\implies {y_p}''=-9a\sin(3t)-9b\cos(3t)[/tex]

Substitute into the ODE:

[tex](-9a\sin(3t)-9b\cos(3t))+3(3a\cos(3t)-3b\sin(3t))=\sin(3t)[/tex]

[tex](-9a-9b)\sin(3t)+(9a-9b)\cos(3t)=\sin(3t)[/tex]

[tex]\implies\begin{cases}-9a-9b=1\\9a-9b=0\end{cases}\implies a=-\dfrac1{18},b=-\dfrac1{18}[/tex]

So, the general solution of the original ODE is

[tex]y(t)=\dfrac{54t^5 - 90t^4 + 120t^3 - 120t^2 + 80t}{405}\\\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,-\dfrac{3t^3+3t^2+2t}{27}e^{-3t}-\dfrac{\sin(3t)+\cos(3t)}{18}[/tex]

The area of the region is -2/3 square units

Since the region is bounded on the left by x = y²/2 and on the right by x = 3y - 4 for 2 ≤ y ≤ 4, the area of the region is given by

[tex]A = \int\limits^4_2 {\frac{y^{2}}{2} } \, dy - \int\limits^4_2 {(3y - 4)} \, dy \\[/tex]

Integrating, we have

A = [y³/6]₂⁴ - [3y²/2 - 4y]₂⁴

A = [4³/6 - 2³/6] - [3(4)²/2 - 4(4) - {3(2)²/2 - 4(2)]}]

A = [64/6 - 8/6] - [3(16)/2 - 16 - {3(4)/2 - 8]}]

A = [64/6 - 8/6] - [3(16)/2 - 16 - {3(4)/2 - 8]}]

A = [64/6 - 8/6] - [3(8) - 16 - {3(2) - 8]}]

A = [(64 - 8)/6] - [3(8) - 16 - {3(2) - 8]}]

A = [56/6] - [24 - 16 - {6 - 8}]

A = [56/6] - [8 - {-2}]

A = [56/6] - [8 + 2]

A = [56/6] - [10]

A = 56/6 - 10

Taking the L.C.M, we have

A = (56 - 10 × 6)/6

A = (56 - 60)/6

A = -4/6

A = -2/3 square units

So, the area of the region is -2/3 square units

Find the graph in the attachment

Learn more about area bounded by region here:

https://brainly.com/question/14510627

Answer:

2.3 (decimal form)

Step-by-step explanation:

Convert 4 1/2 and 2 1/5 into improper fractions.

4 1/2 -> 9/2, 2 1/5 -> 11/5

Then you subtract, find the LCD (Least Common Denominator) and then you can combine.

Decimal form of answer: 2.3

Exact form of answer: 23/10

Mixed number form: 2 3/10

Any of those work! ⬆

9514 1404 393

Answer:

  7. odd angles, 143°; even angles, 37°

  8. odd angles, 159°; even angles, 21°

  9. even angles, 34°; odd angles, 146°

  10. even angles, 29°, odd angles, 151°

Step-by-step explanation:

Angles 1 and 3 are vertical angles, so are congruent. The same can be said of angles 2 and 4. Each odd-numbered angle is supplementary to each even-numbered angle.

__

7. m∠1 = m∠3 = 143°, m∠2 = m∠4 = 180° -143° = 37°

8. m∠1 = m∠3 = 159°, m∠2 = m∠4 = 180° -159° = 21°

9. m∠2 = m∠4 = 34°, m∠1 = m∠3 = 180° -34° = 146°

10. m∠2 = m∠4 = 29°, m∠1 = m∠3 = 180° -29° = 151°

Answer:

[tex]\sf x = 6[/tex]

solving steps:

[tex]\sf in \ a \ rhombus \ the \ opposite \ angles \ are \ equal[/tex]

[tex]\hookrightarrow \sf 7x + 4 = 9x - 8[/tex]

[tex]\hookrightarrow \sf 7x -9x = - 8-4[/tex]

[tex]\hookrightarrow \sf -2x = - 12[/tex]

[tex]\hookrightarrow \sf x = 6[/tex]

Step-by-step explanation:

A Scatter Analysis is used when you need to compare two data sets against each other to see if there is a relationship. Scatter plots are a way of visualizing the relationship; by plotting the data points you get a scattering of points on a graph.

Answer: I'd go with C

Step-by-step explanation:

Answer:

Step-by-step explanation:

-14 - 28i + 4i + 28i^2

-14 - 24i + 28(-1)

-14 - 24i - 28

-42 - 24i

Answer: 21.9

Step-by-step explanation:

-Use Pythagoras theorem-

To find hypotenuse: square root 15 squared plus 16 squared

= 21.9

Step-by-step explanation:

Let an angle = x

x= 70+(90-x)

x= 160-x

2x=160

x=80

So angle is 80 and it's complementary angle would be 10

Answer:

55∘ and 125∘

Step-by-step explanation:

Supplementary angles sum to

180∘

let one angle be [tex]x[/tex]

then the other angle is [tex]x+70[/tex]

summing the 2 angles gives

[tex]x+x+7=180[/tex]

[tex]2x+70=180[/tex]

subtract 70 from both sides

[tex]2x=180 -70=110[/tex]

divide both sides by

[tex]2x=\frac{110}{2} =55[/tex]

thus the angles are

55∘ and  55 + 70= 125∘

Answer:

2. Change from dog/cat to tails/heads.DDC = TTH  CDC = HTH DCD = THT     CCD = HHT DDD = TTT CCC = HHH DCC = THH CDD = HTT

Answer:

Step-by-step explanation:

The function value is the y-coordinate of the point having the given x-value.

f(z-5)=z-5-2

f(z-5)=z-9

Answer: it is (c)

i hope this helped :)

Answer: 68

Step-by-step explanation:

(7-(-1))^2+(-2)^2

8^2+4

68

Answer:

im sry if i get it wrong i think it is 32

Step-by-step explanation:

Answer:

C. X²-4X+6

MY ANSWER(not sure)

Answer:

Step-by-step explanation:

[tex]44:20[/tex]

Cancel common factor : 4

[tex]44 \div 4 = 11 \\ 20 \div 4 = 5 \\ 11:5[/tex]

The ratios are 44:20=11:5

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

The given ratios are  44:20 = ?:5

we have to find the number in question mark place.

Let question mark be taken as x.

The ratios can be written in the form of fraction

44/20=x/5

Apply cross multiplication

44×5=20x

220=20x

Divide both sides by 20

x=220/20

x=11

Hence, the ratios are 44:20=11:5

To learn more on Ratios click:

https://brainly.com/question/13419413

#SPJ2

Answer:

X intercept=(5,0) and Y intercept=(0,15)

Step-by-step explanation:

3x + y = 15

to find the x int, sub in 0 for y and solve for x

3x + 0 = 15

3x = 15

x = 15/3

x = 5....so the x int is (5,0)

to find the y int, sub in 0 for x and solve for y

3(0) + y = 15

y = 15....so the y int is (0,15)

Answer:

p<6

Step-by-step explanation:

this basically means she can buy 6 pounds or less

Answer:

p<7

Step-by-step explanation:

Given parameters:

 Find the slope of the line;

                         -5x + 4y  =  -16

To find the slope of this line, we must express it in linear form according to the equation below;

                        y  = mx + c

Where x and y are the coordinates

                m is the slope

                c is the intercept

 Now let us write the given equation in this form;

                      -5x + 4y  =  -16

                    Take add +5x to both sides;

                    -5x + 4y + 5x  = 5x - 16

                              4y  = 5x - 16

  Now, divide through by 4;

                         [tex]\frac{4y}{4}[/tex]   = [tex]\frac{5x}{4}[/tex]  - [tex]\frac{16}{4}[/tex]

                        y  = [tex]\frac{5x}{4} - 4[/tex]

So the slope of the line is [tex]\frac{5}{4}[/tex]

Answer:

sin(θ) is negative, cos(θ) is positive

Step-by-step explanation:

Cosine corresponds to the x-coordinate within the unit circle, sine corresponds to the y-coordinate. In quadrant I, they are both positive, in quadrant II, x is negative whilst y is positive, and you would just continue by how they correspond as show in the unit circle, therefore, in quadrant IV, x is positive, y is negative.

Answer:

42

Step-by-step explanation:

Its impossible tto calculate x there.

But i can simply the expression for you...

42x²-13x+1

Answer:

See below

Step by step explanation:

Step-by-step explanation:

For cylinder:

r = 9 inches

h = 15 inches

[tex]V_{cylinder}=\pi r^2 h[/tex]

[tex]\implies V_{cylinder}=3.14 (9)^2 (15)[/tex]

[tex]\implies\huge\purple{ V_{cylinder}=3,815.1\:inch^3}[/tex]

[tex]V_{cone}=\frac{1}{3} V_{cylinder}[/tex]

[tex]\implies V_{cone}=\frac{1}{3}\times 3,815.1[/tex]

[tex]\implies \huge\orange{V_{cone}=1,271.7\: inch^3}[/tex]

Cone's volume is one third of the cylinder's volume.

Answer:

ta side from one base to next has  length of x. so we know each side has length x and  the shape they make is a square. This means we are only searching for the diagonal of a square. remember that a diagonal forms and isoscoles right triangle with the 2 sides being equal and the diagonal as the hypotenuse. Using  pythagoream theorem we can say

a^2 + b^2 = c^2 all side lengths are x so we can put x in for a and b  to get

x^2 + x^2 = c^2

2x^2 = c^2

c = x * squareroot(2)

so if the length between bases is 90 ft

c = 90 ft * squareroot(2)

c = 127.28 ft

Step-by-step explanation:

Answer: C 16,200 squared

Step-by-step explanation:

Answer:

2x2 - 7 = 9

Step-by-step explanation:

The factoring method can be chosen to solve the equation 2x2 - 7 = 9. It is one of the easiest methods as we can isolate the variable by factoring out the GCF and obtaining the values.

Answer:

60 lawns

Step-by-step explanation

6/5 lawns per hour times 50 hours = 60 lawns.

rate x time