Consider the system of differential equations

dx/dt= x+ y=1
dy/dt =1- x^2 +y^2

Required:
Sketch the x-nullcline, where solutions must travel vertically. Identify the regions in the plane where solutions will move toward the right, and where solutions move toward the right.

Answer:

t ≥ 72

Step-by-step explanation:

The pool has to be at least 72° or MORE to open, so we are going to have a greater sign with an equal sign under indicating that the temperature has to  at least be 72° or be greater than 72°. (≥)

Answer:

y = ⁷/5x + 13/10

Step-by-step explanation:

Recall: equation in slope-intercept form is given as y = mx + b

Thus, let's rewrite 14x - 10y = -13 in this form.

14x - 10y = -13

Add -14x to both sides

-10y = -14x - 13

Divide both sides by -10

-10y/-10 = -14x/-10 - 13/-10

y = ⁷/5x + 13/10

A quadratic equation is written in the form of ax²+bx+c. The roots of the given quadratic equation are shown in options B and F.

A quadratic equation is an equation whose leading coefficient is of second degree also the equation has only one unknown while it has 3 unknown numbers. It is written in the form of ax²+bx+c.

The roots of a quadratic equation can be found using the formula,

[tex]x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]

Given the quadratic equation 3x²-x+5 = 0. Comparing it with the general quadratic equation the value of a, b, and c will be 3, -1, and 5.

Now, if we substitute the values in the formula of the roots of the quadratic equation,

[tex]x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]

[tex]x = \dfrac{-(-1) \pm \sqrt{(-1)^2 - 4(3)(5)}}{2(3)}\\\\[/tex]

x = (1±√-59)/6

x = (1+√-59)/6, (1-√-59)/6

Hence, the roots of the given quadratic equation are shown in options B and F.

Learn more about Quadratic Equations here:

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9514 1404 393

Answer:

  120 m²

Step-by-step explanation:

If you divide the isosceles triangle into two right triangles, each has a leg and hypotenuse of 8 and 17, respectively. You may recognize these numbers as part of the Pythagorean triple (8, 15, 17). That recognition tells you the triangle's height is 15 m, so its area is ...

  A = 1/2bh

  A = 1/2(16 m)(15 m) = 120 m² . . . . triangle area

__

Alternate solutions

Given the three sides, you can find the smallest angle from the Law of Cosines. It will be ...

  α = arccos((17² +17² -16²)/(2·17·17)) ≈ 56.144°

Then the area is ...

  A = 1/2·ab·sin(C) . . . for triangle with sides a, b, c and opposite angles A, B, C

  A = 1/2sin(α)·17·17 = 120 . . . m²

__

Using Heron's formula:

  s = (17 +17 +16)/2 = 25

  A = √(25(25 -17)(25 -17)(25 -16)) = 5×8×3 = 120 . . . m²

__

If you need to, you can compute the triangle's height from the Pythagorean theorem.

  a² +b² = c² . . . . generic Pythagorean theorem equation

  8² + h² = 17² . . . with relevant values filled in

  h² = 289 -64 = 225

  h = √225 = 15

Answer:

B

Step-by-step explanation:

3/8 + 2/8 = 5/8

Answer:

-C

Step-by-step explanation:

3(C - 2d) - 2(2C - 3d).

Distribute

3C - 6d  - 4C +6d

Combine like terms

3C -4C  -6d +6d

-C

Answer:

-C

Step-by-step explanation:

3(C - 2d) - 2(2C - 3d) =

= 3C - 6d - 4C + 6d

= 3C - 4C - 6d + 6d

= -C

Answer:

The correct options are a and c.

Step-by-step explanation:

Confidence interval:

A confidence interval is given by the sample proportion plus/minus the margin of error. This means that the confidence interval is symmetric, that is, the difference between the upper bound and the sample proportion has to be the same as the difference between the sample proportion and the lower bound.

Sample proportion is 0.55

So options for the confidence interval are:

Lower bound - upper bound

0.54 - 0.56

0.53 - 0.57(which means that option b is wrong)

0.52 - 0.58(which means that option c is right)

...

0.5 - 0.6(which means that option a is right).

The correct options are a and c.

The confidence interval is the range of value between which the true population proportion would lie given a certain margin of error. Hence the correct options are A and C

Hence, the upper and lower boundary would the same error value above and below the mean proportion.

Evaluating the options given :

Error below = 0.50 - 0.55 = -0.05

Error above = 0.60 - 0.55 = 0.05

Error below = 0.53 - 0.55 = -0.02

Error above = 0.59 - 0.55 = 0.04

Error below = 0.52 - 0.55 = -0.03

Error above = 0.58 - 0.55 = 0.03

Error below = 0.60 - 0.55 = 0.05

Error above = 0.70 - 0.55 = 0.15

Error below = 0.45 - 0.55 = -0.10

Error above = 0.60 - 0.55 = 0.05

Therefore, the only options with equal margin of error, above and below the mean are options A and C.

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Answer:

It should be 115.2 meters^3

Step-by-step explanation:

Volume = 1/3 a^2h

             = 1/3 x 12^2 x 2.4

             = 115.2 m ^3

Answer: -7

Step-by-step explanation: -7 x -7 equals 49

Answer:

d = 8

Step-by-step explanation:

For:

(X1, Y1) = (-4, 5)

(X2, Y2) = (-12, 5)

Distance Equation Solution:

d=(−12−(−4))2+(5−5)2−−−−−−−−−−−−−−−−−−−−√

d=(−8)2+(0)2−−−−−−−−−−√

d=64+0−−−−−√

d=6–√4

d=8

Therefore, the distance between (-4,5), (-12,5) is 8.

9514 1404 393

Answer:

  right

Step-by-step explanation:

If you're going to be in the business of classifying triangles based on side lengths, it can be useful to know there is a "form factor" that can help. For sides a, b, c, with long side 'c', it is computed as ...

  f = a² + b² - c²

It has the following interpretation with respect to triangle shape:

  f > 0 . . . acute

  f = 0 . . . right

  f < 0 . . . obtuse

__

In this case, we have ...

  16² +63² -65² = 256 +3969 -4225 = 0

The triangle is a right triangle.

_____

Additional comment

When the triangle is a right triangle, this is equivalent to a statement of the Pythagorean theorem: c² = a² + b².

For triangles of other shapes, the interpretation is consistent with the Law of Cosines. When the form factor is divided by 2ab, the result is the cosine of the largest angle. That is why >0 means acute and <0 means obtuse.

The fourth option is indeed correct on Edge 2021.

The graph that represents the system of nonlinear inequalities is graph (a)

The nonlinear inequalities are given as:

[tex]y \le x^2 - 1[/tex]

[tex]x > y^2 - 6[/tex]

Rewrite the above nonlinear inequalities as:

[tex]y - x^2 \le - 1[/tex]

[tex]x -y^2 > -6[/tex]

[tex]y - x^2 \le - 1[/tex] means that the inequality has a solid line, and the outside part is shaded

[tex]x -y^2 > -6[/tex] means that the inequality has a dotted line, and the inner part is shaded

So, the graph that represents the system of nonlinear inequalities is graph (a)

Read more about the system of nonlinear inequalities at:

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Answer:

6,912 i think that's the answer I'm not sure though

Step-by-step explanation:

Answer:

[tex]8,400in^2[/tex]

Step-by-step explanation:

Area of Trapezoid: [tex]A=h(\frac{b1+b2}{2} )[/tex]

Given: B1, B2 and h

B1 = 18 in

B2 = 24

h = 16 in

Substitute variables for the give numbers:

[tex]A=16(\frac{18+24}{2} )\\A = 336 in^2[/tex]

The 336 in is for one desk, and they want you to find 25 desks. So multiply 336 and 25.

[tex]x = 25(336)\\x = 8,400in^2[/tex]

Answer:

A. 3

Step-by-step explanation:

I just did it on a calculator and got it correct

Answer:

culeous

Step-by-step explanation:

because it gives particular figured area

\

What the person above me said. :)

Answer:

y=5x

Step-by-step explanation:

first, we know that a rising line's slope is always positive, so the first one is incorrect

let's figure out the slope: y-y'/x-x' is the formula.

now, -5-5/-1-1= -10/-2= 5. so the slope of this line is 5.

Answer:

log3x

Step-by-step explanation:

i think it would be y=log3x

Answer:

Step-by-step explanation:

The chord and the segment between the centers form the diagonals of a kite with each pair of side being the radius of the circles.

As we know the long diagonal bisects the shorter one and they are perpendicular.

Using Pythagorean, lets find the distance between the center of a greater circle and the chord:

The distance from the center of smaller circle and the chord is:

Now using Pythagorean again, find the radius of the smaller circle:

Answer:

the second one

Step-by-step explanation:

Answer: Second one

Step-by-step explanation: Because when the plus times the minus it will stay minus.

Answer:

x = 16

Step-by-step explanation:

7x - 12 + 5x = 180

12x = 192

x = 16

Answer:

x = 16

Step-by-step explanation:

180 = (7x-12) + 5x

192 = 12x

16 = x

Answer: [tex]x=13[/tex], one base angle measures [tex]74^{\circ}[/tex]

Step-by-step explanation:

The base angles of an isosceles triangle are congruent, so:

Hence, the measure of one base angle is [tex]5(13)+9=\boxed{74^{\circ}}[/tex]

Answer:

x=30. y=60

Step-by-step explanation:

DG is a straight segment so it sums to 180 degrees. ECG is a right angle so 90 degrees. The rest is described as 2x and x. So 3x=90 degrees. x=30. Eh is also a straight segment. since we know x, we know that ECD is 60 degrees. So y+y=120 degrees. 2y=120. y=60.

Answer:

C.

Step-by-step explanation:

The answer should be less than 15 for x since its the smallest side and C is the only answer that has that.

Answer:

D. 2r = 16

Step-by-step explanation:

r/2 = 16, r=32

8= r/8,    r=64

4r=16,     r=4

2r=16

/2    /2

r=8

Answer:

26 mm

Step-by-step explanation:

1 cm is equal to 10 mm

2.6 cm

> 2.6 x 10

> 26 mm

Answer:

A. 57.8°

Step-by-step explanation:

Reference angle = θ

Length of hypotenuse = 15

Length of adjacent side = 8

Recall, SOHCAHTOA.

Thus, apply CAH to find θ.

Cos θ = Adj/Hyp

Cos θ = 8/15

θ = Cos^{-1}(8/15)

θ = 57.7690474° = 57.8°

Answer:

80

Step-by-step explanation:

because 8 is in tens place

so it´s value is 8*10=80

Answer:

the choices that are solutions are a and d sorry ic im wrong

Answer:

answer is option B) X=0.5

Step-by-step explanation:

happy to help:)