A linear function contains the following points: 0,-3 and 6,15.
WHat is the slope and y-intercept

By applying the theory of separable ordinary differential equations we conclude that the solution of the differential equation [tex]\frac{dy}{dx} \cdot (\ln y)^{2} + y\cdot \sqrt{x} = 0[/tex] with y(0) = e is [tex]y = e^{\sqrt [3]{-2\cdot x^{\frac{3}{2} }+1}}[/tex].

In this question we must separate each variable on each side of the equivalence, integrate each side of the expression and find an explicit expression (y = f(x)) if possible.

[tex]\frac{dy}{dx} \cdot (\ln y)^{2} + y\cdot \sqrt{x} = 0[/tex]

[tex](\ln y)^{2}\,dy = -y \cdot \sqrt{x}\, dx[/tex]

[tex]-\frac{(\ln y)^{2}}{y}\, dy = \sqrt{x} \,dx[/tex]

[tex]-\int {\frac{(\ln y)^{2}}{y} } \, dy = \int {\sqrt{x}} \, dx[/tex]

If u = ㏑ y and du = dy/y, then:

[tex]-\int {u^{2}\,du } = \int {x^{\frac{1}{2} }} \, dx[/tex]

[tex]-\frac{1}{3}\cdot u^{3} = \frac{2\cdot x^{\frac{3}{2} }}{3} + C[/tex]

[tex]u^{3} = -2\cdot x^{\frac{3}{2} } + C[/tex]

[tex](\ln y)^{3} = - 2\cdot x^{\frac{3}{2} } + C[/tex]

[tex]C = (\ln e)^{3}[/tex]

[tex]C = 1[/tex]

And finally we get the explicit expression:

[tex]\ln y = \sqrt [3]{-2\cdot x^{\frac{3}{2} }+ 1}[/tex]

[tex]y = e^{\sqrt [3]{-2\cdot x^{\frac{3}{2} }+1}}[/tex]

By applying the theory of separable ordinary differential equations we conclude that the solution of the differential equation [tex]\frac{dy}{dx} \cdot (\ln y)^{2} + y\cdot \sqrt{x} = 0[/tex] with y(0) = e is [tex]y = e^{\sqrt [3]{-2\cdot x^{\frac{3}{2} }+1}}[/tex].

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Answer:

Look down my answer↓:

Step-by-step explanation:

The coordinates of the turning point of the graph of the quadratic equation is given by: (-6.25, -75.13).

A quadratic equation is modeled by:

[tex]y = ax^2 + bx + c[/tex]

The vertex is given by:

[tex](x_v, y_v)[/tex]

In which:

In this problem, the function is given by:

y = 2x² + 25x + 3.

Hence the coefficients are a = 2, b = 25, c = 3, then the coordinates of the vertex are given as follows:

The coordinates of the turning point of the graph of the quadratic equation is given by: (-6.25, -75.13).

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Answer:

6.25, -75.13

Step-by-step explanation:

it just is

There are 25773 foxes in the region in the year 2008

The given parameters are:

Let the number of years after 2000 be x.

So, the function is

f(x) = a * (1 + r)^x

This gives

f(x) = 15000 * (1 + 0.07)^x

In 2008, we have:

x = 8

So, the equation becomes

f(8) = 15000 * (1 + 0.07)^8

Evaluate

f(8) = 25773

Hence, there are 25773 foxes in the region in the year 2008

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The domain of the function [tex]y=\sqrt{(x+6)}-7[/tex] is given by (B) that is [tex]x \geq-6[/tex]

Domain of a function refers to the values or range of input values of a function for which the function exists in real.

In this problem the given function is

[tex]y=\sqrt{(x+6)}-7[/tex]

Now the above function exists if the expression under square root is greater or equal to 0, since negative number cannot be square rooted in real, that gives imaginary number.

So, for existence of function it is must to

[tex]x+6\geq0[/tex]

[tex]x\geq-6[/tex]

Hence the domain of the given function is given by [tex]x\geq-6[/tex]

Hence the correct option is (B).

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Answer:

All its side lengths are equal

(and all the agle of 60°)

Step-by-step explanation:

What is true of an equilateral triangle? Two of its side lengths are equal. All its side lengths are equal. None of its side lengths are equal. None of its interior angles are equal. What is true of an equilateral triangle ? Two of its side lengths are equal . All its side lengths are equal . None of its side lengths are equal . None of its interior angles are equal .​

Answer:

x

Step-by-step explanation:

[tex]f(g(x)) = 3(\frac{x+2}{3} )-2\\= x + 2 - 2\\= x[/tex]

Answer:

Perimeter = 2(l + b)

= 2(x + 5x³ + 4 - x²)

= 2x + 10x³ + 8 - 2x²

= 10x³ - 2x² + 2x + 8

Hence, ur answer is the first option.

Answer:

A.

Step-by-step explanation:

L = x

W = 5x³ + 4 - x²

P = 2L + 2W

P(x) = 2x + 2(5x³ + 4 - x²) = 2x + 10x³ + 8 - 2x²

P(x) 10x³ - 2x² + 2x + 8

L = x

W = 5x³ + 4 - x²

P= 2L + 2W

P(x) = 2x + 2(5x³ + 4 - x²) = 2x + 10x³ + 8 - 2x²

= P(x) 10x³ - 2x² + 2x + 8

Step-by-step explanation:

both ends are going to the same direction so the degree is even. the right side is going up so the leading coefficient is positive.

Answer: 59

Step-by-step explanation:

The measure of an arc is equal to the measure of the central angle intercepted by it.

Answer:

Step-by-step explanation:

X = 6

Y = (-6)

Answer:

Step-by-step explanation:

(h+k)(1)=h(1)+k(1)=2+(-1)=2-1=1

(k-h)(4)=k(4)-h(4)=0-(-1)=1

(k/h)(3)[tex]=\frac{k(3)}{h(3)} =\frac{-1}{0} =- \infty[/tex]

(h.k)(0)=h(0).k(0)=3(-2)=-6

(k.h)(0)=k(0).h(0)=-2(3)=-6

(h.k)(3)=h(3).k(3)=0(-1)=0

h(k(-2))=h(-3)=0

From the slopes it is confirmed that PQ || RS OR|| SP and therefore it is a parallelogram .

A parallelogram is a quadrilateral in which the opposite sides are parallel.

The coordinates of a quadrilateral is given

To prove that it is a parallelogram

PQ || RS

OR|| SP

The slope of a straight line is given by

[tex]\rm m = \dfrac{y_2 -y_1}{x_2- x_1}[/tex]

For PQ

m = (-1/6) = -1/6

For QR

m = -6/1 = -6

For RS

m = 1/(-6) = -1/6

For SP

m = -6

From the slopes it is confirmed that

PQ || RS

OR|| SP

and therefore it is a parallelogram

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Answer:

(-4, -5)

Step-by-step explanation:

-3x + 4y = -8

+

3x + y = -17

= 5y = -25 = y = -5

-3x + 4(-5) = -8

-3x - 20 = -8

-3x = 12

x = -4

Answer:

Step by step explanation:

Given that,

[tex]f(x) = {x}^{2} [/tex]

[tex]g(x) = x - 1[/tex]

Solution:

Solving for (f•g)(x):

[tex] = f(x) \cdot g(x)[/tex]

Now substitute the given values.

[tex] = x {}^{2} \cdot(x - 1)[/tex]

[tex] = x {}^{2} (x - 1)[/tex]

Apply distributive property:

[tex] = (x ^{2} \cdot x) - x {}^{2} \cdot 1[/tex]

Hence,f•g(x) will be [tex] x {}^{3} - x {}^{2}[/tex].

Answer:

$9

Step-by-step explanation:

Let, the price of pencils is x, and the price of rulers is y.

4x+2y=8.....(i)

2x+4y=10......(ii)

From eq(i),

2(2x+y)=8

2x+y=4

y=4-2x eq(iii)  .....put in eq(ii)

2x+4(4-2x)=10

2x+16-8x=10

-6x=10-16

x=-6/-6

x=1 put in eq (iii)

y=4-2(1)

y=2

Now, the price of 3 rulers and 3 pencils = 3x+3y=3(1)+3(2)

=9

Please give me brainlist.

The sales of skin diving and scuba equipment in the year 2008 is (d) 424,550,000

The regression equation is given as;

y = 7.36x - 14,354.33

In 2008, the value of x is

x = 2008

So, we have:

y = 7.36 * 2008 - 14,354.33

Evaluate

y = 424.55

Hence, the sales of skin diving and scuba equipment in the year 2008 is (d) 424,550,000

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The sales of skin diving and scuba equipment in the year 2008 is (d) 424,550,000.

We have given that,

The table below shows the amount of money spent on skin diving and scuba equipment in some recent years.

The regression equation is given as

y = 7.36x - 14,354.33

In 2008, the value of x is

x = 2008

So, we have y = 7.36 * 2008 - 14,354.33

Evaluate y = 424.55

Hence, the sales of skin diving and scuba equipment in the year 2008 is (d) 424,550,000

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Using the relation between velocity, distance and time, it is found that:

Velocity is distance divided by time, that is:

[tex]v = \frac{d}[t}[/tex]

Flying against the wind, an airplane travels 2520 kilometers in 4 hours, that is:

[tex]v - v_w = \frac{2520}{4}[/tex]

[tex]v - v_w = 630[/tex]

[tex]v = 630 + v_w[/tex]

Flying with the wind, the same plane travels 9450 kilometers in 9 hours, hence:

[tex]v + v_w = \frac{9450}{9}[/tex]

[tex]v + v_w = 1050[/tex]

[tex]v = 1050 - v_w[/tex]

Hence, solving for the wind's speed:

[tex]630 + v_w = 1050 - v_w[/tex]

[tex]2v_w = 420[/tex]

[tex]v_w = \frac{420}{2}[/tex]

[tex]v_w = 210[/tex]

For the plane, we have that:

v = 1050 - 210 = 840.

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Answer:

1. F

2. F

3. T

4. F

5. F

6. T

7. T

8. F

9. F

10. T

Step-by-step explanation:

1. For the rays to be opposite, they need to have the same starting point and go in different directions. Rays AP and BP use Point A and Point B, respectively, for their starting points.

2. They do not lie on the same line.

3. Points A, B, C, D all lie in the same plane therefore making them coplanar.

4. Points X, Y do not lie in the same plane as A, B.

5. Point X does not lie in the same plane as C, D, B

6. A, P, B are all points on the same line therefore any two of them could be used to represent the same line.

7. PX and PY start at the same point and go in the opposite directions, defining them as opposite rays.

8. Plane AXY cannot be defined as point X and Y are not in a plane.

9. Lines AB and CD cannot both be in a different plane.

10. Both rays sum up to equal Line XY.

A function assigns the values. The correct option is D.

A function assigns the value of each element of one set to the other specific element of another set.

The complete question is:

Which pair of statements describe the end behavior of the graph of the function f(x) = x³ + 2x² − 5x − 6?

A.) As x approaches negative infinity, f(x) approaches infinity. As x approaches infinity, f(x) approaches infinity.

B.) As x approaches negative infinity, f(x) approaches infinity. As x approaches infinity, f(x) approaches negative infinity.

C.) As x approaches negative infinity, f(x) approaches negative infinity. As x approaches infinity, f(x) approaches negative infinity.

D.) As x approaches negative infinity, f(x) approaches negative infinity. As x approaches infinity, f(x) approaches infinity.

If we draw the graph of the given function f(x) = x³ + 2x² − 5x − 6, then it can be observed that as x approaches -∞, f(x) approaches -∞. As x approaches ∞, f(x) approaches infinity.

Hence, the correct option is D.

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Answer:

A, D, E

Explanation:

It's right on edge lol

Answer:One of the factors of the given expression is (2h + 1).

Step-by-step explanation:

ed

Answer:

C on edge 23

Step-by-step explanation:

because i said so

The percentage change in G is 21 %

Percentage change is defined as the increase or decrease in the value as compared to the original value multiplied by 100.

It is given that

G = ab

when a is increased by 10% the new a will be = 1.1 a

When b is increased by 10% the new b will be 1.1 b

So,

G' = 1.1a *1.1 b

G' = 1.21 ab

G' = 1.21

(G' - G)*100/G = (1.21-1)*100/1

The percentage change is 21 %

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Answer:

Important- not urgent

Step-by-step explanation:

The research paper is important but since Brandon has two weeks to decide it is not urgent.

Answer: It is not a right angle.

Answer:

y^-1= x +8

Step-by-step explanation:

this may be helpful for you

The slope of line p is -5, so substitute into point-slope form, we get

[tex]\boxed{y-37=-5(x+2)}[/tex]

Answer:

B

Step-by-step explanation:

x = y-4x^2 can be rearranged to get y = 4x^2 + x, which is a function

Using the Factor Theorem, the polynomials are given as follows:

1. [tex]P(x) = x^5 + 2x^4 - 7x^3 + x^2[/tex]

2. [tex]P(x) = 0.8(x^4 - 4x^3 - 16x^2 + 64x)[/tex]

3. P(x) = -0.1(x³ - 4x² - 3x + 18)

The Factor Theorem states that a polynomial function with roots [tex]x_1, x_2, \codts, x_n[/tex] is given by:

[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]

In which a is the leading coefficient.

Item a:

The parameters are:

[tex]a = 1, x_1 = x_2 = 1, x_3 = x_4 = 0, x_5 = -4[/tex]

Hence the equation is:

P(x) = (x - 1)²x²(x + 4)

P(x) = (x² - 2x + 1)(x + 4)x²

P(x) = (x³ + 2x² - 7x + 1)x²

[tex]P(x) = x^5 + 2x^4 - 7x^3 + x^2[/tex]

Item b:

The roots are:

[tex]x_1 = x_2 = 4, x_3 = 0, x_4 = -4[/tex]

Hence:

P(x) = a(x - 4)²x(x + 4)

P(x) = a(x² - 16)x(x - 4)

P(x) = a(x³ - 16x)(x - 4)

[tex]P(x) = a(x^4 - 4x^3 - 16x^2 + 64x)[/tex]

It passes through the point x = 5, P(x) = 36, hence:

45a = 36.

a = 4/5

a = 0.8

Hence:

[tex]P(x) = 0.8(x^4 - 4x^3 - 16x^2 + 64x)[/tex]

Item 3:

The roots are:

[tex]x_1 = x_2 = 3, x_3 = -2[/tex]

Hence:

P(x) = a(x - 3)²(x + 2)

P(x) = a(x² - 6x + 9)(x + 2)

P(x) = a(x³ - 4x² - 3x + 18)

For the y-intercept, x = 0, y = -1.8, hence:

18a = -1.8 -> a = -0.1

Thus the function is:

P(x) = -0.1(x³ - 4x² - 3x + 18)

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