The planets move around the sun in elliptical orbits with the sun at one focus. The point in the orbit at which the planet is closest to the sun is called perihelion, and the point at which it is farthest is called aphelion. These points are the vertices of the orbit. A planet's distance from the sun is 741,000,000 km at perihelion and 817,000,000 km at aphelion. Find an equation for the planet's orbit. (Place the origin at the center of the orbit with the sun on the x-axis. Use the following as necessary: x, y.)

For this one, plug in your x and y intercepts for the corresponding letters and see which one is true.  I always start with the first equation and then see which ones solve it first, that will cut your time down on a test.

Lets start with A. (4,5)

and the first equation y=x+1

5=4+1, which is true so A is a potential answer

B. (2,3)

3=2+1, B is a potential as well

C. (-2,1)

1=-2+1, which is false so C is out

D. (-4,-3)

-3=-4+1, which is true.

To cut down on time, do the same thing with the second equation and your final answer will be A. (4,5)

The simplified form of the expression (25x^2-14xy+4)-(7x^2-9y)+(2xy+7) is 18x^2 - 12xy + 20 + 9y. We achieved this by applying the distributive property, grouping like terms, and simplifying each group.

To simplify the expression (25x^2-14xy+4)-(7x^2-9y)+(2xy+7), we first apply the distributive property and place minus signs before each of the terms inside the bracket:

25x^2 -14xy + 4 - 7x^2 + 9y + 2xy + 7.

From here, group like terms together:

(25x^2 - 7x^2) + (-14xy + 2xy) + (4 + 9y + 7).

Finally, simplify each group of like terms to achieve the simplified expression:

18x^2 - 12xy + 20 + 9y.

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d - e = 2d - e      add e to both sides

d - e + e = 2d - e + e

d = 2d      subtract d from both sides

d - d = 2d - d

0 = d

Answer: D = 0

Thus meaning D has to equal 0.

I hope this helps!

y = x² + 6x + 5

Use the formula: -b/2a

a = 1

b = 6

- 6 / 2

= -3

The x-coordinate of the vertex is -3

Plug the x value back into the original equation to find the y-coordinate of the vertex

y = (-3)² + 6(-3) + 5

y = -4

Answer:

Bus drop him off 64 miles far from the school.

Explanation:

 Total distance traveled by Nigel from Home to school each day = 312 miles

 Distance from bus stop to his home = 14 miles

Distance traveled by Nigel on the city bus = 234 miles.

Distance from bus drop off position to school = X miles

We have Total distance traveled by Nigel = 14+234+X = 248+X

Equating both total distances

          248+X = 312

            X = 64 miles.

 So bus drop him off 64 miles far from the school.

1. The Great Wall of China is 13,170.696

2.how many feet are in a mile= 5,280= 1 mile  

3. 19,536,000=3700 miles

Solving the system, we find [tex]\(x = 2.5\) and \(y = -1\)[/tex]. The product of [tex]\(x\) and \(y\) is \(-2.5\)[/tex]. Answer: C) [tex]\(-\frac{2}{5}\).[/tex]

To find the product of [tex]\(x\) and \(y\)[/tex], we need to solve the given system of equations:

2x - 5y = 10

4x + 3y = 7

Let's solve this system using the substitution method:

From the first equation, we can express [tex]\(x\) in terms of \(y\)[/tex]:

[tex]\[2x = 10 + 5y\][/tex]

[tex]\[x = \frac{10 + 5y}{2}\][/tex]

[tex]\[x = 5 + \frac{5}{2}y\][/tex]

Now, substitute this expression for [tex]\(x\)[/tex] into the second equation:

[tex]\[4(5 + \frac{5}{2}y) + 3y = 7\][/tex]

[tex]\[20 + 10y + 3y = 7\][/tex]

[tex]\[13y = -13\][/tex]

[tex]\[y = -1\][/tex]

Now, substitute [tex]\(y = -1\)[/tex] into the expression for \(x\):

[tex]\[x = 5 + \frac{5}{2}(-1)\][/tex]

[tex]\[x = 5 - \frac{5}{2}\][/tex]

[tex]\[x = 5 - 2.5\][/tex]

[tex]\[x = 2.5\][/tex]

Finally, find the product [tex]\(xy\):[/tex]

[tex]\[xy = 2.5 \times (-1)\][/tex]

[tex]\[xy = -2.5\][/tex]

So, the product of [tex]\(x\) and \(y\) is \(-2.5\)[/tex], which corresponds to option C) [tex]\(-\frac{2}{5}\).[/tex]

I think you can google that really easily.

What is 3/5 of $40 restaurant bill equals $

the answer is $24

Answer:

9/4

Step-by-step explanation:

a pex

Answer:

Real numbers

0≤ t ≤17

Step-by-step explanation:

Khan academy said

The domain of d in the given problem is time (T) in minutes since Tanya left home and is the set of all real numbers greater than or equal to 17.

The domain of d in the given problem is time (T) in minutes since Tanya left home.

Since Tanya walked for 17 minutes, the domain of d is the set of all real numbers greater than or equal to 17.

ANSWER

The factorization of   [tex]100x^2-20x+1[/tex]

 is [tex](10x-1)^2[/tex].

EXPLANATION

We want to factor [tex]100x^2-20x+1[/tex]

Comparing this to [tex]ax^2+bx+c[/tex]

[tex]a=100,b=-20,c=1[/tex]

[tex]ac=100[/tex]

We look for factors of 100  that add up to [tex]-20[/tex].

These factors are [tex]-10,-10[/tex]

We now split the middle term to obtain;

[tex]100x^2-10x-10x+1[/tex]

We factor to obtain;

[tex]10x(10x-1)-1(10x-1)[/tex]

This simplifies to  [tex](10x-1)(10x-1)=(10x-1)^2[/tex]

Answer:B

Step-by-step explanation:

Insert x = 100 and x = 200 in the function

f(100) = 20,000 - 40*100

= 20,000 - 4000

= 16,000

f(2)) = 20,000 - 8,000 = 12,000

So its choice C  ,  All reals between 12,000 and 16,000 inclusive.

Answer:

Option C.

Step-by-step explanation:

The given function is

[tex]f(x)=20000-40x[/tex]

where x represents the number of minutes the painter has worked from the 100-minute mark through the 200-minute mark of the project.

We need to find the practical range of the function.

The value of x lies from 100 to 200.

At x=100,

[tex]f(100)=20000-40(100)=20000-4000=16000[/tex]

At x=200,

[tex]f(200)=20000-40(200)=20000-8000=12000[/tex]

It means the practical range of the function is all real numbers between 12,000 and 16,000 inclusive.

Hence, the correct option is C.

[tex]\frac{-5 + 2x^{2}}{7 - 8x}[/tex]

The denominator cannot equal zero.

7 - 8x ≠ 0

7       ≠  8x

    [tex]\frac{7}{8} \neq \frac{8x}{8}[/tex]

[tex]\frac{7}{8} \neq x[/tex]

Answer: [tex]\frac{7}{8}[/tex] is not in the domain

Answer is BF...hope this helps

$50

the sale price is [tex]\frac{5}{12}[/tex] × $120

[tex]\frac{5(120)}{12}[/tex] = $50

Answer:50

Step-by-step explanation:

you would do number of devisions (denominator of fraction) divided by the number of the original price then multiply it by the numer of the devision (numerator of fraction)

120/12=10*5=50

B. The pickup truck would travel 252 miles in 6 hours.

The truck travels 210 miles in 5 hours.

To find the speed, we divide the distance by the time:

210 miles / 5 hours

= 42 miles/hour.

Now, let's calculate the distance for 6 hours.

The truck travels at 42 miles/hour.

To find the distance in 6 hours, we multiply the speed by the time:

42 miles/hour * 6 hours

= 252 miles.

ANSWER

[tex]2y-x-20=0[/tex]

or

[tex]y=\frac{1}{2}x+10[/tex]

EXPLANATION

Let the rectangle be oriented as shown in the diagram.

The line segment AD passes through [tex]A(2,11)[/tex].

All we need now is the slope of AD then we can find its equation.

Since AD is perpendicular t AB, we determine the slope of AB and then use it to find the slope of AD.

[tex]Slope_{AB}=\frac{1-11}{7-2}[/tex]

[tex]Slope_{AB}=\frac{-10}{5}=-2[/tex]

The slope of AD is the negative reciprocal of the slope of AB because they are perpendicular.

[tex]Slope_{AD}=\frac{-1}{-2}=\frac{1}{2}[/tex]

The equation of AD is given by;

[tex]y-y_1=m(x-x_1)[/tex]

[tex]y-11=\fra[1}{2}(x-2)[/tex]

Multiplying through by 2 gives,

[tex]2y-22=(x-2)[/tex]

[tex]2y-x-22+2=0[/tex]

[tex]2y-x-20=0[/tex]

or

[tex]y=\frac{1}{2}x+10[/tex]

Answer:

1800 ÷ 6

Step-by-step explanation:

18,000 ÷ 60 is the same as;

18,000 ÷ 10 ÷ 6 and is the same as;

1,800 ÷ 6

Answer:

13  all three angles =60 in total they equal 180

14) I believe x = 32.5 Am not sure though.

Step-by-step explanation:

That is the only question i can answer but to help you with this all triangles big or small the total of all the angles combined = 180

First you must know that is i∧2= -1

x∧3-4x∧2+4x-16 = x∧2 (x-4) + 4 (x-4) = (x-4) (x∧2+4) = (x-4) (x∧2-(-4)) =

= (x-4) (x∧2-(-1) *4) = (x-4) (x∧2- i∧2*2∧2) = (x-4) (x∧2-(2i)∧2) = (x-4) (x-2i) (x+2i)

Good luck!!!

An asymptote is a vertical horizontal or oblique line to which the graph of a function progressively approaches without ever touching it.

To answer this question we observe the graph. All the values of x and y must be identified for which the graph of the function tends to infinity.

It is observed that these values are:

x = -1

x = 3

y = 0

The first two corresponds to the equations of a vertical line. The third corresponds to horizontal line, the axis of x. It can be seen that although the graph of the function is very close to these values, it never "touches" them

The asymptotes to the considered function are given as:

Suppose that we have the function f(x) such that it is continuous for all input values < a or > a and have got the values of f(x) going  to infinity or -ve infinity (from either side of [tex]x = a[/tex]) as x goes near a , and being not defined at [tex]x = a[/tex], then at that point, there can be constructed a vertical line [tex]x = a[/tex] and it will be called as vertical asymptote for f(x) at [tex]x = a[/tex]

The line [tex]y = a[/tex] is horizontal asymptote if the function f(x) tends to 'a' from upside of that line y = a, or from downside of that line.

For the given case, the line y = 0 is one of its horizontal asymptote.

If we make two straight lines at x = -1, and x = 3, we get two lines to which the graph of the function is going arbitrarily close, and going to +ve or -ve infinity.

Thus, they are its vertical asymptotes.

Therefore, the asymptotes to the considered function are given as:

Learn more about asymptotes here:

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Answer:

(1,2) (-1,-2)

Step-by-step explanation:

Given the equation of curve as y= 2x³ and slope of tangent line as 6 then

Find dy/dx

[tex]\frac{d}{dx} (y)=\frac{d}{dx}(2x^3)[/tex]

Apply the power rule

[tex]\frac{d}{dx} (x^n)=nx^{n-1}[/tex]

where n=constant

Hence, our equation will be;

[tex]\frac{dy}{dx} =2*3x^{3-1} \\\\\\\frac{dy}{dx} =6x^{2}[/tex]

But you know that dy/dx=slope=6

6x²=6--------------------divide both sides by 6

6x²/6=6/6

x²=1

x=√1=±1

x=1 and -1

Remember y=2x³

Substitute value of x to get value of y

y=2x³

y=2×1³

y=2×1=2

y=2

For x=-1, find y coordinate

y=2×-1³=2×-1=-2

coordinate will be (-1,-2)

Coordinates of the points will be (1,2) ,(-1,-2)