What is an inverse variation graph called?

A system of linear equations: y + 2x = -5 and 8x + 4y = -20  has infinitely many solutions.

The 3 possible solutions of a linear system are:

- Unique or one solution

- Infinite solutions

- No solution

If the linear equations are exactly (or can be transformed to exactly) the same equations, the solution is infinite.

The given linear system is:

y + 2x = -5           ....... (equation 1)

8x + 4y = -20     ..........(equation 2)

Rearrange equation 1 to:

2x + y = -5

Multiply both sides by 4:

8x + y4 = -20

Hence, equation 1 is equivalent to equation 2. Hence, the given linear system has infinitely many solutions.

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Answer:

k = - 2

Step-by-step explanation:

Given α and β are the zeros of x² - 6x + k = 0 , with

a = 1, b = - 6 and c = k , then

α + β = - [tex]\frac{b}{a}[/tex] = - [tex]\frac{-6}{1}[/tex] = 6

αβ = [tex]\frac{c}{a}[/tex] = [tex]\frac{k}{1}[/tex] = k

Then solving

(α + β)² - 2αβ = 40

6² - 2k = 40

36 - 2k = 40 ( subtract 36 from both sides )

- 2k = 4 ( divide both sides by - 2 )

k = - 2

Answer:   The mystery number is 5.5

5.5 converts to the fraction 11/2.

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Explanation:

The phrasing "subtract 10 from the number, then square the result" leads to the expression [tex](\text{x}-10)^2[/tex]

The phrasing "Square the number, then subtract 10 from the result" means we have [tex]\text{x}^2-10[/tex]

Set those expressions equal to one another so we can solve for x like shown in the steps below.

[tex](\text{x}-10)^2 = \text{x}^2-10\\\\\text{x}^2-20\text{x}+100 = \text{x}^2-10\\\\-20\text{x}+100 = -10\\\\-20\text{x} = -10-100\\\\\text{x} = -110/(-20)\\\\\text{x}=11/2\\\\\text{x} = 5.5[/tex]

The x^2 terms cancel out in the third step (since we subtract x^2 from both sides).

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

Check:

[tex](\text{x}-10)^2 = \text{x}^2-10\\\\(5.5-10)^2 = (5.5)^2-10\\\\(-4.5)^2 = (5.5)^2-10\\\\20.25 = 30.25-10\\\\20.25 = 20.25[/tex]

The answer is confirmed.

Answer:

The answer is "Expected Value = - 0.94 (Loss) "

Step-by-step explanation:

Please find the table in the attachment for the complete solution.

Answer:

[tex] \displaystyle \frac{17}{5} [/tex]

Step-by-step explanation:

we are given

[tex] \displaystyle3 \frac{2}{5} \times 3 \times \frac{1}{3} [/tex]

since ⅓ is a reciprocal of 3 therefore if we multiply it we'd get 1

[tex] \displaystyle3 \frac{2}{5} \times \cancel{ \: 3} \times \frac{1}{ \cancel{ \: 3}} [/tex]

[tex] \displaystyle 3\frac{2}{5} [/tex]

remember that

[tex] \displaystyle \rm c\frac{a}{b} \xrightarrow{ \text{improper fraction}} \frac{b \times c + a}{b} [/tex]

so,

[tex] \displaystyle \frac{17}{5} [/tex]

Answer:

3.1 is the answer.

As you can see, 5y is an external angle of triangle ABC

we know that 5y=180-x

since angle B is 40, and angle A=x and C=x, we have

x%2Bx%2B40=180

2x=180-40

x=140%2F2

x=70

so, angle A=70 and C=70

then

5y=180-70

5y=110

y=110%2F5

y=22

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The Filling time is After 25 minutes, both Aquariums will contain same amount of water.

you've fully prepared the aquarium, all you need to do is follow these quick and easy steps and safely fill your aquarium with water.

Calculate the Filling Time of the aquarium Explanation

Given,

Water in Aquarium A = 4.6 gallons

Water in Aquarium B = 54.6 gallons

Filling rate = 1.2 gallons per minute.

Draining rate = 0.8 gallons per minute.

Let,

x represents the minutes.

A(x) = 4.6 + 1.2x

(Because Luis is adding water in the tank.)

B(x) = 54.6 - 0.8x

(Isacc is draining water from the tank.)

For same amount of water;

A(x) = B(x)

4.6+1.2x=54.6-0.8x

1.2x+0.8x=54.6-4.6

2x=50

Dividing both sides by 2

2x/2=50/2

x=25

Therefore, After 25 minutes, both Aquariums will contain same amount of water.

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{x=-1/3-10/3y

5x+20y=5

5(-1/3-10/3y)+20y=5

solve the equation

.

.

Y=5

substitute the value of y into the equation

x=-1/3-10/3×2

.solve the equation

.

.x=-7

(x,y)=(-7,2)

{3×(-7)+10×2=-1

5x(-7)+28×2=5

simplify

{-1=-1

5=5

the ordered pair is asolution

(X,Y)=(-7,2)

That's all!!!!

Answer:

x = -7 y = 2

Step-by-step explanation:

Let's solve this using the elimination method:

3x + 10y = -1. #1

5x + 20y = 5. #2

Multiply Eqtn #1 by -2

-6x - 20y = 2

5x + 20y = 5

Add these two equations together and we will get

-x = 7 or x = -7

Use this value of x into either Eqtn #1 or #2

3(-7) + 10y = -1 ----> 10y = 20 or y = 2

Answer:

4x - 5y = 10

Step-by-step explanation:

We can use the point-slope form to find the line equation:

[tex] \displaystyle{y - y_1 = m(x - x_1)}[/tex]

Where (x1,y1) is the point that the line intersects and m is slope. We know the line passes through (-5,-6) and the slope is parallel to the line 4x - 5y = 35. Meaning the slope of that line is equal to slope of 4x - 5y = 35.

In this equation form Ax + By = C, we can find slope by m = - A/B. Therefore, m = -4/-5 which equals to 4/5. Hence, the slope is 4/5

[tex] \displaystyle{y - y_1 = \dfrac{4}{5}(x - x_1)}[/tex]

And also it intersects the point (-5,-6). Therefore:

[tex] \displaystyle{y - ( - 6) = \dfrac{4}{5}(x - ( - 5))} \\ \\ \displaystyle{y + 6 = \dfrac{4}{5}(x + 5)}[/tex]

Then convert to Ax + By = C to match with the given equation in problem:

[tex] \displaystyle{5(y + 6 )= 5 \left(\dfrac{4}{5}(x + 5) \right)} \\ \\ \displaystyle{5y + 30 = 4(x + 5)} \\ \\ \displaystyle{5y + 30 = 4x + 20} \\ \\ \displaystyle{ \therefore 4x - 5y = 10}[/tex]

Answer:

6 meters

Step-by-step explanation:

^_^

The equation that is modeled to the situation is x - 2y + 2 = 0 and the slope of the line is 1/2.

A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in determining if the lines are parallel, perpendicular, or none at all.      

The slope intercept form of a line is y = mx + c              

Where, c - y-intercept and m - the slope of the line

Given that

The cost of using the internet at an internet cafe is equal to a fee plus a certain rate per minute.

4 minutes of internet costs $ 3

8 minutes of internet costs $ 4  

[ We can represent the given situation as given below ]      

And the coordinates formed are (4, 3) and (8, 4)

The slope of the line formed = (4 - 3)/(8 - 4) = 1/4

Let y = mx + c be the equation to the model situation

=> y = (1/2)x + c

=> 2y = x + c ---- (1)

As we know (1) will pass through (4, 3)

=> 2(3) = 4 + c

=> 6 = 4 + c

=> c = 6 - 4

=> c = 2

=> 2y = x + 2

=> x - 2y + 2 = 0

Therefore,

The equation that is modeled to the situation is x - 2y + 2 = 0 and the slope of the line is 1/2.

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Answer:

7.84  ×  10 ^7

Step-by-step explanation:

If George is trying to fence the garden with less fences possible between the two options given in the question, the first option of measurements i.e 20 feet long and 15 feet wide would take less fencing.

It is the entire distance encircled on all sides by the rectangle.One of the key equations for the rectangle might be regarded to be its perimeter.

The formula for calculating the perimeter of a rectangle is :

P = 2*l + 2 *b where , l and b are the length and breadth of the rectangle.

For the first option, where the garden is 20 feet long and 15 feet wide, the perimeter would be 20+20+15+15 = 70 feet.

For the second option, where the garden is 30 feet long and 10 feet wide, the perimeter would be 30+30+10+10 = 80 feet.

Therefore, the first option where the garden is 20 feet long and 15 feet wide would use less fencing, 70ft in this case, as the perimeter is lower than the other option which is 80 ft.

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Answer:

Step-by-step explanation:

Here is how to solve the given problem above.

Given that the calculator costs $32 and has a tax of 6%, what we are going to do is to find how much is 6% of 32. So 32 times 0.06 is 1.92. So, we add this amount to 32 dollars, and the total price would be 33.92 dollars. Hope this answer helps.

Answer:

33.92

Step-by-step explanation:

32 times 6 divided by 100 gives you 1.92, the sales tax,

add it to 32 and then you get 33.92

P(even) is  50%

It is simple to calculate the likelihood of one die roll.

Calculating the likelihood of experiments happening is one of the branches of mathematics known as probability. We can determine everything from the likelihood of receiving heads or tails when tossing a coin to the likelihood of making a research blunder, for instance, using a probability.

First, keep in mind that a prime number is an integer that has exactly two factors: 1 and the number itself (which is why 1 does not qualify: it has only one factor). The appropriate numbers from 6 onward are 2,3,5. Your response, given that there are six sides, is: P(prime) = 3/6 = 1/2 = 50%

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A positive second derivative means that the solution curve is concave up. Therefore, all solution curves for the given differential equation in Quadrant II are concave up.

(b) To find the second derivative of y with respect to x, we can use the chain rule. Since y is a function of x, we have [tex]dy/dx = f(x) and d^2y/dx^2 = d/dx(dy/dx) = d/dx(f(x)) = f'(x).[/tex]

To find f'(x), we can use the product rule and the given differential equation:

[tex]f'(x) = d/dx(xy^4) = y^4 + xy^4dy/dx = y^4 + xy^4f(x)[/tex]

Now, to determine the concavity of the solution curves, we need to find the sign of f'(x).

In Quadrant II, x and y are both positive, so [tex]x*y^4[/tex] is positive. Therefore, f'(x) is positive as well.

A positive second derivative means that the solution curve is concave up. Therefore, all solution curves for the given differential equation in Quadrant II are concave up.

(c) To find a particular solution to the differential equation with the given initial condition, we can use separation of variables.

The equation can be rewritten as [tex]dy/y^4 = x dx[/tex]

Integrating both sides gives:

[tex]\int\limits^ {} \,dy/y^4 = \int\limits^ {} \, dx* dx\\-1/y^3 = (x^2)/2 + C\\y^3 = -1/(x^2/2 + C)\\y = (-1/(x^2/2 + C))^(1/3)[/tex]

Using the initial condition f(4) = -1, we can find the value of C:

[tex](-1) = (-1/(4^2/2 + C))^(1/3)\\(-1)^3 = -1/(4^2/2 + C)\\-1 = -1/(16/2 + C)\\C = 15/2[/tex]

So the particular solution is:

[tex]y = (-1/(x^2/2 + 15/2))^(1/3)[/tex]

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Complete question is: Consider the differential equation dy/dx=xy^4.

(b) Find ⅆ2yⅆx2 in terms of x and y. Determine the concavity of all solution curves for the given differential equation in Quadrant II. Give a reason for your answer.

(c) Find the particular solution y=f(x) to the given differential equation with initial condition f(4)=−1.

Answer:

x = 3[tex]\frac{1}{3}[/tex]

Step-by-step explanation:

4 + 6 = 10

[tex]\frac{2}{6}[/tex] = [tex]\frac{x}{10}[/tex]

6x = 20

x = 3[tex]\frac{1}{3}[/tex]

Answers:

Rose: y=500

$500

Summer: y=15x+200

$575

Poppy: y=30x

$750

Daisy: y=12.50x+350

$662.5

Violet: y=6x+450

$600

*Make sure you plug the 25 hours in yourself to double check my answers.*

Step-by-step explanation:

I just wrote the equation in number form and plugged the 25 hours in.

Answer:

35 cubic meters along with 35 cubes.

Answer:

The Answer is length 7m Width 5 m Height 1 m number of cubes 35 and volume 35

Step-by-step explanation:

Writing the whole number in the numerator and 1 in the denominator. Fraction in simplest form is 8

How to Find the Most Basic Form

Determine the GCF of the fraction’s numerator and denominator.

Divide the created GCF by the numerator and denominator.

Fill in the blanks with the simplified fraction of the supplied fraction.

The most basic form, If the top and bottom have no common components other than 1, the fraction is in its simplest form. In other words, the top and bottom cannot be divided any further and still remain full numbers. You may sometimes hear the phrase “lowest terms” when referring to the simplest form.

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Answer:

y=-x+2

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(-5-1)/(7-1)

m=-6/6

m=-1

y-y1=m(x-x1)

y-1=-1(x-1)

y-1=-x+1

y=-x+1+1

y=-x+2

Answer:

y = -1 x + 2

Step-by-step explanation:

First of all, remember what the equation of a line is:

y = mx+b

m is the slope, and b is the y-intercept.

Now, to find m, simply substitue here: [tex]m=\frac{y1-y2}{x1-x2}[/tex]

Which means: m = [tex]\frac{-5-1}{7-1} = -1[/tex]

Now, look at our line's equation so far: y=-1x+b.

b is what we want, the -1 is already set and x and y are just two "free variables" sitting there. We can plug anything we want in for x and y here, but we want the equation for the line that specfically passes through the two points (1,1) and (7,-5).

So, why not plug in for x and y from one of our (x,y) points that we know the line passes through? This will allow us to solve for b for the particular line that passes through the two points you gave!

You can use either (x,y) point you want..the answer will be the same:

Either: (1,1). y=mx+b or 1=-1 × 1+b, or solving for b: b=1-(-1)(1). b=2.

Or: (7,-5). y=mx+b or -5=-1 × 7+b, or solving for b: b=-5-(-1)(7). b=2.

both gave us the same answer for b, which is 2.

Therefore, the equation of the line that passes through the points (1,1), and (7,-5) is:

Y = -x + 2

Answer:

C. Is the answer

Answer:

42.92 square

Step-by-step explanation:

The radius of the circles is 5m

So, area of 1 circle is π(5×5)=78.54 square

Two areas will  (78.54+78.54)=157.08 square

Rectangles height is ( 5+5)=10m

Rectangles area is (10×20)=200 square

Shaded region=(200-157.08) square =42.92 square

Answer: 2=who

3=who

4=whom

5=I

Step-by-step explanation:

I don't see the image. Can you send it in the message.

Answer: ≈ 100km/h

Step-by-step explanation:

62 : 0.62 = 100 km

Answer: C= 30

Step-by-step explanation:

A^2+B^2=C^2

C= √(B²+A²)

C= √(18²+24²)

C=30

Answer:

Step-by-step explanation:

48 * [tex]\pi[/tex] / 180 = 0.837758041