1. The graph shows the height of a plant after a certain amount of time measured in days. Do you think that there may be a proportional relationship between the number of days and the height of the plant? Explain your reasoning. The graph shows how much snow fell after a certain amount of time measured in hours. 2. Do you think that there may be a proportional relationship between the number of hours and the amount of snow that fell? Explain your reasoning.

Answer:

[tex]x=-\frac{2}{3}+\frac{\sqrt{2}}{3}i\\\\x=-\frac{2}{3}-\frac{\sqrt{2}}{3}i[/tex]

Step-by-step explanation:

The Quadratic Formula gives us the roots of a quadratic and is defined as: [tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

The discriminant is the part in the square root which is: [tex]b^2-4ac[/tex]

if the discriminant of the quadratic is zero, then the quadratic only has one distinct zero with a multiplicity of 2.

To see why, let's plug in zero for the discriminant: [tex]x=\frac{-b\pm\sqrt{0}}{2a}[/tex]

The square root of zero is just going to be zero: [tex]x=\frac{-b\pm0}{2a}[/tex]

Adding or subtracting zero doesn't change the value: [tex]x=\frac{-b}{2a}[/tex]

As you can see here it doesn't matter if we take the positive or negative solution, we'll get one value.

If the discriminant of the quadratic is positive, then the quadratic will have two distinct real solutions.

Well the solutions are real because the square root has real solutions for positive numbers. The reason we have two distinct solutions is because the square root of a positive number will have a positive and negative solution. These square roots will have a non-zero value and will affect the value of the numerator based on whether you take the negative or positive solution giving you two distinct solutions.

If the discriminant of the quadratic is negative, then the quadratic will have two distinct complex solutions.

To clarify, real numbers are technically complex numbers, since complex numbers are just: [tex]a+bi[/tex], where a=real part, and b=imaginary part. We could use this to represent any real number where b=0.

So when I'm saying "complex solution" I mean a complex solution where b does not equal zero, so there is a non-zero imaginary component to the complex solution.

The reason we have a complex solution in the first place is because we have a negative number in the square root. The square root only has real solutions for positive numbers, since any real number squared will give you a positive number regardless of the sign (positive or negative). The only number that is negative when squared is an imaginary number.

The reason we have two distinct solutions is actually the same reason we have two distinct solutions when the discriminant is positive. Since the square root will yield a non-zero number, so when we add it or subtract it to b, we will get to different values for the numerator, giving us two different values, or two different solutions.

So now let's solve the equation: [tex]3x^2+4x+2=0[/tex]

We have it in standard form where: [tex]ax^2+bx+c=0[/tex]

we want to use the Quadratic Formula: [tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

Plugging in values we get:

[tex]a=3,\ b=4,\ c=2\\\\x=\frac{-4\pm\sqrt{4^2-4(3)(2)}}{2(3)}\\\\x=\frac{-4\pm\sqrt{16-24}}{6}\\\\x=\frac{-4\pm\sqrt{-8}}{6}[/tex]

From here you'll notice the discriminant is -8, and thus we complex solutions since it's negative. We can first break up this square root into multiple square roots using the fact that: [tex]\sqrt{ab}=\sqrt{a}*\sqrt{b}[/tex]

and since -8 can be defined as: -1 * 8, we can split it up like this

[tex]x=\frac{-4\pm\sqrt{-1}*\sqrt{8}}{6}\\\\x=\frac{-4\pm i\sqrt{8}}{6}[/tex]

We can actually simplify the square root a bit more, since we can once more use the identity: [tex]\sqrt{ab}=\sqrt{a}*\sqrt{b}[/tex], to simplify the radical. The number 8 can be represented as 4 * 2, and sqrt(4) can be simplified easily.

[tex]x=\frac{-4\pm i *\sqrt{4}*\sqrt{2}}{6}\\\\x=\frac{-4\pm 2i\sqrt{2}}{6}\\\\x=\frac{(-2 * 2)\pm2i\sqrt{2}}{(3*2)}\\\\x=\frac{-2\pm i\sqrt{2}}{3}[/tex]

Now let's take the positive and negative solution to get the two distinct complex solutions. You can start with either but I'll just do the positive first.

Positive Solution:

[tex]x=\frac{-2+ i\sqrt{2}}{3}[/tex]

You could leave it like this, but generally whenever we have a complex number we want it in the form: [tex]a+bi[/tex] where the real and imaginary part are separate, so we can just distribute the division of 3

Positive Solution Continued:

[tex]x=\frac{-2+ i\sqrt{2}}{3}\\\\x=\frac{-2}{3}+\frac{\sqrt{2}}{3}i[/tex]

I also moved the "i" outside the fraction, so it's a bit easier to see the value of "b"

Negative Solution:

[tex]x=\frac{-2-i\sqrt{2}}{3}\\\\x=\frac{-2}{3}-\frac{\sqrt{2}}{3}i[/tex]

Answer: Yes, the point (-1, 3) makes the equation true.

Step-by-step explanation:

You would need to plug in the coordinates to the following places in the equation.

y=-3x

(3) = -3(-1)

3 = 3

Hope this helps!

Have a great day! :)

The range is 4n - 12≤100.

The inequality is -3 + n≤25. From this, we can find the range of n.

n≤25 + 3

n≤28

Now we have to find the range of 4n - 12. For this, we have to ≤multiply both sides with 4 and then subtract it from 12, in the range of n.

That is;

4n≤ 28×4

4n - 12 ≤112 -12

4n - 12 ≤100

Therefore the range is 4n - 12≤ 100.

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Answer:

-8°

Step-by-step explanation:

-24+16=-8

Answer:

d) 19/4

Step-by-step explanation:

Given mixed number,

→ 4 3/4

Now the improper fraction is,

→ 4 3/4

→ 19/4

Hence, option (d) is correct.

Answer:

Slope: 0

Equation : y = 9

Plsss mark as Brainliest

Slope:

-5-9/-3+3

=-14/0

= 0

Equation:

input gradient and pair of x and y valuesin y = mx +c

9= 0(-3)+c

9 = 0 +c

c = 9

input gradient and c:

y = 9

Simplify them

Answer =11

a= bc-3c-3b/6c

look at the screenshots for steps

[tex]=280-8(-14)-8(x)\\=280+112-8x\\=392-8x[/tex]

Attached is the solution. be alert -8 multiplies everything in the brackets

The equation m/k = x solved for k will be k = m / x.

variable, in algebra, a symbol (usually a letter) that represents an unknown numerical value in an equation. Commonly used variables are x and y (real unknowns), z (complex unknowns), t (time), r (radius), and s (arc length).

There are two types of variables in math:

In mathematics, a variable is an alphabet or term that represents an unknown number or an unknown value or an unknown quantity. Variables are  used especially in algebraic expression or algebra. For example, x 9=. is a linear equation where x is a variable, where 9 and  are constants.

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Step-by-step explanation:

-13x < 65

-13x * -1 < 65 * -1

13x > -65

13x/13 > -65/13

x > -5

Hope this helps! :)

Answer:

12.5 SEK

Step-by-step explanation:

VAT percentage in Sweden is 25% so, 25% of 50 = 12.5

I WILL USE CROSS MULTIPLICATION

[tex]63(4x) = 84(12) \\ 63(4x) = 1008 \\ \frac{63(4x)}{63} = \frac{1008}{63} \\ 4x = 16 \\ \frac{4x}{4} = \frac{16}{4} \\ x = 4[/tex]

ATTACHED IS THE SOLUTION

Answer:

a=1/30

Step-by-step explanation:

6a+4a=1/3

10a=1/3

30a=1

a=1/30

1/30

is the anwser i think.i might be wront tho

Answer: 10 minutes

Step-by-step explanation:

11975 is value of multiplication .

What does multiplication mean in math?

5×395=5×(400×-5)

1975 = 5 * ( - 2000 )

1975 = - 10000

= 10000 + 1975

= 11975

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Answer:

The points scored for each game are approximately normally distributed. The numbers distributed are in order of value from the least to greatest, making it easy to get the medium or mean.

Step-by-step explanation:

Answer:

c 6√5 - 4√5

Step-by-step explanation:

your answer is correct

Answer: 0.187

Step-by-step explanation:

I just did the question

The option which gives the reflection of the triangle (shape) with vertices, (2, -2), (4, -2), and (2, -6) is option a

a. A triangle is shown on ordered pair (2, 2), (4, 2), (2, 6)

A reflection transformation is one in which the line across which the object is reflected acts like a mirror, such that the points are swapped across the line of reflection.

The coordinates of the vertices of the triangle on the coordinate grid are;

Required; The coordinates of a reflection of the shape (the triangle)

Solution; The coordinates of a point (x, y) following a reflection across the y–axis is (-x, y)

The vertices of the image of the triangle following a reflection across the y–axis are therefore;

A reflection of the point (x, y) across the x–axis gives the point (x, -y)

A reflection of the triangle across the x–axis therefore gives;

A reflection of the point (x, y) across the line y = x, gives (y, x)

The vertices of the triangle following a reflection across the line y = x are therefore;

A reflection of the point (x, y) across the line y = -x, gives (-y, -x)

The vertices of the triangle following a reflection across the line y = -x are therefore;

The coordinates of the triangle in the options are;

a) (2, 2), (4, 2), (2, 6)

b) (-2, -2), (-4, -2), (-4, -6)

c) (2, 2), (2, 4), (6, 2)

d) (-2, -4), (-6, -4), (-6, -2)

The correct option is therefore option a with points on the image of the triangle of (2, 2), (4, 2), (2, 6) which corresponds with the coordinates of the triangle following a reflection across the x–axis

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The interquartile range for the given set of numbers {0,2,4,6,8,10,12,14,16,18,20} is 12 .

The interquartile range(IQR) can be calculated by the formula

IQR = Q₃ - Q₁

where Q₃ is the third quartile

and Q₁ is the first quartile

In the question,

the set of numbers is ascending order is given as

0,2,4,6,8,10,12,14,16,18,20

Q₃ means median of the upper half

the upper half of the data is 12,14,16,18,20

the median of the upper half is 16 ,

So Q₃ = 16 .

Q₁ means median of the lower half

the lower half of the data is 0,2,4,6,8

the median of the lower half is 4 ,

So Q₁ = 4 .

Hence , the IQR = Q₃ - Q₁ = 16-4 = 12  .

So, IQR for given set of numbers is 12.

Therefore , the interquartile range for {0,2,4,6,8,10,12,14,16,18,20}  is 12 .

The given question is incomplete , the complete question is

Find the Interquartile range for the given set of numbers 0,2,4,6,8,10,12,14,16,18,20  .

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The equation of the line parallel to 2x + 3y = 18 and passing through point ( 6, 4) is 3y + 2x = 24.

Consider the line 2x + 3y = 18,

The equation of the line in slope-intercept form can be written in the form y = mx + b, where m is the slope of the line.

Therefore,

2x + 3y = 18

Subtracting 2x from each side

2x + 3y - 2x = 18 - 2x

3y = 18 - 2x

Dividing each side by 3.

y = 6 - ( 2/3 )x

y = - (2/3)x + 6

Hence, the slope of the line is - 2/3.

Now, if two lines are parallel then they have the same slope.

Now, the line parallel to 2x + 3y = 18 passes through ( 6,4).

Therefore, using the slope-intercept form:

y = mx + b

4 = ( -2/3 ) × 6 + b

4 = - 4 + b

b = 8

Therefore, the equation of the line parallel to 2x + 3y = 18 is:

y = ( - 2/3 )x + 8

3y = - 2x + 24

3y + 2x = 24

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The missing side of the triangle is 7.2 units

ABC is a triangle.

AD bisects(cut into half) the angle ∠BAC.

Therefore,

AB / BD = AC / DC

Hence,

AB = 12

BD = x

AC = 20

DC = 12

Therefore,

12 / x = 20 / 12

cross multiply

12 × 12 = 20x

144 = 20x

divide both sides by 20

x = 144 / 20

Therefore,

x = 7.2 units.

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Answer:

B is bigger

Step-by-step explanation:

a) 3^2 / 2^3

3*3 / 2*2*2

9/8

b) 9^4 / 4^6

9*9*9*9/4*4*4*4*4

6561 / 4096

1.601807

The time period that Riko would be behind is going to be the inequality 0 ≤ t < 52.5 minutes .

How to solve for the period t that Riko would be behind her brother

The question says that at the time he left the house, Yuto was 5.25 miles ahead of her.

The amount of miles that she would have gained on Yuto within this period would be 0.35 - 0.25 = 0.1 miles on Yuto

Therefore at every mile she would be closing in on 0.1 miles

For her to close the gap that is made here, it would be 5.25 / 0.1

= 52.5 minutes

Therefore we would say that The time that Riko would be behind is going to be  0 ≤ t < 52.5 minutes .

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Answer:

d

Step-by-step explanation:

(x+3)/6 = 5/4

butterfly method

4(x+3) = 5×6

4x+12 = 30

4x = 30-12

4x = 18

x = 18/4

x = 9/2

No, the divisor 0.03 is not a whole number, we should multiply by 10² to get a divisor a whole number.

As given in the question,

Given expression:

13.5 divided by 0.03

Dividend of the given expression = 13.5

Divisor of the given expression = 0.03

No, the divisor 0.03 is not a whole number.

Power of 10 which should be multiply by 0.03 to get a whole number

0.03 = 3 /100

(3/100) should get multiply by 100

100 = 10²

0.03 ×10² =3 whole number

Therefore, the divisor 0.03 is not a whole number, we should multiply by 10² to get a divisor a whole number.

The complete question is:

Is our divisor a whole number? 13.5 divided by 0.03 . By what powers of 10  should you multiply by to get a whole number?

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Answer:

y = 0.835x + 3.58

Step-by-step explanation:

Answer:

25

Step-by-step explanation:

the tens cancle each other out