Which is larger, 3.2 x 104 or 3.2 x 105?

Answer:

s=3k+3j+5/s=3(j+k)+5

Step-by-step explanation:

3 x k=3k

3 x j=3j

bonus question:5

total: 3k+3j+5

If you factorize that then you would get 3(j+k)+5

The equation that represents the situation is s = 3(j + k) + 5.

the correct option is C.

Two algebraic expressions having the same value and symbol '=' in between are called an equation.

Given:

In a trivia game, each correct answer in rounds 1 and 2 is worth 3 points.

The bonus question is worth 5 points.

Lily's team had j correct answers in round 1 and k correct answers in round 2.

They answered the bonus question correctly.

That means,

s = 3j + 3k + 5

s = 3(j + k) + 5

Therefore, the equation is s = 3(j + k) + 5.

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Answer:

C

Step-by-step explanation:

Its c im smart trust me

Answer: C

Step-by-step explanation:

2x - y = 1

-2x         -2x

-y = -2x + 1

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

y = 2x-1

slope is positive 2/1, and the y-intercept is -1

Answer:

c 6√5 - 4√5

Step-by-step explanation:

your answer is correct

Answer:

y = 0.835x + 3.58

Step-by-step explanation:

The distance between points  (-6 , 4 ) and (-5 , -4 ) marked in the graph

is [tex]\sqrt{65}[/tex]

From the given graph the two points are:

      A = ( -6 , 4 )    , B = (-5 , -4 )

we have the distance from A to B ,

to find distance the formula is,

Distance = [tex]\sqrt{(x2 - x1)^{2} + (y2 - y1)^{2} }[/tex]

               = [tex]\sqrt{(-5 - (-6))^{2} + (-4 -4)^{2} }[/tex]

               = [tex]\sqrt{1^{2} + (- 8)^{2} }[/tex]

                = [tex]\sqrt{1 + 64}[/tex]

                = [tex]\sqrt{65}[/tex]

so the distance between points (- 6 , 4 ) and ( -5 , -4 ) is [tex]\sqrt{65}[/tex]

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Answer: y = 4/9 x - 1/3

Step-by-step explanation:

standard form means y = mx + c

so,

4x-8=9y-5

4x-8+5=9y

(4x-3)/9=y

y = (4/9)x - (1/3)

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:

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:

[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]

Simplify them

Answer =11

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

look at the screenshots for steps

Answer:

10

Step-by-step explanation:

The number is 52. If you subtract 2 you get 50, then after dividing by 5 you get 10.

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:

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.

Inverse function of expression is [tex]\frac{1}{2}[/tex]x + 2.

An inverse in mathematics is a function that "undoes" another function. In other words, if f(x) produces y, then y entered into the inverse of f produces x. An invertible function is one that has an inverse, and the inverse is represented by the symbol f1.

In the broadest sense, inverse functions are functions that "reverse" one another. The inverse, f 1 f-1 f1f, start superscript, minus, 1, end superscript, must take b to a, for instance, if f takes a to b.

Given Data

d(x) = 2x -4

Inverse function-

d⁻¹(x)

y = 2x-4

2x = y-4

x = [tex]\frac{y +4}{2}[/tex]

y = [tex]\frac{x+4}{2}[/tex]

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

Inverse function of expression is [tex]\frac{1}{2}[/tex]x + 2.

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Answer:

12.5 SEK

Step-by-step explanation:

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

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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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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Answer:

3

Step-by-step explanation:

Vol = length x width x height

Vol = 3 x 3 x3

Vol = 27

Answer: 10 minutes

Step-by-step explanation:

A clothing store is tracking, adults who are spending on clothes each month from their only store then the adults who buy any clothes consider as population of the store.

So, we cannot consider as population of the store.

So, they are not consider as population of the store.

Therefore,

Adults who buy any clothes consider as population of the store.

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Answer:

y=(0,-45)

x=(-10,0)

Step-by-step explanation:

Answer:

2 and 18

Step-by-step explanation:

2*18 = 36, and 2+18 = 20

Answer:

2 and 18.

Step-by-step explanation:

18 * 2 = 36

18 + 2 = 20

All sides of an equilateral triangle are congruent [equal]

Triangles are categorized into three

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Answer:

-2v+2u+5

Step-by-step explanation:

Distribute the negative sign outside of the parentheses to the values within the parentheses (2v, -2u, and -5). This will give you -2v+2u+5. Let me know if you want a more detailed explanation, hope this helps

To find, let  the no. of kg of mixed nuts that contains 40% peanuts be called  [tex]x[/tex].

We know,

Total peanuts already in the mixture = 18 x [tex]\frac{62}{100}[/tex] = 11.16 kg

The  new mixture contains 52% peanuts, then, [tex]\frac{x_{peanuts} }{x_{total} }[/tex] = 0.52.

Furthermore, 40% must be added.

[tex]x_{peanuts}[/tex] = [tex]0.4x[/tex] + [tex]11.16[/tex]

This gives us the following equation,

[tex]\frac{0.4x + 11.16}{18 + x } = 0.52[/tex]

Total mass =[tex]x + 18[/tex]

⇒ [tex]0.52 x +[/tex] 0.52 x 18 = [tex]0.4x + 11.16[/tex]

⇒ 0.12[tex]x[/tex] = (0.62 - 0.52 ) x 18

⇒ [tex]x[/tex] = 15 kg

Hence, 15 kg must be added.

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Answer:

25

Step-by-step explanation:

the tens cancle each other out

[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 value of x is -64.

An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.

For example, 3x + 5 = 15.

Given:

n(x)=16-0.5x;

n(x)=48

So, equation both

48=16-0.5x

Now, add 0.5 both sides

0.5x+48=16

Now, subtract 48 both sides

0.5x=-32

Divide both side by 0.5

x= -64

Hence, the value of x is -64.

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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