The Great Lakes have a water area of about 2.44 X 105 square
kilometers. One of them, Lake Huron, has a water area of about
6.0 x 104 square kilometers. What approximate fraction of the total
water area of the Great Lakes does Lake Huron represent?

Answer:

12000000000

Step-by-step explanation:

did I add too many zeros????

10 to the 5 is multiply by 10 five times (100,000)

100,000 x 3 = 300,000

For the second thing, 10 to the 4 = 10,000

10,000 x 4 = 40,000

300,000 x 40,000 = 12000000000

Answer:

1/4

Step-by-step explanation:

This is because you want to get x alone, so if you divide -12 on one side you have to do it on the other side, so you get -3/-12 which can be divided by -3 to be simplified to 1/4. Hope this helps!

Answer:

Step-by-step explanation:

-12x = -3

x = 12 : -3

x = 1/4

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

check

-12 * 1/4 = -3

-3 = -3

the answer is good

Answer:

Reflection over y-axis (-x,y)

Step-by-step explanation:

Reflection over y-axis (-x,y)

A (-2 , 4) , A'( 2,4)

you can check the rest.

Step-by-step explanation:

6)

[tex]k = \frac{6}{4} \\ k = \frac{3}{2} [/tex]

7)

[tex] \frac{ab}{mn} = \frac{bc}{no} = \frac{cd}{op} = \frac{da}{pm} [/tex]

8)

[tex]y = 8 ( \frac{3}{2} ) \\ y = 12[/tex]

[tex]z = 6 ( \frac{3}{2} ) \\ z = 9[/tex]

9)

[tex]5k = 8 \\ k = \frac{8}{5} \\ x( \frac{8}{5}) = 32 \\ x = 20ft[/tex]

Step-by-step explanation:

We have that

[tex](x + \frac{1}{x} ) {}^{2} = 3[/tex]

We are trying to find the number value so that we can apply in the later equation.

Qe first simplify.

Remeber that

[tex](a + b) {}^{2} = a {}^{2} + 2ab + {b}^{2} [/tex]

Also remeber that

[tex] \frac{1}{x} = {x}^{ - 1} [/tex]

so

[tex](x + x {}^{ - 1} ) {}^{2} = {x}^{2} + 2x {}^{0} + {x}^{ - 2} = 3[/tex]

We then simply remeber that x^0=1 so

[tex] {x}^{2} + 2 + \frac{1}{ {x}^{2} } = 3[/tex]

Multiply both sides by x^2.

[tex] {x}^{4} + 2 {x}^{2} + 1 = 3 {x}^{2} [/tex]

Subtract both sides by 3x^2

[tex] {x}^{4} - {x}^{2} + 1 = 0[/tex]

Notice that x^4= (x^2)^2.

So our reformed equation is

[tex]( {x}^{2} ) {}^{2} - {x}^{2} + 1 = 0[/tex]

Let a variable , w equal x^2. This means that we subsitute variable, w in for x^2.

[tex]w {}^{2} - w + 1 = 0[/tex]

Now we use the quadratic formula

[tex] w = \frac{ - b + \sqrt{b {}^{2} - 4ac } }{2a} [/tex]

and

[tex]w = - b - \frac { \sqrt{b {}^{2} - 4ac } }{2a} [/tex]

Let a=1 b=-1 and c=1.

[tex]w = \frac{1 + \sqrt{1 - 4(1)} }{2} [/tex]

[tex]w = \frac{1 - \sqrt{1 - 4} }{2} [/tex]

Now, we get

[tex]w = \frac{1}{2} + \frac{i \sqrt{3} }{2} [/tex]

and

[tex]w = \frac{1}{2} - \frac{ i\sqrt{3} }{2} [/tex]

Now since we set both of these to the x^2 we solve for x.

and

[tex] {x}^{2} = \frac{1}{2} + \frac{i \sqrt{3} }{2} [/tex]

and

[tex] {x}^{2} = \frac{1}{2} - \frac{i \sqrt{3} }{2} [/tex]

We can represent both of these as complex number in the form of a+bi. Next we can convert this into trig form which is

[tex] {x}^{2} = 1( \cos(60) + i \: \sin(60) [/tex]

and

[tex] {x}^{2} = 1( \cos(300) + i \: sin(300))[/tex]

Next we take the sqr root of 1 which is 1, and divide the degree by two.

[tex] {x} = 1( \cos(30) + i \: sin \: 30)[/tex]

and

[tex]x = 1( \cos(150) + i \: sin(150)[/tex]

We are asked for the 2nd root so just add 180 degrees to this and we have

[tex]x = 1 \cos(210) + i \: sin \: 210)[/tex]

and

[tex]x = 1( \cos(330) + i \: sin(330)[/tex]

which both simplified to

[tex]x = - \frac{ \sqrt{3} }{2} - \frac{1}{2} i[/tex]

and

[tex]x = \frac{ \sqrt{3} }{2} - \frac{1}{2} i[/tex]

Now we must find

x^18+x^12+x^6+1.

We just use demovire Theorem. Which is a complex number raised to the nth root is

[tex] {r}^{n} (cos(nx) + i \: sin(nx)[/tex]

So let plug in our first root.

[tex]1( \cos(330 \times 18)) + i \: sin \: (330 \times 18))) + 1( \cos(12 \times 330)) + i \: sin(12 \times 330) + 1( \cos(6 \times 330) + i \: sin(6 \times 330))) + 1[/tex]

To save time we multiply the angle and use rules of terminals angle and we get

[tex]1( \cos(180) + i \sin(180) ) + 1( \cos(0) + i \: sin \:( 0) + 1( \cos(180) + i \: sin(180) + 1[/tex]

And we get

[tex] - 1 + 1 + - 1 + 1 = 0[/tex]

So one of the answer is x=0

And the other, let see

[tex]1 \cos(210 \times 18) + i \: \sin(210 \times 18) + 1 \: cos(210 \times 12) + i \: sin(210 \times 12) + 1 \cos(210 \times 6) + \:i sin(210 \times 6) + 1[/tex]

[tex] \cos(180) + i \: sin(180) + 1 \cos(0) + i\sin(0) +1( \cos(0) + i \sin(0) + 1[/tex]

We get

[tex] - 1 + 1 + 1 + 1 = 2[/tex]

So our answer are 2.

So the answer to the second part is

0 and 2.

Answer:

The equation will be. c= 1200 / 240 + 6 = 440. C=440 (I don't know if this is correct)

Answer:

B.(x − 5)(x − 3)(x + 2)

Hope you could get an idea from here.

Doubt clarification - use comment section.

Answer a+ 4 - a-7 a-7 _5 = 37_6

Step-by-step explanation:

Answer:

a=-7

Step-by-step explanation:

Find least common multiplier

LCM=105

Multiply to function

a+4/3 *105- a/7= 105* a+7/5

Simplify

35(a+4)-15x=21(a+7)

Expand

20a+140=21a+147

Subtract 140 from both sides

20a=21a+7

Subtract 21a from both sides

-a=7

Divide both sides by -1

-a/-1=7/-1

a=-7

Answer:

  101

Step-by-step explanation:

To get the largest weighted sum, you want to give the largest weight to the largest possible digit.

  Max( ) = 7·9 +3·8 +2·7 = 63 +24 +14 = 101 . . . . (x, y, z) = (7, 8, 9)

The maximum sum is 101.

Answer:

D.

Step-by-step explanation:

Answer:

discriminant= 100, nature of the root= real numbers.

Step-by-step explanation:

discriminant formula: b^2-4ac

-2^2-4(6)(-4)

4+96=100.

Answer:

2/9.

Step-by-step explanation:

There are 2 multiples of 4 in the 9 cards, 4 itself and 8.

So the required Probability is 2/9.

Answer:

(5, -4)

Step-by-step explanation:

Answer:

(5,-4)

Step-by-step explanation:

((0+10/2),(-2-6/2))

(10/2, -8/2)

(5,-4)

F, G, and H all lie on the same line. If FG/GH = 1, then FG = GH, which is to say the distance between F and G is equal to the distance between G and H. This means either F and H are the same point, or G is the midpoint of F and H.

They're not the same point, because the x-coordinate of H is 7 times that of F. So G must be halfway between F and H.

Then the x-coordinate of G is

(a + 7a)/2 = 8a/2 = 4a

Answer:

Step-by-step explanation:

I will interpret "-\frac{1}{5}−5​" as -(1/5).

We'll look for an equation by starting with the slope intercept format of:

y = mx + b,

where m is the slope and b is the y-intercept (the value of y when x=0).

We are given the slope of -(1/5), I think.  

The equation becomes y = -(1/5)x + b

We want to find a value of b that will force the line to go through point (-5,1).  Do this by putting this point into the equation we have thus far:

y = -(1/5)x + b

1 = -(1/5)*(-5) + b   [point (-5,1)]

1 = 1 + b

b = 0

The equation becomes y = -(1/5)x + 0, or y = -(1/5)x

See the attachment.

The cost of book has to be less than or equal to 26.39.

The amount of money Elena can buy has to be less than or equal to $30. Thus, the inequality sign to be used is the less than or equal to sign.

(1 + tax)cost of books + cost of bus fare ≤ value of the gift

1.08c + 1.5 ≤ 30

In order to determine the maximum cost of books, take the following steps:

Combine similar terms

1.08c  ≤ 30 - 1.5

Add similar terms together

1.08c  ≤ 28.50

Divide both sides of the equation by 1.08

c  ≤ 28.50 / 1.08

c  ≤ 26.39

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Answer:USE SUBSTITUTION METHOD. Algebra work right here

Step-by-step explanation:

Answer:

x = 15

Step-by-step explanation:

(4x - 30) and (2x) are alternate angles and are congruent , then

4x - 30 = 2x ( subtract 2x from both sides )

2x - 30 = 0 ( add 30 to both sides )

2x = 30 ( divide both sides by 2 )

x = 15

Answer:

-71

Step-by-step explanation:

Answer:

-71

Step-by-step explanation:

[-18+(-22)]-43+12

=(-18+22)-43+12

=-40-43+12

=-83+12

=-71

Answer:

gang gang shii

Step-by-step explanation:

gang gang.

Answer:

where is the equation??

pls attach that

Answer:

n = 11

Step-by-step explanation:

n+5=2n-6

you add 6 on both sides and you get

n+11=2n

you then subtract n on both sides and get

11=n

Step-by-step explanation:

n+5 = 2n - 6 -> Original equation

5 = n - 6 -> Take n away from both sides

11 = n -> Add 6 to both sides

n = 11 -> Final answer

*Remember, we are trying to get n by using inverse operations.

Answer:

3(2q+1)

Step-by-step explanation:

6q+2

3(2q+1)

Answer:

-2 - 16 = -18

Step-by-step explanation:

-y+4c

You take the values for c and y and substitute them in the original equation.

It would then look like:

-(2) + 4(-4)

Solving that would be -2 -16 = -18

Answer:

-18

Step-by-step explanation:

-(2)+4(-4)    Plug in the values of y and c.

-2+(-16)       Simplify.

-2-16

-18

Hope this helps you out!! Have an amazing day <3

Answer:

My friend is farthest from my school

Step-by-step explanation:

Let the distance from the movie store to school be x and the distance from the grocery store to school be y

Using Cosine rule,

x²= 10²+7² - 2×10×7Cos120

x²= 149 -140(-0.5)

x²= 149+70

x²= 219

x= √219

= 14.8miles

y²= 10²+7² - 2×10×7Cos100

y²= 149 -140(-0.1736)

y²=149+24.2704

y²=173.2704

y=√173.2704

y=13.4miles

Angles theorem and Reflexive property of congurence

The solution is

Each diagonal of a parallelogram separates it into two congruent triangles

So , ΔABC ≅ ΔCDA

Opposite angles are congruent

So , ∠B ≅ ∠D

What is a Parallelogram?

A parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure

The four types are parallelograms, squares, rectangles, and rhombuses

Properties of Parallelogram

Opposite sides are parallel

Opposite sides are congruent

Opposite angles are congruent.

Same-Side interior angles (consecutive angles) are supplementary

Each diagonal of a parallelogram separates it into two congruent triangles

The diagonals of a parallelogram bisect each other

Given data ,

Let the parallelogram be ABCD

Now , AC is a diagonal of the parallelogram

According to the postulates of parallelogram

Opposite sides are parallel

Opposite sides are congruent

Opposite angles are congruent

Same-Side interior angles (consecutive angles) are supplementary

Each diagonal of a parallelogram separates it into two congruent triangles

The diagonals of a parallelogram bisect each other

And ,

From the figure , we can deduct that ΔABC ≅ ΔCDA by

Angle A is congruent to angle C, and angle D is congruent to angle B

So , from congruent triangle theorem ΔABC ≅ ΔCDA

And ,

∠B ≅ ∠D

Because Opposite angles are congruent of a parallelogram

Hence , Each diagonal of a parallelogram separates it into two congruent triangles

So , ΔABC ≅ ΔCDA

Opposite angles are congruent

So , ∠B ≅ ∠D

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#SPJ2

The standard equation of a line is y = mx+ b

where:

The y-intercept is the point where the line cuts the y-axis

For the equation y = -2x -4

For the equation y = -5/2x

Find the graphs attached.

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Answer:

C) 5 seconds

Step-by-step explanation:

[tex]h = - 16t {}^{2} + 64t + 80[/tex]

When the ball hits the ground, the height is 0.

[tex]0 = - 16t {}^{2} + 64t + 80[/tex]

Factor out the greatest common factor: 16

[tex]0 = - 16(t {}^{2} - 4t - 5)[/tex]

Find numbers whose sum is -5 and product is - 4.

Those numbers are - 5 and 1: - 5 × 1 = - 5, - 5 + 1 = - 4

[tex]0 = - 16(t - 5)(t + 1)[/tex]

[tex]t - 5 = 0[/tex]

Or

[tex]t + 1 = 0[/tex]

So,

[tex]t = 5[/tex]

Or

[tex]t = - 1[/tex]

Since time cannot be a negative value the correct answer is 5 seconds.