The diameter of the sun is about 1.39 × 10^6 kilometers. The diameter of the Earth is about 1.27 × 10^4 kilometers. How many times larger in diameter is the sun than the Earth? Write your answer in scientific notation, and round the coefficient to the nearest hundredths place.

Answer:

Option a

- x + 2y = −10

3x − y = 12

Step-by-step explanation:

step 1

Find the equation of the line with negative slope

we know that

The line with negative slope has a y-intercept at (0,-5)  and passes through the point (2,-6)

Find the slope

[tex]m=(-6+5)/(2-0)=-\frac{1}{2}[/tex]

The equation in slope intercept form is

[tex]y=-\frac{1}{2}x-5[/tex]

Convert to standard form

Multiply by 2 both sides

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

step 2

Find the equation of the line with positive slope

The line with positive slope has a x-intercept at (4,0)  and passes through the point (2,-6)

Find the slope

[tex]m=(-6-0)/(2-4)=3[/tex]

The equation of the line in point slope form is equal to

[tex]y-y1=m(x-x1)[/tex]

we have

[tex]m=3\\point\ (4,0)[/tex]

substitute

[tex]y-0=3(x-4)[/tex]

Convert to standard form

[tex]y=3x-12\\3x-y=12[/tex]

therefore

The system of equations is

- x + 2y = −10

3x − y = 12

Answer:

15: 1

Step-by-step explanation:

Please see attached picture for full solution.

Final answer:

To find how long it takes Miguel to drive 469 miles at the same rate he drove 737 miles, simply divide the distance by his speed. In this case, it would take him 7 hours.

Explanation:

To find the time it would take Miguel to drive 469 miles at the same rate:

Therefore, it would take Miguel 7 hours to drive 469 miles at the same rate.

Answer:

D.Train A by a factor of 1.1

Step-by-step explanation:

To prove MN = 2KL we can use the Multiplication Property of Equality and SAS Similarity Theorem.

In terms of geometry, the triangle is a three-sided polygon with three edges and three vertices. The triangle's interior angles add up to 180°.

It is given that:

K is the midpoint of MJ.

L is the midpoint of NJ.

It is required to prove: MN = 2KL

From the diagram and table given in the picture:

1. K is MJ's midway. L is where NJ splits in half. ~ Given

2. MK, KJ, and NL, LJ: Midpoint Definition

3. Segment Congruence Postulate: MK=KJ and NL=LJ

4. Segment Addition Postulate: MJ = MK + KJ and NJ = NL + LJ

5. Substitution Property of Equality: MJ = 2KJ, NJ = 2LJ

6. The Division Property of Equality: MJ/KJ = NJ/LJ = 2

7. The Reflexive Property of J

8. The SAS Similarity Theorem, JMN, and JKL

9. Corresponding parts of identical triangles have a proportional relationship (MN/KL = MJ/KJ).

10. Substitution: MN/KL = 2

11. The Multiplication Property of Equality: MN = 2KL

Thus, to prove MN = 2KL we can use the Multiplication Property of Equality and SAS Similarity Theorem.

Learn more about the triangle here:

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#SPJ5

Answer:

0.0173913043

Step-by-step explanation:

I used a calculator

Answer:

m∠DEC = 123°

Step-by-step explanation:

First we need to solve for x the equation: x = (x - 45) + (x-12)

x = (x - 45) + (x-12) ⇔ x = 2x -57 ⇔ 0 = x - 57 ⇔ x = 57

since m∠DEC = 180 - x  then   m∠DEC = 180 - 57 = 123

Answer:

The slope is 2

Step-by-step explanation:

y = 2x + 7

Comparing with y = mx + c

Where m is the slope = 2

Answer:

B

Step-by-step explanation:

The equation of line is y=2x+7

Comparing it with the standard equation y=mx+c

Where m is the slope and c is the y-intercept

Hence we get

Slope,m =2

The total cost which includes tip, food cost without tax and sales tax for the considered situation is 19.63 bucks approximately.

Suppose the value of which a thing is expressed in percentage is "a'

Suppose the percent that considered thing is of "a" is b%

Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).

Thus, that thing in number is

[tex]\dfrac{a}{100} \times b[/tex]

For this case, we're specified that:

Pizza cost = 15.95 +7% of tax on 15.95 bucks

Tip  = 15%  of pizza cost

Total cost = Pizza cost + tip

7% of 15.95 is: [tex]\dfrac{15.95}{100} \times 7 = 1.1165[/tex] bucks

Thus, pizza cost = The  (15.95 + 1.1165) = 17.0665

Tip price = 15% of 17.0665 = [tex]\dfrac{17.0665}{100} \times 15 \approx 2.56[/tex] bucks.

Thus, total cost ≈ 17.0665 + 2.56 ≈ 19.63 bucks

Learn more about percent here:

https://brainly.com/question/11549320

Answer:

17

Step-by-step explanation:

a[2]+b[2]=c[2]

8*8+15*15=hypotenuse.

64+225=289

[tex]\sqrt{x} 289[/tex]

hypotenuse=17

Answer:

700

Step-by-step explanation:

Hope this helps!

The problem is a mathematical exercise in determining the total number of movies rented from the provided percentage of those returned. By setting up an equation and solving it, we find that the total number of movies rented was 700.

The student's question is on a mathematical concept related to percentages and determining the whole from a percentage portion. From the information provided, 434 movies, which represent 62% of the total number of movies rented last week, were returned. To calculate the total number of movies rented, we can let the total be x. With this, the equation representing the scenario is 0.62x = 434.

By solving for x, we get x = 434 / 0.62. After the calculation, we find that the total number of movies rented last week was 700. Therefore, the store originally rented out 700 movies.

Remember that when dealing with percentages, the percentage value (in this case, 62%) must be converted into decimal form before performing any calculation. This is done by dividing the percentage by 100, thus 62% becomes 0.62. For clarity, here's the step-by-step procedure:

Answer:

Step-by-step explanation:

In order to graph [tex]y\geq 2[/tex], we first need to graph y = 2.

y = 2 is a straight line which will be parallel to the x-axis.

We need to graph [tex]y \geq 2[/tex].

3, 4, 5......> 2. That is, all these values satisfies [tex]y \geq 2[/tex].

Hence, the will be the area towards the points y = 3 / 4 / 5 / ......

The number of 9-players team formed = 7 teams.

The number of players for substitute = 5 substitute players.

Step-by-step explanation:

step 1: The total number of soccer players = 32 girls + 36 boys = 68 players.

step 2: Each team should have 9 players.

step 3:The number of 9-player teams that can be formed = 68/9 = 7 and Remainder is 5.

step 4: Therefore, The number of 9-players team formed = 7 teams.

The number of players for substitute = 5 substitute players.

Good evening

Answer:

Step-by-step

let c be the total number of cartoons

Cost of purchase = 50c

total sale price = 100(c-15)

profit = total sale price - cost of purchase    

        = 100(c-15) - 50c = 2250 cents

Then (100c-50c) - 1500 = 2250

then 50c = 3750

Then c = 3750/50 = 75

:)

a cube has 6 sides reeeeeeeeeeeeeeeeee

a cube has 6 sides

1 in the front

1 in the back

1 on top                   = 6 sides

1 below

1 to one side

1 to another side

Answer:

  20

Step-by-step explanation:

Let x represent the number of rentals. Then the cost will be the same when ...

  105 +9.50x = 14.75x

  105 = 5.25x

  105/5.25 = x = 20

Each would have to rent a boat 20 times in order to pay the same amount.

Answer:

x=8

Step-by-step explanation:

17=x+9

-9     -9

8=x

Answer:

x=8

Step-by-step explanation:

17-9=8

8+9=17

Answer:

[tex]\frac{15}{17}[/tex]

Step-by-step explanation:

Look at the photo below for the details.

:)

the Distributive Property uses two operations: multiplication and addition. It is an essential key to success in algebra. The Distributive Property allows you to "distribute" a number to each of the addends within parentheses. It offers another way of solving a problem.

Answer:

A math property.

Step-by-step explanation:

Say you have a two big number and you don't know the answer on top of your head. You use distributive property to break it apart.

Answer:

Step-by-step explanation:

1) pentagon; n= 5

Sum of interior angles = 180*(n -2) = 180* (5-2) = 180 * 3 = 540

2) Sum of interior angles of a polygon = 1080

180*(n-2) = 1080

n - 2 = 1080/180

n -2 = 6

n = 6+2

n = 8

Polygon has 8 sides

3) Sum of interior angles of a polygon = 6840

180*(n-2) = 6840

n - 2 =6840/180

n -2 = 38

n = 38 + 2

n = 40

Polygon has 40sides

4)Sum of interior angles of an octagon = 180*(n-2) = 180* (8-2) = 180 - 6 = 1080

The sum of the interior angles of the 10-sided polygon on the left is 1440 °.

The answer is : 1440

Option C

For x = 1.5 we get f(x) = -2

Solution:

Given function is:

[tex]f(x) = 3.4x - 7.1[/tex]

We have to find the value of "x" so that f(x) = -2

Substitute f(x) = -2 in given function

[tex]-2 = 3.4x - 7.1[/tex]

Solve for "x" by moving the constants to one side and variables to other side

[tex]3.4x = -2 + 7.1\\\\3.4x = 5.1\\\\ \text{Divide both the sides of equation by 3.4 }\\\\x = \frac{5.1}{3.4}\\\\x = 1.5[/tex]

For x = 1.5 we get f(x) = -2

We can verify by substituting x = 1.5 in given function

[tex]f(1.5) = 3.4(1.5) - 7.1\\\\f(1.5) =5.1-7.1\\\\f(1.5) = -2[/tex]

Thus for x = 1.5 we get f(x) = -2

You can park in the garage for 5 hours 30 minutes

Solution:

Given that, shopping mall parking garage charges $2 for the first half hour and $1.20 for each additional half hour (even if it is under 30 minutes)

Therefore,

Cost for first half an hour = $ 2

Cost for each additional half an hour = $ 1.20

Let "x" be the number of each additional half hour

Therefore, total cost to pay is given as:

Total cost = Cost for first half an hour + (Cost for each additional half an hour)(number of each additional half hour)

Total cost = 2 + 1.20x

Given you have $ 8 in cash

[tex]8 = 2 + 1.20x\\\\1.20x = 8 - 2\\\\1.20x = 6\\\\x = \frac{6}{1.20}\\\\x = 5[/tex]

Total hours parked = first half an hour + 5

Thus you can park in the garage for 5 hours 30 minutes

Answer:

2

Step-by-step explanation:

see the image for the explanation

Answer:

I think its B. because if you put 6/4and reduce it it would be 3/2

Step-by-step explanation:

Answer:

C. 5/8

Step-by-step explanation:

P(red) = 6/16

p(blue) = 4/16

p(red or blue) = P(red) + p(blue) = (6+4)/16 = 10/16 = 5/8

Answer:

45°

Step-by-step explanation:

We know ∠ Y +∠ S = 90

and ∠ S= 5 ( ∠ Y)-180  so

leave S alone for both

90- ∠Y = 5 ( ∠Y) -180

270 = 6( ∠Y )

45= ∠ Y

∠S = 5( 45) -180

     =225-180

     =45

Final answer:

The measure of angle Y (m∠Y) is 45°, following the equation derived from the facts that angles S and Y are complementary and m∠S equals 5 times m∠Y minus 180°.

Explanation:

If ∠S and ∠Y are complementary angles, then the sum of their measures is 90°. According to the given information, m∠S = 5(m∠Y) − 180°. Since m∠S + m∠Y = 90°, we can set up the equation:

5(m∠Y) − 180° + m∠Y = 90°

Combining like terms to solve for m∠Y:

6(m∠Y) = 90° + 180°

6(m∠Y) = 270°

m∠Y = 270° / 6

m∠Y = 45°

The measure of angle Y, m∠Y, is 45°.

Answer:

18

Step-by-step explanation:

Solve for  x  by simplifying both sides of the equation, then isolating the variable.

Answer:

18

Step-by-step explanation:

1/3x=6

x=6/(1/3)

x=(6/1)(3/1)

x=18/1

x=18

Answer: he spent $100.10 and gained $42.90

Step-by-step explanation:

Option A

[tex]\left(y^{\frac{4}{3}} \cdot y^{\frac{2}{3}}\right)^{\frac{-1}{2}} = \left(y^{2}\right)^{\frac{-1}{2}}[/tex]

Solution:

Given expression is:

[tex]\left(y^{\frac{4}{3}} \cdot y^{\frac{2}{3}}\right)^{\frac{-1}{2}}[/tex]

Product of powers property:

The product of powers property tells us that when you multiply powers with the same base you just have to add the exponents

Which is represented as,

[tex]a^m.a^n = a^{m+n}[/tex]

Therefore, the given expression becomes,

[tex]\left(y^{\frac{4}{3}+\frac{2}{3}}\right)^{\frac{-1}{2}}[/tex]

Now add the exponents, we get

[tex]\left(y^{\frac{4+2}{3}}\right)^{\frac{-1}{2}}[/tex]

Simplify the above expression

[tex]\left(y^{\frac{6}{3}}\right)^{\frac{-1}{2}}[/tex]

Simplify the exponent of y, we get

[tex]\left(y^{2}\right)^{\frac{-1}{2}}[/tex]

Thus Option A is correct

Answer:

The answer is A

Step-by-step explanation:

Answer:

Step-by-step explanation:

Height of wall = 10ft

Length of ladder = 12ft

Angle of elevation be x

Sin x = opp/hyp

Sin x = wall height/length of ladder

Sin x = 10/12

Sin x = 0.83

X = Sin-¹ (0.83)

X = 56.44°