Let $F,$ $G,$ and $H$ be collinear points on the Cartesian plane such that $\frac{FG}{GH} = 1.$ If $F = (a, b)$ and $H = (7a, c)$, then what is the $x$-coordinate of $G$?

This is the number 80 thousand

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Explanation:

1/2, aka 2/4, of the original fund was given to his wife and 1/4 was given to his son. That totals 3/4 since 2/4+1/4 = (2+1)/4 = 3/4.

In short, 3/4 of the fund is distributed between the wife and son. That leaves 1/4 of the fund for the two brothers to share equally.

Imagine a cake cut into quarters. Then cut each slice in half to get eighths, i.e. there are 8 equal slices. This means each brother gets 1/8 of the fund.

Since each brother got Rs 10000, this must mean the original fund is worth 8*10000 = 80000

Taking 1/8 of Rs 80000 will get us Rs 10000 for each brother.

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Checking the answer:

original fund amount = 80000

1/2 of 80000 = 40000 is the amount the wife gets

1/4 of 80000 = 20000 is the amount the son gets

That totals 40000+20000 = 60000 leaving 80000-60000 = 20000 leftover for the two brothers to share. Cut that 20 thousand figure in half to arrive at Rs 10000 for each brother. These steps help confirm the answer.

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Another method using algebra:

x = original amount of the fund

W = x/2 = 2x/4 = half of the fund = amount wife gets

S = x/4 = quarter of the fund = amount the son gets

W+S = (2x/4) + (x/4) = (2x+x)/4 = 3x/4

W+S represents the sum of the wife's and son's amounts.

We'll subtract this from the original amount x to find out what's left

x - (W+S) = x - (3x/4) = (4x/4) - (3x/4) = (4x-3x)/4 = x/4

This shows that 1/4 of the fund is left over after distributing to the wife and son.

The amount x/4 is then cut in half to get x/8 to represent the amount each brother gets. We're told that amount is Rs 10000

So,

x/8 = 10000

x = 8*10000

x = 80000

The original fund is worth Rs 80000

Answer:

y= 32

Step-by-step explanation:

HOPE THIS HELPS :)

Answer:

Step-by-step explanation:

The diagonal is the hypotenuse of the right triangle whose sides are the sides of the rectangle. The Pythagorean theorem applies.

  height² + base² = diagonal²

  height² +24² = 26²

  height² = 676 -576 = 100

  height = √100 = 10

__

The area is the product of the base and height.

  A = bh

  A = (24)(10) = 240

The height is 10 units; the area is 240 square units.

Answer:

I don't know

Step-by-step explanation:

Answer:

Part A: The origin would be (0, 0)

Part B:

(-1, 1)  starting from the origin (0,0), would move left 1 on the x-axis  then you would move up 1 on the y-axis

(1, -1.5)  starting from the origin (0,0), you would move to the right 1 on the x-axis, then you would move down 1.5 on the y-axis

(2, 1/4) starting from the origin (0,0), you would move to the right 2 on the x-axis, then you would move up 1/4 (.25).

a) The origin would be (0, 0).

Coordinates are a pair of integers (Cartesian coordinates), or sporadically a letter and a number, that identify a certain place on a grid, also referred to as a coordinate plane. The x axis (horizontal) and y axis (Verticle) are the two axes that make up a coordinate plane.

Given:

a) The origin would be (0, 0).

b) First, (-1, 1) move left 1 on the x-axis then you would move up 1 on the y-axis

Second, (1, -1.5) move to the right 1 on the x-axis, then move down 1.5 on the y-axis

Third, (2, 1/4) move to the right 2 on the x-axis, then move up 1/4 (.25).

Learn more about Coordinates here:

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Answer:

30 hours 48 minutes

Step-by-step explanation:

Using the relationship

average speed = [tex]\frac{distance}{time}[/tex] = [tex]\frac{375}{15}[/tex] = 25 Km / hour

Then

time = [tex]\frac{distance}{speed}[/tex] = [tex]\frac{770}{25}[/tex] = 30.8 hours = 30 hours 48 minutes

Answer:

30.8 or 30 hours and 48 mins

Step-by-step explanation:

375 km > 15 Hours

Divide 375 and 15, equals to 25.

So, to proof that 375 is equals to 15 hours, divide 375 and 25 then you will get the answer 15. :)

Now, divide 770 and 25 to get the time taken to travel 770km.

And the answer is 30.8 hrs or... 30hrs and 48mins

Welcome ;)

Answer:

  (b)  y -4 = 3(x -2)

Step-by-step explanation:

You are given the form

  y -y1 = m(x -x1)

and the values

  y1 =4, m =3, x1 =2

Putting these in their places gives ...

  y -4 = 3(x -2)

Answer:

what questions?

Step-by-step explanation:

Answer:

N=3

Step-by-step explanation:

use cross multiplication to find 28N=84 and then divide both sides by 28 to get N=3

Answer:

N = 3

Step-by-step explanation:

Given Δ ABC is similar to Δ DEF , then the ratios of corresponding sides are in proportion, that is

[tex]\frac{AB}{DE}[/tex] = [tex]\frac{BC}{EF}[/tex] , substitute values

[tex]\frac{21}{N}[/tex] = [tex]\frac{28}{4}[/tex] = 7 ( multiply both sides by N to clear the fraction )

21 = 7N ( divide both sides by 7 )

3 = N

Answer:

  A, D, F

Step-by-step explanation:

It is convenient to let a calculator or spreadsheet evaluate the function for you. Reflection over the y-axis means x is replaced by -x in the original function definition.

The values that show up on the reflected graph are ...

  (-7, -10.206)

  (0.5, -0.221)

  (9, -0.003)

The equation of the line for the graph that has y-intercept (0, 6) and contains the point (2, 1) is; y = -2.5x + 6

The general form of the equation of a Line in Slope Intercept form is;

y = mx + c

where;

m is slope

c is y-intercept

We are told that the graph has the points (0, 6) and (2, 1). Thus, the formula for slope is;

m = (y₂ - y₁)/(x₂ - x₁)

m = (1 - 6)/(2 - 0)

m = -5/2

m = -2.5

Now, since the y-intercept is at (0, 6), then it means that;

c = 6

Thus, the equation of the line is; y = -2.5x + 6

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Answer:lol

Step-by-step explanation:

Answer:

The test  has 10 3-point questions and 14 5-point questions.

Step-by-step explanation:

x + y = 24

3x + 5y = 100

From the first equation:

3x + 3y = 72

Subtracting:

3x - 3x + 5y - 3y = 100 -72

2y = 28

so y = 14

x + 14 = 24 so x = 10.

10*3 + 5*14

= 30 + 70 = 100 points.

Based on his score last week and his score this week, we can say that Jacob increased his score by 180%

Jacob scored 25 in his test last week and then this week scored 70.

The increase can be found as:

= (New score - Old score) / Old score x 100%

Solving gives:

= (70 - 25) / 25 x 100%

= 180%

In conclusion, Jacob increased by 180%

Find out more at https://brainly.com/question/22444616.

Answer:One minute is 60 times as long as one hour i guess?

Hey there!

Guide to follow

“Difference” means subtract

“Is” means equal to

“Product” means multiply

“Quotient” means divide

“Sum” means add

Answering your question….

“The [QUOTIENT] of [-4] and [y]

Remember we said “quotient” means divide

So we’re dividing -4 from y and that will be your answer.

Answer

-4 ÷ y

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

Answer:

9 lol

Step-by-step explanation:

comming from a highscholer its 12% of 12 =9

hope this helps

Answer:

x = 12

Step-by-step explanation:

y= -4x+48

0=-4x+48

4x=48

x=12

Answer:

what you need to know is all lines equal up to 180

so basically it's 180 - 115

which is 65

comment down below if you need more explanation

Step-by-step explanation:

110 is the initial fee.

intial fee is the y-intercept.

Answer:

The answer is I don't know

Answer:

Step-by-step explanation:

Rule: the largest angle is ALWAYS opposite the longest side, and the converse is also true: the longest side is always opposite the largest angle. So the largest side is E which is B

Answer: what? What’s the question?

Answer:

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

Step-by-step explanation:

x - 5(x - 1) = x - (2x - 3) ← distribute parenthesis and simplify both sides

x - 5x + 5 = x - 2x + 3

- 4x + 5 = - x + 3 ( add x to both sides )

- 3x + 5 = 3 ( subtract 5 from both sides )

- 3x = - 2 ( divide both sides by - 3 )

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

Answer:

B 71 & 71

Step-by-step explanation:

OP is an angle bisector

Answer:

B

Step-by-step explanation:

Since angles MOP and NOP are both labeled as 2x+1, they must both be equivalent. The only answer choice which shows them to be equivalent is B.

Verification:

(2x+1)+(2x+1)=142

4x=140

x=35

(substitution)

2(35)+1 = 71

Answer:

a. 3x = 2x + 10, b. x = 10, c. 30 degrees

Step-by-step explanation:

Angle 4 and angle 6 = 180 degrees, so

3x = 2x + 10

x = 10

Angle 7 is congruent to angle 6, so it is also 2x + 10, x = 10, so it is 30 degrees.

Answer:

see explanation

Step-by-step explanation:

∠ 4 and ∠ 6 are same- side interior angles and sum to 180° , that is

(a)

3x + 2x + 20 = 180 , simplifying

(b)

5x + 20 = 180 ( subtract 20 from both sides )

5x = 160 ( divide both sides by 5 )

x = 32

(c)

∠ 6 and ∠ 7 are vertically opposite angles and are congruent , then

∠ 7 = 2x + 20 = 2(32) + 20 = 64 + 20 = 84°