All categories

3 years ago

O is the midpoint of segment FG. FO=3x+17, OG=7x-15. 98 points

Mathematics

2 answers:

gulaghasi [49]3 years ago

7 0

Hey!

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

Find the value of x:

OG and FO need to be equal first.

~Create an inequality

7x - 15 = 3x + 17

~Subtract 3x to both sides

7x - 15 - 3x = 3x + 17 - 3x

~Simplify

4x - 15 = 17

~Add 15 to both sides

4x - 15 + 15 = 17 + 15

~Simplify

4x = 32

~Divide 4 to both sides

4x/4 = 32/4

~Simplify

x = 8

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

Substitute for the inequality:

7x - 15 = 3x + 17

7(8) - 15 = 3(8) + 17

56 - 15 = 24 + 17

41 = 41

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

Add together:

41 + 41 = 82

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

Answer:

$\large\boxed{Midpoint~is~42~units!}$

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

Hope This Helped! Good Luck!

AlladinOne [14]3 years ago

5 0

O is the midpoint so both sides FO and OG need to equal each other.

3x + 17 = 7x - 15

Subtract 3x from both sides:

17 = 4x -15

Add 15 to both sides:

32 = 4x

Divide both sides by 4:

x = 32/4

X = 8

Now you have the value of X, solve for the lengths:

FO = 3x +17 = 3(8) +17 = 24 +17 = 41

OG = 7x -15 = 7(8) -15 = 56-15 = 41

Total length would be 41 + 41 = 82

You might be interested in

__,__, 8.16,32,64 what is the arithmetic sequence?

seraphim [82]

Answer:

2,4,8,16,32,64

Step-by-step explanation:

There are a couple of ways one could approach this. The goal is to find out the factor by which the numbers are increasing. Looking at going from 8 -> 16, we have either added 8, or doubled 8. So the factor is either +8 or x2. Going from 16 -> 32, adding 8 no longer holds true, while multiplying by 2 (doubling 16) does. To confirm what we have found, we can further check our math by using the final two numbers, 32 -> 64, to confirm that the sequence pattern is to double the current number to achieve the next number.

Working backwards, we can half each number to find out the first two numbers in the sequence. 64/2 = 32, 32/2 = 16, 16/2 = 8, 8/2 = 4, 4/2 = 2

8 0

3 years ago

On a piece of paper, use a protractor to construct right triangle DEF with DE=4 in. , m∠D=90° , and m∠E=45° . What statement is

Makovka662 [10]

I think the second one hope this helps

3 0

3 years ago

The functions f(x) and g(x) are described using the following equation and table: f(x) = −6(1.05)x x g(x) −4 −9 −2 −6 0 −3 2 2 W

kiruha [24]

Based on our examination of the y-intercepts, we can deduce that the y-intercept of function f(x) is equivalent to two times the y-intercept of function g. (x)

<h3>What is the examination of the y-intercept?</h3>

The value of the function at the point where the value of x is equal to zero is known as the y-intercept.

f(x)=-6(1.05)^x

Considering x

x=0

f(0)=-6(1.05)^0

f(0)=-6(1)

f(0)=-6

Therefore, the y-intercept is point (0,-6)

Generally, the equation for the function of the y-intercept of g(x) is mathematically given as

From table

at x=0

The y-intercept is the point (0,-3)

Based on our examination of the y-intercepts, we can deduce that the ty-intercept of function f(x) is equivalent to two times the y-intercept of function g. (x)