All categories

2 years ago

Point F is on line segment EG given EG=5x + 7, EF=5x, and FG=2x - 7, determine the numerical length of FG

Mathematics

1 answer:

myrzilka [38]2 years ago

5 0

Answer:

$FG = 7$

Step-by-step explanation:

Given

$EG = 5x + 7$

$EF = 5x$

$FG = 2x - 7$

Required

Determine the length of FG

Since, F is on segment EG, then

$EG= EF + FG$

Substitute values for EG, EF and FG

$5x + 7 = 5x + 2x - 7$

Collect Like Terms

$5x - 5x - 2x = -7 - 7$

$- 2x = -14$

Solve for x

$x = -14/-2$

$x = 7$

Substitute 7 for x in $FG = 2x - 7$

$FG = 2 * 7- 7$

$FG = 14- 7$

$FG = 7$

You might be interested in

If you withdraw part of your money from a certificate of deposit before the date of maturity, you must pay an interest penalty.

s344n2d4d5 [400]

Answer:

$\frac{3}{12} *100=25\\$

8,3*0,25=2,10%(2d.p)

Step-by-step explanation:

7 0

2 years ago

You and a friend have a hula hoop competition. you win 3 out of every 7 trials. your friend wins 5 more trials than you. how man

Ivenika [448]

Answer:

Total number of trials is 35.

Step-by-step explanation:

Given : Me and my friend have a hula hoop competition. I win 3 out of every 7 trials. My friend wins 5 more trials than me.

To find : How many trials are in the competition?

Solution :

Probability of my winning is 3 out of 7 trials $=\frac{3}{7}$

and probability of my friend's winning is $=1-\frac{3}{7}=\frac{4}{7}$

Let there be n numbers of trials.

Therefore, my score after n trials $=\frac{3n}{7}$

and my friend's score after n trials $=\frac{4n}{7}$

Now, the number of trials my friend won more than me is

$\frac{4n}{7}-\frac{3n}{7}=\frac{n}{7}$

We know, that my friend won 5 more trials than me so comparing the actual and given we get,

$\frac{n}{7}=5\\n=7\times5=35$

Therefore, total number of trials is 35.

We can also verify our answer by placing value of n,

After 35 trials I will win $\frac{3\times 35}{7}=15$ trials

and my friend will win $\frac{4\times 35}{7}=20$ trials.

Hence, my friend won 5 more trials than me.

3 0

2 years ago

Help plz

Ber [7]

Answer:

Definition of bisector

Angle addition postulate

same side interior angles theorem

subtraction property of equality

Step-by-step explanation:

It is given that m║n, m∠1 = 65°,m∠2=60° and BD --> bisects ∠ABC . Because of triangle sum theorem, m∠3 = 55°. By the definition of bisector , ∠3 ≅∠4, so m∠4= 55°. Using the angle addition postulate , m∠ABC = 110°, m∠5 = 110° because vertical angles are congruent . Because of same side interior angles theorem, m∠5 +m∠6 = 180°. Substituting gives 110°+ m∠6 =180°, so by the subtraction property of equality , m∠6 = 70°.

5 0

2 years ago

alice drew two triangles on the coordinate plane as shown. Which series of transformation proves the two triangles are congruent

Nimfa-mama [501]

Answer:

idk i just really neeed the points

Step-by-step explanation:

alice drew two triangles on the coordinate plane as shown. Which series of transformation proves the two triangles are congruent?

8 0

2 years ago

A geometry teacher asked Radric to define "parallel lines." Radric said that parallel lines are lines in a plane that do not hav

UkoKoshka [18]

Answer: The answer is Yes.

Step-by-step explanation: Given in the question that Radric was asked to define "parallel lines" and he said that parallel lines are lines in a plane that do not have any points in common. We are to decide whether Radric's definition is valid or not.

Parallel lines are defined as lines in a plane which never meets or any two lines in a plane which do not intersect each other at any point are called parallel.

Thus, Radric's definition is valid.

6 0

2 years ago

Read 2 more answers