All categories

3 years ago

If EF bisects CD, CG = 5x-1, GD = 7x-13, EF = 6x-4 and GF = 13, Find EG

Mathematics

2 answers:

My name is Ann [436]3 years ago

8 0

The length of $EG$ will be 19.

Explanation

According to the below diagram, line $EF$ bisects the line $CD$ at point $G$ .

That means, $CG= GD$

Given that, $CG = 5x-1$ and $GD = 7x-13$

So, we will get......

$5x-1=7x-13\\ \\ 5x-7x=-13+1\\ \\ -2x=-12\\ \\ x=\frac{-12}{-2}=6$

Also given that, $EF= 6x-4$ and $GF= 13$

According to the diagram, $EG= EF-GF= (6x-4)-13= 6x-17$

Now plugging the value $x=6$ in the above expression......

$EG=6(6)-17=36-17= 19$

Thus the length of $EG$ will be 19.

zavuch27 [327]3 years ago

6 0

Segment EG is equal to 19

You might be interested in

The expression n2 + n represents the total number of blocks used in the nth figure of a pattern. Use the equation n2 + n = 56 to

Brrunno [24]

We have to solve this quadratic equation $n^{2}+n=56$ for n to get which figure has 56 blocks.

$n^{2}+n=56\\n^{2}+n-56=0$

For middle term factorization, we need two numbers that multiplied gives us -56 and added gives us 1 (coefficient of n).

Such two numbers are 8 and -7. We can now write,

$n^{2}+n-56=0\\(n+8)(n-7)=0\\n=-8, 7$

"There is no negative figure number possible, so we disregard -8"

Our answer is 7.

ANSWER: The 7th figure has 56 blocks.

3 0

3 years ago

Read 2 more answers

2/7x = 10 show work plz

Rashid [163]

Answer:

x = 35

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

2/7*x-(10)=0

Simplify —

(— • x) - 10 = 0

Subtracting a whole from a fraction

Rewrite the whole as a fraction using 7 as the denominator :

10 10 • 7

10 = —— = ——————

1 7

Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

2x - (10 • 7) 2x - 70

————————————— = ———————

7 7

Pull out like factors :

2x - 70 = 2 • (x - 35)

2 • (x - 35)

———————————— = 0

When a fraction equals zero ...

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

2•(x-35)

———————— • 7 = 0 • 7

Now, on the left hand side, the 7 cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :

2 • (x-35) = 0

Solve : 2 = 0

This equation has no solution.

A a non-zero constant never equals zero.

Solve : x-35 = 0

Add 35 to both sides of the equation :

x = 35

4 0

3 years ago

Read 2 more answers

The length of a 1-inch paperclip is about 1.6 x 10−5 miles. It takes about 1.5 x 1010 paperclips linked together to reach the mo

son4ous [18]

Answer:

Distance from the moon is 2.4 × 10⁵ miles

Step-by-step explanation:

Length of 1-inch paperclip = $1.6\times 10^{-5}$ miles

Number of paperclips used to reach the moon = 1.5 × 10¹⁰

Total distance from the moon = Number of paper clips used × Length of one clip

= (1.5 × 10¹⁰) × (1.6 × 10⁻5)

= (1.5 × 1.6) (10¹⁰× 10⁻⁵)

= 2.4 × 10⁽¹⁰⁻⁵⁾ miles

= 2.4 × 10⁵ miles

Distance from the moon is 2.4 × 10⁵ miles.

5 0

3 years ago

You and your four friends go to the water park. it is $10 each for tickets, and y dollars for lunch.

xeze [42]

Answer:

56 dollars

Step-by-step explanation:

idfk 56 dollars is the answer tho

6 0

3 years ago

Which system of equations is shown by the graph?

marta [7]

Answer:

y-x=15 and 25+2x=y

Step-by-step explanation:

7 0

3 years ago