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Lelu [443]
2 years ago
12

B is the midpoint of AC. AB=x^ 2 . BC=4x+5 Find AC

Mathematics
1 answer:
S_A_V [24]2 years ago
6 0

Answer:

AC = 50

Step-by-step explanation:

Since, B is the midpoint of AC.

\therefore AB = BC\\\therefore x^2 = 4x + 5\\\therefore x^2 - 4x - 5 =0\\\therefore x^2 - 5x + x - 5= 0\\\therefore x(x - 5) +1(x - 5)=0\\\therefore (x - 5)(x + 1) =0\\\therefore x - 5 = 0\: or \: x + 1 = 0\\\therefore x = 5 \: or \: x = - 1\\ \because x = - 1 \:  doesn't \: satisfy\: the\: \\condition \: of \: midpoint  \\ \therefore x =5\\\because AC = AB + BC\\\therefore AC = x^2 + 4x + 5\\\therefore AC = x^2 + 4x + 5 \\\therefore AC = 5^2 + 4\times 5 + 5\\\therefore AC = 25 + 20 +5\\\huge \red {\boxed {\therefore AC = 50}}

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6. The area of a rectangular sheet of paper is 300 cm squared. The length is 5 cm more than the width
konstantin123 [22]

Answer:

Step-by-step explanation:

width = x

length= x + 5

a)  x + 5

b) x * (x+5) = 300

x^2 + 5x = 300

x^2 + 5x - 300 = 0

Δ = 25 + 1200 = 1225

width = (-5 + 35)/2 = 15 cm

lenght = 15 + 5 = 20 cm

8 0
2 years ago
Read 2 more answers
Which equations are correct? select three options. n = 10 n = 7 cf = 59 fe = 42 cd = 30
pashok25 [27]

Based on the calculations on this parallelogram, the correct equations are:

  1. n = 10
  2. CF = 59
  3. FE = 42

<h3>The properties of a parallelogram.</h3>

Based on the image of the parallelogram shown in the image attached below, we can logically deduce that the opposite sides of this parallelogram are all equal. Thus, we have:

Side DE = Side CF

6n - 1 = 5n + 9

6n - 5n = 9 + 1

n = 10.

From Side CF, we have:

CF = 5n + 9

CF = 5(10) + 9

CF = 59.

For the measure of side FE, we have

FE = 4n + 2

FE = 4(10) + 2

FE = 42.

Read more on parallelogram here: brainly.com/question/16743544

#SPJ1

Complete Question:

Figure CDEF is a parallelogram.

Parallelogram C D E F is shown. The length of F C is 6 n minus 1, the length of C D is 4 n + 2, and the length of D E is 5 n + 9.

Which equations are correct? Select three options.

n = 10

n = 7

CF = 59

FE = 42

CD = 30

5 0
1 year ago
|
alekssr [168]

Answer: the answer is infinite solutions

Step-by-step explanation:Systems of Equations Level 1:

Question 1

Two linear equations are given below.

Exactly how many solutions does this system of equations have?

Select one:

4 0
2 years ago
Select all the common denominators for
Vitek1552 [10]

Answer:

B, E

Step-by-step explanation:

There are a few ways to check for common denominator.

Here is one method

Take the 4 and 10 and see if both numbers will  go into the numbers evenly. If they do, it is a common denominator

<u>Will 4 and 10 divide evenly into 10 ?</u>

4 will not go into 10 evenly

10 is not a common denominator.

<u>Will 4 and 10 divide evenly into 20?</u>

4 will go into 20 evenly. 20 /4 = 5

10 will go into 20 evenly 20 / 10 =  2

So 20 is a common denominator

<u>Will 4 and 10 divide evenly into 24?</u>

4 will go into 24 evenly 24 / 4 = 6

10 will not go into 24 evenly

24 is not a common denominator

<u>Will 4 and 10 divide evenly into 32?</u>

4 will go into 32 evenly 32 / 4 = 8

10 will not go into 32 evenly

32 is not a common denominator

<u>Will 4 and 10 divide evenly into 40?</u>

4 will go into 40 evenly 40/4 = 10

10 will go into 40 evenly 40 / 10 = 4

40 is a common denominator

3 0
2 years ago
Help me with this plz.
kondaur [170]
The answer is F because my brother is in high school and he knows the's things
7 0
3 years ago
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