All categories

3 years ago

If BD = 7x-10, BC = 4x-29, and CD = 5x-9, find each value.

Mathematics

2 answers:

pshichka [43]3 years ago

7 0

Answer:

$x=14$ , $BD=88$ , $BC=27$ , $CD=61$ .

The value of CD is 61 units.

Step-by-step explanation:

Given information: BD = 7x-10, BC = 4x-29, and CD = 5x-9,

From the given figure it is clear that Points B, C and D collinear. Point C lies on line segment BD.

$BD=BC+CD$

Substitute BD = 7x-10, BC = 4x-29, and CD = 5x-9 in the above equation.

$7x-10=(4x-29)+(5x-9)$

On combining like terms we get

$7x-10=(4x+5x)+(-29-9)$

$7x-10=9x-38$

Add 38 on both sides.

$7x-10+38=9x$

$7x+28=9x$

Subtract 7x from both sides.

$28=9x-7x$

$28=2x$

Divide both sides by 2.

$14=x$

Therefore the value of x is 14.

$BD = x-10=7(14)-10=88$

The value of BD is 88 units.

$BC = 4x-29=4(14)-29=27$

The value of BC is 27 units.

$CD = 5x-9=5(14)-9=61$

The value of CD is 61 units.

ICE Princess25 [194]3 years ago

4 0

BD = BC + CD
7x - 10 = (4x - 29) + (5x - 9)
7x - 10 = 9x - 38
2x = 28
Ans: x = 14
BC = 4x - 29
= 4(14) - 29
= 27
Ans: BC = 27
CD = 5x - 9
= 5(14) - 9
= 61
Ans: CD = 61
BD = 61 + 27
= 88
Ans: BD = 88

You might be interested in

If Mason wants to consider his short-term and long-term goals, which question should he ask? If I buy this bike, will I give up

melamori03 [73]

Answer: Second option is correct.

Step-by-step explanation:

Short term goals are those goals which are meant for short period that is not more than one year.

Long term goals are those goals which are meant for long period that takes more than 4 to 5 years.

So, He should ask " Do I want this bike this month, or should I save up over the summer? "

Here, purchasing a bike is short term goal or saving money is long term goal.

Hence, Second option is correct.

3 0

3 years ago

Read 2 more answers

HELP I NEED THESE ANSWERED!!!

levacccp [35]

1) b=1

-3+1=3b-5

Add 3b to both sides.

1=6b-5

Add 5 to both sides

6=6b

Divide both sides by 6

b=1

2) t=11

(1/2)t+7=(3/2)t-4

Subtract 1/2t from both sides.

7=t-4

Add 4 to both sides.

t=11

3) x=-0.878

-2.3 +1.2x=5.9-2.9x

Subtract 1.2x from both sides

-2.3=5.9-4.1x

Add 5.9 to both sides.

3.6=-4.1x

Divide by -4.1

x=-0.878

4)No solution

-7y-21=-3y-21

Add 3y to both sides.

-4y-21=-21

Add 21 to both sides

-4y=0

5 0

4 years ago

X+2y-z=5<br> -X-y+2z=-13<br> 2x+y-2z=14

faltersainse [42]

Answer:

$x+2y-z=5 ...(1)\\ -x-y+2z=-13...(2) \\ 2x+y-2z=14...(3) \\ \\ add \: (2) + (3) \\\boxed{x= 1} \\ 2 \times (1) + (2) \\ x + 3y = - 3 \\ 1 + 3y = - 3 \\ 3y = - 4 \\ \boxed{y = - \frac{4}{3} }\\ solve \: for \: z \\ x + 2y - z = 5 \\ 1-\frac{4}{3}(2)-z=5\\3-8-3z=15\\3z=-20\\\boxed{z = - \frac{20}{3} }$

3 0

3 years ago

Prove that in any pythagorean triple, one of the side lengths is divisible by 5

victus00 [196]

The trick is to realize what your choices are.

if m or n or both are divisible by 5, then 2mn will be divisible by 5
I don't know if you know about x mod(5), but in that case there can only be 4 possibilities for m and n
m mod (5) = +/- 2 or m mod(5) = +/- 1
In the first case m^2 = 4 mod(5) and in the second case m^2 = 1 mod(5) N has the same considerations.
If m and n have the same modular results (both are [say] 2 ) then m^2 - n^2 which be 0
If they are different, then (m^2 + n^2) mod 5 = 0

7 0

3 years ago

Compute:<br> a. (−10 + 9i) + (7 − 5i)

Aleonysh [2.5K]

Answer:

4i - 3

Step-by-step explanation:

-10 + 9i + 7 - 5i

Collect like terms: 4i - 3

4 0

3 years ago