MATHEMATICS COLLEGE

If BC = x − 2, CD = 19, and BD = 3x − 11, what is BD? Simplify your answer and write it as a proper fraction, mixed number, or integer. Could you please type the answer in a step by step.

Answers

Answer 1

Answer:

Answer:

UV = 15

BD= 31

Step-by-step explanation:

Since, U is the midpoint of TV.

Therefore,

TU = UV

x + 10 = 3x

x - 3x = - 10

-2x = - 10

x = - 10/-2

x = 5

UV = 3x = 3*5

UV = 15

BD = BC + CD

3x - 11 = x - 2 + 19

3x - 11 = x + 17

3x - x = 11 + 17

2x = 28

x = 28/2

x = 14

BD = 3x - 11 = 3*14-11 = 42 - 11

BD= 31

Answer 2

Answer:

Final answer:

We used the relationship that BC + CD = BD and then solved for x, which we found to be 14. We then substituted 14 for x in the equation for BD, which gave us a result of 31.

Explanation:

In the given question, we have a piece of a line divided into different sections: BC, BD, and CD with their respective lengths. BD is represented through a variable equation. We know that BC + CD = BD, this is a fundamental property of geometry that the sum of the lengths of two consecutive sections of a line is equal to the total length. So, substitute the given values:

x − 2 + 19 = 3x − 11

Simplify the equation by combining like terms: x + 17 = 3x - 11. Now, let's solve for x:

First, consolidate x's on one side by subtracting 'x' on both sides. We get 17 = 2x - 11.

Next, add 11 on both sides to solve for x. We get, 28 = 2x.

Finally, divide by 2 on both sides to find x, x = 14.

Now, we can find BD by substituting x into the equation 3x - 11, we get:

BD = 3*14 - 11 = 42 - 11 = 31.

Learn more about Algebraic Equations here:

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Answers

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God bless you have a beautiful blessed day and I hope this makes it!

Kareem says that the ratio 4 : 1 is equivalent to the ratio 12 : 9 because 4 1 8 5 12 and 1 1 8 5 9. Is Kareem correct? Explain how you know.

Answers

4 : 1 and 12 : 9 are not equivalent

Kareem is wrong

Correct question:

Kareem says that the ratio 4:1 is equivalent to the ratio 12:9 because

4 + 8 = 12 and 1 + 8 = 9. Is Kareem correct? Explain how you know

4 : 1 is in its simplest form already

12 : 9

= 12/9

= 4/3

= 4 : 3

Therefore,

4 : 1 and 12 : 9 are not equivalent

Kareem is wrong based on his assumption that 4 + 8 = 12 and 1 + 8 = 9

brainly.com/question/17352744

$\bf Step-by-step~explanation:$

Kareem's statement: 4:1 is equal to 12:9. Let's see if this is correct.

$\bf Step ~1:$

We have to simplify the ratios. Since 4:1 is already simplified, we do not have to do anything with it. 12:9 could be simplified. To do so, we need to find the greatest common factor (GCF) of both numbers. The GCF of 12 and 9 is 3. Since 3 is the GCF for both numbers, we divide them by 3.

$\bf 12 /3=4\n9/3=3$