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2 years ago

What is the value of x in the equation ? 2.5(6x-4)=10+4(1.5+0.5x)

Mathematics

1 answer:

lukranit [14]2 years ago

4 0

Step 1: Rewrite

2.5(6x-4)=10+4(1.5+0.5x)

Step 2: Distribute

Multiply 2.5 by 6 and then do the same to -4. MAKE SURE TO MULTIPLY 2.5 BY NEGATIVE 4 OR THE ANSWER WILL BE WRONG.

You should get:

15x-10=10+4(1.5+0.5x)

Step 3: Combine Like Terms

Look over the left side of the equation. If there are no numbers to combine, go to the right side. 10 and 4 are like terms. You may go ahead and combine them.

You should get:

15x-10=21+7x

Step 5: Combine Like Terms again

Now that you have no like terms on either side of the equation, you will combine them together. Confusing? Let me explain, you have a 15x and 7x on two sides of the equation and they are like terms. Since they are on different sides of the equation, you need to do the opposite of what you'd do if they were on the same side.

You should get:

8x=31

What I did was take the 7x (since its the lesser value) and subtract it by 15x and I got 8x. I then took the -10 and added it to 21.

Step 6: Divide

Now that you have 8x=31, you can simply divide and get your answer.

You should get:

x=3.875

Now, depending on what your problem is asking for, you would either round to the tenths or hundreths place.

There you go!

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2 years ago

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andreev551 [17]

Answer:

D) 54 cm

Step-by-step explanation:

We can use the Centroid Theorem to solve this problem, which states that the centroid of a triangle is $\frac{2}{3}$ of the distance from each of the triangle's vertices to the midpoint of the opposite side.

Therefore, $R$ is $\frac{2}{3}$ of the distance from $U$ to $V$ , since the latter is the midpoint of the side opposite to $U$ . We know this because $R$ belongs to $UV$ , so $R$ must be $QS$ 's midpoint due to the fact that by definition, the centroid of a triangle is the intersection of a triangle's three medians (segments which connect a vertex of a triangle to the midpoint of the side opposite to it).

We can then write the following equation:

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Substituting $VR = 18$ into the equation gives us:

$18=\frac{1}{3} UV$

Solving for $UV$ , we get:

$18=\frac{1}{3} UV$

$3 *18=3*\frac{1}{3}UV$ (Multiply both sides of the equation by $3$ to get rid of $UV$ 's coefficient)

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Therefore, the answer is D. Hope this helps!

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2 years ago

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Step-by-step explanation:

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