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Paladinen [302]

2 years ago

13

What are the coordinates of the point on the directed line segment from (1, -6) to (8, 8) that partitions the segment into a rat

io of 4 to 3?

1 answer:

vlada-n [284]2 years ago

3 0

9514 1404 393

Answer:

(5, 2)

Step-by-step explanation:

Line segment AB is partitioned by point P into segments of the ratio m : n when point P satisfies ...

P = (mB +nA)/(m+n)

Here we want ...

P = (4(8, 8) +3(1, -6))/(4 +3) = (32 +3, 32 -18)/7 = (35/7, 14/7)

P = (5, 2)

The point (5, 2) partitions the segment into a ratio of 4 : 3.

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Solve the equation<br> 3x-2<br> 4<br> -<br> 2x - 5- 1 + x<br> 3 6

Nataly_w [17]

Answer:

$\boxed{\sf x=12}$

Step-by-step explanation:

$\sf \cfrac{3x-2}{4}-\cfrac{2x-5}{3}=\cfrac{1+x}{6}$

First, let's find the LCM of 4, 3, and 6.

<u>How to find the LCM:</u>

→ List multiples of each number.

→ Find the smallest number on each list.

4: 4, 8, 12, 16, 20, 24..

3: 3, 6, 9, 12, 15, 18, 21, 24, 27....

6: 6, 12, 18, 24, 30, 36, 42...

<u>LCM: 12</u>

<u>_________</u>

Now, we'll Multiply by LCM:

$\sf \cfrac{3x-2}{4}\times \:12-\cfrac{2x-5}{3}\times \:12=\cfrac{1+x}{6}\times \:12$

Simplify:

$\sf 3\left(3x-2\right)-4\left(2x-5\right)=2\left(x+1\right)$

Now, expand, Apply the Distributive property:

$\bold{ 3\left(3x-2\right)-4\left(2x-5\right)}$

$\sf 9x-6-8x+20$

Combine like terms:

$\sf x+14$

________

$\bold{ 2\left(x+1\right)}$

$\sf 2x+2$

$\sf x+14=2x+2$

Subtract 14 from both sides:

$\sf x+14-14=2x+2-14$

Simplify:

$\sf x=2x-12$

Subtract 2x from both sides:

$\sf x-2x=2x-12-2x$

Simplify:

$\sf -x=-12$

Divide both sides by -1:

$\sf \cfrac{-x}{-1}=\cfrac{-12}{-1}$

$\sf x=12$

<h3><u>____________________________</u></h3>

7 0

2 years ago

2/3 is what percent of 1/4

asambeis [7]

Answer:

267%

Step-by-step explanation:

you need to divide the second number by the first. This will give you the percentage.

2/3 ÷ 1/4 = 8/3 = 2.67 = 267%

6 0

3 years ago

What is the answer to this?

katrin [286]

Answer:

$\huge\boxed{-28}$

Step-by-step explanation:

We can substitute the given values of $a$ , $b$ , and $c$ to find the value of this expression.

$-4 | a + b - c|$

$-4 | 3 + (-2) - (-6)|$

We know that <em>two negatives make a positive. </em>This means that $-2 - (-6)$ will be the same this as $-2+6$

$-4 | 3 + -2 + 6|$

Adding a negative is the same as subtracting a positive.

$\4 | 3-2+6|\\\\3-2+6 = 7$

$-4 \cdot 7 = -28$

Hope this helped!

7 0

2 years ago

Read 2 more answers

H<br> nlaced inside a cylinder as shown. The radius of the cone is half the radius of the cylinder.

Sophie [7]

Answer:

umm what or we doing?

Step-by-step explanation:

5 0

2 years ago

An electrician needs 3/4 roll of electrical wire to wire each room in a house . How many rooms can he wire with 6 rolls

Makovka662 [10]

Answer:

8

Step-by-step explanation:

number of rooms=6÷3/4=6×4/3=8

7 0

2 years ago