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3 years ago

V is the midpoint of UW. If UV = x + 2 and VW = 2x, what is VW?

Mathematics

2 answers:

erica [24]3 years ago

8 0

Answer:

VW = 4

Step-by-step explanation:

Since V is the midpoint of line UW, we can say that the measure of UV is equal to VW (see def. of midpoint). Thus, we can generate the equation using the statements provided, leading us to this equation: x+2 = 2x. We can then subtract x on both sides, leading us to 2 = x, or x = 2.

We were given that VW = 2x, thus the measure of VW is equal to 2(2) or 4.

(BONUS: since we know that VW ≅ UV, then the measure of UV is also equal to 4, which when applied to the formula for UV (x+2) we get the equation for UV, x+2=4. This is a way to prove that x=2, as 2+2=4. We can also use this knowledge to find the total length of this line segment, which would be 8, as 4+4=8)

Elan Coil [88]3 years ago

3 0

Answer:

8 units

Step-by-step explanation:

x + 2 = 2x

2 = 2x - x

x = 2

uW = 2(2+2) = 8

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Find the 6th term of the arithmetic sequence X – 9, -X – 11, -3.3 – 13, ...

MrMuchimi

Answer:

$-13x-23$

Step-by-step explanation:

Given sequence: $x-9, -x-11, -3x-13$

Therefore,

$a_1=x-9$
$a_2=-x-11$
$a_3=-3x-13$

General form of an arithmetic sequence: $a_n=a+(n-1)d$

(where a is the first term and d is the common difference)

To find the common difference, subtract a term from the next term:

$\begin{aligned}d & =a_2-a_1\\ & =(-x-11)-(x-9)\\ & = -x-11-x+9\\ & = -2x-2\end{aligned}$

Therefore,

$a_n & =(x-9)+(n-1)(-2x-2)$

To find the 6th term, input n = 6 into the equation:

$\begin{aligned}\implies a_6 & =(x-9)+(6-1)(-2x-2)\\ & = (x-9)+7(-2x-2)\\ & = x-9-14x-14\\ & = -13x-23\end{aligned}$

3 0

3 years ago

Simplify: 3x + 4y + 7x - 2y

tresset_1 [31]

Answer:

10x+2y

Step-by-step explanation:

combine like terms

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3 years ago

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alexandr1967 [171]

Answer:

Equation: 7x - 23 = 25 + x

Solution: x = 8

Step-by-step explanation:

7x - 23 = 25 + x

1. Subtract 25 from both sides:

7x - 23 - 25 = 25 - 25 + x

7x - 48 = x

2. Subtract 7x from both sides to get x on one side:

7x - 7x - 48 = x - 7x

- 48 = -6x

3. Divide both sides by -6 to get x by itself:

8 = x

8 is the solution

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3 years ago

If y varies directly as x, and x = 48 when y = 6, find y<br> when x = 12.

pentagon [3]

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3 years ago

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Rosa is attending an event where prizes are being given away. The probability of winning a T‐shirt is 0.89 and the probability o

vagabundo [1.1K]

Answer:

It is very likely that Rosa wins both prizes.

Step-by-step explanation:

The probability of winning a T‐shirt is 0.89 and the probability of winning a $20 gift certificate is 0.05. Which statement correctly describes the chances of Rosa winning a T‐shirt or a $20 gift certificate?

We have these three possibe outcomes.

Win t-shirt(0.89 probability) and lose the gift certiciate(1 - 0.05 = 0.95 probability)

Lose t-shirt(0.11 probability) and win the gift certiciate(0.05 probability).

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$p = 0.89*0.95 + 0.11*0.05 + 0.89*0.05 = 0.8955$

0.8955 = 89.55% probability of Rosa winning a T‐shirt or a $20 gift certificate, which is considered a very likely probability. So the answer is:

It is very likely that Rosa wins both prizes.

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