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11Alexandr11 [23.1K]
2 years ago
14

Solve for x: −3x + 3 < 6 x > −1 x < −1 x < −3 x > −3

Mathematics
2 answers:
Misha Larkins [42]2 years ago
7 0

Answer:

x > -1

Step-by-step explanation:

Ad libitum [116K]2 years ago
7 0

\bf{-3x+3 < 6}

Subtract 3 from both sides.

  • \bf{-3x < 6-3 }

Subtract 3 from 6 to get 3.

  • \bf{-3x < 3}

Divide both sides by -3. Since −3 is < 0, the inequality direction is changed.

  • \bf{x > \dfrac{3}{-3}  }

Divide 3 by -3 to get -1.

  • \bf{x > -1 \ \ \to \ \ \ Answer }

Therefore, the correct option is the first.

\red{\boxed{\green{\boxed{\boldsymbol{\purple{Pisces04}}}}}}

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Determine whether the three segment lengths will produce a triangle. Type yes or no in the space provided.
tresset_1 [31]

Answer:

20 , 20 , 30 will produce a triangle

Step-by-step explanation:

* Lets study how to know if the lengths of the three segments

 can formed a triangle

- It is a fact that in any triangle the sum of the smallest two sides

 must be greater than the largest side

- Lets study some examples

# If the lengths of the three segments are 5 , 6 , 7

∵ 5 and 6 are the smallest

∴ 5 + 6 = 11

∵ 11 > 7 ⇒ the sum greater than the 3rd side

∴ 5 , 6 , 7 can formed a triangle

# If the lengths of the three segments are 5 , 7 , 12

∵ 5 and 7 are the smallest

∴ 5 + 7 = 12

∵ 12 = 12 ⇒ the sum equal the 3rd side

∴ 5 , 7 , 12 can not formed a triangle

# If the lengths of the three segments are 10 , 12 , 24

∵ 10 and 12 are the smallest

∴ 10 + 12 = 22

∵ 22 < 24 ⇒ the sum less than the 3rd side

∴ 10 , 12 , 24 can not formed a triangle

* Now lets solve the problem

∵ The length of the three segments are 20 , 20 , 30

∵ 20 and 20 are the smallest

∴ 20 + 20 = 40

∵ 40 > 30 ⇒ the sum greater than the 3rd side

∴ 20 , 20 , 30 will produce a triangle

5 0
2 years ago
Thetime(inhours)requiredtorepairamachineis an exponentially distributed random variable with parameter λ = 1 . What is 2 (a) the
mihalych1998 [28]

Answer:

a) 0.1353

b) 0.3679

Step-by-step explanation:

Let's start by defining the random variable T.

T : ''The time (in hours) required to repair a machine''

T ~ exp (λ)

T ~ exp (1)

The probability density function for the exponential distribution is

(In the equation I replaced λ = L)

f(x)=Le^{-Lx}

With L > 0 and x ≥ 0

In this exercise λ = 1 ⇒

f(x)=e^{-x}

For a)

P(T>2)

P(T>2)=1-P(T\leq 2)

P(T>2)=1-\int\limits^2_0 {e^{-x} } \, dx

P(T>2)=1-(-e^{-2}+1)

P(T>2)=e^{-2}=0.1353

For b)

P(T\geq 10/T>9)

The event (T ≥ 10 / T > 9) is equivalent to the event T ≥ 1 so they have the same probability of occur

P(T\geq 10/T>9)=P(T\geq 1)

P(T\geq 1)=1-P(T

P(T\geq 1)=1-(-e^{-1}+1)=e^{-1}=0.3679

4 0
3 years ago
Which of the following numbers can be expressed as a decimal that<br> terminates 9/7 5/3 3/2 6/4
podryga [215]

Answer:

Last 2 terminate

Step-by-step explanation:

9/7 does not terminate: 1.285724285724285724...

5/3 does not terminate: 1.66666666666666666...

3/2 does terminate: 1.5

6/4 same thing as 3/2 = 1.5

C and D terminate.

8 0
2 years ago
Find the missing side This is due in a hour
loris [4]

Answer:

The Arch is 630 ft tall

Step-by-step explanation:

3 0
3 years ago
What is the value of a in the equation 3.5a-2= -1.5a+4
Natali5045456 [20]
6/5 because you add 1.5 to both sides, the. Add 2 to both sides, then divide to get a by itself
4 0
3 years ago
Read 2 more answers
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