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3 years ago

Choose the missing step in the given solution to the inequality −x − 10 > 14 + 2x.

Mathematics

1 answer:

Drupady [299]3 years ago

6 0

Step-by-step explanation:

-3x - 10 > 14

-3x > 24 (add 10 to both sides)

x < -8 (divide by -3, flip inequality sign)

The missing step is -3x > 24.

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Two cars start out together from the same place. they travel in opposite directions, with one of them traveling 5 miles per hou

Mashutka [201]

Annotation
General formula for distance-time-velocity relationship is as following
d = v × t
The velocity of the first car will be v₁, the time is 2 hours, the distance will be d₁.
The velocity of the second car will be v₂, the time is 2 hours, the distance will be d₂.

One of them traveling 5 miles per hour faster than the others. That means the velocity of the first car is 5 miles per hour more than the velocity of the second car.
v₁ = v₂ + 5 (first equation)

The distance of the two cars after two hours will be 262 miles apart. Because they go to opposite direction, we could write it as below.
d₁ + d₂ = 262 (second equation)

Plug the d-v-t relationship to the second equation
d₁ + d₂ = 262
v₁ × t + v₂ × t = 262
v₁ × 2 + v₂ × 2 = 262
2v₁ + 2v₂ = 262

Plug the v₁ as (v₂+5) from the first equation
2v₁ + 2v₂ = 262
2(v₂ + 5) + 2v₂ = 262
2v₂ + 10 + 2v₂ = 262
4v₂ + 10 = 262
4v₂ = 252
v₂ = 252/4
v₂ = 63
The second car is 63 mph fast.

Find the velocity of the first car, use the first equation
v₁ = v₂ + 5
v₁ = 63 + 5
v₁ = 68
The first car is 68 mph fast.

Answer
$\boxed{\boxed{ v_{1}=68mph} }$
$\boxed{\boxed{ v_{2}=63mph} }$

7 0

4 years ago

What is 1 hour : 45 minutes in a ratio?

Afina-wow [57]

1 hour is 60 minutes. The ratio of 60 minutes to 45 minutes is 4:3 .

3 0

3 years ago

Customer- I recently saw an advertisement that said your company would give 5% discount to anyone who enrolls in your automatic

Darya [45]

Answer: $3.75

Step-by-step explanation:

The amount that you would save is 5% of your monthly bill of $75.

This amount is:

= 75 * 5%

= $3.75

The total amount that you would pay is:

= 75 - 3.75

= $71.25

4 0

3 years ago

Which Decimal is equivalent to 47/250

Masja [62]

Answer:

0.188?

Step-by-step explanation:

3 0

3 years ago

1.Could 18 in, 6 in, and 13 in, form a triangle?

lianna [129]

Answer:

1. yes

2. yes

3. no

4. no

5. yes

Step-by-step explanation:

The questions you're asking relate to the Triangle Inequality Theorem, which states that the two smallest sides (ex. 6 and 13) have to be of greater value than the largest side (ex. 18)

1. 6+13>18

2. 34+27>58

3. 29+9=38 (since the value of the two smallest sides are equal, it does not apply to the Triangle Inequality Theorem, and therefore won't be a triangle)

4. 12+12<25

5. 19+14>31

Happy to help <3

3 0

3 years ago