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2 years ago

|3y-1|>5 Solve the absolute value inequalities by making a compound inequality

Mathematics

1 answer:

Fantom [35]2 years ago

7 0

Hi there!

We can begin by solving the inequality using the positive and negative terms:

3y - 1 > 5

Add 1 to both sides:

3y > 6

Divide both sides by 3:

y > 2

Now, solve the negative:

-(3y - 1) > 5

Distribute the -1:

-3y + 1 > 5

Subtract 1 from both sides:

-3y > 4

Divide both sides by -3. REMEMBER to flip the sign.

y < -4/3

'y' has to be LESS than -4/3 and greater than 2, so:

y < -4/3, y > 2

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The lengths of the sides of a triangle are in ratio 5 : 7 : 9. The middle-in-length side is 35 cm. Find the perimeter of the tri

ipn [44]

Answer:

The perimeter of the triangle is 105 cm.

Step-by-step explanation:

The ratio of sides of a triangle is $5:7:9$ .

The length of middle side is 35 cm.

Let first side of the tringle is $x$ , length of third side is $y$ . middle side is of 35 cm.

So, the ratio of length of sides can be written as,

$x:35:y=5:7:9$

Compare the ratio to get the value of $x$ and $y$ .

$x:35:y=25:35:45\\x=25\\y=45$

Now, the sides of the triangle are 25 cm, 35 cm and 45 cm.

Thus, the perimeter of the triangle will be the sum of all sides and can be calculated as,

$p=25+35+45\\p=105$

Therefore, the perimeter of the triangle is 105 cm.

For more details, refer the link:

brainly.com/question/20955459?referrer=searchResults

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3 years ago

Use the graph below to determine a1 and d for the sequence.

Aliun [14]

Answer:

a₁ = 2 and d = 3

Step-by-step explanation:

Consider the sequence given by the values of y, that is

2, 5, 8, 11, 14, 17

The first term in the sequence is a₁ = 2

The common difference is

d = 17 - 14 = 14 - 11 = 11 - 8 = 8 - 5 = 5 - 2 = 3

Thus a₁ = 2 and d = 3

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3 years ago

On a residential single lane road there was a wreck that backed up traffic for 4 miles. 70% of the traffic consists of cars and

kolezko [41]

Answer:

There are approximately 1145 vehicles are stuck in the traffic jam. It is very close to option C.

Step-by-step explanation:

To determine:

Estimate how many vehicles are stuck in the traffic jam.

Information Fetching and Solution Steps:

On a residential single lane road there was a wreck that backed up traffic for 4 miles.

70% of the traffic consists of cars and 30% of the traffic consists of trucks.

The average distance between vehicles is 3 feet.

The average length of a car is 13.5 feet.

The average length of a truck is 20 feet.
There are 5280 feet in 1 mile

Let 'n' be the total number of vehicles stuck in the traffic jam.

So, the equation becomes

$0.7n\cdot \:13.5+0.3n\cdot \:20+3n-3=4\cdot \:5280$

$\mathrm{Multiply\:the\:numbers:}\:0.7\cdot \:13.5=9.45$

$9.45n+20\cdot \:0.3n+3n-3=4\cdot \:5280$

$\mathrm{Multiply\:the\:numbers:}\:0.3\cdot \:20=6$

$9.45n+6n+3n-3=4\cdot \:5280$

$\mathrm{Add\:similar\:elements:}\:9.45n+6n+3n=18.45n$

$18.45n-3=4\cdot \:5280$

$\mathrm{Multiply\:the\:numbers:}\:4\cdot \:5280=21120$

$18.45n-3=21120$

$\mathrm{Multiply\:both\:sides\:by\:}100$

$18.45n\cdot \:100-3\cdot \:100=21120\cdot \:100$

$\mathrm{Refine}$

$1845n-300=2112000$

$1845n-300+300=2112000+300$

$1845n=2112300$

$\frac{1845n}{1845}=\frac{2112300}{1845}$

$n=\frac{46940}{41}$

$n=1144.87804$

Estimating to get the integer vehicle number and rounding it to the nearest integer.

$n\:\approx \:1145$ vehicles

Therefore, there are approximately 1145 vehicles are stuck in the traffic jam, which is very close to option C.

Keywords: word problem

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3 0

3 years ago