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3 years ago

Solve the following compound inequality. 5x+7<=-3 or 3x-4>=11

Mathematics

1 answer:

Kobotan [32]3 years ago

4 0

Answer:

$x\leq -2$ or $x\geq 5$

Step-by-step explanation:

$5x+7\leq -3$ or $3x-4\geq 11\\$

$5x+7\leq -3\\5x\leq -10\\x\leq -2$

$3x-4\geq 11\\3x\geq 15\\ x\geq 5$

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On the first day of travel, a driver was going at a speed of 40 mph. The next day, he increased the speed to 60 mph. If he drove

gogolik [260]

Velocity, distance and time:

This question is solved using the following formula:

$v = \frac{d}{t}$

In which v is the velocity, d is the distance, and t is the time.

On the first day of travel, a driver was going at a speed of 40 mph.

Time $t_1$ , distance of $d_1$ , v = 40. So

$v = \frac{d}{t}$

$40 = \frac{d_1}{t_1}$

The next day, he increased the speed to 60 mph. If he drove 2 more hours on the first day and traveled 20 more miles

On the second day, the velocity is $v = 60$ .

On the first day, he drove 2 more hours, which means that for the second day, the time is: $t_1 - 2$

On the first day, he traveled 20 more miles, which means that for the second day, the distance is: $d_1 - 20$

Thus

$v = \frac{d}{t}$

$60 = \frac{d_1 - 20}{t_1 - 2}$

System of equations:

Now, from the two equations, a system of equations can be built. So

$40 = \frac{d_1}{t_1}$

$60 = \frac{d_1 - 20}{t_1 - 2}$

Find the total distance traveled in the two days:

We solve the system of equation for $d_1$ , which gets the distance on the first day. The distance on the second day is $d_2 = d_1 - 20$ , and the total distance is:

$T = d_1 + d_2 = d_1 + d_1 - 20 = 2d_1 - 20$

From the first equation:

$d_1 = 40t_1$

$t_1 = \frac{d_1}{40}$

Replacing in the second equation:

$60 = \frac{d_1 - 20}{t_1 - 2}$

$d_1 - 20 = 60t_1 - 120$

$d_1 - 20 = 60\frac{d_1}{40} - 120$

$d_1 = \frac{3d_1}{2} - 100$

$d_1 - \frac{3d_1}{2} = -100$

$-\frac{d_1}{2} = -100$

$\frac{d_1}{2} = 100$

$d_1 = 200$

Thus, the total distance is:

$T = 2d_1 - 20 = 2(200) - 20 = 400 - 20 = 380$

The total distance traveled in two days was of 380 miles.

For the relation between velocity, distance and time, you can take a look here: brainly.com/question/14307500

3 0

3 years ago

Use the Pythagorean Theorem to find the missing length and then round the result to the nearest tenth.

motikmotik

A^2+B^3=c^2
6^2+8^2=c^2
36+16=c^2
52=c^2
Square root both sides
7.2=C

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2 years ago

When Meriden made a cake she used a recipe calling for 3/4 cup of sugar. She was planning to make a huge cake for a family get-t

soldi70 [24.7K]

Meriden would need 2 1/4 cups of sugar because 3*3/4=2 1/4

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3 years ago

Find the geometric mean between each pair of numbers. sq root 49 and sq root841

vodomira [7]

<u>Answer:</u>

The geometric mean between each pair of numbers $\bold{\sqrt{49} \text { and } \sqrt{841} \text { is } 14.24}$

<u>Solution:</u>

The Geometric mean between two numbers a and b is given as Geometric mean = $\bold{\sqrt{ab}}$ --- eqn 1

The Geometric Mean is a special type of average where we multiply the numbers together and then take a square root for the numbers.

From question, given that two numbers are $\sqrt{49} and \sqrt{841}$

Hence we can say “a” = $\sqrt{49}$ =7

Similarly “b” = $\sqrt{841}$ = 29

We have to find the geometric mean between “7” and “29”

By using equation 1,

Geometric mean between 7 and 29 = $\sqrt{7 \times 29} = \sqrt{203}$ = 14.24

Hence the geometric mean between $\sqrt{49} \text { and } \sqrt{841} \text { is } 14.24$

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3 years ago

Does 2x-7=1/3(6x-12) + (-3) have one solution, infinitely many solutions, or no solutions? Please show how you got the answer an

salantis [7]

Answer:

Infinetly many solutions. No matter what you plug in, it always comes out equal.

Step-by-step explanation:

7 0

3 years ago

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