The one on the bottom asap! 6th grade math pre-ap

Mathematics

1 answer:

Nikitich [7]2 years ago

6 0

100 puzzles were sold

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Find two positive numbers if their ratio is 8:5 and the difference is 150.

natima [27]

Let's call the two numbers x and y. We can write a system of equations to describe the situation:

5x = 8y

x - y = 150

Let's solve the first equation for x:

x = 8y/5

Now we can use substitution to solve the system by plugging 8y/5 in for x in the second equation:

(8y/5) - y = 150

Simplify:

3y/5 = 150

3y = 750

y = 250

If y = 250, then x is:

x = 8(250)/5 = 400

The answer is 250 and 400.

7 0

2 years ago

6 more than a number is at most 10.<------Put as an inequality.The sum of a number and 14 is at least 18<----Put as an ine

lord [1]

X+6 less than or equal to 10
X+14 greater than or equal to 18

6 0

2 years ago

The wheels on Darlene's car have on 11-inch radius. If the wheels are rotating at a rate of 378 rpm, find the linear speed in mi

elena-s [515]

Answer:

The linear speed in which Darlene is traveling is 24.74 miles per hour.

Step-by-step explanation:

The wheel experiments rolling, which is a combination of translation and rotation. The point where linear speed happens is located at geometrical center of the wheel and instantaneous center of rotation is located at the point of contact between wheel and ground. The linear speed ( $v$ ), measured in inches per second, is defined by following expression:

$v = R\cdot \omega$ (1)

Where:

$R$ - Radius of the wheel, measured in inches.

$\omega$ - Angular speed, measured in radians per second.

If we know that $R = 11\,in$ and $\omega \approx 39.584\,\frac{rad}{s}$ , then the linear speed, measured in miles per hour, in which Darlene is traveling is: