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3 years ago

Eight times a number is not less than the sum of the number and fifty

1 answer:

4 0

If the number is n, then 8 times n ≥ n+50, and by subtracting n from both sides we get 8n-n ≥ 50 and 7n ≥50. Therefore, by dividing by 7, n ≥50/7

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A line perpendicular to y=1/4x+3 passes through the point (0,6). Which other point lies on the line

leonid [27]

A line perpendicular to y = (1/4)x+3 will have slope -4.
This is because when you multiply the slopes of the original line and the perpendicular line, you get -1. (1/4)(-4)=-1 
The equation of the perpendicular line is 
y=-4x+b 
This line pases through (0,6) 
6=-4(0)+b 
b=6 
y=-4x+6 is the line

3 0

3 years ago

A submarine is exploring the Pacific Ocean. At 502.5 feet below sea level, the water temperature is 6 1/4 °F. The submarine dive

Whitepunk [10]

Step-by-step explanation:

At the elevation 617.5 feet below the sea level temperature of the water was °F

Step-by-step explanation:

At 502.5 feet below the sea level temperature of the water is °F

When submarine dives down 115 feet deeper, water temperature drops by °F

Elevation after the submarine dove = -502.5 - 115 = -617.5 feet

This negative sign represents the elevation below the sea level.

And the temperature will be =

= °F

Therefore, at the elevation 617.5 feet below the sea level temperature of the water was °F

4 0

3 years ago

Read 2 more answers

the counter on a tape recorder registers 520 after the recorder has been running for 20 minutes. what would the counter register

valkas [14]

The answer would be 1,560

8 0

3 years ago

The spherical balloon is inflated at the rate of 10 m³/sec. Find the rate at which the surface area is increasing when the radiu

rjkz [21]

The balloon has a volume $V$ dependent on its radius $r$ :

$V(r)=\dfrac43\pi r^3$

Differentiating with respect to time $t$ gives

$\dfrac{\mathrm dV}{\mathrm dt}=4\pi r^2\dfrac{\mathrm dr}{\mathrm dt}$

If the volume is increasing at a rate of 10 cubic m/s, then at the moment the radius is 3 m, it is increasing at a rate of

$10\dfrac{\mathrm m^3}{\mathrm s}=4\pi (3\,\mathrm m)^2\dfrac{\mathrm dr}{\mathrm dt}\implies\dfrac{\mathrm dr}{\mathrm dt}=\dfrac5{18\pi}\dfrac{\rm m}{\rm s}$

The surface area of the balloon is

$S(r)=4\pi r^2$

and differentiating gives

$\dfrac{\mathrm dS}{\mathrm dt}=8\pi r\dfrac{\mathrm dr}{\mathrm dt}$

so that at the moment the radius is 3 m, its area is increasing at a rate of

$\dfrac{\mathrm dS}{\mathrm dt}=8\pi(3\,\mathrm m)\left(\dfrac5{18\pi}\dfrac{\rm m}{\rm s}\right)=\dfrac{20}3\dfrac{\mathrm m^2}{\rm s}$

4 0

3 years ago

Sara receives a 9% commission on every car she sells. The car dealership paid $20,000 for a car from an auction. The next day th

Paladinen [302]

Hey there! Your answer to this problem is 2160..

Explanantion:

Since every car Sara sells, she gets 9% of the commission, this means that at the last few step, we would have to give 9% of the total cost to Sara.

If 100% is 20,000, then 50% would be 10,000. But we have to find the cost of 20%. So what we would actually be doing is multiplying 20 with 0.01. 20x0.01 is 0.2 or 0.20.

Then you add the 4,000 to the 20,000 because it states, “the next day, they sold the car 20% more than they paid. This means that you’ll have to add it. 20,000 plus 4000 would be 24,000. So 24,000 would be the cost of the car they sold.

However they didn’t wanna know the cost of the car, they wanted to know how much Sara would get. So you would have to take 9% of the cost of the cost which would be 2,160.

Final result: $2,160

4 0

3 years ago