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3 years ago

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A motorboat travels 9 miles downstream (with the current) in 30 minutes. The return trip upstream (against the current) takes 90

minutesWhich system of equations can be used to find x, the speed of the boat in miles per hour, and y, the speed of the current in miles per hour? Recall the formula d = rt..

1 answer:

Ksju [112]3 years ago

8 0

Answer:

Option B

Step-by-step explanation:

When moving with the current, the speeds of the boat and current will add up. The first situation can then be represented by:

9 = 0.5(x + y)

While opposing the current, the speeds will be subtracted. Forming:

9 = 1.5(x - y)

The second option contains this equation system, so it is correct.

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Crank

3/5 of 300 is 180. 180 coupons were unused.

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3 years ago

Find the distance between the two points and simplest rational form (3,-4) (6,-7))

pychu [463]

Answer:

$D = 3\sqrt{2}$

Step-by-step explanation:

Given

$(x_1,y_1) = (3,-4)$

$(x_2,y_2) = (6,-7)$

Required

Determine the distance between the two points

Distance (D) is calculated as:

$D = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

Substitute values for x's and y's

$D = \sqrt{(6 - 3)^2 + (-7 - (-4))^2}$

$D = \sqrt{(6 - 3)^2 + (-7 +4)^2}$

$D = \sqrt{(3)^2 + (-3)^2}$

$D = \sqrt{9+9}$

$D = \sqrt{18}$

Express as 9 * 2

$D = \sqrt{9*2}$

Split:

$D = \sqrt{9}*\sqrt{2}$

$D = 3*\sqrt{2}$

$D = 3\sqrt{2}$

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2 years ago

Given f(x) = x^3-3 , find f(-2).<br> Show work please

Tasya [4]

(-2)×3-3=-9
f(x) = -9

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3 years ago

The total number of? restaurant-purchased meals that the average person will eat in a? restaurant, in a? car, or at home in a ye

zmey [24]

Answer:

<em>The number of restaurant-purchased meals eaten in a restaurant is 75, the number eaten in a car is 33 and the number eaten at home is 55.</em>

Step-by-step explanation:

Suppose, the number of meals eaten in a restaurant is $x$ , in a car is $y$ and at home is $z$

The total number of meals eaten in a restaurant, in a car or at home is given as 163. So, the first equation will be......

$x+y+z=163 .............................(1)$

The total number meals eaten in a car or at home exceeds the number eaten in a restaurant by 13. So, the second equation will be......

$y+z=x+13 ................................(2)$

Twenty more restaurant-purchased meals will be eaten in a restaurant than at home. So, the third equation will be......

$x= z+20..................................(3)$

First, <u>substituting equation (2) into equation (1)</u>, we will get........

$x+(x+13)=163\\ \\ \Rightarrow 2x+13=163\\ \\ \Rightarrow 2x=163-13=150\\ \\ \Rightarrow x=\frac{150}{2}=75$

<em>Now plugging this $x=75$ into equation (3)</em>, we will get......

$75=z+20\\ \\ \Rightarrow z=75-20= 55$

<em>Plugging $x=75$ and $z=55$ into equation (1)</em> .........

$75+y+55=163\\ \\ \Rightarrow y+130=163\\ \\ \Rightarrow y=163-130=33$

So, the number of restaurant-purchased meals eaten in a restaurant is 75, the number eaten in a car is 33 and the number eaten at home is 55.

8 0

3 years ago

A scale on a blueprint drawing of a house shows that 10 centimeters represents 2 meters. What number of actual meters are repres

nata0808 [166]

Answer:

<u>3.6 meters</u> are represented by 18 centimeters on the blueprint.

Step-by-step explanation:

Given:

A scale on a blueprint drawing of a house shows that 10 centimeters represents 2 meters.

Now, to find the actual meters represented by 18 centimeters.

Let the actual meters represented by 18 centimeters be $x.$

As, given the scale on a blueprint drawing of a house shows that 10 centimeters represents 2 meters.

So, 10 centimeters equivalent to 2 meters.

Thus, 18 centimeters equivalent to $x.$

Now, to solve by using cross multiplication method:

$\frac{10}{2}=\frac{18}{x}$

<em>By cross multiplying we get:</em>

$10x=36$

<em>Dividing both sides by 10 we get:</em>

$x=3.6\ meters.$

Therefore, 3.6 meters are represented by 18 centimeters on the blueprint.

3 0

3 years ago