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uysha [10]
3 years ago
13

A sailboat travels 48 miles upstream in 6 hours and return back downstream in 4 hours. What is the speed of the boat in still wa

ter?
Mathematics
1 answer:
Kipish [7]3 years ago
4 0
Let s be the speed of the boat in still water.
Let c be the speed of the current.
s - c = 48/6 = 8
s + c = 48/4 = 12
Adding the two equations, we get:
2s = 20
s = 10
The answer is 10 miles per hour.
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(02.03 MC)
vodomira [7]

Answer:

So the Solution is

x = 4\ , x = -2

Step-by-step explanation:

Solve for x: 4|2x − 2| + 10 = 34.

Step 1. Subtracting 10 on both the sides we get

4|2x-2|+10-10=34-10\\\\4|2x-2|=24

Step 2. Dividing both the side by 4 we get

\dfrac{4|2x-2|}{4}=\dfrac{24}{4}\\\\|2x-2|=6

Step 3. Removing Modulus sign we get two values

2x-2=6\ or\ 2x-2=-6\\\\2x=6+2\ or\ 2x=-6+2\\\\2x=8\ or\ 2x=-4\\\\x=\dfrac{8}{2} \ or\ x=\dfrac{-4}{2} \\\\x=4\ or\ x=-2\\

So the Solution is

x = 4\ , x = -2

4 0
3 years ago
If a = 5 and b = 6, evaluate the following expression:<br> 20 - 5a + 3b
aliya0001 [1]

Answer:

20-5 × 5 + 3 × 6

20-25 + 36

Step-by-step explanation:

6 0
3 years ago
Two students in your class, Ralph and Bobby, are disputing a function. Ralph says that for the function, between x = −1 and x =
marshall27 [118]

Answer:

Ralph and Bobby both are correct about slope. Because slope for both is 0.

Step-by-step explanation:

We are given a function that has two values of x's between x = −1 and x = 1.

And the average rate of change between x=-1 and x=1 is 0.

We know that x=-1 and x=1 are the points on x-axis.

If we joint x=-1 and x=1 points, we would get a straight line horizontal line on x-axis.

And note, the slope of a horizontal line is 0 always.

So, according to Bobby the graph goes up through a turning point, and then back down that means the point (-1,0) gets horizontally shift by 2 unit at (1,0).

Therefore, rise/run = 0/2, that is also equal to 0.

Therefore, Ralph and Bobby both are correct about slope.

Because slope for both is 0.

7 0
3 years ago
The equation x^2+ (k - 3)x + (3 - 2k) = 0, where k is a constant, has two distinct real roots.
Lisa [10]

Step-by-step explanation:

For quadratic equation ax^2 + bx + c = 0 to have two distinct real roots,

b^2 - 4ac must be positive.

b^2 - 4ac > 0

(k - 3)^2 - 4(3 - 2k) > 0

k^2 - 6k + 9 - 12 + 8k > 0

k^2 + 2k - 3 > 0

4 0
3 years ago
Mrs. Cleaver mixes 1.24 liters of red paint with 3 times as much blue paint to make purple paint. She pours the paint equally in
otez555 [7]

The amount of blue paint in each container is \fbox{\begin\\\ 0.744 liters \end{minispace}}.

Further explanation:

The mixture mixed by Mrs. Cleaver contains 1.24 litres of red paint with 3 times blue paint to obtain purple paint.

So, the amount of blue paint is calculated as,

{3} \times {1.24}=3.72 \text { liters}

Therefore, the total amount of paint mixture is the sum of blue paint and red paint.

\fbox{\begin \\\begin{aligned} \text{Total paint}= 1.24+3.72\\=4.96 \text{ liters}\\\end{aligned}\\\end{minispace}}

Now, as Mrs. Cleaver divides the paint mixture equally in 5 containers so the amount of paint in one container is calculated as,

\boxed{\begin{aligned}\text{Amount of paint in one container}&= \dfrac{4.96}{5}\\ &=0.992 \text{ liters} \end {aligned}}

Since amount of blue paint mixed is three times the red paint so the fraction of blue paint to the total paint is \dfrac{3}{4}.  

Now, as it is known that the fraction of blue paint to the total paint is \dfrac{3}{4} and the amount of paint in a container is 0.992 \text{ liters} then the blue paint in one container is calculated as,

\boxed{\begin{aligned}\text{Blue paint in one container} =\dfrac{3}{4} \times 0.992\\=0.248 \text{ liters}\end{aligned}}

Thus, the amount of blue paint in each of the five containers is \fbox{\begin\\\ 0.744 liters \end{minispace}}.

Learn more:  

1. To solve one variable linear equation brainly.com/question/1682776

2. Linear equation application brainly.com/question/2479097

3. Composite functions brainly.com/question/2142762

Answer details  

Grade: Middle school  

Subject: Mathematics  

Chapter: Mixtures and ratios

Keywords: mixture, paint, red paint, blue paint, Mrs. Cleaver, purple paint, fraction, each container, five containers, divides, times, equally divide, mixes, liters.

3 0
3 years ago
Read 2 more answers
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