A boat travel 312 miles each way downstream and back. The trip downstream took 13 hours. the trip back took 26 hours. What is the speed of the boat in still water. what is the speed of the current.

The larger number is (-7+14)/2 = 3.5.

The smaller number is (-7-14)/2 = -10.5.

_____

The two equations a+b=-7, a-b=14 can be solved to get these results. It is genrally convenient to solve them by adding one to the other, or subtracting one from the other.

Final answer:

The equation 'x over five equals three over four' is solved by cross-multiplying to get 4x = 15, and then dividing both sides by four to find x = 3.75.

Explanation:

The equation presented by the student 'x over five equals three over four' translates to the algebraic equation x/5 = 3/4. Solving this involves finding the value of x that makes the equation true. To solve for x, we can cross-multiply to get 4x = 15, and then divide both sides of the equation by four to isolate x, giving us x = 15/4 or x = 3.75. Thus, the solution to the equation x/5 = 3/4 is x = 3.75.

Answer:

(d-5)

Step-by-step explanation:

we know that

The phrase"five fewer than d days" is equal to subtract 5 from the number d

so

d minus 5-----> (d-5)

Answer:

d-5

Step-by-step explanation:Just trust

Answer:

The equation for new function is [tex]y=\frac{1}{3}|x|[/tex]

Step-by-step explanation:

We have been given the absolute value parent function f(x) = |x| and this function is vertically compressed by a factor 3.

If we multiply the function with a constant (say a) then the parent function will get stretch/compressed vertically.

We have below conditions for vertical stretch and compression.

a > 1 => vertically stretch

0 < a < 1 => vertically compression

Hence, in order to vertical compression by a factor 3, we have to multiply the whole function by 1/3

Therefore, the equation for new function is [tex]y=\frac{1}{3}|x|[/tex]

Answer:

g(x) = 1/3 |x| !

Step-by-step explanation:

I hope this helps!

PQ = 2 units

height = 4 units

 area = 2*4 = 8/2 = 4 square units

The six sections would be 1/12

Final answer:

Lisa needs to score at least 12 points to win, so the inequality to represent this scenario is 'p >= 12', where 'p' is the number of points she scores on her next turn.

Explanation:

To represent the number of points Lisa needs to win the game with an inequality, we can let p stand for the points she will score on her next turn.

Since she needs to score at least 12 points, the inequality would be p \">= 12".

This reads as 'p is greater than or equal to 12,' meaning Lisa needs to score 12 or more points to win.

Answer:

The volume of the box is 0.09375 inches cube.

Step-by-step explanation:

Given : This box is 3/4 inches long, 1/2 inches wide, and 1/4 inches deep.

To find : What is the volume of the box ?          

Solution :

The dimension of the box is,

Length = [tex]l=\frac{3}{4}[/tex] inches

Breadth = [tex]b=\frac{1}{2}[/tex] inches

Height = [tex]h=\frac{1}{4}[/tex] inches

The formula of volume of the box is

[tex]V=l\times b\times h[/tex]

[tex]V=\frac{3}{4}\times \frac{1}{2}\times\frac{1}{4}[/tex]

[tex]V=\frac{3}{4\times 2\times 4}[/tex]

[tex]V=\frac{3}{32}[/tex]

[tex]V=0.09375in^3[/tex]

Therefore, The volume of the box is 0.09375 inches cube.

The volume of the box is 3/32 cubic inches.

Given

This box is 3/4 inches long, 1/2 inches wide, and 1/4 inches deep.

The volume of the box is given by-product of length, width, and height.

The volume of the box is determined by the following formula;

[tex]\rm Volume \ of \ box =Height\times Width \times length[/tex]

Substitute all the values in the formula;

[tex]\rm Volume \ of \ box =Height\times Width \times length\\\\\rm Volume \ of \ box =\dfrac{3}{4}\times \dfrac{1}{2} \times \dfrac{1}{4}\\\\\rm Volume \ of \ box =\dfrac{3}{32} \ cubic \ inches[/tex]

Hence, the volume of the box is 3/32 cubic inches.

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In 30 minutes, 250 gallons are filled in the swimming pool. In the same rate in 1 hours (which means 60 minutes), 500 gallons will be filled.

Let x be the number of hours it will take to fill the entire swimming pool which has the capacity of 25,000 gallons.

We need to set up a proportion like given below:

[tex] \frac{Number \; of \; Hours }{Amount \; of\; water \; in\; gallons} =\frac{x}{25,000} =\frac{1}{500} [/tex]

Solving the equation for x:

[tex] \frac{x}{25000} =\frac{1}{500} \\ Multiply \; 25000\; on\; both\; sides\; of\; the \; equation\\ \\ 25000 \times \frac{x}{25000} =\frac{1}{500} \times 25000\\ Simplify \; on \; both \; sides\\ \\ x \; = \; \frac{25000}{500} \; = 50 \; hours [/tex]

Conclusion:

The number of hours that will take to fill the pool is 50 hours !

Answer:

10 soccer club members are going to the tournament.

Step-by-step explanation:

Let x be the number of soccer club members who are going to the  tournament,

Given,

The cost of transportation of x students = $ 192

⇒ The cost of transportation of 1 student = [tex]\frac{192}{x}[/tex]

⇒ The cost of transportation of (x+2) student = [tex]\frac{192}{x-2}[/tex]

According to the question,

[tex]\frac{192}{x}-\frac{192}{x+2}=3.20[/tex]

[tex]192(\frac{1}{x}-\frac{1}{x+2})=3.20[/tex]

[tex]192(\frac{x+2-x}{x(x+2)})=3.20[/tex]

[tex]\frac{384}{x^2+2x}=3.20[/tex]

[tex]3.2x^2+6.4x=384[/tex]

[tex]3.2x^2+6.4x-384=0[/tex]

By the quadratic formula,

[tex]x=\frac{-6.4\pm \sqrt{40.96+4915.2}}{6.4}[/tex]

[tex]\implies x = \frac{-6.4\pm 70.4}{6.4}[/tex]

[tex]\implies x = 10\text{ or } x = -12[/tex]

Since, the number can not be negative,

Hence, 10 soccer club members are going to the tournament.

To find the number of soccer club members going to the tournament, we set up an equation based on the total cost of the van and the drop in cost per person when two additional students join. Solving the quadratic equation reveals that the number of soccer club members is 10.

The question asks us to determine the number of soccer club members going to the tournament given that the cost of the van is $192 and that the cost per person drops by $3.20 when 2 additional students join the trip. Let's denote the number of club members as 'x'. Before the 2 students join, the cost per person is $192 / x. After they join, the cost per person becomes $192 / (x + 2), which is $3.20 less than the original cost per person, so:

192 / x - 192 / (x + 2) = $3.20

Multiplying through by x(x + 2) to clear the denominators gives us:

192(x + 2) - 192x = 3.20x(x + 2)

This simplifies to:

192x + 384 - 192x = 3.20x^2 + 6.4x

The term 192x cancels out on both sides, so we have:

384 = 3.20x^2 + 6.4x

To solve for 'x', we divide both sides by 3.20:

120 = x^2 + 2x

Now we solve the quadratic equation x^2 + 2x - 120 = 0. Factoring this equation, we get (x + 12)(x - 10) = 0. Thus, x can be -12 or 10. However, since we can't have a negative number of club members, the number of soccer club members is 10.

Final answer:

The total distance walked by someone from home to school and back depends on the distance covered in each direction, for example, if a person walks 2 kilometers to school and 2 kilometers back, the total distance walked is 4 kilometers.

Explanation:

The total distance walked by the guy from his house to school and back depends on the exact distance he covers in each direction. If he walks 2 kilometers to school and 2 kilometers back, then the total distance walked would be 4 kilometers.

The equation of line is slope intercept form is y = 2x + 3

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

2x - y = -3   be equation (1)

Adding 3 on both sides of the equation , we get

2x - y + 3 = 0

Adding y on both sides of the equation , we get

y = 2x - 3

Now , equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

Therefore , the value of A is 2x - 3  , where the slope is m = 2

Hence , the equation of line is y = 2x - 3

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Final answer:

To convert the equation 2x-y=-3 into slope-intercept form, y must be isolated. The steps involve rearranging the equation to solve for y, resulting in the slope-intercept form y = 2x + 3, where the slope (m) is 2 and the y-intercept (b) is 3.

Explanation:

To convert the equation 2x-y=-3 into slope-intercept form, we need to solve for y. The slope-intercept form of a linear equation is y = mx + b, where m represents the slope, and b represents the y-intercept.

Let's solve for y:

Therefore, the equation 2x - y = -3 in slope-intercept form is y = 2x + 3.