a boat traveled 336 miles downstream and back.the trip downstream took 12 hours.the trip back took 14 hours.what is the speed of the boat in still water?what is the speed of the.current?

Answers

Answer 1

Answer: Boat speed speed =x mph
current speed =y mph
against current 14 hours
with current 12 hours

Distance against 336 miles distance with 336 miles
t=d/r against current -
336 / ( x - y )= 14
14 ( x - y ) = 336
14 x - 14 y = 336 ....................1

336 / ( x + y )= 12
12 ( x + y ) = 336
12 x + 12 y = 336 ...............2
Multiply (1) by 6
Multiply (2) by 7

we get
84 x + -84 y = 2016
84 x + 84 y = 2352
168 x = 4368
/ 168
x = 26.00 mph

plug value of x in (1) y
14 x -14 y = 336
364 -14 -364 = 336
-14 y = 336
-14 y = -28 mph
y = 2.00
Boat speed speed 26.00 mph
current speed 2.00 mph

Answer 2

Answer: It took an avg of 13 mi total 15 mi/hr is the answer for the still water 11 mi/hr is the upstream speed I added 2 and subtracted two because it made sense because there is a difference of two in the hrs it took to go upstream and downstream

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A university's freshman class has 5000 students. 80% of those students are majoringin Computer Science. How many students in the freshman class are Computer
Science majors?

Answers

Answer:

4000 students

Step-by-step explanation:

Number of computer science majors = 80% of 5000

= 0.8 * 5000

= 4000

Answer:

4000

Step-by-step explanation:

5000 * .8 is 4000

5(2x-3)=155 solve for x

Answers

5(2x-3)=155
10x-15=155(solve/multiply 5 by the numbers/variables in the parentheses first)
10x=170(add 15 to each side)
Divide 170 by 10x
170÷10x=17
x=17

5(2x - 3) = 155
10x - 15 = 155
10x = 155 + 15
10x = 170
x = 170/10
x = 17

Using the completing-the-square method, find the vertex of the function f(x) = 5x2 + 10x + 8 and indicate whether it is a minimum or a maximum and at what point.a. maximum (1,8)
b. minimum (1,8)
c. maximum (-1,3)
d. minimum (-1,3)

Answers

Answer : d. minimum (-1,3)

$f(x) = 5x^2 + 10x + 8$

The vertex form of quadratic function is

$f(x) = a(x-h)^2 + k$ , where (h,k) is the vertex

To get vertex form we apply completing the square method

To apply completing the square method , there should be only x^2

So we factor out 5 from from first two terms

$f(x) = 5(x^2 + 2x) + 8$

Now we take the number before x (coefficient of x) and divide by 2

$(2)/(2)$ =1

Now square it

$(1)^2 =1$

Add and subtract 1 inside the parenthesis

$f(x) = 5(x^2 + 2x + 1 - 1) + 8$

Now we take out -1 by multiplying 5

$f(x) = 5(x^2 + 2x + 1) -5 + 8$

$f(x) = 5(x^2 + 2x + 1) + 3$

Now we factor x^2 +2x+1 as (x+1)(x+1)

$f(x) = 5(x+1)(x+1) + 3$

$f(x) = 5(x+1)^2 + 3$

h=-1 and k=3

So vertex is (-1,3)

When the value of 'a' is negative , then it is a maximum

When the value of 'a' is positive , then it is a minimum

$f(x) = 5x^2 + 10x + 8$ is in the form of $f(x) = ax^2 + bx + c$

The value of a is 5

5 is positive so it is a minimum

f(x) is minimum at point (-1,3)

The vertex form is a(x-h)²+k, where (h,k) are the coordinates of the vertex.

$f(x)= \n 5x^2+10x+8= \n5(x^2+2x)+8= \n5((x^2+2x+1)-1)+8= \n5((x+1)^2-1)+8= \n5(x+1)^2-5+8= \n5(x+1)^2+3$

The coordinates of the vertex are (-1,3).

The coefficient of x² is positive, so the parabola opens upwards and the vertex is the minimum of the function.

The answer is d.

2) If the original price of an antique chair was $41, what is the best estimate of an offer to purchase the chair at 124% of the original price?a.) The chair will be purchased at $20.
b.) The chair will be purchased at $40.
c.) The chair will be purchased at $50.
d.) The chair will be purchased at $90.

3) Which fraction could be used to determine an estimate of 76% of the people who attended the play?

a.) 1/2 of the people
b.) 3/4 of the people
c.) 2/3 of the people
d.) 1/10 of the people

4) Which mixed number could be used to determine an estimate of a 249% increase in value of a ring?

a.) 1/2 the value of the ring
b.) 3/4 the value of the ring
c.) 2 1/2 times the value of the ring
d.) 3 1/3 times the value of the ring

Answers

2) d.) The chair will be purchased at $90.
3) b.) 3/4 of the people
4) c.) 2 1/2 times the value of the ring

2) 50.84 ≈ 50 c

3) b.) 3/4 of the people

4) c.) 2 1/2 times the value of the ring

If the hypotenuse of a right triangle is 2 cm and one leg is √ 3 cm, the exact length of the other leg is _______ cm. A. √ 3
B. 1
C. 3
D. 4

Answers

Answer:

The length of the other leg is 1 cm.

Step-by-step explanation:

By using the pythagorean theorem

Hypotenuse² = Perpendicular² + Base²

As given

If the hypotenuse of a right triangle is 2 cm and one leg is √ 3 cm.

Let us assume that the unknown length be x.

Thus

2² = Perpendicular² + Base²

$4^(2)= (√(3))^(2) + x^(2)$

$(√(3))^(2) = 3$

4 = 3 + x²

x² = 4 -3

$x = √(1)$

x = 1 cm

Therefore the length of the other leg is 1 cm.

The exact length of the other leg is B. 1 cm.

The quotient of the difference of a number and 24 divided 8 is the same as the number divided by 6

Answers

The number that satisfies the given condition is -72.

Let's break down the given statement step by step:

The difference of a number and 24:

Let's assume the number is represented by 'x'.

The difference of 'x' and 24 can be written as (x - 24).

Divided by 8: We divide the difference of 'x' and 24 by 8, which gives us ((x - 24) / 8).

The quotient of the difference of a number and 24 divided by 8: So, the quotient is ((x - 24) / 8).

The number divided by 6: We divide the number 'x' by 6, which gives us (x / 6).

The given statement says that the quotient obtained in step 3 is equal to the number divided by 6.

Mathematically, we can represent this as:

((x - 24) / 8) = (x / 6)

To solve this equation for 'x', we can cross-multiply:

6(x - 24) = 8x

Now, we can simplify and solve for 'x':

6x - 144 = 8x

Subtracting 6x from both sides:

-144 = 2x

Dividing by 2:

x = -72

Therefore, the number that satisfies the given condition is -72.

Learn more about expression click;

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$x-the\ number\n\n(x-24)/(8)=(x)/(6)\ \ \ \ |multiply\ both\ sides\ by\ 24\n\n3(x-24)=4x\n\n3x-72=4x\ \ \ \ |subtract\ 3x\ from\ both\ sides\n\n\boxed{x=-72}$

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