Find the slope of the linear equation 2y = -18x + 10

9514 1404 393

Answer:

  boat speed: (7t -95)/(6t² -110t +500)

  stream speed: (37t -345)/(6t² -110t +500)

Step-by-step explanation:

The relation between time, speed, and distance is ...

  time = distance/speed

The boat speed (b) is added to the stream speed (s) going downstream. The stream speed is subtracted going upstream. The given relations tell us ...

  25/(b-s) +44/(b+s) = t

  15/(b-s) +22/(b+s) = 5

This gives us 2 equations in 3 unknowns, so we can only provide a solution in terms of one of the unknowns. Since we are asked for the speeds, they will be provided in terms of t.

Subtracting the first equation from 2 times the second gives ...

  2(15/(b-s) +22/(b+s)) -(25/(b-s) +44/(b+s)) = 2(5) -(t)

  5/(b-s) = 10 -t

  5/(10 -t) = b -s

Substituting for b-s in the second equation gives ...

  15/(5/(10-t)) +22/(b+s) = 5

  30 -3t +22/(b+s) = 5

  22/(b+s) = 3t -25

  22/(3t -25) = b+s

Adding the equations for the sum and difference of speeds, we get ...

  (b-s) +(b+s) = 5/(10-t) +22/(3t -25)

  2b = (5(3t -25) +22(10 -t))/((10-t)(3t-25)) = (95 -7t)/((10-t)(3t-25))

  b = (7t -95)/(6t² -110t +500)

Subtracting the equations for sum and difference of speeds, we get ...

  (b+s) -(b-s) = 22/(3t -25) -5/(10 -t)

  2s = (22(10-t) -5(3t -25))/((10-t)(3t-25))

 s = (37t -345)/(6t² -110t +500)

__

The speed of the boat in still water is (7t -95)/(6t² -110t +500) km/h.

The speed of the stream is (37t -345)/(6t² -110t +500) km/h.

__

Note that these solutions only make sense for values of t between 25/3 and 345/37, approximately 8.33 < t < 9.32. For t=9 hours, the boat speed is 8 km/h and the stream speed is 3 km/h.

rectangle base: 24 x 15 = 360

triangle: 15 x 3 x 1/2= 45 x 1/2 = 22.5 x 4 (each side) 90 inches

total: 360 + 90 = 450 inches :)

Answer:

[tex]\frac{3}{20}[/tex] = 0.15

Step-by-step explanation:

15 + 20 + 40 + 15 + 10 = 100

[tex]\frac{15}{100} = \frac{3}{20}[/tex] = 0.15

Answer:

1). y = 4(1.75)ˣ

2). y = (2)ˣ

Step-by-step explanation:

1). Let the equation of the given exponential graph is,

y = a(b)ˣ

Graph of the given equation passes through two points (0, 4) and (0+1, 4+3)

For point (0, 4),

4 = a(b)⁰

a = 4

For point (1, 7),

7 = 4(b)¹

b = [tex]\frac{7}{4}[/tex]

b = 1.75

Therefore, equation of the function is,

y = 4(1.75)ˣ

2). Similarly, equation of the second graph will be same in the form of

y = a(b)ˣ

Second graph passes through the points (0, 1) and (2, 4)

For (0, 1),

1 = a(b)⁰

a = 1

For (2, 4),

4 = 1(b)²

b = 2

Therefore, exponential function representing the graph will be,

y = 1(2)ˣ

y = 2ˣ

Answer:

380 cubic inches

Step-by-step explanation:

The basic formula is length x width x height, so it's pretty simple, you just do 4 x 19 x 5! The order doesn't matter as long as it's just the length worth and height

I, sometimes do length x width, then use the answer for that and multiply it by the height (So that I can break it down)

Answer:

a displacement of 3 meters.

Step-by-step explanation:

you move 6 meters to the right, then 3 meters to the left

6 - 3 = 3

displacement is the distance away from the starting point

The ball traveled a total displacement of 3m.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

      <------------6m----------------->

Ball ____________________

                       Ball_________

                             <------3m------>

Distance traveled by the ball.

= 6 m + 3m

= 9 m

Displacement is the shortest distance traveled by the ball.

= 6 - 3

= 3m

Thus,

Displacement is 3m.

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ2

Answer:  

2, 3, 4,

Step-by-step explanation:

I took the k12 quiz and i remeber putting these as my answer.

Hope this helps!

Answer:

the number of orange sodas be 60

Step-by-step explanation:

Let us assume the orange ones be x

And, the cola ones be y

Now according to the question

x + y = 100

y = 100 - x.........(1)

35x + 38y = $3,620........(2)

Now put the value of equation 1 in equation 2

So,

35x + 38(100- x) = 3620

35x + 3800 - 38x = 3620

-3x = -180

x = 60

Hence, the number of orange sodas be 60

Answer:

3

plz follow me

potphcloysidyodoyzyozlhph

Answer:

x=12

Step-by-step explanation:

1/2x - 5 = 10 - 3/4x ---> move like terms to the same side

1/2x + 3/4x = 10 + 5 ---> calculate

5/4x = 15 ---> multiply both sides by 4/5

x = 12

Answer: $510

Step-by-step explanation:

Total monthly budget = $3,400.

Percentage of total budget spent on utilities = 15%

The amount that the Riddle Family spending on utilities each month will then be:

= 15% × $3400

= 15/100 × $3400

= 0.15 × $3400

= $510

Answer:

0.15 * 3400 = $________ utilities cost per month

Multiply the monthly cost by 12.

Answer:

lgma

Step-by-step explanation:

Answer:

6 pounds and 9 ounces

or 7 pounds when rounded

Answer:

1) 4.5 x 10^3 =4,500

2)5.78 x 10^-2

3) 5.7 x 10^1 = 57

4) 6.256 x 10^-3 = 0.006256

5) 7.3 x 10^2 = 730

6) 4.2 x 10^-5 = 0.000042

7) 7x10^-3 = 0.007

8) 2.563 x 10^1

9) 3.0025 x 10^2 = 300.25

10) 1.456 x 10^-1

Answer:

x²+y²=225

Step-by-step explanation:

when centered at the origin the equation of a circle is x²+y²=r²

we are given x and y so 9²+12²=r²

[tex]r^{2} =9^{2} +12^{2}\\ =81+144\\ =225[/tex]

Answer:

g(x)=2(x-4)+7

2g(-6)=2[2(-6-4)+7]

=2[2(-10)+7]

=2(-20+7)

=2(-13)

=-26

Answer:

17 nickles !

Step-by-step explanation:

First, identify the variables:

n = amount of nickels

d = amount of dimes

Next, setup the equations based on what you know.  The first equation is:

n + d = 28

For the second equation, we know that a dime is worth 10¢ and a nickel is 5¢, so it should be:

0.05n + 0.10d = 1.95

This a three-step answer:

In one formula (you can use any of them; most people use the simplest one), single out the variable on one side

Apply the first formula into the second formula, and solve it to get the value of one variable

Apply the answer from the second formula into the first formula, and solve it to get the value of the other variable

======

Step One:

n + d = 28

n + d - d = 28 - d

n = 28 - d

Step Two:

0.05n + 0.10d = 1.95

(0.05 * (28 - d)) + 0.10d = 1.95

1.40 - 0.05d + 0.10d = 1.95

1.40 + 0.05d = 1.95

1.40 - 1.40 + 0.05d = 1.95 - 1.40

0.05d = 0.55

d = 11

Step Three:

n = 28 - d

n = 28 - 11

n = 17

======

Your answer should be 17 nickels and 11 dimes.

You can double check by applying the variables into both formulas.

n + d = 28

17 + 11 = 28

28 = 28

0.05n + 0.10d = 1.95

(0.05 * 17) + (0.10 * 11) = 1.95

0.85 + 1.10 = 1.95

1.95 = 1.95

I hope this helped.

Answer:

28 girls

Step-by-step explanation:

Let total students be ‘X’

No of girls = (X-20)

Girls/Boys=7/5=(X-20)/20

7(20) =5(X-20)

140=5X-100

5X=240

X = 240/5

X =48

So, Total Students are 48

No of girls = (X-20) = 48-20 = 28

Answer:

pi/3+2pin, 2pi/3+2pi(n)

Answer:

the next one is c - pi/2

Step-by-step explanation:

Answer:

John did not make a mistake

Step-by-step explanation:

he did everything correct

Triangle 1 and 4 are similar using AAA

number one and four.......

Answer:

Im not sure

Step-by-step explanation:

GOOD LOOK ON YOUR TEST HE DISCONN-ECTED

Answer:

Step-by-step explanation:

The following statements are true:

1.  A quadratic function can have up to two x-intercepts.

2.  An x-intercept of a quadratic function is also called a zero of the function

Answer:

45 i think

Step-by-step explanation:

Answer:

2nd option

Step-by-step explanation:

If AB  is a tangent to the circle then ∠ B is right angle

Using the converse of Pythagoras' identity.

If the square of the longest side is equal to the sum of the squares on the other 2 sides, then the triangle is right

longest side = 52 and 52² = 2704

48² + (10 + 10)² = 48² + 20² = 2304 + 400 = 2704

Then AB  is a tangent to the circle since ∠ B is a right angle