Water goes over Niagara Falls at a rate of 180 million cubic feet every 30 minutes. How much water goes over the Falls in 1 minute?

Answer:

Step-by-step explanation:

Given:

Principal value of loan = $1,245

Rate of interest = 5%

To find:

The total amount that will be repaid if the loan described is paid in 2 years.

Solution:

The formula for amount is

[tex]A=P\left(1+\dfrac{r}{100}\right)^t[/tex]

Where, P is the principal, r is the rate of interest, t is the number of years.

Putting P=1245, r=5 and t=2, we get

[tex]A=1245\left(1+\dfrac{5}{100}\right)^2[/tex]

[tex]A=1245\left(1+0.05\right)^2[/tex]

[tex]A=1245\left(1.05\right)^2[/tex]

On further simplification, we get

[tex]A=1245(1.1025)[/tex]

[tex]A=1372.6125[/tex]

[tex]A\approx 1372.61[/tex]

Therefore, the total amount that will be repaid if the loan described is paid in 2 years is $1372.61.

Answer:

x = 7

Step-by-step explanation:

5x - 2 + x = 9 + 3x + 10

5x + x - 2 = 9 + 10 + 3x

5x + x - 3x - 2 = 9 + 10 + 3x - 3x (substracted 3x from both sides)

3x - 2 = 19

3x = 19 + 2

3x = 21

x = 21 : 3

x = 7

Answer (assuming it can be in slope-intercept format):

[tex]y = -\frac{3}{5} x+7[/tex]  

Step-by-step explanation:

When knowing the y-intercept of a line and its slope, we can write an equation representing it in slope-intercept form, or [tex]y = mx + b[/tex].

1) First, find the slope of the equation. Use the slope formula, [tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex], to find the slope. Substitute the x and y values of the given points into the formula and simplify:

[tex]m = \frac{(4)-(7)}{(5)-(0)} \\m = \frac{4-7}{5-0} \\m = \frac{-3}{5}[/tex]

Thus, the slope is [tex]-\frac{3}{5}[/tex].

2) Usually, we would have to use one of the given points and the slope to put the equation in point-slope form. However, notice that the point (0,7) has an x-value of 0. All points on the y-axis have an x-value of 0, thus (0,7) must be the y-intercept of the line. Now that we know the slope of the line and its y-intercept, we can already write the equation in slope-intercept format, represented by the equation  [tex]y = mx + b[/tex]. Substitute [tex]m[/tex] and [tex]b[/tex] for real values.

Since [tex]m[/tex] represents the slope, substitute [tex]-\frac{3}{5}[/tex]  in its place in the equation. Since [tex]b[/tex] represents the y-intercept, substitute 7 in its place. This gives the following equation and answer:

[tex]y = -\frac{3}{5} x+7[/tex]

Answer and Step-by-step explanation:

The measure of angle D is 64.

This is true by the vertical angles theorem, which states that angles that are vertical to each other, they are equal.

#teamtrees #WAP (Water And Plant)

Answer:

(0, 4)

Step-by-step explanation:

To find the intersection of two lines, we want to find the value when they equal each other. To do this, we want to set the equations equal to each other.

First, let's simplify y = x + 4x + 4 by combining the x's.

y = 5x + 4

Now let's set the equations equal to each other. Since they both equal y, we can set the opposite sides equal to each other.

5x + 4 = 2x + 4

Now you want to combine the terms.

[subtract 4] 5x = 2x

[subtract 2x] 3x = 0

Now you want to isolate the x.

[divide by 3] x = 0

Now we want to find y by plugging x = 0 back into the equations.

y = 5(0) + 4

[multiply] y = 0 + 4

[add] y = 4

Check this with the other equation.

y = 2(0) + 4

[multiply] y = 0 + 4

[add] y = 4

Your answer is correct!

(0, 4)

Answer:

5.1

Step-by-step explanation:

cos 65° = [tex]\frac{x}{12}[/tex]  

x = 12 cos 65°

cos 65° ≈ 0.422618261741

x ≈ 5.07 ≈ 5.1

Answer:

6.651*10^9

Step-by-step explanation:

6.68*10^9-2.9*10^7

You can factor out 10^7 to get

(6.68*10^2-2.9)*10^7

(668-2.29)*10^7

665.71*10^7

Scientific notation would be 6.651*10^9

Answer:

this makes no sense

Step-by-step explanation:

Answer:

x = 240 ft

Step-by-step explanation:

20/80 = 60/x

20x = 2400

x = 240 ft

Set up 2 equations:

Kyle: 5h + 3f = 14.50

Myles: 4h + 2f = 11.00

Lets get the two h's to cancel out.

Multiply Kyle by 4 and Myles by -5:

Kyle: 20h + 12f = 58

Myles: -20h - 10f = -55

Now add the two equations together:

2f = 3

Divide both sides by 2:

f = 3/2

f = 1.50

1 french fry cost $1.50

Now solve for the price of a hot dog:

5h + 3(1.50) = 14.50

5h + 4.50 = 14.50

Subtract 4.50 from both sides:

5h = 10.00

Divide both sides by 5:

h = 2

One hot dog cost $2.00

nope they are not similar

as in order to say that triangles are similar their sides should be in proportion or angles to be equal but here

here only one angle is equal the other one is not

So they are not similar

Step-by-step explanation:

Yes the given two triangles are similar because all the corresponding angles are equal.

in the first figure let the remaining angle be x then

x + 37 + 110 = 180

x = 33

In the second figure let the remaining angle be y then

y + 33 + 110 = 180

y = 37

Here we come to the conclusion that all the corresponding angles are equal so they are similar triangles.

Hope it will help :)❤

Step-by-step explanation:

Just think of these as your building blocks for geometry success.

Diagram for success. ...

Know your properties and theorems.

Understand Euclid's postulates.

Learn the language of math.

Know your angles. ...

Know your triangles. ...

Figure out what you want and what you're given. ...

Now fill in the rest.

Step-by-step explanation:

when y=1 then,

y=1+X

X=1-y .

I'm assuming the equations are o that you solve in your own:

x = y + 1 = 1+1 = 2

x = y -1 = 1-1 = 0

x = 1*y = 1*1 = 1

x = y*1 = 1*1 = 1

x = y/1 = 1/1 = 1

x = 1/y = 1/1 = 1

An equality relationship between two expressions written on both sides of the equal to sign.

There are many situations in which equations can be used. Whenever an unknown quantity has to be found, an equation can be formed and solved.

Learn more about Equation here

https://brainly.com/question/13763238

#SPJ2

Answer: 47.5

Step-by-step explanation:

Answer:

PRESSURE: 1.08 kg/cm

VOLUME OF THE GAS: 47.5ML

THE PRODUCT OF P x V: 51.3

Step-by-step explanation:

RATE AND THANK IF IT HAS HELPED YOU!

Answer: 0.49 mi

Step-by-step explanation:

First find the half circumference of the circular pond as this will show the total distance your friend has to walk:

= (π * diameter) / 2

= (22/7 * 0.85) / 2

= 1.34 mi

Your friend is going to walk 1.34 and you will walk 0.85.

Difference is:

= 1.34 - 0.85

= 0.49 mi

Answer:

fnjfc ij vcd d GB hhv

Step-by-step explanation:

tb f thg. kufc if fyi uuj

Answer:

You multiply by 6 and the 5th term is 60

Step-by-step explanation:

15*4 = 60

Answer:

multiply by 4 & the unknown number is 60

Step-by-step explanation:

3×4=12

6×4=24

9×4=36

12×4=48

15×4=60

Answer:

2 cm

Step-by-step explanation:

the sum of the two shorter sides must be longer than the third side

Answer:A cafe makes ten 8-ounce fruit smoothies. Each smoothie is made with 4 ounces of soy milk and 1.3 ounces of banana flavoring. the rest is blueberry juice. How much of each ingredient will be necessary to make the 10 smoothies?

Step-by-step explanation:

A cafe makes ten 8-ounce fruit smoothies. Each smoothie is made with 4 ounces of soy milk and 1.3 ounces of banana flavoring. the rest is blueberry juice. How much of each ingredient will be necessary to make the 10 smoothies?

Answer:

A cafe makes ten 8-ounce fruit smoothies. Each smoothie is made with 4 ounces of soy milk and 1.3 ounces of banana flavoring. the rest is blueberry juice. How much of each ingredient will be necessary to make the 10 smoothies?

Step-by-step explanation:

Answer:

1) 225

2) 2304

Step-by-step explanation:

1)

Use geometric mean of legs

[tex]x = \sqrt{(16+9)^2 * 9^2} = \sqrt{25^2 * 9^2} = 25 * 9 = 225[/tex]

2)

Use geometric mean of altitude

[tex]x = \sqrt{(100-36)^2 * 36^2} = \sqrt{64^2 * 36^2} = 64 * 36 = 2304[/tex]

Answer:

(7, 2).

Step-by-step explanation:

The median from A intersects BC at it's midpoint.

To find the midpoint of BC:

This is (x1, y1) where x1 = (sum of the x_values of B and C) / 2)  and where y1

= (sum of the y_values of B and C) / 2)

This is (2+12)/2,  (1 + 3)/2

= (7, 2).

Answer:

Jenny's age = 8 yr

Sam's age = 17 yr

Step-by-step explanation:

Let x = Jenny's age now

then x + 9 = Sam's age now

x - 5 = Jenny's age 5 years ago

x + 9 - 5 = x + 4 = Sam's age 5 years ago

4(x - 5) = x + 4

4x - 20 = x + 4

3x = 24

x = 8 = Jenny's age now

x + 9 = 8 + 9 = 17 Sam's age now

Check:  5 yrs ago Jenny was 3 and Sam was 12

4(3) = 12, so the answer is correct.

Answer:

there are 6 boys in the class

Step-by-step explanation:

Answer:

There are 14 boys in the class. Yes, we can use what we know to figure out how many boys are in the class.

Step-by-step explanation:

think about the ratio as a fraction if the fraction is 2/3 and then compare it to x/21 21/3 is 7 and 7*2 is 14

Answer: 5

Step-by-step explanation: unless this was somehow a trick question