There was 1 liter of water in the water bottle. Tom drank 200 milliliters of water. How many liters of water are left?

Answer:

[tex]90^\circ[/tex]

Step-by-step explanation:

Given two non zero vectors, [tex]\vec a, \vec b[/tex].

Let the angle between the two vectors = [tex]\theta[/tex]

Given that:

[tex]|\vec a+\vec b|=|\vec a-\vec b|[/tex]

Let us have a look at the formula for magnitude of addition of two vectors:

[tex]|\vec x+\vec y|=\sqrt{x^2+y^2+2xycos\theta}[/tex]

Where [tex]\theta[/tex] is the angle between the two vectors.

formula for magnitude of subtraction of two vectors:

[tex]|\vec x-\vec y|=\sqrt{x^2+y^2-2xycos\theta}[/tex]

As per the given condition:

[tex]\sqrt{a^2+b^2+2abcos\theta}=\sqrt{a^2+b^2-2abcos\theta}[/tex]

Squaring both sides:

[tex]a^2+b^2+2abcos\theta=a^2+b^2-2abcos\theta\\\Rightarrow 2abcos\theta=-2abcos\theta\\\Rightarrow cos\theta = -cos\theta\\\Rightarrow 2cos\theta = 0\\\Rightarrow cos\theta = 0\\\Rightarrow \theta = 90^\circ[/tex]

So, the angle between the two vectors is: [tex]90^\circ[/tex]

Answer:

20

Step-by-step explanation:

The total gains of Jack if, In the first play, he gained 12 yards, in the second play lost 15 yards, in the third play gained 25 yards, and in the fourth play lost 2 yards is 20 yards.

The action of subtracting a matrix, vector, or other quantity from another according to predetermined rules in order to find the difference.

In math, addition is the process of adding two or more integers together. Addends are the numbers that are added, while the total refers to the outcome of the operation.

Given:

In the first play, he gained 12 yards, in the second play lost 15 yards, in the third play gained 25 yards, and in the fourth play lost 2 yards.

Assume the gains can be denoted by positive and loss by negative,

Gains = 12 yards, 25 yards.

Total gain = 12 + 25 = 37 yards

Loss = -15 yards, -2 yards

Total loss = -15 + (-2) = -17 yards

Calculate the total gain as shown below,

Total gain = total gain + total loss

Total gain = 37 + (-17)

Total gain = 20 yards.

To know more about subtraction:

https://brainly.com/question/28008319

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Answer:

[tex]n=26[/tex]

Step-by-step explanation:

So we have the equation:

[tex]-413.4=-15.9n[/tex]

To figure out the value of n, divide both sides by -15.9. The right will cancel. Thus:

[tex]n=(-413.4)/(-15.9)[/tex]

Use a calculator:

[tex]n=26[/tex]

So, the answer is 26.

So, yes, you are very correct!

Answer:

n=26

Step-by-step explanation:

We are given the equation:

[tex]-413.4=-15.9n[/tex]

We want to solve for the unknown variable, which is n. Therefore, we must isolate n on one side of the equation.

n is being multiplied by -15.9. The inverse of multiplication is division. Divide both sides of the equation by -15.9

[tex]\frac{-413.4}{-15.9} =\frac{-15.9n}{-15.9}[/tex]

[tex]\frac{-413.4}{-15.9}=n[/tex]

[tex]26=n[/tex]

Let's check our solution. Plug 26 in for n and solve.

[tex]-413.4=-15.9n[/tex]

[tex]-413.4=-15.9(26)[/tex]

Multiply -15.9 and 26.

[tex]-413.4=-413.4[/tex]

This checks out, so we know our solution is correct.

The solution to this equation is n=26 and you are correct!

Answer:

$4.44

Step-by-step explanation:

Cost per yard = $10/2.25

= $4.44 (nearest cent)

the answer $ 4.44

explanation :

so first of all you need to divide 10 by 2 1/4

when you divide both number you'll get 4 4/9

4 4/9 can also be written as 4.44444444444

which is also 4.4 recurring

now we can round this off

when you round it off, you should round it off to two decimal points cause the answer should be in dollars

you should get 4.44 as an answer

so the answer will be $ 4.44

really hope that helped :)

Answer:

$170.14

Step-by-step explanation:

4,861 / 1,000 = $4.861 per gallon

35 x $4.681 = $170.135, so you need to round up to the nearest penny

Step-by-step explanation:

For 1000 gallons=$4861

For 1 gallon =$4861/1000

For 35 gallons=$4861/1000 x 35=170.135

Answer:

The coordinates of point P are (2,5)

Step-by-step explanation:

We know that point P divides AB internally in the ratio 3:2, that is AP/PB = 3/2,

we thus use the formula for internal division.

Let A = (x₁, y₁) = (-4, 8), B = (x₂, y₂) = (6, 3) and P = (x, y)  

So x = (mx₂ + nx₁)/(m + n)

y = (my₂ + ny₁)/(m + n)

where m = 3 and n = 2

Substituting the values of the x coordinates of A and B into x, we have

x = (mx₂ + nx₁)/(m + n)

x = (3 × 6 + 2 × (-4))/(3 + 2)

x = (18 - 8)/5

x = 10/5

x = 2

Substituting the values of the y coordinates of A and B into y, we have

y = (my₂ + ny₁)/(m + n)

y = (3 × 3 + 2 × 8)/(3 + 2)

y = (9 + 16)/5

y = 25/5

y = 5

Therefore, the coordinates of point P are (2,5)

Answer:

The other lockers that were changed exactly 3 times are:

Locker 1 and Locker 7

Step-by-step explanation:

Question: What other lockers were changed exactly 3 times?

Answer: Lockers 1 and 7

How?

Locker 1 was opened by a student other than student 1; it was closed by a student other than student one; and it was opened by student 1.

Same happened with Locker 7.

The relationship between these numbers is an associative relationship.

Answer:

Step-by-step explanation:

150 students/3 classes= 50 students per class

Answer:

$50 is profit because every $50 it intersects.

X would be the $50 so 10x50=500-150=which would be $350.

I think this is right hope this helps!

Answer:

Step-by-step explanation:

Answer:

The number of years needed is 15.75 years.

Step-by-step explanation:

The investment amount (present value) = $200

Interest rate =4.5%

Double of investment = $400

Now we have to find the time or number of years in which the investment amount will be doubled. So, just use the below formula to find the number of years.

Future value = present value ×(1+interest rate)^n

400 = 200×(1+4.5%)^n

N = 15.75 years

The number of years required to double the amount is 15.75 years.

Answer:

Any number less than -13.

Step-by-step explanation:

If the number is real and rational and non-natural, this means that it can be any number in the negative number space.

Additionally, since the number has to be less than -13, then the number could be any number less than -13.

With all these things considered, the number is any number less than -13 that is real and rational.

Cheers.

Answer:

the last one is the only one with a y intercept of -1

Step-by-step explanation:

Answer:

9 - 21x  

Step-by-step explanation:

Simplify the following:

7 (1 - 3 x) + 2

Hint: | Distribute 7 over 1 - 3 x.

7 (1 - 3 x) = 7 - 21 x:

7 - 21 x + 2

Hint: | Add the numbers in -21 x + 2 + 7 together.

Add like terms. 2 + 7 = 9:

9 - 21 x

Hint: | Factor out the greatest common divisor of the coefficients of 9 - 21 x.

Factor 3 out of 9 - 21 x:

Answer: 3 (3 - 7 x)

(of the given solutions it's the only correct one, but can be further simplifued to 3 (3 - 7 x)

Any two parallel lines always have the same slope (but different y intercepts)

The equation of the green line is y = (8/5)x+6

The equation of the red line is y = (8/5)x-3

Slope intercept form is y = mx+b with m as the slope and b as the y intercept.

The slopes must be the same so that each time the line goes up some amount, we move to the right the same amount. Think of a set of stairs to possibly visualize what I mean. If the slopes are different (even slightly), then the lines will intersect at some point and we wouldn't have parallel lines.

Answer:

4096

Step-by-step explanation:

Answer:

4096

Step-by-step explanation:

4 to the third power is 64 and 64 to the 2nd power is 4096 so that should be your answer

Answer:the answer would be 2.5/5

Answer:

4 pints

Step-by-step explanation:

16 oz in a pint

Answer:

-12

Step-by-step explanation:

a + b

a = -46

b = 34

-46 + 34 = -12

Answer:4782984

Step-by-step explanation:

Answer:4782984

Step-by-step explanation:

Answer:

x^2 - 8x + 9

Step-by-step explanation:

Please write x2+9-8x as x^2 + 9 - 8x.  The " ^ " indicates exponentiation.

Next, please write x^2 + 9 - 8x in descending powers of x:

x^2 - 8x + 9

Answer:

4/5*3/4&6/7*2/5

Step-by-step explanation:

4/5*3/4=12/20

6/7*2/5=12/35

Answer:

thousands place

Step-by-step explanation:

Answer:

[tex]\displaystyle \int \sec\left(\frac{x}{2}\right)\tan^5\left(\frac{x}{2}\right)dx=\frac{2\sec^5\left(\dfrac{x}{2}\right)}{5}-\frac{4\sec^3\left(\dfrac{x}{2}\right)}{3}+2\sec\left(\frac{x}{2}\right)+C[/tex]

Step-by-step explanation:

We want to find the integral:

[tex]\displaystyle \int \sec\left(\frac{x}{2}\right)\tan^5\left({\frac{x}{2}\right)dx[/tex]

First, perform the substitution y = x / 2. This yields:

[tex]\displaystyle dy = \frac{1}{2} \, dx \Rightarrow dx = 2\, dy[/tex]

Hence, the integral becomes;

[tex]\displaystyle =2\int \sec y\tan^5 y \, dy[/tex]

Next, as you had done, let's expand the tangent term but to the fourth:

[tex]\displaystyle =2\int \sec y\tan^4 y\tan y\, dy[/tex]

Recall that:

[tex]\tan^2(y)=\sec^2(y)-1[/tex]

Hence:

[tex]\displaystyle =2\int \sec y(\sec^2 y-1)^2\tan y\, dy[/tex]

We can use substitution once more. This time, let u = sec(y). Hence:

[tex]\displaystyle du = \sec y \tan y \, dy[/tex]

Rewrite:

[tex]\displaystyle =2\int \left((\sec^2y-1)^2\right)\left(\sec y \tan y\right)dy[/tex]

Therefore:

[tex]\displaystyle = 2\int (u^2 - 1)^2\, du[/tex]

Expand:

[tex]\displaystyle =2\int u^4-2u^2+1\, du[/tex]

Reverse Power Rule:

[tex]\displaystyle = 2\left(\frac{u^5}{5} - \frac{2u^3}{3} + u\right) + C[/tex]

Simplify:

[tex]\displaystyle = \frac{2u^5}{5} - \frac{4u^3}{3} + 2u + C[/tex]

Back-substitute:

[tex]\displaystyle = \frac{2\sec^5 y }{5}-\frac{4\sec^3 y}{3}+2\sec y+C[/tex]

Back-substitute:

[tex]\displaystyle =\frac{2\sec^5\left(\dfrac{x}{2}\right)}{5}-\frac{4\sec^3\left(\dfrac{x}{2}\right)}{3}+2\sec \left(\frac{x}{2}\right)+C[/tex]

Therefore:

[tex]\displaystyle \int \sec\left(\frac{x}{2}\right)\tan^5\left(\frac{x}{2}\right)dx=\frac{2\sec^5\left(\dfrac{x}{2}\right)}{5}-\frac{4\sec^3\left(\dfrac{x}{2}\right)}{3}+2\sec\left(\frac{x}{2}\right)+C[/tex]

Answer:

= 2 (sec (x/2) - 2sec³(x/2) +  sec⁵(x/2) ) + C

                              3                     5

Step-by-step explanation:

∫sec(x/2) tan⁵(x/2) dx

apply u substitute u = x/2

= ∫sec(u) tan⁵(u) * 2du

= 2 *  ∫sec(u) tan⁴(u) tan(u) du

= 2 *  ∫sec(u) (tan²(u))² tan(u) du

= 2 *  ∫sec(u) (-1 + sec²(u))² tan(u) du

apply u substitute v = sec(u)

= 2 * ∫(-1 + v²)² dv

expand

= 2 * ∫1 - 2v² + v⁴ dv

sum

= 2 (v - 2v³ + v⁵ )

             3      5

substitute it back

= 2 (sec (x/2) - 2sec³(x/2) +  sec⁵(x/2) )

                              3                     5

add constant to the solution.

= 2 (sec (x/2) - 2sec³(x/2) +  sec⁵(x/2) ) + C

                              3                     5

Answer:

92%

Step-by-step explanation:

The answer to your question is 4.8 kilometers. Brainliest?

Answer:

1.86

Step-by-step explanation:

Answer:

Equation to represent all number of points = |4|

Step-by-step explanation:

We are told that a player either wins or loses 4 points during each turn. This means a player could either gain 4 points or loose 4 points. When writing this in Mathematical terms its means either -4 or +4.

Now, since possible number of turns is -4 or 4, then we can represent this with the absolute value symbol.

Thus, it's |4|

Answer: 3 seconds

Step-by-step explanation: the pump fills 1 tire per second