Finn bought a 2-liter bottle of soda. If he poured 4 cups of soda filled with 350 milliliters each, how many milliliters of soda are left in the bottle?

Answer:

15 units

Step-by-step explanation:

you have to use pythagoras to solve (c²=a²+b²)

AB is the longest side of the triangle which is c in the pythagoras

so counting the units for AC, you get 9 units, and CB you get 12 units

now solve for c in pythagoras

c²=9²+12²

c = 15 units

Answer:

completing the division operation: numerator divided by denominator.

Step-by-step explanation:

If you have a rate, such as price per some number of items, and the quantity in the denominator is not 1, you can calculate unit rate or price per unit by completing the division operation: numerator divided by denominator.

Answer:

See below!

Explanation:

equation for distance:

Lets Ben hours be x and Landon hours be y,

60x + 56y = 820 .........equation 1

equation for time:

[tex]\frac{60x}{60}+ \frac{56x}{56} =14[/tex]

x + y = 14 .........equation 2

Make x the subject:

60x + 56y = 820

x = (820 - 56y)/60 ..........equation 3

x + y = 14

x = 14 - y ........equation 4

Solve equation 3 and 4 simultaneously:

             [ Therefore Landon drove 5 hours ]

Extra's further investigated:

if y = 5

              [ Therefore Ben drove 9 hours ]

Answer:

Landon drove 5 hours (and Ben drove 9 hours)

Step-by-step explanation:

Let B = number of miles Ben drove

Let L = number of miles Landon drove

Given The trip took them 14 hours

⇒ B + L = 14

Given, Ben averaged 60 miles per hour and Landon averaged 56 miles per hour. Ben and Landon took turns driving on a 820 mile road trip:

⇒ 60B + 56L = 820

Rewrite B + L = 14 to make B the subject, substitute into 60B + 56L = 820, and solve for L:

⇒ B = 14 - L

⇒ 60(14 - L) + 56L = 820

⇒ 840 - 60L + 56L = 820

⇒ 20 = 4L

⇒ L = 5

Therefore, Landon drove for 5 hours

Answer:

10

Step-by-step explanation:

There are several ways to solve this problem which I’ll demonstrate these ways and see which method is way easier to understand.

First Method

This method is to convert the fractional expression to a single exponent expression using a law of exponent.

[tex]\displaystyle \large{\frac{m^a}{m^b} = m^{a-b}}[/tex]

In words, it means if both divisor (denominator) and dividend (numerator) have same values or are same, we can subtract the exponent from dividend (numerator) with divisor (denominator).

The dividend (numerator) exponent is unknown, let’s say it’s got ‘x’ as an exponent and this ‘x’ is what we are going to find since we don’t know its value.

Now we have the equation:

[tex]\displaystyle \large{\frac{m^x}{m^7} = m^3}[/tex]

Apply the exponent rules above.

[tex]\displaystyle \large{m^{x-7} = m^3}[/tex]

Solve an exponential equation - If both sides of equation have same base, we can solve the exponents.

Since LHS (Left-Handed Side) and RHS (Right-Handed Side) both have same base which is ‘m’ therefore, solve exponents.

[tex]\displaystyle \large{x-7=3}\\\displaystyle \large{x=7+3}\\\displaystyle \large{x=10}[/tex]

Therefore, the missing exponent is 10.

Additional Info

You can also use logarithm to solve an exponential equation.

[tex]\displaystyle \large{m^{x-7} = m^3}[/tex]

Take a logarithm of base ‘m’ both sides so we can apply other properties.

[tex]\displaystyle \large{\log_m m^{x-7} = \log_m m^3}[/tex]

From the property [tex]\displaystyle \large{\log_a b^n = n \log_a b}[/tex]

[tex]\displaystyle \large{(x-7) \log_m m = 3 \log_m m}[/tex]

From the property [tex]\displaystyle \large{\log_a a = 1}[/tex]

[tex]\displaystyle \large{(x-7)1 = 3 \cdot 1}\\\displaystyle \large{x-7=3}\\\displaystyle \large{x=10}[/tex]

______________________________

Second Method

This method is to isolate the term with missing exponent.

[tex]\displaystyle \large{\frac{m^x}{m^7} = m^3}[/tex]

Transport m^7 to multiply with m^3 via transportation property.

[tex]\displaystyle \large{m^x = m^3 \cdot m^7}[/tex]

We also have to apply another law of exponent as well.

[tex]\displaystyle \large{m^a \cdot m^b = m^{a+b}}[/tex]

Similar to the one with division (fraction), this one, when same bases multiply each other, we have to add both exponents while the other one subtracts exponents.

[tex]\displaystyle \large{m^x = m^{3+7}}\\\displaystyle \large{m^x = m^{10}}[/tex]

In the first method, we know that when solving an exponential equation, if two bases from left and right sides are same, we solve the exponent.

Therefore, [tex]\displaystyle \large{m^x = m^{10} \to \boxed{x=10}}[/tex]

______________________________

Summary

  Laws of Exponent

[tex]\displaystyle \large{a^m \cdot a^n = a^{m+n}}\\\displaystyle \large{\frac{a^m}{a^n} = a^m \div a^n = a^{m-n}}\\[/tex]

For what I demonstrate in my explanation only.

  Exponential Equation

When two bases from left side and right side are same, we can solve through exponents.

Examples:

[tex]\displaystyle \large{2^{x-3} = 2^{4}}\\\displaystyle \large{x-3=4}\\\displaystyle \large{x=4+3}\\\displaystyle \large{x=7}[/tex]

You can also substitute x-value in an equation to see if both sides are equal or not.

[tex]\displaystyle \large{2^{x-4} =2^3}[/tex]

Substitute x = 7 for check.

[tex]\displaystyle \large{2^{7-4} = 2^3}\\\displaystyle \large{2^3 = 2^3 \ \ \checkmark}[/tex]

  Logarithm

This is not necessary used in this question. This is mostly used for converting to exponential and more advanced mathematics.

[tex]\displaystyle \large{\log_a b^n = n\log_a b}\\\displaystyle \large{\log_a a = 1}[/tex]

Only from what I demonstrate in my explanation.

______________________________

If you are still stuck or need clarification regarding my answer and explanation, you may ask in comment below.

Hope this helps! And wish you luck in your assignment.

Answer:

Step-by-step explanation:

r = 10

h = 6

[tex]Volume =\dfrac{1}{3}\pi r^{2}h\\\\\\ =\dfrac{1}{3}*3.14*10*10*6\\\\=3.14 * 10 * 10 * 2\\\\= 628 \ cubic units[/tex]

Based on the amount Peyton invested, and the interest rate, the amount in the account 15 years later would be $2,848.09.

The amount in the account after 15 years would be:

= Amount x ( 1 + rate) ^ number of years

Solving gives:

= 1,700 x ( 1 + 3.5%)¹⁵

= $2,848.09

Find out more on future value at https://brainly.com/question/24978019.

Answer:

2848.1

Step-by-step explanation:

Answer:

Two points, (0,4) & (8,5)

Step-by-step explanation:

In this equation, we can easily find the first point by looking at the +4 in this equation. This should automatically signal to you that the point is (0,4)

Now, we have to look at the 1/8x in the equation.

This 1/8 means that the slope is 1/8!

Now we use the slope and to rise/run to find our next point

We go up 1 from 4 (this is the rise) to get to 5 on the y-axis

Next, we go over 8 horizontally to get to 8 for your x-axis point.

So therefore, our next point is, (8,5)

You can use this rise/run system infinitely and is very useful

Answer: x= -20/3 and y= 34/3

hope this helps :)

Step-by-step explanation:

Answer:

$35.436

Step-by-step explanation:

Hope this helps! :)

Answer:

$35.436

Step-by-step explanation:

Hope you like bro !!!!!!!!!!!

PLS MARK ME THE BRAINLIEST

Answer:

total area = 132 units²

Step-by-step explanation:

Area of largest rectangle = 4 x 15 = 60 units²

Area of smallest rectangle = 4 x 6 = 24 units²

Area of largest triangle = 1/2 x (15 - 6) x (4 + 4) = 36 units²

Area of smallest triangle = 1/2 x 6 x 4 = 12 units²

Total area of the figure = sum of areas of 2 rectangles and 2 triangles

⇒ area = 60 + 24 + 36 + 12 = 132 units²

Step-by-step explanation:

I'll do it on my laptop.......

Answer:

[tex]x = 22.5[/tex]

Explanation:

Given Sides:

-----------------------------

using all these sides, create similarities equation:

[tex]\frac{HB}{HD} = \frac{HM}{HT}[/tex]

[tex]\frac{6}{21} = \frac{9}{9+x}[/tex]

[tex]6(9+x) = 9(21)[/tex]

[tex]54 + 6x = 189[/tex]

[tex]6x = 189 - 54[/tex]

[tex]6x = 135[/tex]

[tex]x = \frac{135}{6}[/tex]

[tex]x = 22.5[/tex]

Answer:

[tex]f(x)=2x-6[/tex]

[tex]f^{-1}(x)=\dfrac{x+6}{2}[/tex]

Step-by-step explanation:

Using slope-intercept form of linear function:  [tex]y = mx + b[/tex]

[tex]\implies f(x)=mx+b[/tex]

[tex]\textsf{if} \ \ f(1) = -4[/tex]

[tex]\implies m + b=-4[/tex]

[tex]\implies b = -4-m[/tex]

Find inverse of slope-intercept form:

swap x and y:  [tex]x = my + b[/tex]

Make y the subject:

[tex]\implies x - b = my[/tex]

[tex]\implies y = \dfrac{x-b}{m}[/tex]

[tex]\implies f^{-1}(x) = \dfrac{x-b}{m}[/tex]

[tex]\textsf{if} \ \ f^{-1}(0) = 3[/tex]

[tex]\implies \dfrac{0-b}{m}=3[/tex]

[tex]\implies b=-3m[/tex]

[tex]\textsf{equation 1:} \ \ b = -4-m[/tex]

[tex]\textsf{equation 2:} \ \ b=-3m[/tex]

Equate the equations and solve for [tex]m[/tex]:

[tex]\implies b=b[/tex]

[tex]\implies -4-m=-3m[/tex]

[tex]\implies -4=-2m[/tex]

[tex]\implies m=2[/tex]

Substitute found value for [tex]m[/tex] into one of the equations and solve for [tex]b[/tex]:

[tex]b = -4-2=-6[/tex]

Substitute found values of [tex]m[/tex] and [tex]b[/tex] into equations for [tex]f(x)[/tex] and [tex]f^{-1}(x)[/tex]:

[tex]f(x)=2x-6[/tex]

[tex]f^{-1}(x)=\dfrac{x+6}{2}[/tex]

Answer:

B

Step-by-step explanation:

put both sides under square root.

x^2 + y^2 = 64

sqrt ( x^2 + y^2 ) = sqrt(64)

x + y = 8

r = 8.

[tex]\underline{r^2=x^2+y^2} \\\\\\ x^2+y^2=64\implies r^2=64\implies r=\sqrt{64}\implies r=8[/tex]

Answer:

21 can not the 3rd side

Step-by-step explanation:

because the sum of 2 sides of triangle are always greater -it is a fact or theorem

Answer:

1st row = 10 = y

2nd row = 12 = y

3rd row = 18 = y

4th row = 22 = y

Step-by-step explanation:

Given:

y = 4x + 6

since the y-intercept is 6, we know that when the input value(x) is equal to 0, the output value(y) is equal to 6.

so now we plug in the equation for each row,

starting with the first one.

in the first row it says x is equal to 1 so the equation would look like this:

y = 4(1) + 6

simplified the equation to get

y = 4 + 6  = 10

meaning for the first row, y = 10!

since the x value is constant, and only goes up by 1 each row, this means we can just add 4 more each time.

However, I am going to write the equation for each row anyways.

Second row:

y = 4(2) + 6

simplifys into

y = 8 + 6   =  12

y = 12

Third row:

y = 4(3) + 6

simplifys into

y = 12 + 6 = 18

y = 18

Fourth row:

y = 4(4) + 6

simplifys into

y = 16 + 6 = 22

y = 22

So to recap, the answers to each row are...

1st row = 10 = y

2nd row = 12 = y

3rd row = 18 = y

4th row = 22 = y

I hoped this helped and have a good day :D!!!

Answer:

F=40h+25

a) 40 per hour

b) 25

c) hours

d) how much it costs

Answer:

1) c

2) b

Step-by-step explanation:

1) translated 6 units to the left will be negative = x-6

5 units up will be positive = y+5

2) when reflecting across the x-axis, the x-values of each original point will remain the same and the y-values will become opposite. For example one point is (-5, 3) which will be (-5, -3) as the opposite of 3 is -3 which is in the form (x,-y)

Answer:

The answer is 6/7

Step-by-step explanation:

Step-by-step explanation:

let's name the 2 sides of the bisected angle a and b.

and the 2 segments (created by the bisector) of the opposite side x and y.

then we have

a/b = x/y

question 1

14/21 = x/15

1/3 = x/15

15/3 = x = 5

question 2

8/y = 4/6

8×6 = 4y

48 = 4y

y = 12

question 3

3/4.5 = z/1.5

3×1.5 = 4.5z

4.5 = 4.5z

z = 1

question 4

16.5/p = 11/(29-11) = 11/18

16.5×18 = 11p

297 = 11p

p = 27

question 5

7/13 = (15-x)/x

7x = 13×(15-x) = 195 - 13x

20x = 195

x = 195/20 = 39/4 = 9.75

Answer:

Marcus can do more jumping jacks per minute.

Step-by-step explanation:

By 3 more jumping jacks.

Answer:

ryan can do the most

Step-by-step explanation:

by 3

Answer:

y = - 6x - 8

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 3, 10) and (x₂, y₂ ) = (- 1, - 2) ← 2 points on the line

m = [tex]\frac{-2-10}{-1-(-3)}[/tex] = [tex]\frac{-12}{-1+3}[/tex] = [tex]\frac{-12}{2}[/tex] = - 6

the line crosses the y- axis at (0, - 8 ) ⇒ c = - 8

y = - 6x - 8 ← equation of line

Answer:

[tex]a + b = a + b[/tex]

Step-by-step explanation:

plugging in a and b for anything will work, thus resulting in infinite amount of solutions

Answer:

Yes

Step-by-step explanation:

Domain : 0 ≤ x ≤ 8

Range : 0 ≤ y  ≤ 56

The inequality that represents all the possible combinations he can buy is $12x + $10y ≤ $60.

What do inequality signs mean?

> means greater than

< means less than

≥ means greater than or equal to

≤ less than or equal to

The inequality sign to use is ≤ less than or equal to. This is because he does not want to spend more than $60.

$12x + $10y ≤ $60.

To learn more about inequality, please check: https://brainly.com/question/5031619