Larry and Cathy study for a total of 24 hours each week. Larry studies 3 less than twice the hours than Cathy studies. How many hours does Cathy study per week?

Nick's first step was to subtract 4x from both sides of the equation:

     3x - 4x + 9 = 4x - 4x - 5

             -x + 9 =  - 5

Charlie's first step was to subtract 3x from both sides:

     3x - 3x + 9 = 4x - 3x - 5

                    9 = x - 5

Nick's first step is to bring 4x left and Charlie's is to take 3x right-hand side.

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.

More than one variable may be present inside a linear equation. An equation is said to be linear if the maximum power of the variable is consistently unity.

A formula known as an equation uses the same sign to denote the equality of two expressions.

Given the equation,

3x+9=4x− 5

1. The result of Nick's first step was −x + 9 = −5

So,

3x - 4x + 9 = -5 ⇒ -x + 9 = -5

2. The result of Charlie's first step was 9 = x - 5

3x+9=4x−5

9 = 4x - 3x - 5 ⇒ 9 = x - 5

Hence "Nick's first step is to bring 4x left and Charlie's is to take 3x right-hand side".

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Answer:

z = -70

Explanation:

-12.2z-13.4z=1792

-25.6z=1792

Divide both sides by (-25.6)

z = -70

Answer:

g = 1

Step-by-step explanation:

1/2 (3g - 2) = g/2

3g - 2 = g

3g = g + 2

3g - g = 2

2g = 2 ÷ 2

g = 1

Answer:

Approximately [tex]50\; \rm m \cdot s^{-2}[/tex], assuming that air resistance is negligible and that the rock was released with zero initial velocity.

Step-by-step explanation:

Let [tex]g[/tex] denote the gravitational acceleration on this planet.

Let [tex]x[/tex] denote the displacement of this rock during this fall. Let [tex]t[/tex] denote the duration of this fall. Assume that the rock was released with an initial velocity [tex]v_{0} = 0\; \rm m \cdot s^{-1}[/tex].

Assume that the air resistance is negligible (such that gravity is the only force on this rock). The acceleration [tex]a[/tex] of the rock during the fall would be constantly equal to the gravitational acceleration [tex]g[/tex].  

Since the acceleration of the rock during the fall was constantly [tex]a = g[/tex], the following SUVAT equation would apply:

[tex]\displaystyle x = \frac{1}{2}\, a \, t^{2} + v_{0}\, t[/tex].

Rearrange this equation to find an expression for acceleration [tex]a[/tex]:

[tex]\begin{aligned}a &= \frac{x - v_{0}\, t}{t^{2} / 2}\end{aligned}[/tex].

Convert the height and duration of this fall to standard units:

[tex]\begin{aligned}h &= 89\; \rm km \times \frac{10^{3}\; \rm m}{1\; \rm km} \\ &= 8.9\times 10^{4}\; \rm m\end{aligned}[/tex].

[tex]\begin{aligned}t &= 0.99\; \rm min \times \frac{60\; \rm s}{1\; \rm min} \\ &= 59.4\; \rm s\end{aligned}[/tex].

Substitute in the values to find the value of acceleration [tex]a[/tex]:

[tex]\begin{aligned}a &= \frac{x - v_{0}\, t}{t^{2} / 2} \\ &= \frac{89000\; \rm m}{(59.4\; \rm s)^{2} / 2} && (\text{Note that $v_{0} = 0\; \rm m\cdot s^{-1}$.}) \\ &\approx 50\; \rm m\cdot s^{-2} \end{aligned}[/tex].

By the assumptions above, the acceleration of this rock during this fall would be equal to the gravitational acceleration on this planet. Thus, [tex]g \approx 50\; \rm m\cdot s^{-2}[/tex] on this planet.

Answer:

95 apples

Step-by-step explanation:

given:

John has 13 boxes of apples

each apples can have 10 apples

6 box= full -10 apples

7 box= half full-10÷2=5 apples

•°• John has= (6×10) + (7×5)

= 60+35

=95 apples

Answer:

1

Step-by-step explanation:

just add the values,,,, i.e,

-3+8-4=1

Step-by-step explanation:

calculate the difference in level of water : (68.1-52.5)mL = 15.6mL ( volume)

mass of the rock = 27.69g

density = mass/volume

=> (ρ) = 27.69/15.6 = 1.775g/mL or 1.775g/cm³(1cm³=1mL).

hope this helps you.

Answer:

4.8 cm

Step-by-step explanation:

To find the answer, lets use the information we have. We need to find the width, or w. We know that is 2.5 times smaller than its length, and that the length is 12. So lets make an equation to solve:

12/2.5=w

We did this because we know that the length is 2.5 times bigger than the width, so to find the width we need to go 2.5 times smaller than the length, and the length is 12.

Now solve:

4.8=w

So the width of the rectangle is 4.8 centimeters.

Answer:

width = 4.8 cm

Step-by-step explanation:

let width be w then length = 2.5w

Given length = 12 cm , then

2.5w = 12 ( divide both sides by 2.5 )

w = 4.8

That is width = 4.8 cm

Answer:

Where is your attachment ?

       For us to write the equation for this line, we need to (1) find the slope of the line, and (2) use one of the points to write an equation:  

       The question gives us two points (one of which is the y-intercept), (4.5,-4.25), and (0, 2.5), from which we can find the slope and later the equation of the line.

Finding the Slope    

The slope of the line (m) = (y₂ - y₁) ÷ (x₂ - x₁)    

                                        =  (2.5 - (- 4.25)) ÷ (0 - 4.5)

                                        =  −1.5

 Finding the Equation

Now that we know the slope and the y-intercept, we can write the equation of the line in the point-slope form (y = mx + b)

                                            y = −1.5x + 2.5

Checking my answer:

I used Desmos to graph the line I got and the points. Since the line passes through the points then the line is correct.

Answer:

13.

Step-by-step explanation:

So, if you need to feed 52 people and each pizza feeds 4 people the equation would be: # of people/ 4 = number of pizzas you need.

Answer:its 6 because 3 + 6 is 9 + 6 is 15

Step-by-step explanation:

The number of stenciled wooden boxes needed so as to maximize profit is 6 small boxes and 6 large boxes.

Let x represent small boxes  and y represent large boxes.

Since you have no more than 30 hours available to stencil, hence:

2x + 3y ≤ 30

Also, at least 12 boxes are required to sell, hence:

x + y ≥ 12

The solution to this problem gives:

x = 6, y = 6

Hence 6 small boxes and 6 large boxes are needed.

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Answer:

Step-by-step explanation:

you will multiply the amount of small boxes which will be 12 x 8 = 96

Then the amount of small boxes which will be 17 x 3 = 51

You add them two tg 96+51 = 147

Answer:

5/12

Step-by-step explanation:

2/3 +1/4 = 8/12 + 3/12= 11/12

11/12 - 1/2 = 11/12 - 6/12 = 5/12 less

Answer:

17

1234

4567

56783

56743

180 in 40 seconds ; 180/40 = 4.5

For 30 seconds, divide by 2.

Answer:

60

Step-by-step explanation:

Answer:

[tex]f(q) = y = 9 {(q + 6)}^{3} \\ q = 9 {(y + 6)}^{3} \\ \frac{ \sqrt[3]{q} }{ \sqrt[3]{3} } = y + 6 \\ y = \frac{ \sqrt[3]{q} }{ \sqrt[3]{3} } \frac{ \sqrt[3]{3} }{ \sqrt[3]{3} } - 6 \\ y = \frac{ \sqrt[3]{q} \sqrt[3]{3}}{ {3} } - 6 = {f}^{ - 1} (q)[/tex]

Step-by-step explanation:

please mark me as brainlest

Answer:

14 red crayons

Step-by-step explanation:

since we already know the ratios of the crayons we are going to use ratio and proportion to solve our question B:R is 32:28 and they are directly proportional meaning we can scale the quantities by multiplying.32:28 and 16:R , r is the unknown quantity ,then we cross multiply  the 2 ratios to get 32R= 448, then we divide by32 both sides so we can remain with the value of R which is 14

Answer:

4

Step-by-step explanation:

Answer:

$2.93

Step-by-step explanation:

67.50/23=2.9347826087 sorry had to use 20 characters in the explanation

Answer:

$2.93

Step-by-step explanation:

$67.50 for 23 gallons

$? for 1 gallon

$67.50 ÷ 23 = $2.93478

Rounded to the nearest cent: $2.93

Answer:

7^3 x 7^8

Step-by-step explanation:

I used a calculator, pls let me know if im incorrect

Answer: 3:5

Step-by-step explanation:

So, taking the ratio of the time taken by Henry to the time taken by Gavin is: (36 mins/ 60 mins) = (36/60) = 3:5 [Taking minutes as the common unit for both of the cases.] Thus the ratio is 3:5 in simplest form.

Answer:

(4, -4) = (x, y) = A

Step-by-step explanation:

 5x + 2y = 12

- (5x - 2y = 28)

4y = -16

y = -4

5x + 2(-4) = 12

5x - 8 = 12

5x = 20

x = 4

Answer:

18

Step-by-step explanation:

Write the information algebraically:

6b + 3s = 126

3b = 2s

(b = bags, s = shirts)

The second line in bold means that we can replace 6b with 4s

3b = 2s (multiply both sides by 2)

∴ 6b = 4s

so, 4s + 3s + 126

Now simplify:

7s = 126

We can now find s by dividing both sides by 7:

s = 126 ÷ 7 = 18

1 shirt costs 18