A 10 kg ball is traveling at the same speed as a 1 kg ball. Compared to the 10 kg ball, the 1 kg ball has...

Jermaine, Keira, and Leon are buying supplies for an art class. Jermaine bought 2 canvases, 4 tubes of paint, and 2 paint brushe

maria [59]

Answer:

canvas $3

tube of paint $5

paint brush $4

Step-by-step explanation:

We need to choose variables for the prices of the different items, translate the sentences into equations, and solve a system of equations.

1. Define variables

Let c = price of 1 canvas, t = price of 1 tube of paint, and b = price of 1 brush.

2. Translate sentences into equations

"Jermaine bought 2 canvases, 4 tubes of paint, and 2 paint brushes for $34."

2c + 4t + 2b = 34

"Keira spent $22 on 1 canvas, 3 tubes of paint, and 1 paint brush."

c + 3t + b = 22

"Leon already has plenty of paint, so he bought 3 canvases and 2 paint brushes for $17."

3c + 2b = 17

The system of equations is

2c + 4t + 2b = 34 Eq. 1

c + 3t + b = 22 Eq. 2

3c + 2b = 17 Eq. 3

Since the third equation has only the variables c and b, we use the first equations to eliminate variable t and give us an equation in only c and b.

3 * Eq. 1 - 4 * Eq. 2

2c + 2b = 14

c + b = 7 Eq. 4

Eq. 3 and Eq. 4 form a system of equations in two variables.

3c + 2b = 17 Eq. 3

c + b = 7 Eq. 4

Solve Eq. 4 for b.

b = 7 - c Eq. 5

Substitute into Eq. 3.

3c + 2(7 - c) = 17

3c + 14 - 2c = 17

c = 3

Plug in c = 3 into Eq. 5.

b = 7 - 3

b = 4

Plug in c = 3 and b = 3 into Eq. 2.

c + 3t + b = 22 Eq. 2

3 + 3t + 4 = 22

3t + 7 = 22

3t = 15

t = 5

Answer:

canvas $3

tube of paint $5

paint brush $4

7 0

3 years ago

There once was a student named chandler. In 5 minutes, chandler texted 435 words. At the rate how many words did chandler text p

Sergio [31]

Answer:

87

Step-by-step explanation:

7 0

3 years ago

Explain how to evaluate f(g(0)).

alekssr [168]

Answer as a fraction: 17/6

Answer in decimal form: 2.8333 (approximate)

==================================================

Work Shown:

Let's use the two black points to determine the equation of the red f(x) line.

Use the slope formula to get...

m = slope

m = (y2-y1)/(x2-x1)

m = (4-0.5)/(2-(-1))

m = (4-0.5)/(2+1)

m = 3.5/3

m = 35/30

m = (5*7)/(5*6)

m = 7/6

Now use the point slope form

y - y1 = m(x - x1)

y - 0.5 = (7/6)(x - (-1))

y - 0.5 = (7/6)(x + 1)

y - 0.5 = (7/6)x + 7/6

y = (7/6)x + 7/6 + 0.5

y = (7/6)x + 7/6 + 1/2

y = (7/6)x + 7/6 + 3/6

y = (7/6)x + 10/6

y = (7/6)x + 5/3

So,

f(x) = (7/6)x + 5/3

We'll use this later.

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

We ultimately want to compute f(g(0))

Let's find g(0) first.

g(0) = 1 since the point (0,1) is on the g(x) graph

We then go from f(g(0)) to f(1). We replace g(0) with 1 since they are the same value.

We now use the f(x) function we computed earlier

f(x) = (7/6)x + 5/3

f(1) = (7/6)(1) + 5/3

f(1) = 7/6 + 5/3

f(1) = 7/6 + 10/6

f(1) = 17/6

f(1) = 2.8333 (approximate)

This ultimately means,

f(g(0)) = 17/6 as a fraction

f(g(0)) = 2.8333 as a decimal approximation

8 0

3 years ago

What is the 2nd term when -3f^3+9f+6f^4-2 f^2 is arranged in descending order

Pavel [41]

The second term would be -3f^3 because when in descending order it is
6f^4 - 3f^3 - 2f^2 + 9f

3 0

3 years ago

A school district wants to determine the most effective way to prepare seniors for the SAT. They randomly select senior level ma

My name is Ann [436]

Answer:

In the SAT; Pedagogical relationships are not traditional but those of a group of people working together towards a common goal. Students and tutor challenge specific problems together and face a style of encounter that opens the way to self-learning.

● Within the SAT group, which is at the same time a group of neighbors who share possibilities and problems, learning to dialogue is both an educational objective and a means of training.

Step-by-step explanation:

The purpose of the SAT is for graduates to be competent to perform in their own communities at different levels of activity. The Booster, for example, works at the level of improvement of productive projects within its own productive units or those of its neighbors. The Pilot, in addition to the previous capacity, can organize different types of activities for the common good (health projects, the environment, work with children, recreation, production in solidarity). These two levels are approved by law with the basic secondary. At the Bachelor level, graduates are trained to participate in more complex organizations and develop long-term initiatives in both productive and organizational aspects.

To achieve greater ease and adaptation to the SAT, <em><u>I consider that the group that is being taught with the non-traditional method and where the students work in groups, can easily adapt to the SAT learning system.</u></em>

4 0

3 years ago