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2 years ago

What property of operations can be used to justify that the two expressions in this equation are equivalent? 6x^2 +4x=4x + 6x^2

Mathematics

1 answer:

lorasvet [3.4K]2 years ago

8 0

Answer:

Commutative

Step-by-step explanation:

There are four basic property of operations to solve an algebraic expressions. They are associative, commutative, distributive and identity.

The expression given is : $6x^2 + 4x=4x+6x^2$

So the given algebraic expression is a commutative property of operations. The commutative property states that when any two numbers are added in an expression the sum of the numbers are the same regardless of the order of the numbers that are added.

Thus the sum of the above expression will be same in which ever order the numbers are added.

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At her job, mary works 4 hours on monday, 3 hours on wednesday, and 6 hours on saturday. her boss adds a $10 bonus to her payche

Andru [333]

She worked 4+3+6 hours = 13 hoursso 13x+10 = 120.50
13x=110.50
x=8.5
so she makes $8.50 an hour which is A.

8 0

3 years ago

A bacteria colony increases in size at a rate of 4.0581e1.6t bacteria per hour. If the initial population is 36 bacteria, find t

Harrizon [31]

Answer:

1560

Step-by-step explanation:

The rate of Increase of the population (P) of the bacteria is given as:

$\frac{dP}{dt} =4.058e^{1.6t}$

$dP =4.058e^{1.6t}}dt\\Taking\: Integrals\\\int dP =4.058 \int e^{1.6t}dt\\P(t)=\frac{4.058}{1.6} (e^{1.6t} +K)\\P(t)=2.53625 (e^{1.6t} +K)$

Where k is a constant of Integration.

At t=0, P(t)=36

$36=2.53625 (e^{1.6*0} +K)\\36=2.53625 (e^{0} +K)\\36=2.53625 (1 +K)\\36=2.53625 +2.53625K\\K=13.19$

Therefore:

$P(t)=2.53625 (e^{1.6t} +13.19)\\At \: t=4\\P(4)=2.53625 (e^{1.6*4} +13.19)\\=1559.88\\P(4)=1560$

3 0

3 years ago

Ashley and Keely shared some Hershey Kisses in the ratio of 5:2. If Keely had 12 Hershey Kisses, how many did Ashley have?

wolverine [178]

Answer:

Ashely had 30 kisses! Muah!

Step-by-step explanation:

Ratio of Ashely to Keely is 5 : 2 and we know Keely had 12. Keely represents the 2 in this ratio, and how do we get from 2 to 12? We multiply by 6. We have to multiply by 6 on the other side too then. 5 times 6 is 30, so Ashely had 30 hershey kisses.

In real life, not in ratio form, Ashely had 30 kisses and Keely had 12.

Please mark brainliest if possible, have a nice day! :)

8 0

2 years ago

304 students went on a field trip .7 buses were filled and 17 students traveled in cars. How many students were in each bus?? Sh

Gemiola [76]

304-17= 287.
287 divided by 7= 41 students per bus.

8 0

3 years ago

Read 2 more answers

Evan tosses a ball from the roof of a building. The path of the ball can be modelled

DiKsa [7]

Answer:

Please find attached sketch of the path of the ball, having plot area and plot points, created with MS Excel

Step-by-step explanation:

Question;

The equation representing the path of the ball obtained from a similar question posted online are;

h₁ = -4·(t + 1)·(t - 5), h₂ = -4·(t - 2)² + 36, h₃ = -4··t² + 16·t + 20

The above equations represent the same path

The equation, h₁ = -4·(t + 1)·(t - 5), gives the roots of the height function, h(t), used in determining the height of the ball after time <em>t</em>

At (t + 1) = 0 (t = -1) or at (t - 5) = 0 (t = 5), the ball is at ground level

The ball reaches the ground, is at ground level at t = 1, and at t = 5 seconds after being tossed, where h(t) = 0

The equation of the path of the ball in vertex form, y = a·(x - 2)² + k, is h₂ = -4·(t - 2)² + 36, where, by comparison, we have;

The vertex of the ball = The maximum height reached by the ball = (h, k) = (2, 36)

The coefficient of the quadratic term, t², is negative, therefore, the shape of the parabola is upside down, ∩, shape

The sketch of the path of the ball created with MS Excel, used in plotting the vertex, the initial value and the root points of the parabola, through which the ball passes and joining of the points with a 'smooth' curve is attached

5 0

2 years ago