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3 years ago

Rewrite in simplest terms: (3x + 2) + (-10x – 3)

Mathematics

1 answer:

Andre45 [30]3 years ago

8 0

Answer:

$\boxed {\tt -7x-1}$

Step-by-step explanation:

We are given the expression:

$(3x+2)+(-10x-3)$

Combine like terms.

The terms with variables can be combined, then the terms without variables (constants) can be combined.

$(3x+-10x)+(2+-3)$

$(3x-10x)+(2-3)$

Subtract 10x from 3x.

$(-7x)+(2-3)$

Subtract 3 from 2.

$(-7x)+(-1)$

$-7x-1$

The simplified expression is -7x-1

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The water level in a pool is currently at 1/2 of an inch. Every hour, the water level increases 4.75 inches. How many hours will

____ [38]

Answer:

7.1 hours

Step-by-step explanation:

Given data

Let the number of hours taken to fill the pool be x

the current quantity is 1/2 the capacity of the pool

we are given that the rate of flow = 4.75 in per hour

let the total amount of water after x hours be y, the expression for the quantity of water is given as

$y= 0.5+4.75x$

if y= 33.75 in, let us find x

$33.75= 0.5+4.75x\\\\33.75-0.5= 4.75x\\\\33.25= 4.75x\\\\$

divide both sides by 4.75

$x= 33.75/4.75\\\\x= 7.10$

Hence, it will take 7.1 hours

6 0

3 years ago

Find a decomposition of a=⟨−5,−1,1⟩ into a vector c parallel to b=⟨−6,0,6⟩ and a vector d perpendicular to b such that c+d=a.

dezoksy [38]

The projection of vector A parallel to vector B is $\langle -3, 0, 3\rangle$ and the projection of vector A perpendicular to vector B is $\langle -2, -1, -2\rangle$ .

In this question, we need to determine all projections of a vector with respect to another vector. In this case, the projection of vector A parallel to vector B is defined by this formula:

$\vec a_{\parallel , \vec b} = \frac{\vec a \,\bullet\,\vec b}{\|\vec b\|^{2}}\cdot \vec b$ (1)