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2 years ago

Simplify -4 + (-3) + 6

1 answer:

3 0

Start off with: -4 + (-3) + 6

First of all, when there is a, + sign and a - sign next to each other, the - side wins. E.g. 1 +- 3 = 1 - 3

So, apply this to our one:
-4 -3 +6

From there you solve, you can do this using the number line method or whatever you are into:
=-7 + 6
=-1
The answer is -1

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Sara has a stack of 8 plates, each plate is 0.5 inches tall and she is trying to wrap them as a gift.

AlekseyPX

Answer:

The plates will not fit into the box.

Step-by-step explanation:

Each plate is 0.5 inches tall; therefore, the stack of 8 plates will have a height of $0.5in*8 = 4inches$ .

Also, the diameter of the largest plate is 10 inches or has a radius of 5 inches, which matches the radius of the cylindrical box; therefore, we know that the stack of plates can fit into the base area of the cylindrical box.

What we want to figure out now is the height of the cylindrical box to see if it is greater than or equal to 4 inches—the height of the stack of plates.

The volume of a cylinder is $\pi R^2h$ , and since for our cylindrical box the volume is 150 cubic inches; therefore,

$\pi R^2h = 150in^3$

putting in $R = 5in$ and solving for height $h$ we get

$h = \dfrac{150in^3}{\pi (5)^2}$

$h = 1.91\: inches$ ,

which is not greater than 4 inches, which means the plates will not fit into the box since the height of the stack is greater than the height of the box.

5 0

3 years ago

A local ice rink is hosting a skating competition that will determine whether or not skaters qualify to compete regionally. The

Zinaida [17]

Answer:

Function: $f(x) =\left \ {{150x;\ 0\le x\ \le 50} } \right.$

Domain: $0 \le x\ \le 50$

Step-by-step explanation:

Given

Registration Fee = 150

Entrants = 50 (maximum)

Solving (a): Create a function

Let the number of entrants be x.

If 1 entrant pays 150, then x entrants will pay 150x.

So:

$f(x) = 150x$

The minimum entrant is 0 (i.e. no entrant shows up) and from the question, the maximum is 50

So, the domain can be represented as: $0 \le x\ \le 50$

Hence, the function is: $f(x) =\left \ {{150x;\ 0\le x\ \le 50} } \right.$

(b) : The domain

The domain has been described above as:

"The minimum entrant is 0 (i.e. no entrant shows up) and from the question, the maximum is 50"

"So, the domain can be represented as: $0 \le x\ \le 50$ "

3 0

3 years ago

Square the binomial (x + y).

Zepler [3.9K]

Answer:

$x^2 + 2xy + y^2$

Step-by-step explanation:

$(x+y)^2 = (x+y)(x+y)$

F.O.I.L. the equation (first, outer, inner, last)

$(x+y)(x+y) = (x*x) + (x*y) + (x*y) + (y*y)$

$(x*x) + (x*y) + (x*y) + (y*y) = x^2 + xy +xy+y^2 = x^2 +2xy+y^2$

7 0

2 years ago

Which of the following statements are true?

olchik [2.2K]

Answer:

II, III, and IV

Step-by-step explanation:

Define:

Similar polygons:

Corresponding angles are equal
Corresponding sides are in a constant proportion

Congruent polygons:

Corresponding angles are equal
Corresponding sides are equal

Let's break each statement down one-by-one:

I. Corresponding sides of similar figures are the same.

False - Corresponding sides of similar figures are in a constant proportion, but not necessarily the same. Congruent figures have equal corresponding sides, but similar figures only have their corresponding sides in a constant proportion.

II. Corresponding sides of congruent figures are the same.

True - By definition, corresponding figures have equal sides and angles. Therefore, this statement is true.

III. Corresponding angles of congruent figures are the same.

True - By definition, corresponding figures have equal sides and angles. Therefore, this statement is true.

IV. Corresponding angles of similar figures are the same.

True - While corresponding sides of similar figures may not be the same, their angles are. This is what gives them the similar characteristic. All similar polygons have equal angles, therefore this statement is true.

7 0

3 years ago

If I ship travels at 120 miles in five hours how far can it travel in two hours

zalisa [80]

So 120 miles in 5 hrs so 120 divided by 5 is 24 times 2 is 48 is the ship travels 48 in 2 hrs and happy valentines

3 0

3 years ago