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Delicious77 [7]
3 years ago
11

1. There are 532 pieces of art at the show.

Mathematics
2 answers:
Svetllana [295]3 years ago
8 0

Answer:

213 pieces are not paintings.

Step-by-step explanation:

532 pieces of art at the show.

-319 pieces of art are paintings.

_____________________

213 pieces are not paintings.

Irina-Kira [14]3 years ago
7 0

<u>Answer: </u>

There are 532 pieces of art at the show. 319 pieces of art are paintings. Number of pieces of art which are not paint is 213

<u>Solution: </u>

Total number of pieces of art at the show = 532

Number of pieces of art which are painting = 319

Let number of pieces of arts which are not painting = x

From given information, we can say that total number of arts will be summation of number of pieces of arts which are painting and number of pieces of arts which are not painting.  so we get,

Total number of arts = number of pieces of arts which are painting + number of pieces of arts which are not paint

532 = 319 + x

On subtracting 319 both sides

532 – 319 = 319 + x - 319

x = 213

Hence number of pieces of art which are not paint is 213

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Mr. Trainer is building a bookcase. He has two wooden boards that are each 8 feet long. He needs to cut the wooden boards into p
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Answer:

12

Step-by-step explanation:

Length of one of the boards = 8 feet

Converting to inches

1\ \text{foot}=12\ \text{inches}\\\Rightarrow 8\ \text{feet}=8\times 12=96\ \text{inches}

One cut is 16 inches

So, we divide the length of the board by 16

\dfrac{96}{16}=6

So, one board is cut into 6 pieces.

The other board is also 8 feet long.

So, the number of pieces the other board is cut into is also 6.

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8 0
2 years ago
Rachel plays a game by rolling two number cubes with sides numbered 1 through 6 to win the game the sum of the numbers facing up
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The probability that Rachel will win the game is: 1/12

Step-by-step explanation:

The number cubes has six sides numbered between 1 to 6. the chances of each number are equally likely

Let S be the sample space

The sample space has 6*6 = 36 outcomes.

Now, Let A be the event that the sum of numbers on both number cubes is 10

A = {(4,6),(5,5), (6,4)

n(A) = 3

P(A)= \frac{n(A)}{n(S)}\\=\frac{3}{36}\\=\frac{1}{12}

The probability that Rachel will win the game is: 1/12

Keywords: Probability, Sample

Learn more about probability at:

  • brainly.com/question/9729310
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3 years ago
1.) Determine the type of solutions for the function (Picture 1)
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Answer:

1) 2 nonreal complex roots

2) 1 Real Solution

3) 16

4) Reflected, narrower by a factor of 2/5, slides right 4 units and slides up 6 (units)

Step-by-step explanation:

1) The graph does not intercept the x-axis, therefore, there are no real solutions at the point y = 0

We get;

y = a·x² + b·x + c

At y = 6, x = -2

Therefore;

6 = a·(-2)² - 2·b + c = 4·a - 2·b + c

6 = 4·a - 2·b + c...(1)

At y = 8, x = 0

8 = a·(0)² + b·0 + c

∴ c = 8...(2)

Similarly, we have;

At y = 8, x = -4

8 = a·(-4)² - 4·b + c = 16·a - 4·b + 8

16·a - 4·b = 0

∴ b = 16·a/4 = 4·a

b = 4·a...(3)

From equation (1), (2) and (3), we have;

6 = 4·a - 2·b + c

∴ 6 = b - 2·b + 8 = -b + 8

6 - 8 = -b

∴ -b = -2

b = 2

b = 4·a

∴ a = b/4 = 2/4 = 1/2

The equation is therefor;

y = (1/2)·x² + 2·x + 8

Solving we get;

x = (-2 ± √(2² - 4 × (1/2) × 8))/(2 × (1/2))

x =( -2 ± √(-12))/1 = -2 ± √(-12)

Therefore, we have;

2 nonreal complex roots

2) Give that the graph of the function touches the x-axis once, we have;

1 Real Solution

3) The given function is f(x) = 2·x² + 8·x + 6

The general form of the quadratic function is f(x) = a·x² + b·x + c

Comparing, we have;

a = 2, b = 8, c = 6

The discriminant of the function, D = b² - 4·a·c, therefore, for the function, we have;

D = 8² - 4 × 2 × 6 = 16

The discriminant of the function, D = 16

4.) The given function is g(x) = (-2/5)·(x - 4)² + 6

The parent function of a quadratic equation is y = x²

A vertical translation is given by the following equation;

y = f(x) + b

A horizontal to the right by 'a' translation is given by an equation of the form; y = f(x - a)

A vertical reflection is given by an equation of the form; y = -f(x) = -x²

A narrowing is given by an equation of the form; y = b·f(x), where b < 1

Therefore, the transformations of g(x) from the parent function are;

g(x) is a reflection of the parent function, with the graph of g(x) being narrower by 2/5 than the graph of the parent function. The graph of g(x) is shifted right by 4 units and is then slides up by 6 units.

7 0
2 years ago
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