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Artist 52 [7]
2 years ago
11

4. Add f(x)= 4x?+5x-1 g(x) = 2x2 + 5x+3

Mathematics
1 answer:
Maurinko [17]2 years ago
6 0
<h3>Answer:</h3>

A. 3x² +6

<h3>Explanation:</h3>

(f-g)(x) = f(x) -g(x) = (4x²+1) -(x²-5) . . . . . substitute the function definitions

... = 4x² +1 -x² +5 . . . . . . . . . . . eliminate parentheses

... = (4-1)x² +(1+5) . . . . . . . . . . . collect like terms

... = 3x² +6

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The coordinates of the vertices of quadrilateral DEFG are D(−2, 5) , E(2, 4) , F(0, 0) , and G(−4, 1) .
daser333 [38]

Answer: The correct option is a.Quadrilateral DEFG is a rhombus because opposite sides are parallel and all four sides have the same length.

Explanation:

It is given that  coordinates of the vertices of quadrilateral DEFG are D(−2, 5) , E(2, 4) , F(0, 0) , and G(−4, 1) .

The distance formula for two points is given below,

D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

DE=\sqrt{(2+2)^2+(4-5)^2}=\sqrt{17}

EF=\sqrt{(0-2)^2+(0-4)^2}=\sqrt{20}

FG=\sqrt{(-4-0)^2+(1-0)^2}=\sqrt{17}

DG=\sqrt{(-4+2)^2+(1-5)^2}=\sqrt{20}

Slope formula,

m=\frac{y_2-y_1}{x_2-x_1}

Slope of DE,

m_1=\frac{4-5}{2+2}= \frac{-1}{4}

Slope of EF,

m_2=\frac{0-4}{0-2}= 2

Slope of FG,

m_3=\frac{1-0}{-4-0}= \frac{-1}{4}

Slope of DG,

m_4=\frac{1-5}{-4+2}= 2

The slope of opposite sides are equal, it means the opposite sides are parallel.

All four sides do not have the same length. It means it is not a rhombus.

From the figure it is noticed that the opposite sides are parallel.

Therefore, the correct option is a.Quadrilateral DEFG is a rhombus because opposite sides are parallel and all four sides have the same length.

3 0
3 years ago
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Which of the following is a proportional relationship? SELECT ALL THAT APPLY
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Answer:

a

Step-by-step explanation:

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4 0
2 years ago
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The table shows the cost for movie tickets. Find the rate of change of price to number of tickets.
zalisa [80]

C. 13.00 per ticket (:

4 0
3 years ago
Identify the terms and like terms in the expression - x - 9x*2 + 12x*2 + 7
alexgriva [62]
The expression - x - 9x^2 + 12x^2 + 7 has 4 terms:
-x, -9x^2, 12x^2, 7

Like terms are:
-9x^2, 12x^2
4 0
3 years ago
Sandra swims the 100-meter freestyle for her school’s swim team. Her state’s ranking system awards 3 points for first place, 2 p
Elina [12.6K]

Answer:

2.25

Step-by-step explanation:

The total frequency is:

20 + 12 + 6 + 2 = 40

Calculate the probability of each score:

P(X=3) = 20/40 = 0.50

P(X=2) = 12/40 = 0.30

P(X=1) = 6/40 = 0.15

P(X=0) = 2/40 = 0.05

So the expected value is:

E = (3)(0.50) + (2)(0.30) + (1)(0.15) + (0)(0.05)

E = 2.25

5 0
2 years ago
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