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3 years ago

Simplify x²-49/3x+21

2 answers:

5 0

$x^2-49=x^2-7^2=(x-7)(x+7)\\\\\text{Used}\ a^2-b^2=(a-b)(a+b)\\\\3x+21=3\cdot x+3\cdot7=3(x+7)\\\\\dfrac{x^2-49}{3x+21}=\dfrac{(x-7)(x+7)}{3(x+7)}=\dfrac{x-7}{3}$

Vera_Pavlovna [14]3 years ago

3 0

First, you factor and simplify (respectively) the numerator and denominator. Your equation becomes:

$\frac{(x-7)(x+7)}{3(x + 7)}$

Notice, there is a (x + 7) on both the top and the bottom. Because of this, they cancel each other out. What is left is your answer:

$\frac{(x-7)}{3}$

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A child gets 20 heads out of 30 tosses of a coin. If he declared the chance of getting a head with that coin were 2/3, that woul

Komok [63]

Answer: Experimental probability

Step-by-step explanation:

There are two kinds of probability: Theoretical probability and Experimental probability.

To calculate theoretical probability we divide favorable outcomes by total outcomes.

To calculate experimental probability we divide number of times an event occurs by the total number of trials or times the activity is performed.

Here, A child gets 20 heads out of 30 tosses of a coin. If he declared the chance of getting a head with that coin were 2/3, which is dependent on the activity he performed, thus it is an experimental probability.

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3 years ago

Find the equation of the line passing through the points (7, 16) and (2, −4). Then state the slope and coordinates of the x- and

Elanso [62]

Answer:

Equation point-slope model is: y-16 = 4 (x-7)

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Step-by-step explanation:

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3 years ago

I don’t understand this someone pls help me! (Question 10)

Likurg_2 [28]

Answer:

a. f(n) = n(n+1)/2

b. 351

c. 19

d. no; n would not be an integer for f(n) = 17.

Step-by-step explanation:

a. The terms are 1, 3, 6, 10, ...

Each term has the term number added to the previous term. That is, first differences are 3-1 = 2, 6-3 = 3, 10-6 = 4. These differences have a constant difference of 1.

When the 2nd differences are constant, a 2nd degree polynomial can describe the sequence. It is a little bit of trouble to find that polynomial.

For the polynomial ...

$f(n)=an^2+bn+c$

We can substitute values for n and f(n) to get 3 equations in 3 unknowns:

$1=a\cdot1^2+b\cdot1+c\\\\3=a\cdot2^2+b\cdot2+c\\\\6=a\cdot3^2+b\cdot3+c$

Solving these equations by your favorite method gives ...

(a, b, c) = (1/2, 1/2, 0)

That is, the function representing the relationship is ...

f(n) = n(n+1)/2 . . . . the function describing the relationship

b. f(26) = 26(27) = 13(27) = 351 . . . . the number of squares in term 26

c. The number of the term having 190 squares can be found by solving ...

n(n +1)/2 = 190

n(n +1) = 380 = 19(20)

The 19th term will have 190 squares.

d. Terms 5 and 6 are 15 and 21.

17 is not the value of one of the terms in this sequence.

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2 years ago

Given: line hg is the perpendicular bisector of segment JK. Which conclusion is valid?

Varvara68 [4.7K]

JG = GK
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H
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3 years ago

3. The graph of an equation intersects the y-axis at some point. What do the coordinates of the intersection indicate?

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Answer:

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Number of edges: 3

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Step-by-step explanation:

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2 years ago