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bulgar [2K]
3 years ago
8

Simplify the expression –3(x + 3)2 – 3 + 3x. What is the simplified expression in standard form?

Mathematics
2 answers:
serious [3.7K]3 years ago
8 0

hello :
<span>–3(x + 3)² – 3 + 3x = -3( x² +6x+9) -3 +3x
                               =-3x² -18x -27 -3 +3x
                               = -3x² - 15x -30.. ( </span><span>standard form)</span>
VARVARA [1.3K]3 years ago
6 0

Answer with explanation:

The given expression is

 -3(x + 3)^2 -3 + 3 x\\\\=-3*(x^2+2*3*x+3^2)-3 +3 x\\\\=-3 x^2-3*6 x-3*9-3+3 x\\\\=-3 x^2-18 x-27-3+3 x\\\\=-3 x^2-15 x-30\\\\ =-3(x^2+5 x+10)

This is standard form of the expression given.

→→Used the following properties and Identity to solve the expression :

1. (a+b)²=a²+2 a b +b²

2. Distributive property of multiplication with respect to addition and subtraction,which is

1. a × (b+c)=a × b + a × c

2.  a × (b - c)=a × b - a × c

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3 years ago
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$600 invested with compound interest at a rate of 4% per year for 10 years <br> formula:M= P(1+i)^n
makkiz [27]
Answer: M = 2100$

Explanation:

M = P(1 + I)^n

P = 600$, I = 4% = 0.04, n = 10

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8 0
2 years ago
What is the y-intercept, axis of symmetry and vertex of the following function.
Pepsi [2]

Complete the square:

F(x) = -3x² - 6x - 5

F(x) = -3 (x² + 2x) - 5

F(x) = -3 (x² + 2x + 1 - 1) - 5

F(x) = -3 ((x + 1)² - 1) - 5

F(x) = -3 (x + 1)² + 3 - 5

F(x) = -3 (x + 1)² - 2

The y-intercept has x-coordinate equal to 0, so it corresponds to the value of F(0) :

F(0) = -3 (0 + 1)² - 2 = -3 - 2 = -5

The axis of symmetry is the vertical line running through the vertex of this parabola, so we'll come back to this.

The vertex of the parabola is (-1, -2). This represents the maximum value of F(x), which follows from

(x + 1)² ≥ 0   ⇒   -3 (x + 1)² ≤ 0   ⇒   -3 (x + 1)² - 2 ≤ -2

This is to say, every point on the parabola has a y-coordinate no greater than -2.

As mentioned earlier, the axis of symmetry is the vertical line through the vertex, and its equation is determined by the x-coordinate of the vertex. Hence the AoS is the line x = -1.

4 0
2 years ago
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drek231 [11]

Answer:

y=3x+1, or the second option

Step-by-step explanation:

We can see on the graph the line converges with the y-axis at (0, 1), so we can cross out the last two answers. Then we can also see that the slope is 3 on the graph and an equation that has x^2 must be a parabola. The answer is then narrowed down to the second option.

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The population of a type of local dragonfly can be found using an infinite geometric series where a1 = 65 and the common ratio i
hram777 [196]
In mathematics, number sequencing of the same pattern are called progression. There are three types of progression: arithmetic, harmonic and geometric. The pattern in arithmetic is called common difference, while the pattern in geometric is called common ratio. Harmonic progression is just the reciprocal of the arithmetic sequence.

The common ratio is denoted as r. For values of r<1, the sum of the infinite series is equal to

S∞ = A₁/(1-r), where A1 is the first term of the sequence. Substituting A₁=65 and r=1/6:

S∞ = A₁/(1-r) = 65/(1-1/6)
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3 years ago
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