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3 years ago

Which expression is equivalent to 6m+(m-2)(m+7)+3

Mathematics

1 answer:

Vika [28.1K]3 years ago

5 0

Answer:

$m^{2}$ + 11m - 11

Step-by-step explanation:

6m+(m-2)(m+7)+3 = 6m + [ m*m - 14 -2m + 7m] + 3

= 6m + mm - 14 + 5m + 3

= mm + 11m - 11

6m+(m-2)(m+7)+3 = $m^{2}$ + 11m - 11

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3 years ago

What is the explicit formula for this sequence? 2,10,50,250,1250

Valentin [98]

Answer:

$a_n = 2(5)^{n-1}$

Step-by-step explanation:

Explicit Geometric Formula: $a_n = a_1r^{n-1}$

a₁ is 1st term

r is common ratio

n is term number

Step 1: Find common ratio r

r = 10/2 = 5

Step 2: Plug variables into formula

$a_n = 2(5)^{n-1}$

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4 years ago

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ALGEBRA QUESTION PLS HELPS

cluponka [151]

The value of x is –7.

Solution:

Given expression:

$$\left(\frac{1}{x+3}+\frac{6}{x^{2}+4 x+3}\right) \cdot \frac{x+3}{x+1}$

Let us factor $x^2+4x+3$ .

$x^2+4x+3=(x+1)(x+3)$

Substitute this in the fraction.

$$\left(\frac{1}{x+3}+\frac{6}{(x+1)(x+3)}\right) \cdot \frac{x+3}{x+1}$

To make the denominator same, multiply and divide the first term by (x +1).

$$\left(\frac{(x+1)}{(x+1)(x+3)}+\frac{6}{(x+1)(x+3)}\right) \cdot \frac{x+3}{x+1}$

Denominators are same, you can add the fractions.

$$\left(\frac{x+1+6}{(x+1)(x+3)}\right) \cdot \frac{x+3}{x+1}$

$$\frac{x+7}{(x+1)(x+3)} \cdot \frac{x+3}{x+1}$

Cancel the common term in the numerator and denominator.

$$\frac{x+7}{x+1} \cdot \frac{1}{x+1}$

Multiply the fractions.

$$\frac{x+7}{(x+1)^2}$

$$\frac{x+7}{x^2+2x+1}$

The expression is simplified to one rational expression.

Suppose the expression is equal to 0.

$$\frac{x+7}{x^2+2x+1}=0$

Do cross multiplication.

$${x+7}=0\times (}{x^2+2x+1})$

Any number or variable multiplied by 0 gives 0.

$${x+7}=0$

Subtract 7 from both sides of the equation.

$${x+7-7}=0-7$

x = –7

The value of x is –7.

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3 years ago

32 is 40% of what number? Enter your answer in the box.

Whitepunk [10]

32 is 40% of 80...…....

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3 years ago

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What is the poinet-slope form of the equation for the line in the graph?

Ne4ueva [31]

Answer:

$y -5 = \frac{9}{13}(x - 7)$

Step-by-step explanation:

Given :

Two points are given in graph (-6, -4) and {7, 5).

The point-slope form of the equation of a straight line is:

$y -y_{1} = m(x - x_{1})$ ------------(1)

Let $(x_{1}, y_{1})=(7,5)$ and $(x_{2}, y_{2})=(-6,-4)$

The slope of the line $m=\frac{y_{2}- y_{1}}{x_{2}- x_{1}}$

Put all known value in above equation.

$m=\frac{-4- 5}{-6- 7}$

$m=\frac{-9}{-13}$

$m=\frac{9}{13}$

The slope of the line $m=\frac{9}{13}$

We know m, and also know that $(x_{1}, y_{1})=(7,5)$ , so we put these value in equation 1.

$y -5 = \frac{9}{13}(x - 7)$

Therefore, the equation of the line is $y -5 = \frac{9}{13}(x - 7)$ .

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3 years ago