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3 years ago

Find the sum of the terms.

Mathematics

1 answer:

kow [346]3 years ago

5 0

Answer:

Step-by-step explanation:

Given

$\frac{x}{x^2+3x+2}$ + $\frac{3}{x+1}$ ← factor the denominator of first fraction

= $\frac{x}{(x+1)(x+2)}$ + $\frac{3}{x+1}$

Multiply the numerator/ denominator of second fraction by (x + 2)

= $\frac{x}{(x+1)(x+2)}$ + $\frac{3(x+2)}{(x+1)(x+2)}$

The denominators are now common, so add the numerators leaving the denominator, that is

= $\frac{x+3x+6}{(x+1)(x+2)}$

= $\frac{4x+6}{(x+1)(x+2)}$ → with numerator 4x + 6 → C

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PLEASE I NEED HELP ASAP

Annette [7]

The coordinates of the vertex that A maps to after Daniel's reflections are (3, 4) and the coordinates of the vertex that A maps to after Zachary's reflections are (3, 2)

<h3>How to determine the coordinates of the vertex that A maps to after the two reflections?</h3>

From the given figure, the coordinate of the vertex A is represented as:

A = (-5, 2)

<u>The coordinates of the vertex that A maps to after Daniel's reflections</u>

The rule of reflection across the line x = -1 is

(x, y) ⇒ (-x - 2, y)

So, we have:

A' = (5 - 2, 2)

Evaluate the difference

A' = (3, 2)

The rule of reflection across the line y = 2 is

(x, y) ⇒ (x, -y + 4)

So, we have:

A'' = (3, -2 + 4)

Evaluate the difference

A'' = (3, 4)

Hence, the coordinates of the vertex that A maps to after Daniel's reflections are (3, 4)

<u>The coordinates of the vertex that A maps to after Zachary's reflections</u>

The rule of reflection across the line y = 2 is

(x, y) ⇒ (x, -y + 4)

So, we have:

A' = (-5, -2 + 4)

Evaluate the difference

A' = (-5, 2)

The rule of reflection across the line x = -1 is

(x, y) ⇒ (-x - 2, y)

So, we have:

A'' = (5 - 2, 2)

Evaluate the difference

A'' = (3, 2)

Hence, the coordinates of the vertex that A maps to after Zachary's reflections are (3, 2)

Read more about reflection at:

brainly.com/question/4289712

#SPJ1

8 0

1 year ago

9966 [12]

Answer:

(b) -m, m + 3

Step-by-step explanation:

x² − 3x − m(m + 3) = 0

x² − 3x = m(m + 3)

x² − 3x + 9/4 = m(m + 3) + 9/4

(x − 3/2)² = m(m + 3) + 9/4

(x − 3/2)² = m² + 3m + 9/4

(x − 3/2)² = (m + 3/2)²

x − 3/2 = ±(m + 3/2)

x − 3/2 = m + 3/2, -m − 3/2

x = m + 3, -m

6 0

3 years ago

A certain bookstore chain has two stores, one in San Francisco and one in Los Angeles. It stocks three kinds of books: hardcover

victus00 [196]

Answer:

Answer:

a. Sales from January to June: Matrix B6

Hard Soft Plastic

San Francisco 4,200 7,200 12,000

Los Angeles 2,400 1,200 3,000

b) Ending Inventory: Matrix D:

Hard Soft Plastic

San Francisco 400 4,800 3,000

Los Angeles 1,600 7,800 3,000

Step-by-step explanation:

a) Data and Calculations:

Stock on January 1: Matrix A

Hard Soft Plastic

San Francisco 1,000 3,000 6,000

Los Angeles 1,000 6,000 3,000

Sales in January: Matrix B

Hard Soft Plastic

San Francisco 700 1,200 2,000

Los Angeles 400 200 500

Restocking: Matrix C

Hard Soft Plastic

San Francisco 600 1,500 1,500

Los Angeles 500 500 500

Total Sales over the first 6 months =

Matrix B * 6 = Matrix B6

Sales in January: Matrix B

Hard Soft Plastic

San Francisco 700 1,200 2,000

Los Angeles 400 200 500

* 6

Sales from January to June: Matrix B6

Hard Soft Plastic

San Francisco 4,200 7,200 12,000

Los Angeles 2,400 1,200 3,000

Matrix C6 = Matrix C * 6

Restocking: Matrix C6

Hard Soft Plastic

San Francisco 3,600 9,000 9,000

Los Angeles 3,000 3,000 3,000

Inventory at the end of June =

Matrix A + Matrix C6 - Matrix B6

= Matrix D

Stock on January 1: Matrix A

Hard Soft Plastic

San Francisco 1,000 3,000 6,000

Los Angeles 1,000 6,000 3,000

Restocking: Matrix C6

Hard Soft Plastic

San Francisco 3,600 9,000 9,000

Los Angeles 3,000 3,000 3,000

Sales from January to June: Matrix B6

Hard Soft Plastic

San Francisco 4,200 7,200 12,000

Los Angeles 2,400 1,200 3,000

Ending Inventory: Matrix D:

Hard Soft Plastic

San Francisco 400 4,800 3,000

Los Angeles 1,600 7,800 3,000

3 0

2 years ago

A flock of geese is flying north for the summer while a bird watcher is observing. He notices that they are flying in the shape

nata0808 [166]

Answer:

y = -¼│x − 5│+ 3

Step-by-step explanation:

y = a│x − h│+ k

(h, k) is the vertex of the absolute value graph. In this case, it's (5, 3).

y = a│x − 5│+ 3

One point on the graph is (1, 2). Plug in to find the value of a.

2 = a│1 − 5│+ 3

2 = 4a + 3

a = -¼

Therefore, the graph is:

y = -¼│x − 5│+ 3

4 0

3 years ago

A quadratic function is given. f(x) = 1 + x − 7 x2 (a) Use a graphing device to find the maximum or minimum value of the quadrat

Virty [35]

Answer:

a) $P (x,y) \approx (0.1,1.05)$ , b) $P(x,y) = (0.07,1.04)$ .

Step-by-step explanation:

a) The graphic is enclosed to the problem. By visual inspection, an absolute maximum is found.

$P (x,y) \approx (0.1,1.05)$

b) The exact method consists in the application of the First and Second Derivative Tests. First and second derivatives are, respectively:

$f'(x) = 1 - 14\cdot x$

$f''(x) = -14$

The First Derivative Test consists in equalizing the first derivative to zero and solving the expression:

$1 - 14\cdot x = 0$

$x = 0.07$

According to the second derivative, the critical point leads to a maximum. The remaining component is determined by evaluation the polynomial:

$y = 1 +0.07-7\cdot (0.07)^{2}$

$y = 1.04$

The exact solution is $P(x,y) = (0.07,1.04)$ , indicating that graphic solution leads to a good approximation.

6 0

3 years ago