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3 years ago

A _________ is a minute (very small) area of illumination on a display screen. Fill in the blanks!!! Thanks♡

Mathematics

1 answer:

Monica [59]3 years ago

5 0

Answer:

A Pixel is a minute area of illumination on a display screen

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What two rational expressions sum to 2x+3/x^2-5x+4

Anni [7]

Answer:

$\frac{2x + 3}{(x- 1)(x - 4)} = \frac{-5}{3(x- 1)} + \frac{11}{3(x - 4)}$

Step-by-step explanation:

Given the rational expression: $\frac{2x + 3}{x^2 - 5x + 4}$ , to express this in simplified form, we would need to apply the concept of partial fraction.

Step 1: factorise the denominator

$x^2 - 5x + 4$

$x^2 - 4x - x + 4$

$(x^2 - 4x) - (x + 4)$

$x(x - 4) - 1(x - 4)$

$(x- 1)(x - 4)$

Thus, we now have: $\frac{2x + 3}{(x- 1)(x - 4)}$

Step 2: Apply the concept of Partial Fraction

Let,

$\frac{2x + 3}{(x- 1)(x - 4)}$ = $\frac{A}{x- 1} + \frac{B}{x - 4}$

Multiply both sides by (x - 1)(x - 4)

$\frac{2x + 3}{(x- 1)(x - 4)} * (x - 1)(x - 4)$ = $(\frac{A}{x- 1} + \frac{B}{x - 4}) * (x - 1)(x - 4)$

$2x + 3 = A(x - 4) + B(x - 1)$

Step 3:

Substituting x = 4 in $2x + 3 = A(x - 4) + B(x - 1)$

$2(4) + 3 = A(4 - 4) + B(4 - 1)$

$8 + 3 = A(0) + B(3)$

$11 = 3B$

$\frac{11}{3} = B$

$B = \frac{11}{3}$

Substituting x = 1 in $2x + 3 = A(x - 4) + B(x - 1)$

$2(1) + 3 = A(1 - 4) + B(1 - 1)$

$2 + 3 = A(-3) + B(0)$

$5 = -3A$

$\frac{5}{-3} = \frac{-3A}{-3}$

$A = -\frac{5}{3}$

Step 4: Plug in the values of A and B into the original equation in step 2

$\frac{2x + 3}{(x- 1)(x - 4)} = \frac{A}{x- 1} + \frac{B}{x - 4}$

$\frac{2x + 3}{(x- 1)(x - 4)} = \frac{-5}{3(x- 1)} + \frac{11}{3(x - 4)}$

7 0

3 years ago

a store is having a sale on walnuts and chocolate chips. for 3 pounds of walnuts and 5 pounds of chocolate chips, the total cost

Step2247 [10]

Answer:

Walnuts - $1.25, chocolate chips - $3.25

Step-by-step explanation:

Let walnuts = x, chocolate chips = y

Set a system and solve:

3x + 5y = 20
6x + 2y = 14

Double the first equation and subtract the second one from it:

6x + 10y - 6x - 2y = 40 - 14
8y = 26
y = 26/8
y = 3.25

Find the value of x:

6x + 3.25*2 = 14
6x = 14 - 6.5
6x = 7.5
x = 7.5/6
x = 1.25

7 0

2 years ago

Rectangle

Viefleur [7K]

Answer:

21 square units

Step-by-step explanation:

The sides of the rectangle are aligned with the coordinate grid, so we can easily find its dimensions.

AB lies on the line y = -2, so the horizontal extent is the difference in x-values:

6 - 3 = 3

BC lies on the line x = 6, so the vertical extent is the difference in y-values:

5 -(-2) = 7

The area is the product of these two dimensions:

A = LW = (7)(3) = 21 . . . . square units

The area of the rectangle is 21 square units.

3 0

3 years ago

Read 2 more answers

Evaluate the function. f(x) = -2x2 + 7 Find f(-5)

Alla [95]

-2(-5)^2 + 7
-2 • 5^2 + 7
-2 • 25 + 7
-50 + 7
-43

6 0

3 years ago

PLEASE ANSWER THIS QUESTION AND EXPLAIN IF YOU CAN

jekas [21]

Factor out -1
-1(x^2+x-6)

Factor the inner trinomial
-1(x+3)(x-2)

Final answer: B

6 0

3 years ago

Read 2 more answers

A _________ is a minute (very small) area of illumination on a display screen. Fill in the blanks!!! Thanks♡​

A _________ is a minute (very small) area of illumination on a display screen. Fill in the blanks!!! Thanks♡