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1 year ago

11

A ) Rotate Trapezoid ABCD 90° counterclockwise around the origin .

1 answer:

FinnZ [79.3K]1 year ago

8 0

Answer:

A" (3,3)

B" (3,5)

C" (5,7)

D" (5,1)

Yes they are congruent as they are similar and have the same shape and size.

Step-by-step explanation:

-y,x is the formula for a 90° counter clockwise rotation, And since the shape nor size doesnt change it is congruent.

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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

you have $18 to buy peppers. peppers cost $1.50 each. write and solve an inequality that represents the number of peppers you ca

Nezavi [6.7K]

At most 12 peppers can be bought with $18

Step-by-step explanation:

Given

Total amount for peppers = $18

Cost per pepper = $1.50

Let p be the number of peppers that can be bought from $18 at $1.50 per pepper

So,

$1.50p\leq 18$

Dividing both sides by 1.50

$\frac{1.50p}{1.50}\leq \frac{18}{1.50}\\p\leq 12$

Hence,

At most 12 peppers can be bought with $18

Keywords: Inequality, solution

Learn more about inequalities at:

#LearnwithBrainly

5 0

3 years ago

Can someone please help me in this question.

mestny [16]

Answer:

a) $2^{3}$

b) $2^{5}$

c) $2^{8}$

d) $\frac{5}{2^{3} }$

e) $2^{4} + 2^{3}$

Step-by-step explanation:

a) 8 = 2 x 2 x 2

b) 32 = 2 x 2 x 2 x 2 x 2

c) 256 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2

d) 5 x 2^3 / 64 = 5 x 8 / 64

= 40/64

= 5/8

= $\frac{5}{2^{3} }$

e) 16 - (-2)^3 = 16 - (-8)

= 16 + 8

= $2^{4} + 2^{3}$

6 0

3 years ago

To branily ani't buy the plus so please stop i don't want it

mario62 [17]

Answer:

fr tho

Step-by-step explanation:

like bro i dont need no brainly plus

7 0

3 years ago

The difference between a number and 8 is less than -15

Olenka [21]

Answer:

x-8<-15

Step-by-step explanation:

8 0

3 years ago