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3 years ago

A² + b² = 7b and b² + (2b-a)² = 7² find (a - b)².

Mathematics

1 answer:

Mamont248 [21]3 years ago

4 0

Answer:

(a - b)^2 = 49 - 4b^2 +2ab

Step-by-step explanation:

Given: a^2 + b^2 = 7b (assuming A is really “a”)

b^2 + (2b - a)^2 = 7^2

Find; (a - b)^2

Plan: Use Algebraic Manipulation

Start with b^2 + (2b - a)^2 = 7^2 =>

b^2 + 4b^2 - 4ab + a^2 = 49 by expanding the binomial.

a^2 + b^2 + 4b^2 - 4ab = 49 rearranging terms

a^2 + b^2 -2ab - 2ab + 4b^2 = 49 =>

a^2 - 2ab + b^2 = 49 - 4b^2 +2ab rearranging and subtracting 4b^2 and adding 2ab to both sides of the equation and by factoring a^2 - 2ab + b^2

(a - b)^2 = 49 - 4b^2 +2ab

Double Check: recalculated ✅ ✅

(a - b)^2 = 49 - 4b^2 +2ab

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A glass top of an office table is in the form of rectangle. The diagonal of the table have length 5x-11 and 2x+25

3241004551 [841]

Answer:

1) The value of $x$ is 12.

2) The length of the diagonal is 49.

Step-by-step explanation:

1) If the glass is a rectangle, then both diagonal must have the same length, that is, the following equation must be solved:

$5\cdot x - 11 = 2\cdot x + 25$ (1)

We need some algebraic handling to determine the value of $x$ :

$5\cdot x - 11 = 2\cdot x + 25$

$5\cdot x - 2\cdot x = 25 +11$

$[5+(-2)] \cdot x = 36$

$3\cdot x = 36$

$x = 12$

The value of $x$ is 12.

2) If we know that $x = 12$ , then the length of the diagonal ( $d$ ) is:

$d = 2\cdot x + 25$

$d = 49$

The length of the diagonal is 49.

4 0

3 years ago

24x-45y=34x (rp) have a great day

nirvana33 [79]

24x-45y=34x

To solve for y, subtract 24x:
-45y=10x

Divide by -45:
y=-10/45x

Reduce:
y=-2/9x

To solve for x, subtract 24x:
-45y=10x

Divide by 10:
-45/10y=x

Reduce:
-9/2y=x

4 0

3 years ago

Read 2 more answers

Which expression is m.m.m.m.m rewritten in exponential form

Anastaziya [24]

Answer: M^5

Step-by-step explanation: M•M•M•M•M

3 0

3 years ago

Complete the graph to model this situation

lianna [129]

I think you would just add 50 to each line on the bottom and add 4 on the y axis line

Hope this helps!! And that I'm right!

3 0

3 years ago

Pleeeeeeeeeease

xxMikexx [17]

Answer:

The final equation is $y = \frac{4}{3}x - \frac{16}{3}$

Step-by-step explanation:

The slope of the line CB where, C(0,3) and B(12,-6) will be

$M = \frac{- 6 - 3}{12 - 0} = - \frac{3}{4}$

Now, if the line perpendicular to the line CB has slope N, then M × N = - 1

⇒ $N = \frac{4}{3}$ {Since $M = - \frac{3}{4}$ }

Now, equation of the straight lines which are perpendicular to CB will be in slope-intercept form

$y = \frac{4}{3}x + c$ {Where, c is the y-intercept}

If this straight line passes through the point (7,4), then

$4 = \frac{4}{3} \times 7 + c$

⇒ 12 = 28 + 3c

⇒ 3c = - 16

⇒ $c = - \frac{16}{3}$

Therefore, the final equation is $y = \frac{4}{3}x - \frac{16}{3}$ (Answer)

7 0

4 years ago