Ask question

Ask question

All categories

3 years ago

15

If x + y = 4 and x2 − y2 = 64, what is the value of (x − y)?

1 answer:

murzikaleks [220]3 years ago

7 0

The value of (x-y) is 16

Further explanation:

We have to use the given values to find the value

Given

$x+y=4\\and\\x^2-y^2=64$

We will use:

$x^2-y^2=64$

Simplifying by using: $x^2-y^2=(x+y)(x-y)$

So,

$(x+y)(x-y)=64$

As we know that x+y=4

Putting the value in equation

$(4)(x-y)=64$

Dividing both sides by 4

$\frac{4(x-y)}{4}=\frac{64}{4}\\x-y=16$

The value of (x-y) is 16

Keywords: Algebraic formulas, Simplification

Learn more about algebraic expressions at:

#LearnwithBrainly

You might be interested in

5p + 9c = p for c <br><br> Help out with this problem

Rom4ik [11]

Answer:

Step-by-step explanation:

5p + 9c = p

9c = p - 5p

9c = -4p

c = -4p/9

c= $\frac{-4p}{9}$

5 0

1 year ago

Read 2 more answers

If you have a cubic polynomial of the form y = ax^3 + bx^2 + cx + d and lets say it passes through the points (2,28), (-1, -5),

nikklg [1K]

Step-by-step explanation:

<u>Step 1: Solve using the first point</u>

<em>(2, 28)</em>

$28 = a(2)^3 + b(2)^2 + c(2) + d$

$28 = 8a + 4b + 2c + d$

<u>Step 2: Solve using the second point</u>

<em>(-1, -5)</em>

$-5 = a(-1)^3 + b(-1)^2 + c(-1) + d$

$-5 = -a + b - c + d$

<u>Step 3: Solve using the third point</u>

<em>(4, 220)</em>

$220 = a(4)^3 + b(4)^2 + c(4) + d$

$220 = 64a + 16b + 4c + d$

<u>Step 4: Solve using the fourth point</u>

<em>(-2, -20)</em>

$-20 = a(-2)^3 + b(-2)^2 + c(-2) + d$

$-20 = -8a + 4b - 2c + d$

<u>Step 5: Combine the first and fourth equations</u>

<u /> $28 - 20 = 8a - 8a + 4b + 4b + 2c - 2c + d + d$

$8 = 8b + 2d$

$8 - 8b = 8b - 8b + 2d$

$(8 -8b)/2 = 2d/2$

$4 - 4b = d$

<u>Step 6: Solve for c in the second equation</u>

$-5 + 5 = -a + b - c + d + 5$

$0 + c = -a + b - c + c + d + 5$

$c = -a + b + d + 5$

<u>Step 7: Substitute d with the stuff we got in step 5</u>

$c = -a + b + (4 - 4b) + 5$

$c = -a + b + 4 - 4b + 5$

$c = -a - 3b + 9$

<u>Step 8: Substitute d and c into the first equation</u>

<u /> $28 = 8a + 4b + 2(-a - 3b + 9) + (4 - 4b)$

$28 = 8a + 4b - 2a - 6b + 18 + 4 - 4b$

$28 - 22 = 6a - 6b + 22 - 22$

$6 / 6 = (6a - 6b) / 6$

$1 + b = a - b + b$

$1 + b = a$

<u>Step 9: Substitute a, b, and c into the third equation</u>

$220 = 64(1 + b) + 16b + 4(-(1 + b) - 3b + 9) + (4 - 4b)$

$220 = 64 + 64b + 16b + 4(-1 - b - 3b + 9) + 4 - 4b$

$220 - 100 = 60b + 100 - 100$

$120 / 60 = 60b / 60$

$2 = b$

<u>Step 10: Find a using b = 2</u>

$a = b + 1$

$a = (2) + 1$

$a = 3$

<u>Step 11: Find c using a = 3 and b = 2</u>

$c = -a - 3b + 9$

$c = -(3) - 3(2) + 9$

$c = -3 - 6 + 9$

$c = 0$

<u>Step 12: Find d using b = 2</u>

$d = 4 - 4b$

$d = 4 - 4(2)$

$d = 4 - 8$

$d = -4$

Answer: $a = 3, b = 2, c = 0,d = -4$

6 0

2 years ago

Read 2 more answers

Find the directional derivative of the function at the given point in the direction of the vector v. F(x, y, z) = xey + yez + ze

Vitek1552 [10]

no rurio greob tryo yeu

7 0

3 years ago

Find area of rhombus . please./.

lilavasa [31]

Answer: 126

Step-by-step explanation:

6 0

2 years ago

I really need help asap please

gizmo_the_mogwai [7]

We can use the substitution method to solve this problem.

The second equation is $\sf y=2x$ , so we can plug in 2x for 'y' in the first equation:

$\sf 5x-2y=3$

$\sf 5x-2(2x)=3$

Multiply:

$\sf 5x-4x=3$

Combine like terms:

$\sf x=3$

This is the x-value of our solution, we can plug this into any of the two equations to find the y-value:

$\sf y=2x$

$\sf y=2(3)$

Multiply:

$\sf y=6$

This is the y-value of our solution. So our entire solution is (3, 6).

5 0

2 years ago