All categories

3 years ago

Find two consecutive positive even integers such that the square of the first decreased by 64 equals 3 times the second.

Mathematics

1 answer:

IRINA_888 [86]3 years ago

8 0

Answer:

10 and 12

Step-by-step explanation:

let the consecutive even integers be n and n + 2 , then

n² - 64 = 3(n + 2) ← distribute parenthesis

n² - 64 = 3n + 6 ( subtract 3n + 6 from both sides )

n² - 3n - 70 = 0 ← in standard form

(n - 10)(n + 7) = 0 ← in factored form

Equate each factor to zero and solve for n

n - 10 = 0 ⇒ n = 10

n + 7 = 0 ⇒ n = - 7

Since n must be a positive even integer then n = 10 and n + 2 = 10 + 2 = 12

The 2 numbers are 10 and 12

You might be interested in

HURRY PLEASE I WILL GIVE BRAINLIEST

Sergeu [11.5K]

Answer:

About 40% of students own a cat

Step-by-step explanation:

7 0

3 years ago

Which of the following functions has a vertex of (-4,3) and a line of symmetry of x=-4

Bogdan [553]

2(x+4)^2+4

That is the answer!

8 0

4 years ago

Consider the surface defined by the equation x3 + y3 + z3 = 3xyz. Use implicit differ- ∂z entiation to find ∂x. (Note z is not a

Aloiza [94]

Answer:

$\frac{∂z}{∂x}=\frac{(3yz-3x^{2})}{3z^{2} -3xy}$

Step-by-step explanation:

Given equation is $x^{3}+y^{3}+z^{3}=3xyz$ ………………(1)

we use derivative formula $\frac{d}{dx}(x^{n}) = n x^{n-1}$

$\frac{d}{dx}(x^{3)} = 3 x^{2}$

$\frac{d}{dx}(z^{3)} = 3 z^{2}$

And also apply 'u v' formula

$\frac{d}{dx}(uv}) = u\frac{d}{dx}(v)+v\frac{d}{dx}(u)$

Differentiating equation (1) partially with respective to 'x' , we treated 'y' as constant.

$(3x^{2} +0+3z^{2}\frac{∂z}{∂x}) =3y(x\frac{∂z}{∂x}+z(1))$ ( here y treated as constant so the derivative of constant function is zero in addition but in multiplication the constant is keep as like 'y').

on simplification , we get

$(3x^{2} +0+3z^{2}\frac{∂z}{∂x}) =(3yx\frac{∂z}{∂x}+3yz)$

again simplification, we get

$3z^{2}\frac{∂z}{∂x}- 3yx\frac{∂z}{∂x}=3yz-3x^{2}$

taking common ' $\frac{∂z}{∂x}$ on left on side , we get

$(3z^{2}- 3yx)\frac{∂z}{∂x}=3yz-3x^{2}$

dividing ' $(3z^{2}- 3yx)$ on both sides, we get

$\frac{∂z}{∂x}=\frac{(3yz-3x^{2})}{3z^{2} -3xy}$

<u>Final answer</u>:-

$\frac{∂z}{∂x}=\frac{(3yz-3x^{2})}{3z^{2} -3xy}$

6 0

3 years ago

14) Which equation represents the line that passes through the point (4,1) and (20,-3)?

guapka [62]

Answer:

All of the options are in standard form (ax+by=c). But none of the answers is an option. The correct answer is <u>x+4y=8.</u>

Step-by-step explanation:

The following screenshot is a graphing website to prove that the equation x+4y=8 passes through the points (4,1) and (20,-3).

I don’t know if the equation x+4y=8 is an option for you, because I don’t see it as an option to choose out of the four.

But I hope this helps and answers your question :)

8 0

3 years ago

Read 2 more answers

What do e and f equal?

Aleks04 [339]

They both equal 78 degrees because they are the same angle which means that they have the same degrees for f and e.

6 0

3 years ago