Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

If
m^(2)+p^(2)=x and
4mp=y, which of the following is equivalent to
4x+2y ?
Choose 1 answer:
(A)
(2m+p)^(2)
(B)
(2m+2p)^(2)
(C)
(4m+2p)^(2)
(D)
(4m+8p)^(2)

If $m^{2}+p^{2}=x$ and $4 m p=y$ , which of the following is equivalent to $4 x+2 y$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $(2 m+p)^{2}$ $\newline$ (B) $(2 m+2 p)^{2}$ $\newline$ (C) $(4 m+2 p)^{2}$ $\newline$ (D) $(4 m+8 p)^{2}$

View step-by-step help

View step-by-step help

Compare linear and exponential growth

Full solution

Q. If

m^{2}+p^{2}=x

and

4 m p=y

, which of the following is equivalent to

4 x+2 y

?

\newline

Choose

1

answer:

\newline

(A)

(2 m+p)^{2}

\newline

(B)

(2 m+2 p)^{2}

\newline

(C)

(4 m+2 p)^{2}

\newline

(D)

(4 m+8 p)^{2}

Given Equations: We are given two equations: $\newline$ $1$ . $m^2 + p^2 = x$ $\newline$ $2$ . $4mp = y$ $\newline$ We need to find an equivalent expression for $4x + 2y$ using these equations.
Express $4x$ : First, let's express $4x$ in terms of $m$ and $p$ using the first equation: $\newline$ $4x = 4(m^2 + p^2)$
Express $2y$ : Now, let's express $2y$ in terms of $m$ and $p$ using the second equation: $\newline$ $2y = 2(4mp)$
Combine Expressions: Combine the expressions for $4x$ and $2y$ : $\newline$ $4x + 2y = 4(m^2 + p^2) + 2(4mp)$
Simplify Expression: Simplify the expression by distributing the constants: $4x + 2y = 4m^2 + 4p^2 + 8mp$
Factor Expression: Now, let's try to factor this expression to match one of the answer choices. We are looking for a perfect square since all the answer choices are in the form of a squared binomial.
Identify Perfect Square: We notice that $4m^2 + 4p^2 + 8mp$ can be written as $(2m + 2p)^2$ because: $\newline$ (\(2\)m + \(2\)p)^\(2\) = (\(2\)m)^\(2\) + \(2\)\times(\(2\)m)\times(\(2\)p) + (\(2\)p)^\(2\)\(\newline\) = \(4\)m^\(2\) + \(8\)mp + \(4\)p^\(2\) $\newline$ Which matches our expression for $4x + 2y$ .
Final Equivalent Expression: Therefore, the equivalent expression for $4x + 2y$ is $(2m + 2p)^2$ , which corresponds to answer choice $(B)$ .

More problems from Compare linear and exponential growth

Question

Jill bought a used motorcycle from a seller online for $1,200. The seller will charge her $5 a day to store the motorcycle at his house until she is able to pick it up. You can use a function to describe the total amount of money Jill will owe the seller if she waits

x

days to pick up the motorcycle.

\newline

Write an equation for the function. If it is linear, write it in the form

g(x) = mx + b

. If it is exponential, write it in the form

g(x) = a(b)^x

\newline

g(x) = \underline{\hspace{3em}}

Posted 5 months ago

Question

f(t)=-2t-7

change over the interval from

t=-7

t=-6

\newline

\newline

\left[\text{f(t) decreases by } 2\right]

\newline

\left[\text{f(t) increases by } 2\right]

\newline

\left[\text{f(t) increases by } 200\%\right]

\newline

\left[\text{f(t) decreases by a factor of } 2\right]

Posted 5 months ago

Question

g(t)=9^t

change over the interval from

t=1

t=3

\newline

\newline

\left[\text{g(t) decreases by a factor of } 81\right]

\newline

\left[\text{g(t) increases by a factor of } 81\right]

\newline

\left[\text{g(t) increases by } 18\%\right]

\newline

\left[\text{g(t) decreases by } 9\%\right]

Posted 5 months ago

Question

Both of these functions grow as

x

gets larger and larger. Which function eventually exceeds the other?

\newline

\newline

(A)f(x) = 8x + 3.3

\newline

(B)g(x) = 3.3^x - 5

Posted 6 months ago

Question

Both of these functions grow as

x

gets larger and larger. Which function eventually exceeds the other?

\newline

\newline

(A) \ f(x) = 2x + 9

\newline

(B)\ g(x) = 2^x

Posted 6 months ago

Question

f(x)

g(x)

are differentiable.

\newline

h(x)

h(x)=\frac{g(x)}{f(x)}

\newline

f(8)=1

f'(8)=-6

g(8)=8

g'(8)=-10

h'(8)

\newline

Simplify any fractions.

\newline

h'(8)=

Posted 6 months ago

Question

p(x)

q(x)

are differentiable.

\newline

r(x)

r(x)= \frac{p(x)}{q(x)}

\newline

p(3)= 2

p'(3)= 4

q(3)= 6

q'(3)= 9

r'(3)

\newline

Simplify any fractions.

\newline

r'(3)=

Posted 7 months ago

Question

u(x)

v(x)

are differentiable.

\newline

w(x)

w(x)= \frac{u(x)}{v(x)}

\newline

u(5)= 3

u'(5)= -2

v(5)= 7

v'(5)= 1

w'(5)

\newline

Simplify any fractions.

\newline

w'(5)=

Posted 7 months ago

Question

a(x)

b(x)

are differentiable.

\newline

c(x)

c(x)= \frac{a(x)}{b(x)}

\newline

a(2)= 4

a'(2)= 5

b(2)= 1

b'(2)= -3

c'(2)

\newline

Simplify any fractions.

\newline

c'(2)=

Posted 7 months ago

Question

m(x)

n(x)

are differentiable.

\newline

o(x)

o(x)= \frac{m(x)}{n(x)}

\newline

m(7)= 2

m'(7)= -1

n(7)= 4

n'(7)= 8

o'(7)

\newline

Simplify any fractions.

\newline

o'(7)=

Posted 7 months ago

Related topics

Algebra - Order of Operations Algebra - Distributive Property `X` and `Y` Axes Geometry - Scalene Triangle Common Multiple Geometry - Quadrant