Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

49x^(2)-64=0
What are the solutions to the given equation?
Choose 1 answer:
(A)
x=(64)/(49)
(B)
x=-(64)/(49) and
x=(64)/(49)
(C)
x=(8)/(7)
(D)
x=-(8)/(7) and
x=(8)/(7)

$49 x^{2}-64=0$ $\newline$ What are the solutions to the given equation? $\newline$ Choose $1$ answer: $\newline$ (A) $x=\frac{64}{49}$ $\newline$ B $x=-\frac{64}{49}$ and $x=\frac{64}{49}$ $\newline$ (C) $x=\frac{8}{7}$ $\newline$ (D) $x=-\frac{8}{7}$ and $x=\frac{8}{7}$

View step-by-step help

View step-by-step help

Compare linear and exponential growth

Full solution

Q.

49 x^{2}-64=0

\newline

What are the solutions to the given equation?

\newline

Choose

1

answer:

\newline

(A)

x=\frac{64}{49}

\newline

B

x=-\frac{64}{49}

and

x=\frac{64}{49}

\newline

(C)

x=\frac{8}{7}

\newline

(D)

x=-\frac{8}{7}

and

x=\frac{8}{7}

Identify equation type and method: Identify the type of equation and the method to solve it. $\newline$ The given equation is a quadratic equation in the standard form $ax^2 + bx + c = 0$ , where $a = 49$ , $b = 0$ , and $c = -64$ . $\newline$ To solve for $x$ , we can factor the equation or use the quadratic formula. Since the equation is already in a form that suggests factoring, we will attempt to factor it.
Factor the quadratic equation: Factor the quadratic equation. $\newline$ The equation $49x^2 - 64$ can be factored as a difference of squares because both $49x^2$ and $64$ are perfect squares. $\newline$ $(7x)^2 - 8^2 = 0$ $\newline$ $(7x + 8)(7x - 8) = 0$
Solve for x: Set each factor equal to zero and solve for x. $\newline$ $7x + 8 = 0$ or $7x - 8 = 0$ $\newline$ For the first factor: $\newline$ $7x + 8 = 0$ $\newline$ $7x = -8$ $\newline$ $x = -\frac{8}{7}$ $\newline$ For the second factor: $\newline$ $7x - 8 = 0$ $\newline$ $7x = 8$ $\newline$ $x = \frac{8}{7}$
Check solutions in original equation: Check the solutions in the original equation. $\newline$ Substitute $x = -\frac{8}{7}$ into the original equation: $\newline$ $49\left(-\frac{8}{7}\right)^2 - 64 = 49\left(\frac{64}{49}\right) - 64 = 64 - 64 = 0$ $\newline$ Substitute $x = \frac{8}{7}$ into the original equation: $\newline$ $49\left(\frac{8}{7}\right)^2 - 64 = 49\left(\frac{64}{49}\right) - 64 = 64 - 64 = 0$ $\newline$ Both solutions satisfy the original equation.

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