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2 years ago

What method would you choose to solve the equation 2x2 – 7 = 9? Explain why you chose this method.

2 answers:

8 0

Sample Response/Explanation: I would use the square root property of equality. Because there is no x term, I would just add and divide to get x2 by itself. Then I would take the square root.

oksano4ka [1.4K]2 years ago

7 0

I would add 7 to get ...

... 2x² = 16

then divide by 2 to get

... x² = 8

Now, I would take the square root, recognizing that both positive and negative values will solve the problem.

... x = ±√8

The root can be simplified, so we have ...

... x = ±2√2

_____

The above method seemed the most obvious method to me. One could use the quadratic formula, but that seems to involve more operations.

... 2x² -16 = 0 . . . . subtract 9

... x = (-0 ± √(0² -4·2·(-16)))/(2·2) . . . . put the coefficients into the formula

... x = ±(√128)/4 = ±√8 = ±2√2 . . . . . simplify the result

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What is the equation of the quadratic function with a vertex at (2,-25) and an x-intercept at (7,0)?

skelet666 [1.2K]

Answer: f(x) = (x + 3)(x – 7)

Step-by-step explanation: Use "standard form" of the function and insert values given: vertex (2,-25) intercept point (7,0)

f(x) = a(x-h)² + k from vertex, h is 2 y is -25 from intercept, x is 7 f(x) is 0

to find a, 0 = a(7-2)² +(-25) 0 = a(7-2)² -25 add 25 to both sides

25 = a(5)² 25 = 25a 25/25 = a 1=a (seems useless but verifies implied "a"coefficient is 1)

f(x) = a(x-h)² + k solve to get the quadratic form

f(x) = (x-2)² -25 (x - 2)² is x² -4x +4

f(x) = x² -4x +4 -25 simplify

f(x) = x² -4x - 21 then factor

f(x) = (x + 3)(x - 7)

8 0

2 years ago

The power 3 Superscript negative 3 equals StartFraction 1 Over 27 EndFraction . Which expression is equivalent to 3 Superscript

SpyIntel [72]

Answer:

Option a: \frac{m^{5} }{162n} is the equivalent expression.

Explanation:

The expression is \frac{(3m^{-2} n)^{-3}}{6mn^{-2} } where m\neq 0, n\neq 0

Let us simplify the expression, to determine which expression is equivalent from the four options.

Multiplying the powers, we get,

\frac{3^{-3}m^{6} n^{-3}}{6mn^{-2} }

Cancelling the like terms, we have,

\frac{3^{-3}m^{5} n^{-1}}{6 }

This equation can also be written as,

\frac{m^{5}}{3^{3}6 n^{1} }

Multiplying the terms in denominator, we have,

\frac{m^{5} }{162n}

Thus, the expression which is equivalent to \frac{(3m^{-2} n)^{-3}}{6mn^{-2} } is \frac{m^{5} }{162n}

Hence, Option a is the correct answer. 23

Step-by-step explanation:

4 0

1 year ago

Read 2 more answers

A lab technician is tested for her consistency by making multiple measurements of the cholesterol level in one blood sample. The

Zanzabum

Step-by-step explanation:

Given precision is a standard deviation of s=1.8, n=12, target precision is a standard deviation of σ=1.2

The test hypothesis is

H_o:σ <=1.2

Ha:σ > 1.2

The test statistic is

chi square = $\frac{(n-1)s^2}{\sigma^2}$

= $\frac{(12-1)1.8^2}{1.2^2}$

=24.75

Given a=0.01, the critical value is chi square(with a=0.01, d_f=n-1=11)= 3.05 (check chi square table)

Since 24.75 > 3.05, we reject H_o.

So, we can conclude that her standard deviation is greater than the target.

5 0

2 years ago

Malachi took cans to the recycling plant and put them into the can-crusher one at a time. after he had already crushed some of t

ioda

2/3
it is 2/3 or not I don't know

3 0

2 years ago

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Triangular numbers can be represented with equilateral triangles formed by dots. The first five triangular numbers are 1, 3, 6,

Alisiya [41]

Direct variation is y = kx where y would be the value of the number and x would be its position in the sequence, k is a constant

so for consecutive values y/x would be a constant k
In this case its not true becuse for example 3/1 = 3 and 6/3 = 2

so there is no direct variation here.

7 0

2 years ago

Read 2 more answers