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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A gymnast dismounts the uneven parallel bars. Her height, h, depends on the time, t, that she is in the air h = −162 + 24t + 16.

dimulka [17.4K]

That is when h=0
so assuming yo meant
h(t)=-16t²+24t+16
solve for t such that h(t)=0
because when height=0, the gymnast hits the ground

so
0=-16t²+24t+16
using math (imma complete the square
0=-16(t²-3/2t)+16
0=-16(t²-3/2t+9/16-9/16)+16
0=-16((t-3/4)²-9/16)+16
0=-16(t-3/4)²+9+16
0=-16(t-3/4)²+25
-25=-16(t-3/4)²
25/16=(t-3/4)²
sqrt both sides
+/-5/4=t-3/4
3/4+/-5/4=t
if we do plus (because minus would give us negative height)
8/4=t
2=t
it takes 2 seconds

5 0

1 year ago

Find the average value of the function f(x, y, z) = 5x2z 5y2z over the region enclosed by the paraboloid z = 4 − x2 − y2 and the

S_A_V [24]

The paraboloid meets the x-y plane when x²+y²=9. A circle of radius 3, centre origin.

Use cylindrical coordinates (r,θ,z) so paraboloid becomes z = 9−r² and f = 5r²z. 

If F is the mean of f over the region R then F ∫ (R)dV = ∫ (R)fdV 

∫ (R)dV = ∫∫∫ [θ=0,2π, r=0,3, z=0,9−r²] rdrdθdz 

= ∫∫ [θ=0,2π, r=0,3] r(9−r²)drdθ = ∫ [θ=0,2π] { (9/2)3² − (1/4)3⁴} dθ = 81π/2 

∫ (R)fdV = ∫∫∫ [θ=0,2π, r=0,3, z=0,9−r²] 5r²z.rdrdθdz 

= 5∫∫ [θ=0,2π, r=0,3] ½r³{ (9−r²)² − 0 } drdθ 

= (5/2)∫∫ [θ=0,2π, r=0,3] { 81r³ − 18r⁵ + r⁷} drdθ 

= (5/2)∫ [θ=0,2π] { (81/4)3⁴− (3)3⁶+ (1/8)3⁸} dθ = 10935π/8 

∴ F = 10935π/8 ÷ 81π/2 = 135/4

3 0

1 year ago

An investment of $500 increases at a rate of 12.5% per year. What is the value of the investment after 30 years? Round to the ne

NemiM [27]

Here's the equation:
0.125(500) + 500
But because it is 30 years:
30(0.125(500)) + 500
3.75(500) + 500
We can make it simpler:
4.75(500)
2375
You will have $2375

7 0

2 years ago

Shawna is making smoothies. The recipe calls for 2 parts yogurt to 3 parts blueberries. Shawna wants to make 10 cups of smoothie

vesna_86 [32]

20 cups yogurt and 30 cups blueberry

7 0

2 years ago

In a completely randomized experimental design involving three assembly methods, 30 employees were randomly selected and 10 were

AnnZ [28]

Answer:

$F = \frac{MSR}{MSE} =\frac{45.89}{6.27}=7.32$

So then the best option is:

a. 7.32

Step-by-step explanation:

Previous concepts

Analysis of variance (ANOVA) "is used to analyze the differences among group means in a sample".

The sum of squares "is the sum of the square of variation, where variation is defined as the spread between each individual value and the grand mean"

If we assume that we have $3$ groups and on each group from $j=1,\dots,10$ we have $10$ individuals on each group we can define the following formulas of variation: