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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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Bonita has a standard of 2 hours of labor per unit, at $12 per hour. In producing 2600 units, Bonita used 5050 hours of labor at

Eduardwww [97]

Answer:

1800

Step-by-step explanation:

Labor quantity variance= Actual quantity ×standard price - standard quantity ×standard price

Standard quantity=2×2600=5200

Labor quantity variance

5050×12-5200×12=1800

3 0

2 years ago

Your utility company charges 13 cents per kilowatt-hour of electricity. What is the daily cost of keeping lit a 75 watt light bu

Tresset [83]

we know that

$1 Kw=1000 w$

The company charges $13$ cents per kilowatt-hour of electricity

$13 cents=0.13 dollars\\\\ 75w=\frac{75}{1000} kw\\\\ 15w=\frac{15}{1000} kw$

Step $1$

Find the cost for the light bulb

a) in one day

$\frac{75}{1000} *12=0.9\ kw\ hour$

$Cost=0.13*0.9$

Cost=$ $0.117$

b) In a year

$\frac{75}{1000} *12=0.9\ kw\ hour$

$0.9*365=328.5\ kw\ hour$

$Cost=0.13*328.5$

Cost=$ $42.71$

Step $2$

Find the cost for the led bulb

a) in one day

$\frac{15}{1000} *12=0.18\ kw\ hour$

$Cost=0.13*0.18$

Cost=$ $0.0234$

b) In a year

$\frac{15}{1000} *12=0.18\ kw\ hour$

$0.18*365=65.7\ kw\ hour$

$Cost=0.13*65.7$

Cost=$ $8.54$

Step $3$

Find the difference in cost

$Save=42.71-8.54\\ Save=34.17 dollars$

therefore

the answer is

$34.17 dollars$

3 0

2 years ago

Read 2 more answers

The volume of a fish tank is given by the function V(x)=(x+7)(x-4)(x+3). Write a function describing a fish tank that has the sa

Aleksandr [31]

Answer:

V(x)=(x+9) * (x-4) * (x+6)

Step-by-step explanation:

A fish tank is normally in the shape of a rectangular prism. The volume of a rectangular prism can be calculated using the following formula

V = w * h * l

where w represents the width, h represents the heigh, l represents the length, and V represents the volume of the rectangular prism/fish tank. Therefore, we can use the function provided in the question and simply add 3 units to the length and 2 units to the width in order for it to work for our new fish tank.

V(x)=(x+9) * (x-4) * (x+6)

3 0

2 years ago

According to a study in a medical journal, 202 of a sample of 5,990 middle-aged men had developed diabetes. It also found that m

tekilochka [14]

Answer:

0.0588 = 5.88% probability that a middle-aged man with diabetes is very active

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

In which

P(B|A) is the probability of event B happening, given that A happened.

$P(A \cap B)$ is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Has diabetes.

Event B: Is very active.

Probability of having diabetes:

To find this probability, we take in consideration that:

It also found that men who were very active (burning about 3,500 calories daily) were a fourth as likely to develop diabetes compared with men who were sedentary. Assume that one-fifth of all middle-aged men are very active, and the rest are classified as sedentary.

So the probability of developing diabetes is:

x of 4/5 = x of 0.8(not active)

x/4 = 0.25x of 1/5 = 0.2(very active). So

$P(A) = 0.8x + 0.25*0.2x = 0.85x$

Probability of developing diabetes while being very active:

0.25x of 0.2. So

$P(A \cap B) = 0.25x*0.2 = 0.05x$

What is the probability that a middle-aged man with diabetes is very active?

$P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.05x}{0.85x} = \frac{0.05}{0.85} = 0.0588$

0.0588 = 5.88% probability that a middle-aged man with diabetes is very active

4 0

2 years ago

According to the Rational Root Theorem, the following are potential fox) 2x2 +2x 24.roots of -4, -3, 2, 3, 4Which are actual roo

aksik [14]

Correct Answer: First Option

Explanation:

There are two ways to find the actual roots:

a) Either solve the given quadratic equation to find the actual roots

b) Or substitute the value of Possible Rational Roots one by one to find out which satisfies the given equation.

Method a is more convenient and less time consuming, so I'll be solving the given equation by factorization to find its actual roots. To find the actual roots set the given equation equal to zero and solve for x as given below:

$2x^{2} +2x-24=0\\ \\ 2(x^{2} +x-12)=0\\ \\ x^{2} +x-12=0\\ \\ x^{2} +4x-3x-12=0\\ \\ x(x+4)-3(x+4)=0\\ \\ (x-3)(x+4)=0\\ \\ x-3=0, x=3\\ \\ or\\\\x+4=0, x=-4$

This means the actual roots of the given equation are 3 and -4. So first option gives the correct answer.

7 0

2 years ago

Read 2 more answers