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2 years ago

Use the quadratic formula to solve the equation -4x^2-3x+2=0

Mathematics

2 answers:

Karolina [17]2 years ago

7 0

The quadratic formula is hard to type on this
3 (+ , -) (sqroot of 41)
---------------------------
8

Stolb23 [73]2 years ago

5 0

Answer:

The solution to the quadratic equations are:

$x=-\frac{3+\sqrt{41}}{8},\:x=\frac{\sqrt{41}-3}{8}$

Step-by-step explanation:

Consider the provided quadratic equation.

$-4x^2-3x+2=0$

$\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}\\x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

Substitute a=-4, b=-3 and c=2 in above formula.

$x_{1,\:2}=\frac{-\left(-3\right)\pm \sqrt{\left(-3\right)^2-4\left(-4\right)2}}{2\left(-4\right)}$

$x_{1,2}=\frac{3\pm\sqrt{9+32}}{-8}$

$x_{1,2}=-\frac{3\pm\sqrt{41}}{8}$

Hence, the solution to the quadratic equations are:

$x=-\frac{3+\sqrt{41}}{8},\:x=\frac{\sqrt{41}-3}{8}$

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Suppose that a merchant buys a patio set from the wholesaler for $260

Alina [70]

Answer:

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Step-by-step explanation:

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2 years ago

The mean life of a television set is 119119 months with a standard deviation of 1414 months. If a sample of 7474 televisions is

Pepsi [2]

Answer:

0.5034 = 50.34% probability that the sample mean would differ from the true mean by less than 1.1 months

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central limit theorem:

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sample means with size n of at least 30 can be approximated to a normal distribution with mean

In this problem, we have that:

$\mu = 119, \sigma = 14, n = 74, s = \frac{14}{\sqrt{74}} = 1.6275$

What is the probability that the sample mean would differ from the true mean by less than 1.11 months?

This is the pvalue of Z when X = 119 + 1.1 = 120.1 subtracted by the pvalue of Z when X = 119 - 1.1 = 117.9. So

X = 120.1

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$

$Z = \frac{120.1 - 119}{1.6275}$

$Z = 0.68$

$Z = 0.68$ has a pvalue of 0.7517

X = 117.9

$Z = \frac{X - \mu}{s}$

$Z = \frac{117.9 - 119}{1.6275}$

$Z = -0.68$

$Z = -0.68$ has a pvalue of 0.2483

0.7517 - 0.2483 = 0.5034

0.5034 = 50.34% probability that the sample mean would differ from the true mean by less than 1.1 months

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2 years ago

You borrow $2000 from the bank at 1% annual interest compounded monthly. The monthly payment is $100. What is the balance after

Blizzard [7]

Answer:

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Step-by-step explanation:

If you start with the balance being $2000, the monthly payment is $100 with the percentage rate being 1%. You would way 0.84 per month and if you multiply that by three months, you get $2.52.

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2 years ago

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Gala2k [10]

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2 years ago

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vesna_86 [32]

Answer:

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Step-by-step explanation: