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4 years ago

Use the quadratic formula to find the solutions to the equation. 7- 3x+1=0

Mathematics

2 answers:

Anni [7]4 years ago

7 0

Answer:

Option b) is correct

ie., $x=\frac{3\pm \sqrt{5}}{2}$

Step-by-step explanation:

Given quadratic equation is $x^{2}-3x+1=0$

To find the solutions of given equation:

Solution of quadratic equation $ax^{2}+bx+c=0$

$x=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}$ where a,b, are coefficients of $x^{2}$ and x respectively and c is constant.

From the given quadratic equation a=1, b=-3 and c=1

$x=\frac{-(-3)\pm \sqrt{(-3)^{2}-4(1)(1)}}{2(1)}$

$x=\frac{3\pm \sqrt{9-4}}{2}$

$x=\frac{3\pm \sqrt{5}}{2}$

Therefore Option b) is correct

ie., $x=\frac{3\pm \sqrt{5}}{2}$

irina [24]4 years ago

5 0

Answer:

Step-by-step explanation:

quadratic formula:

x = [-b ± sqrt(b^2 - 4ac)] / 2a

1. find a, b, and c

a = 1

b = -3

c = 1

2. plug values into formula

x = [3 ± sqrt(9-4•1•1)] / 2

3. simplify

x = [3 ± sqrt(5)] / 2

This is B.

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URGENT!!! please help me with these two problems, and solve with statement-reasoning. Thank you!!!

iren [92.7K]

Answer:

See below.

Step-by-step explanation:

By definition the median of the triangle bisects the base of the isosceles triangle.

We need to prove that the 2 triangles formed by the median are congruent.

If the 2 triangles are ABD and ACD where BD is the median and < ABC is the angle from which BD is drawn.

BD = BD ( the common side)

AD = DC ( because BD is the median).

AB = AC ( because ABC is an isosceles triangle).

So Triangles ABD and ACD are congruent by SSS.

Therefore m < ABD = m < CBD, so BD is the bisector of < ABC.

To prove BD is also the altitude:

Triangles ABD and CBD are congruent as we have just proven. Therefore the

of measure of the base angle ABD = m < CBD . Also they are adjacent angles ( on the same line) so they add up to 180.

Therefore angles ABD and CBD are both right angles and BD is the altitude of triangle ABC.

8 0

4 years ago

The mean weight of an adult is 69 kilograms with a variance of 121. If 31 adults are randomly selected, what is the probability

amid [387]

Answer:

0.2236 = 22.36% probability that the sample mean would be greater than 70.5 kilograms.

Step-by-step explanation:

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

Also, important to remember that the standard deviation is the square root of the variance.

Normal probability distribution:

Problems of normally distributed samples are 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 $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$

In this problem, we have that:

$\mu = 69, \sigma = \sqrt{121} = 11, n = 31, s = \frac{11}{\sqrt{31}} = 1.97565$

What is the probability that the sample mean would be greater than 70.5 kilograms?

This is 1 subtracted by the pvalue of Z when X = 70.5. So

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

By the Central limit theorem

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

$Z = \frac{70.5 - 69}{1.97565}$

$Z = 0.76$

$Z = 0.76$ has a pvalue of 0.7764

1 - 0.7764 = 0.2236

0.2236 = 22.36% probability that the sample mean would be greater than 70.5 kilograms.

8 0

3 years ago

Answer the following questions with the chart below.

MariettaO [177]

Answer:

Q1)$-95.75

Q2)$140.20

Q3)D

Q4)D

6 0

2 years ago

Read 2 more answers

Special Triangles

natulia [17]

Since this is a 45-45-90 triangle, n = 9 and m = x

6 0

4 years ago

Suppose brine containing 0.2 kg of salt per liter runs into a tank initially filled with 500 L of water containing 5 kg of salt.

Oliga [24]

Answer:

(a) 0.288 kg/liter

(b) 0.061408 kg/liter

Step-by-step explanation:

(a) The mass of salt entering the tank per minute, x = 0.2 kg/L × 5 L/minute = 1 kg/minute

The mass of salt exiting the tank per minute = 5 × (5 + x)/500

The increase per minute, Δ/dt, in the mass of salt in the tank is given as follows;

Δ/dt = x - 5 × (5 + x)/500

The increase, in mass, Δ, after an increase in time, dt, is therefore;

Δ = (x - 5 × (5 + x)/500)·dt

Integrating with a graphing calculator, with limits 0, 10, gives;

Δ = (99·x - 5)/10

Substituting x = 1 gives

(99 × 1 - 5)/10 = 9.4 kg

The concentration of the salt and water in the tank after 10 minutes = (Initial mass of salt in the tank + Increase in the mass of the salt in the tank)/(Volume of the tank)

∴ The concentration of the salt and water in the tank after 10 minutes = (5 + 9.4)/500 = (14.4)/500 = 0.288

The concentration of the salt and water in the tank after 10 minutes = 0.288 kg/liter

(b) With the added leak, we now have;

Δ/dt = x - 6 × (14.4 + x)/500

Δ = x - 6 × (14.4 + x)/500·dt

Integrating with a graphing calculator, with limits 0, 20, gives;

Δ = 19.76·x -3.456 = 16.304

Where x = 1

The increase in mass after an increase in = 16.304 kg

The total mass = 16.304 + 14.4 = 30.704 kg

The concentration of the salt in the tank then becomes;

Concentration = 30.704/500 = 0.061408 kg/liter.

6 0

3 years ago