All categories

3 years ago

Find the roots. 3x2 - 5x+ 2 =0

Mathematics

1 answer:

tigry1 [53]3 years ago

5 0

Answer:

see explanation

Step-by-step explanation:

Given

3x² - 5x + 2 = 0

Consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term

product = 3 × 2 = 6 and sum = - 5

The factors are - 3 and - 2

Use these factors to split the x- term

3x² - 3x - 2x + 2 = 0 ( factor the first/second and third/fourth terms )

3x(x - 1) - 2(x - 1) = 0 ← factor out (x - 1) from each term

(x - 1)(3x - 2) = 0

Equate each factor to zero and solve for x

x - 1 = 0 ⇒ x = 1

3x - 2 = 0 ⇒ 3x = 2 ⇒ x = $\frac{2}{3}$

Roots are x = 1, x = $\frac{2}{3}$

You might be interested in

Joe multiplies a number by 4, adds 1, and then divides by 3, getting a result of 7. sue divides the same original number by 3, a

Sidana [21]

Let's translate this from words to equations: So (4x+1)/3=7 is our first equation. Multiply by 3, subtract 1, then divide by 4 to get x. Notice it is the exact opposite of what Joe did to get back to where he started. Once you get x, just follow the instructions, so divide by 3, add 1 and multiply by 4. You will end up with a fraction since the original number is not evenly divisible by 3.

8 0

3 years ago

Deepak is a landscaper who charges $30 for each job he does plus an additional $15 for each hour he works. He only accepts jobs

BartSMP [9]

Answer:

$30+15x\geq 90$

Step-by-step explanation:

Deepak charges for each Job = $30

An additional charges for working each hour = $15

Let x be the number of hours he worked for each job.

So,additional charges for working x hours = 15 x

So,he earns in total at each job = $30+15x$

We are also given that He only accepts jobs if he will earn at least $90 the job.

This means he must earn $90 or more than that .

So, the inequality becomes:

$30+15x\geq 90$

Hence an inequality to determine x, the number of hours he must work during each job in order to accomplish this is $30+15x\geq 90$

4 0

3 years ago

Read 2 more answers

An automobile manufacturer claims that its car has a 28.0 miles/gallon (MPG) rating. An independent testing firm has been contra

d1i1m1o1n [39]

Answer:

The calculated value z = 1.3145 < 2.326 at 0.02 level of significance

The null hypothesis is accepted

Hence An automobile manufacturer claims that its car has a 28.0 miles/gallon (MPG) rating.

Step-by-step explanation:

Step(i):-

An automobile manufacturer claims that its car has a 28.0 miles/gallon (MPG) rating.

The mean of the Population 'μ' = 28.0miles/gallon

Given data after testing 270 cars, they found a mean MPG of 27.8. Assume the variance is known to be 6.25.

The sample size 'n' = 270

Mean of the sample 'x⁻' = 27.8

Given Population variance 'σ² = 6.25

The standard deviation of Population 'σ' = √6.25 = 2.5

Step(ii):-

Null hypothesis :H₀: 'μ' = 28.

Alternative hypothesis :H₁: 'μ' ≠28.

The test statistic

$Z = \frac{x^{-}-mean }{\frac{S.D}{\sqrt{n} } }$

$Z = \frac{27.8-28 }{\frac{2.5}{\sqrt{270} } } = \frac{-0.2}{0.15214}$

Z = -1.3145

|Z| = |-1.3145|= 1.3145

Step(iii):-

The tabulated value of z-score at 0.02 level of significance = 2.326

The calculated value z = 1.3145 < 2.326 at a t 0.02 level of significance

The null hypothesis is accepted

Hence An automobile manufacturer claims that its car has a 28.0 miles/gallon (MPG) rating.

8 0

3 years ago

The probability that a farmer is in debt is 0.700. The probability that a farmer is in debt and also lives in the Midwest is 0.2

bogdanovich [222]

Answer:

0.4

Step-by-step explanation:

Given that:

P(debt) = P(D) = Probability of being in debt = 0.7

P(debt n Midwest) = P(Dn M) = probability of being in debt and lives in Midwest = 0.280

The probability that a randomly selected farmer lives in the Midwest given that he is in debt is?

P(M | D) = p(D n M) / p(D)

P(M | D) = 0.280 / 0.7

P(M | D) = 0.4

5 0

3 years ago

A data set contains three points, and two of the residuals are -12 and 24. what is the third residual?

barxatty [35]

We know that
the sum of the residuals must be equal to zero

let
x------> the third residual

-12+24+x=0
12+x=0-----> add -12 both sides
x=-12

the answer is
 the third residual is -12

5 0

3 years ago

Read 2 more answers