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2 years ago

Which of the following is the complete factorization of 10x - 3 - 3x 2?

1 answer:

5 0

-3x^2+10x-3

This is of the form ax^2+bx+c. We need to find two values, j and k, such that:

jk=ac=9 and j+k=b=10, so j and k must be 1 and 9.

Now replace bx with jx and kx in the original equation...

-3x^2+x+9x-3 now factor 1st and 2nd pair of terms

-x(3x-1)+3(3x-1)

(-x+3)(3x-1) or equivalently...

-(x-3)(3x-1) or as they put it:

-(3x-1)(x-3)

You might be interested in

Find the sum of natural number from 1 to 30

Ierofanga [76]

Answer:

1. sum of term = 465

2. nth term of the AP = 30n - 10

Step-by-step explanation:

1. The sum of all natural number from 1 to 30 can be computed as follows. The first term a = 1 and the common difference d = 1 . Therefore

sum of term = n/2(a + l)

where

a = 1

l = last term = 30

n = number of term

sum of term = 30/2(1 + 30)

sum of term = 15(31)

sum of term = 465

2.The nth term of the sequence can be gotten below. The sequence is 20, 50, 80 ......

The first term which is a is equals to 20. The common difference is 50 - 20 or 80 - 50 = 30. Therefore;

a = 20

d = 30

nth term of an AP = a + (n - 1)d

nth term of an AP = 20 + (n - 1)30

nth term of an AP = 20 + 30n - 30

nth term of the AP = 30n - 10

The nth term formula can be used to find the next term progressively. where n = number of term

The sequence will be 20, 50, 80, 110, 140, 170, 200..............

6 0

3 years ago

A pet shop has rabbits and gerbils for sale. They have 20 animals altogether. They sell two rabbits. Then one of the gerbils has

Triss [41]

20 animals - 2 rabbits = 18 animals
18 animals + 2 gerbils = 20 animals.
20 animals / 4 = 5 animals
There are 5 rabbits and 15 gerbils now.
At the start 2 rabbits were sold so add that on.
5 + 2 = 7
There were 7 rabbits.
There weren't any twin gerbils then.
15 - 2 = 13.
There were 13 gerbils and 7 rabbits to start with.

Hope This Helps You!
Good Luck Studying :)

4 0

2 years ago

Use the confidence level and sample data to find a confidence interval for estimating the population mu. Round your answer to th

inysia [295]

Answer:

c. 9.5 lb < mu < 11.1 lb.

Step-by-step explanation:

Confidence interval can be stated as M±ME where

M is the sample mean (10.3)
ME is the margin of error

margin of error (ME) around the mean can be calculated using the formula

ME= $\frac{z*s}{\sqrt{N} }$ where

z is the corresponding statistic in 95% confidence level (1.96)

s is the standard deviation of the sample (2.4)

N is the sample size (37)

Putting thesenumbers in the formula we get:

ME= $\frac{1.96*2.4}{\sqrt{37} }$ ≈ 0.7733 ≈ 0.8

Then the 95% confidence interval would be 10.3 ± 0.8

7 0

3 years ago

which one in the following is the correct option for fill in the blank :conduction, induction, electromagnetism>?the process

lana [24]

The answer is conduction

7 0

2 years ago

Solve each triangle. Round your answers to the nearest tenth.<br>show work If possible

kvasek [131]

<h2>Answer:</h2>

∠ABC = 76°

BC = 20.1

CA = 28.0

<h2>Step-by-step explanation:</h2>

Solving the triangle means finding all unknown angles and sides of the triangle.

(i) Two of the angles (∠BCA = 60° and ∠CAB = 44°) are given. To find the third angle (∠ABC), use one of the theorems stating <em>that the sum of angles of a triangle is equal to 180°.</em>

Therefore, the sum of angles of the triangle ABC is 180°. i.e

∠ABC + ∠BCA + ∠CAB = 180°

=> ∠ABC + 60° + 44° = 180°

=> ∠ABC + 104° = 180°

=> ∠ABC = 180° - 104°

=> ∠ABC = 76°

(ii) One side (BA) of the triangle is given. To get the other sides, we use the sine rule as follows;

=> $\frac{sin60}{25} = \frac{sin44}{BC} = \frac{sin76}{CA}$

=> $\frac{sinBCA}{BA} = \frac{sinCAB}{BC} = \frac{sinABC}{CA}$

<em>Substitute the necessary values</em>

$\frac{sin60}{25} = \frac{sin44}{BC} = \frac{sin76}{CA}$ ---------------------(ii)

(a) To get side BC, use the first two terms of equation (ii)

$\frac{sin60}{25} = \frac{sin44}{BC}$

<em>Cross multiply</em>

BC x sin 60 = 25 x sin 44

BC x 0.8660 = 25 x 0.6947

0.8660 x BC = 17.3675

BC = $\frac{17.3675}{0.8660}$

BC = 20.05

=> BC = 20.1 to the nearest tenth

(b) To get CA, use any two terms of equation (ii). Using the first and third terms, we have;

$\frac{sin60}{25} = \frac{sin76}{CA}$

<em>Cross multiply</em>

CA x sin 60 = 25 x sin 76

CA x 0.8660 = 25 x 0.9703

0.8660 x CA = 24.2575

CA = $\frac{24.2575}{0.8660}$

CA = 28.01

=> CA = 28.0 to the nearest tenth

5 0

3 years ago