All categories

3 years ago

When factorising a quadratic trinomial of the form ax^2 + bx + c, we need to find two numbers which ???? (see image for options)

Mathematics

1 answer:

kupik [55]3 years ago

3 0

Answer: Choice E

multiply to give a*c and add to get b

===========================================

This is known as the AC factoring method based on how you multiply the first and last coefficients (a and c) and use that product to figure out which factors add to the middle coefficient.

---------

An example:

6x^2 + 35x + 50

We have a = 6, b = 35, c = 50

Multiply a and c and we get: a*c = 6*50 = 300

We need to find factors of 300 that pair up and add to 35

Through trial and error you should find,

15 * 20 = 300

15 + 20 = 35

The two numbers are therefore 15 and 20.

So we break 35x into 15x+20x and use the factor by grouping method

6x^2 + 35x + 50

6x^2 + 15x + 20x + 50

(6x^2 + 15x) + (20x + 50)

3x(2x + 5) + 10(2x + 5)

(3x + 10)(2x + 5)

We see that 6x^2 + 35x + 50 factors to (3x + 10)(2x + 5)

Use the FOIL method or the box method or distribution to help see that (3x + 10)(2x + 5) expands back to 6x^2 + 35x + 50.

You might be interested in

Complete the table so that the cost per banana remains the same.

Aneli [31]

Step-by-step explanation:

No. of banana Cost Unit price

4 2 0.50

6 3 0.50

7 3.5 0.50

20 10 0.50

33 16.50 0.50

Cost = No of banana x unit price

Cost = 4 x 0.50 = 2

Cost = 6 x 0.50 = 3

Cost = 7 x 0.50 = 3.50

Cost = 20 x 0.50 = 10

No of banana = Cost / Unit price

No of banana = 10 / 0.50 = 20

No of banana = 16.50 / 0.50 = 33

3 0

3 years ago

A person on a runway sees a plane approaching. The angle of elevation from the runway to the plane is 11.1° . The altitude of th

Gnoma [55]

Answer:

The horizontal distance from the plane to the person on the runway is 20408.16 ft.

Step-by-step explanation:

Consider the figure below,

Where AB represent altitude of the plane is 4000 ft above the ground , C represents the runner. The angle of elevation from the runway to the plane is 11.1°

BC is the horizontal distance from the plane to the person on the runway.

We have to find distance BC,

Using trigonometric ratio,

$\tan\theta=\frac{Perpendicular}{base}$

Here, $\theta=11.1^{\circ}$ ,Perpendicular AB = 4000

$\tan\theta=\frac{AB}{BC}$

$\tan 11.1^{\circ} =\frac{4000}{BC}$

Solving for BC, we get,

$BC=\frac{4000}{\tan 11.1^{\circ} }$

$BC=\frac{4000}{0.196}$ (approx)

$BC=20408.16$ (approx)

Thus, the horizontal distance from the plane to the person on the runway is 20408.16 ft

8 0

3 years ago

ALGEBRA 2- If f(x)= √x-3 , which inequality can be used to find the domain of f(x)?

Fed [463]

B, because you can't get the square root of a negative number

8 0

3 years ago

Read 2 more answers

Show all work please!!!!!!

sergij07 [2.7K]

The midpoint formula is:
(point1 + point2)/2

1) (-2 + 12)/2 = 5

2) (-1 +5)/2 = 2
    (0+2)/2 = 1
     (2,1)

3) Sqrt of (x2-x1)^2 + (y2 - y1)^2
     sqrt of (7 -1)^2 + (-7 - 1)^2
     sqrt of (6)^2 + (-8)^2
     sqrt of 36 + 64
     sqrt of 100
     10

Hope this helps!

7 0

3 years ago

A premature infant is gaining 2.5 ounces a day. At that rate, how many days will it take for him to gain 8 ounces

Ann [662]

Answer:

3.2 days

Step-by-step explanation:

All you have to do is divide 8 by 2.5

8 ÷ 2.5 = 3.2

5 0

3 years ago