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3 years ago

What is the factorization of 2x^2 + 7x + 6?

Mathematics

1 answer:

qaws [65]3 years ago

6 0

Answer:

( x + 2)(2x + 3)

Step-by-step explanation:

$2 {x}^{2} + 7x + 6 \\ \\ = 2 {x}^{2} + 4x + 3x + 6 \\ \\ = 2x(x + 2) + 3(x + 2) \\ \\ = ( x + 2)(2x + 3)$

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I can’t figure out, can someone please explain how to get the correct answer?

Karolina [17]

Answer:

a) CD = 9

b) AB = 20

Step-by-step explanation:

In this geometry, all of the right triangles are similar. This means The ratio of short side to long side is the same for all of the triangles.

You are given the short and long sides of ΔADB, and the long side of ΔCDA. You are asked for the short side of ΔCDA, so you can write the proportion ...

CD/AD = AD/BD

CD/12 = 12/16

CD = 12(12/16)

CD = 9

There are a couple of options for finding AD. One you may be familiar with is the Pythagorean theorem.

AB² = AD² +DB²

AB² = 12² +16² = 144 +256 = 400 . . . . fill in known values

AB = √400 = 20 . . . . . take the square root

Alternatively, you can use the same proportional relationship that is described above. Here, we make use of the ratio of the hypotenuse to the long side.

AB/BD = CB/AB

AB² = BD·CB = 16·(16+9) = 16·25 . . . . cross multiply; fill in known values

AB = √(16·25) = 4·5 . . . . . take the square root

AB = 20

_____

<em>Additional comment</em>

This geometry, where the altitude of a right triangle is drawn, has some interesting properties. We have hinted at them above.

You can write three sets of proportions for this geometry: the ratios of short side and long side; the ratios of short side and hypotenuse; and the ratios of long side and hypotenuse. When you look at the way the sides touching the longest hypotenuse relate to that hypotenuse, you see three similar relations:

AC = √(CD·CB)

AD = √(DC·DB)

AB = √(BD·BC) . . . . . . . . the relation used in part (b) above

This "square root of a product" is called the <em>geometric mean</em>. In effect, the length of a side touching the longest hypotenuse is the geometric mean of the two segments of that hypotenuse that it touches.

7 0

2 years ago

Sddddddddddddddddddddddddddddssa

Semenov [28]

Answer:

sdddddddddddddddddddddddddssa

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

How do you do 17x+4?

DerKrebs [107]

Answer:

unclear man, u cant add them together sorry

Step-by-step explanation:

5 0

3 years ago

Calcula la longitud en YARDAS de

tatiyna

Answer:

Las longitudes solicitadas en yardas son:

<u>Trayecto A = 109.361 yardas.</u>
<u>Trayecto B = 20.231785 yardas.</u>

Step-by-step explanation:

Para hacer la conversión de unidades que requieres en el ejercicio, debes saber que:

1 metro = 1.09361 yardas

Con ese factor de conversión tú puedes hacer reglas de tres para calcular las medidas que requieres. En el caso del trayecto A:

Si:

1 metro = 1.09361 yardas
100 metros = X

Entonces:

$x=\frac{100m *1.09361yardas}{1m}$

Cancelamos metros y obtenemos:

x = 100 * 1.09361 yardas
<u>x = 109.361 yardas</u>

En este caso, <u>el trayecto A en yardas corresponde a 109.361 yardas</u>. El mismo procedimiento puede aplicarse para el trayecto B:

Si:

1 metro = 1.09361 yardas
18.50 metros = X

Entonces:

$x = \frac{18.50m*1.09361yardas}{1m}$

Cuando se cancelan los metros se obtiene:

x = 18.50 * 1.09361 yardas
<u>x = 20.231785 yardas</u>

Así, <u>el trayecto B en yardas corresponde a 20.231785 yardas</u>.

4 0

3 years ago

What is sin 45°? O A. 1/2 12 1 OB. NI O C. 1 O D. O E. 1 3 O F. 13 ap.ex

andrew-mc [135]

1/√2

Step-by-step explanation:

Imagine a right-angled triangle, for e.g. Triangle ABC,

Where

B = 90°

Remember your Toa Cah Soh.

sin 45° = opposite / hypotenuse

If theta = 45°

Angles A and C = 45° (Sum of angles in a triangle equal = 180°)

Since theta are the same, we can also deduce that the length AB and BC are the same.

Take for example AB = BC = 1 = opposite

By the Pythagorean theorem,

AB² + BC² = AC²

1² + 1² = AC²

2 = AC²

AC = √2 = hypotenuse

Therefore:

sin 45° = opposite / hypotenuse

sin 45° = 1/√2

6 0

3 years ago