(ab+bc+ca)³=abc(a+b+c)³

Determine the value of a, b, and c for the quadratic equation: 4x2- 8x = 3

Rufina [12.5K]

Answer:

B. a = 4, b = -8, c = -3

Step-by-step explanation:

The quadratic equation given is:

$4x^2- 8x = 3$

The general form of a quadratic equation is given as:

$ax^2 + bx +c = 0$

Let us put the given equation in this form and then compare with the general form of the quadratic equation.

$4x^2- 8x = 3\\\\4x^2 - 8x - 3 = 0$

Therefore, by comparing:

a = 4

b = -8

c = -3

The correct option is B

4 0

3 years ago

Find the dimensions of an American football field. The length is 200 ft more than the width, and the perimeter is 1,040 ft. Find

natka813 [3]

Answer:

The width of the football field is 160 feet.

The length of the football field is 360 feet.

Step-by-step explanation:

Let w represent width of the football field.

We have been given that the length is 200 ft more than the width, so the length of the field would be $w+200$ .

We are also told that the perimeter is 1,040 ft. We know that football field is in form of rectangle, so perimeter of field would be 1 times the sum of length and width. We can represent this information in an equation as:

$2(w+w+200)=1040$

Let us solve for w.

$2(2w+200)=1040$

$4w+400=1040$

$4w+400-400=1040-400$

$4w=640$

$\frac{4w}{4}=\frac{640}{4}$

$w=160$

Therefore, the width of the football field is 160 feet.

Upon substituting $w=160$ in expression $w+200$ , we will get length of field as:

$w+200\Rightarrow 160+200=360$

Therefore, the length of the football field is 360 feet.

7 0

3 years ago

Complete the statement. Round to the nearest hundredth if necessary. 48 ft =_____yd

TiliK225 [7]

Answer: 16

Step-by-step explanation:

there are 3 feet in one yard so divided 48 by 3 and you get 16

8 0

3 years ago

Read 2 more answers

Can someone help 12 points on the line

ANTONII [103]

Answer:

x=6

Step-by-step explanation:

We can write this as a ratio

x 9

---- = --------

10 15

Using cross products

15x = 10*9

15x = 90

Divide by 15

15x/15 = 90/15

x =6

7 0

3 years ago

Can someone help me with this please

Bingel [31]

Answer:

A.1: ∠BAC ≅ ∠BDC ≅ ∠EDF, ∠ACD ≅ ∠ABD ≅ ∠BDE ≅ ∠CDF

A.2: ∠1 ≅ ∠4, ∠2 ≅ ∠3 ≅ ∠5 ≅ ∠6

A.3: ∠2 ≅ ∠3

B.1: ∠ACD ≅ ∠CAB, ∠CDA ≅ ∠ABC, ∠DAC ≅ ∠BCA

B.2: ∠1 ≅ ∠3 ≅ ∠5, ∠2 ≅ ∠4 ≅ ∠6

see "additional comment" regarding listing pairs

Step-by-step explanation:

There are a number of ways angles can be identified as congruent. In each case, the converse of the proposition is also true.

opposite angles of a parallelogram are congruent
corresponding angles where a transversal crosses parallel lines are congruent
alternate interior angles where a transversal crosses parallel lines are congruent
vertical angles are congruent
any two angles with the same measure are congruent

In these exercises, pairs of angles need to be examined to see which of these relations may apply.

__

ABCD is a parallelogram, so the congruent angles are opposite angles and any that are vertical or corresponding:

∠BAC ≅ ∠BDC ≅ ∠EDF ≅ 110° (3 pairs)

∠ACD ≅ ∠ABD ≅ ∠BDE ≅ ∠CDF ≅ 70° (6 pairs)

<u>Center</u>

∠1 ≅ ∠4 ≅ 66° (1 pair) . . . . vertical angles

∠2 ≅ ∠3 ≅ ∠5 ≅ ∠6 ≅ 57° (6 pairs) . . . . marked with the same measure, and their vertical angles

<u>Right</u>

Assuming that lines appearing to go in the same direction actually do go in the same direction, the only pair of congruent angles in the figure is ...

∠2 ≅ ∠3

__

Corresponding angles in congruent triangles are congruent. Here, the congruent triangles are ΔACD ≅ ΔCAB. So, the pairs of congruent angles are ...

∠ACD ≅ ∠CAB (30°)

∠CDA ≅ ∠ABC (90°)

∠DAC ≅ ∠BCA (60°)

<u>Right</u>

The corresponding angles and any vertical angles are congruent. This means all the odd-numbered angles in the figure are congruent, and all the even-numbered angles in the figure are congruent. The marked 72° angles show the "horizontal" segments are parallel by the converse of the corresponding angles theorem.

∠1 ≅ ∠3 ≅ ∠5 (72°) (3 pairs)

∠2 ≅ ∠4 ≅ ∠6 (108°) (3 pairs)

_____

<em>Additional comment</em>

The question asks you to list pairs of congruent angles. When 3 things are congruent, they can be arranged in 3 pairs:

a ≅ b ≅ c ⇒ (a≅b), (a≅c), (b≅c)

Similarly, when 4 things are congruent, they can be arranged in 6 pairs:

a ≅ b ≅ c ≅ d ⇒ (a≅b), (a≅c), (a≅d), (b≅c), (b≅d), (c≅d)

In the above, we have elected not to list all of the pairs, but to list the set of congruences from which pairs can be chosen.

6 0

3 years ago

(ab+bc+ca)³=abc(a+b+c)³​

(ab+bc+ca)³=abc(a+b+c)³