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3 years ago

Two sets of quadratic expressions are shown below in various forms:

Mathematics

2 answers:

Elan Coil [88]3 years ago

6 0

Solution:

1. $x^2 + 3 x +2= x^2 + 2 x + x + 2= x(x+2)+1(x+2)=(x+1)(x+2)\\\\ x^2 + 3 x + 2=(x+\frac{3}{2})^2-(\frac{3}{2})^2+2=(x+\frac{3}{2})^2-2.25+2=(x+\frac{3}{2})^2-0.25$

2. $x^2 + 5 x + 6 =x^2+ 3 x + 2 x+6=x(x+3)+2(x+3)= (x + 2)(x + 3)\\\\ x^2 + 5 x + 6 =(x+\frac{5}{2})^2-(\frac{5}{2})^2+6=(x+\frac{5}{2})^2-6.25+6=(x+\frac{5}{2})^2-0.25$

Line 1: x² + 3 x + 2= (x + 1)(x + 2)= (x + 1.5)² − 0.25 contains three equivalent expressions.

Ray Of Light [21]3 years ago

3 0

Line one is equivalent

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Miguel volunteers at a library. He needs to arrange 576 books on shelves for a book sale. There are 16 empty shelves. Miguel put

Sergeeva-Olga [200]

Answer:

The equal number of books that is arranged on 16 empty shelves is 36 .

Step-by-step explanation:

Given as :

The total number of books Miguel need to arrange = 576

The total number of empty shelves = 16

Let The total number of books arrange on each shelves = x

So , According to question

The total number of books Miguel need to arrange = The total number of empty shelves × The total number of books arrange on each shelves

I.e 576 = 16 × x

Or, x = $\frac{576}{16}$

∴ x = 36

Hence The equal number of books that is arranged on 16 empty shelves is 36 . Answer

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3 years ago

At 5.45p.M .,lixin,khairul and Devil are at the starting point of a 1-km circular path. Lixin Takes 18 minutes to walk one round

sweet [91]

Answer:

$Meeting\ Time = 6:03\ pm$

Step-by-step explanation:

Given

$Start\ Time= 5:45pm$

$Lixin = 18\ min/round$

$Khairul = 360\ seconds/round$

$Devi = 4minutes/2\ rounds$

Required

Determine their next meeting time

First, we need to get their unit rate in minutes per round

$Lixin = 18\ min/round$

$Khairul = 360\ seconds/round$

Convert 360 seconds to minutes

$Khairul = \frac{360}{60} min/round$

$Khairul = 6 min/round$

$Devi = 4minutes/2\ rounds$

Divide by 2/2

$Devi = 2mins/round$

So, we have:

$Lixin = 18\ min/round$

$Khairul = 6 min/round$

$Devi = 2mins/round$

Next, is to determine the LCM of 18, 6 and 2

$18=2 * 3 * 3$

$6 = 2 * 3$

$3 = 3$

Their LCM is:

$LCM = 2 * 3 * 3$

$LCM = 18$

This means that they will meet 18 minutes after their initial time of departure.

So:

$Meeting\ Time = 5:45\ pm + 18\ minutes$

$Meeting\ Time = 6:03\ pm$

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3 years ago

What is the value of the expression below? 32^3/5 O A. 6/5 B. 6 O c. 96/5 O D. 8

Hoochie [10]

Answer:

D. 8

Step-by-step explanation:

32^(3/5) is the same as $\sqrt[5]{32}$ ^3.

$\sqrt[5]{32}$ = 2 because 2^5=32

2^3 = 8

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2 years ago

Read 2 more answers

Trigonometry

Alchen [17]

The area of the triangle PQR is 17.6 square units.

Explanation:

Given that the sides of the triangle are PQ = 12 and PR = 3 and $m\angle P = 78^{\circ}$

We need to determine the area of the triangle PQR

Area of the triangle:

The area of the triangle can be determined using the formula,

$\text {Area}=\frac{1}{2} qr \sin P$

Substituting the values, we get,

$\text {Area}=\frac{1}{2}(12)(3) \sin 78$

Simplifying, we have,

$\text {Area}=\frac{1}{2}(36)(0.98)$

Multiplying the terms, we have,

$\text {Area}=\frac{35.28}{2}$

Dividing, we get,

$\text {Area}=17.64$

Rounding off to the nearest tenth, we have,

$Area=17.6$

Thus, the area of the triangle PQR is 17.6 square units.

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3 years ago

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Consider the polynomial function g(x)=x³-3x²+6x+8. Divide g by x+1.

irina [24]

Answer:

Quotient ( x² -4x +10)

Reminder -2

Step-by-step explanation:

We have to consider the polynomial function g(x) = x³ - 3x² + 6x + 8

Now, we have to divide g(x) by (x+1)

Let us arrange the terms of g(x) to get (x+1) as common.

x³ - 3x² + 6x + 8

= x³ +x² -4x² -4x +10x +10 -2

= x² (x +1) -4x (x +1) +10 (x +1) -2

= (x +1)( x² -4x +10) -2

Hence, if we divide g(x) by (x +1) then the quotient will be ( x² -4x +10) and the reminder will be -2. (Answer)

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3 years ago