What is the area of the triangle having sides 3 cm 4 cm and 5 cm?

Answer:

For quadratic equations that cannot be solved by factorising, we use a method which can solve ALL quadratic equations called completing the square. We use this later when studying circles in plane analytic geometry.

Completing the square comes from considering the special formulas that we met in Square of a sum and square of a difference earlier:

(x + y)2 = x2 + 2xy + y2 (Square of a sum)

(x − y)2 = x2 − 2xy + y2 (Square of a difference)

To find the roots of a quadratic equation in the form:

\displaystyle{a}{x}^{2}+{b}{x}+{c}={0}ax

2

+bx+c=0,

follow these steps:

(i) If a does not equal \displaystyle{1}1, divide each side by a (so that the coefficient of the x2 is \displaystyle{1}1).

(ii) Rewrite the equation with the constant term on the right side.

(iii) Complete the square by adding the square of one-half of the coefficient of x to both sides.

(iv) Write the left side as a square and simplify the right side.

(v) Equate and solve.

Example 1

Find the roots of x2 + 10x − 4 = 0 using completing the square method.

Answer

Example 2

Solve 4x2 + x = 3 by completing the square.

Answer

Exercises

Solve the following quadratic equations by completing the square

Q1. \displaystyle{2}{s}^{2}+{5}{s}={3}2s

2

+5s=3Answer

Q2. \displaystyle{3}{x}^{2}={3}-{4}{x}3x

2

=3−4xAnswer

Q3. \displaystyle{9}{v}^{2}-{6}{v}-{2}={0}9v

2

−6v−2=0Answer

Q4. \displaystyle{a}{x}^{2}+{b}{x}+{c}={0}ax

2

+bx+c=0Answer

1. Solving Quadratic Equations by Factoring

3. The Quadratic Formula

Answer: is this correct

Step-by-step explanation:

25% is 50% of 50.

Explaination is on the picture.

50% of 100 is 50.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100.

Let x be a number such that

50% of x is 50

This forms an equation in one variable which can be solved by transposition.

[tex]50/100\times x = 50[/tex]

x/2=50

On multiplying 2 both sides,

[tex]X/2\times 2 =50\times 2[/tex]

X=100

Thus, 50% of 100 is 50.

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Correct question:

50% of what is 50.

Answer:

4 lol

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

C. 14

iedujdd

Step-by-step explanation:

i think i searched

Answer:

9

Step-by-step explanation:

Triangle DCE and ACD are similar (they share the angle at A, and since DE║CB, ∠D=∠C and ∠E=∠B (corresponding angles))

That means the side lengths are in ratio:

12/(8+12)=?/(6+?)

0.6(6+?)=?

3.6+0.6?=?

0.4?=3.6

?=9

Answer:

y = 5x + 4

Step-by-step explanation:

y - 4 = 5(x - 0)

That is point-slope form. I'm not sure if you want it in slope intercept form, but slope intercept form of the equation is y = 5x + 4

Answer:

y=5x+4

Step-by-step explanation:

y=mx+b

Answer:

The answer is 1.024

Step-by-step explanation:

5.12 divided by 5 = 1.024

Hope this helps.

Answer:

20 ft

A=wl

l=A/W=240/12=20ft

Answer:

2 kg cashews

6 kg pecans

Step-by-step explanation:

System of Equations:

c + p = 8

8c + 7p = 8(7.25)

let c = 8-p

8(8-p) + 7p = 58

64 - 8p + 7p = 58

-p = -6

p = 6

The composite score range for the ACT is D) 1 to 36.

The composite score range for the ACT (American College Testing) is the total score achieved by an individual after taking all four sections of the ACT, which include English, math, reading, and science. The composite score ranges from 1 to 36, with 36 being the highest possible score.

The ACT score is used by colleges and universities in the United States to assess the readiness of a student to enter college. A high composite score indicates that the student has the skills and knowledge needed to succeed in college-level courses. Therefore, the correct answer is D) 1 to 36.

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Answer:

480 toy boats per hour

Step-by-step explanation:

1. Divide 360 by 45 to find unit rate per MINUTE.

360 / 45 = 8

2. One hour = 60 minutes, so multiply 8 and 60.

8 * 60 = 480

Answer:

x^2-3x+36

Step-by-step explanation:

Answer:

-0.4

Step-by-step explanation:

to solve use the formula m=y2-y1/x2-x1

Answer:

Step-by-step explanation:

Where are the equations to choose from?

14 pounds × (1 bag)/(¼ pound) = 56 bags

Answer:

8

Step-by-step explanation:

∡AB + ∡BC + ∡CD = 180°

∡CD = ∡AE

∡AB + ∡BC + ∡AE = 180°

(8x + 6)° + (6x + 2)° + (7x + 4)° = 180°

8x + 6 + 6x + 2 + 7x + 4 = 180

21x + 12 = 180

21x = 180 - 12

21x = 168

x = 8

Answer:

Step-by-step explanation:

[tex]\sqrt{(6-1)^{2}+(3-5)^{2} }[/tex]=[tex]\sqrt{29}[/tex]

                               =5.39(correct to nearest hundredth)

Answer:248

Step-by-step explanation:

First you need to find the unit rate by dividing 93 by 3 which would be 31 then take that number (which is how many miles for one gallon) and multiply it by 8 which would get you 248( if you need this as an equation here 93\3= 31 31*8 = 248). If they gave you the distance instead you would have had to divide by 31 instead of using multiplication. Hope this helps!

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Answer:

100 pounds

Step-by-step explanation:

Answer:

Let's use the slope-intercept form of the equation of a line describe the slope and the y-intercept:

y = mx + b where m=slope and b=y-intercept

the answer is: x= -111/182

Answer:

x= -0.60989010989

Step-by-step explanation:

Answer:

The orders of magnitude are numbers of the form:

10^n

where n can be any integer number.

So we can write something like:

"A is n orders of magnitude above B

Now we have the quantities:

Amjed cards = 223

Latif cards = 8741

We want to find how many times more trading cards does Latif  have than Amjed.

Then we need to look at the quotient between the number of cards of Latif and Amjed.

8741/223 = 39.2

Now we need to approximate this to the nearest 10^n number.

(..., 0.1, 1, 10, 100, 1000, ...)

The nearest one to 39.2 is 10.

So we can say that Latif's collection is 10.

and 10 = 10^1

then n = 1

Then we can say that Latif's collection is one order of magnitude above Amjed's collection.

The domain is the set of input values for which the function is real and defined.

Find non negative values for the radicals.

For y = sqrt(3-x) if x is greater than the 3 the value under the square root would be negative which would result in a non real number.

The answer needs to be x <= 3 ( less than or equal to)

For y = sqrt(3x), if x is less than 0, the number under the sqrt root would be negative resulting in a non real number.

The answer is x >= 0 ( greater than or equal to)

Answer: 24x2+26x−104 or -104

Step-by-step explanation:

Step-by-step explanation:

angle 2 = 49

angle 1 = 131

angle 3 = 112

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Answer: 13 m

Step-by-step explanation:

distance from starting point = root{(5)^2 + (12)^2 }

=root{ 25 + 144}

= 13

Answer:

Step-by-step explanation:

Between south direction and east direction we have right angle, so we can use Pythagorean theorem:

a² + b² = c²

a = 5 m

b = 12 m

c = the distance

[tex]5^2+12^2=c^2\\\\c^2=25+144\\\\c^2=169\\\\c=\sqrt{169}=13\,m[/tex]

Answer:

x < -9 or x > 10.

Step-by-step explanation:

x + 10 > 20

x  > 10.

x + 12 < 3

x < -9.

Answer:

144 =4

=>144=2×2×2×3×3

OK

OK i know this only

enjoy your day

Answer:

12.56 in.

Step-by-step explanation:

A=Pi*R to the 2nd power

A=3.14*2 to the 2nd power

A=3.14*4

A=12.56

Let me know if im wrong

Area of the circle is 12.56 square units which has radius 2 inches.

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

Given that radius of a circle is 2 inches.

We need to find the area of circle.

Radius= 2 inches.

π=3.14

We know that area of circle=πr²

Area of circle=3.142×2²

=3.142×4

=12.56 square inches.

Hence, area of the circle is 12.56 square units which has radius 2 inches.

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