Factors of 2x^2-13x+21

A perfect square trinomial is represented by the equation [tex]x^2-6x+9[/tex] and this can be determined by using the factorization method.

Given :

A perfect square trinomial can be represented by a square model with equivalent length and width.

The following steps can be used in order to determine the polynomial that can be represented by a perfect square model:

Step 1 - First, check option a) [tex]x^2-6x+9[/tex] is a perfect square or not.

Step 2 - Try to factorize the above equation.

[tex]x^2-6x+9 = x^2-3x-3x+9[/tex]

[tex]x^2-6x+9 = x(x-3)-3(x-3)[/tex]

[tex]x^2-6x+9 = (x-3)^2[/tex]

Step 3 - The equation in option a) represents the perfect square trinomial.

From, the above steps, it can be concluded that the correct option is a).

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Answer:

the answer is 4

Step-by-step explanation:

16×7= 112

112÷28=4

The value of a in the equation is 10

The root of the equation is determined using the equation shown below:

[tex]x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]

Given the quadratic equation ax^2+x-24=0;

The product of the quadratic equation is c/a

Product = c/a

- 2 2/5 = -24/a

-12/5 = -24/a

-12a = 5 * -24

-12a = -120

a = 10

Hence the value of a in the equation is 10

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Compare to ax^2+bx+c

Product of roots=c/a

ATQ

[tex]\\ \tt\hookrightarrow \dfrac{c}{a}=-2\dfrac{2}{5}[/tex]

[tex]\\ \tt\hookrightarrow \dfrac{-24}{a}=\dfrac{-12}{5}[/tex]

[tex]\\ \tt\hookrightarrow \dfrac{24}{a}=\dfrac{12}{5}[/tex]

[tex]\\ \tt\hookrightarrow 12a=120[/tex]

[tex]\\ \tt\hookrightarrow a=10[/tex]

Answer:

2

Step-by-step explanation:

4+14=18

18/9=2

Answer:

2.4 inches a year

Step-by-step explanation:

It took 5 years for the bush to grow 22 inches, and it went up by 12 inches in 5 years. So, the easiest thing to do is 12 / 5 = 2.4 inches a year. :)

(Brainliest ??)

Answer:

false

Step-by-step explanation:

I hope this helps!!

Answer:

Step-by-step explanation:

The total amount Rita spent is ...

  (18.54x +23) +(25) = 18.54x +48 . . . total spent

__

When x=2, that is approximately ...

  (18.5)(2) + 48 = 37 +48 = (40 -3) +(50 -2) = (40 +50) -(3 +2) = 90 -5 = 85

Rita spent about $85 if she bought 2 items.

_____

Additional comment

Estimation is often done using 1 significant figure. In this case, that would mean rounding the equation to 20x+50, so it would give a value of 90 when x=2.

An additional task when estimating is to estimate the error in the estimate. Here, using 20x+50 has an error of approximately 1.5x+2 (too high), so the error for 2 items will be about (1.5(2)+2) = 5. That is, the estimate of 90 is approximately 5 too high. Even this estimate has a remaining small error of 0.04x (too low).

Answer:

  P

Step-by-step explanation:

The SI prefixes nano- and pico- stand for ...

  nano- = 10^-9

  pico- = 10^-12

2500 picometers is 2500·10^-12 = 2.5·10^-9 = 2.5 nanometers.

25 nanometers is greater than 2.5 nanometers, so is the greater length. Organism P has the greater length.

The amount of water that should be added to 5 gallons of 50% acid to get 20% solution is 7.5 gallons.

Word problems in mathematics requires crucial understanding and mathematical knowledge to be able to solve real life cases.

From the information given:

∴

The amount of water to be added can computed by using the relation:

[tex]\mathbf{\dfrac{2.5}{x+5} = 20\%}[/tex]

[tex]\mathbf{2.5= 0.2(x+5)}[/tex]

2.5 = 0.2x + 1

2.5 - 1 = 0.2x

1.5 = 0.2x

x = 1.5/0.2

x = 7.5

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Answer:

y = -1/4x + 2

Step-by-step explanation:

using the slope-intercept form (y=mx+b) m is the slope of the line which is -1/4 because it is decreasing and b is the y-intercept of the line which is 2

Answer:

1050

Step-by-step explanation:

bylon 3 x 68 =204

wool (3x3) x 94 =846

204 + 846 = 1050

he spent 1050 $ on materials

Answer:

$846

Step-by-step explanation:

I think it is sry if u got it wrong

Given that ΔQSR and ΔTSU are similar triangles, therefore, the length of SU is: 20.

Recall:

Thus, given the figure attached below, ΔQSR and ΔTSU are similar to each other.

SR/SU = QR/TU

SR = RU + SU = 12 + SU

SU = ?

QR = 40

TU = 25

Plug in the values

[tex]\frac{12 + SU}{SU} = \frac{40}{25}[/tex]

[tex](12 + SU)25 = 40(SU)\\\\300 + 25SU = 40SU\\\\300 = 40SU - 25SU\\\\300 = 15SU\\\\\mathbf{SU = 20}[/tex]

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Answer:

Step-by-step explanation:

sum of ratio=3+7=10

total=120 ml

first part=3/10×120=36 ml

second part=7/10×120=84 ml

In mathematics, a constant rate of change is a rate of change that stays the same and does not change.

Answer:

I'm not sure but I'll try help you work it out

Step-by-step explanation:

You need to do 300 x 0.75

Then you need to do 0.75 + 0.75, 300 x 1.50

Now compare the answers

A reasonable domain could be a bake sale <3

Sorry I tried to help

Answer:

2*2*2*3*5

Step-by-step explanation:

It is saying that 120 is the same as 24*5, and that 24* 5 is the same as 5 *2*12, which is that same as 5*2*3*4, which is then the same as 5*2*3*2*2.

Answer:

2 x 2 x 2 x 3 x 5

Step-by-step explanation:

Answer:

hope it helps you ✨✨✨✨✨✨

Answer:

Step-by-step explanation:

x = 7/11, y = -16/11

Whole part = 2

Fractional part = 5/18

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

Explanation:

4/9 = 8/18 after multiplying top and bottom by 2

1/6 = 3/18 after multiplying top and bottom by 3

So the fractional parts subtract to:

4/9 - 1/6 = 8/18 - 3/18 = (8-3)/18 = 5/18

The whole parts subtract to

3-1 = 2

Overall, we end up with the mixed number of [tex]2 \frac{5}{18}[/tex]

We can write this as 2 & 5/18 or as 2 5/18

Side note: This mixed number converts to the improper fraction of 41/18.

Answer:

You got this just keep trying

Step-by-step explanation:

Answer:

It might be 80

Step-by-step explanation:

first you put 64% and $80 as a fraction. 64%/$80. Then next to the fraction, you put x/100. Then you cross multiply. 64 times 100 is 6400. 6400 divided by 80 is 80. Therefore, the answer is 80. Hope this helps!

Answer:

b,c

Step-by-step explanation:

hello, the answer to this is / and ----- or b and c I got this right on my test :)

Answer:

the next is -2 × 5 = - 10

Step-by-step explanation:

the sequence is times 5

Answer:

39

Step-by-step explanation:

detailed explanation showed in the diagram above

Answer:

10/3

Step-by-step explanation:

[tex] \bf \huge \: Question:[/tex]

Find the value of x

[tex]\bf \huge \: Equation \: provided:[/tex]

[tex]\sf \dfrac{2}{3} +5/6= 3\dfrac{1}{3} [/tex]

[tex]\bf \huge \: Solution:[/tex]

[tex] \bf \: Convert\: The\: mixed \: fraction \: to \: improper \: f raction:[/tex]

[tex]\sf \longmapsto \: \dfrac{2}{3} x + \dfrac{5}{6} = \dfrac{10}{3} [/tex]

[tex]\underline{\bf Subtract \: 5/6 \: from \: both \: sides : }[/tex]

[tex]\sf \longmapsto \dfrac{2}{3 }x + \dfrac{5}{6} - \red{ \dfrac{5}{6} } = \dfrac{10}{3} - \red{ \dfrac{5}{6} }[/tex]

[tex] \bf \: On \: Simplification:[/tex]

[tex]\sf \longmapsto \dfrac{2}{3} x + 0 = \dfrac{20 -5 }{ 6 } [/tex]

[tex]\sf \longmapsto \dfrac{2}{3} x = \dfrac{5}{2} [/tex]

[tex]\underline{ \bf \: Multiply \: both \: sides \: by \: 3/2:}[/tex]

[tex]\sf \longmapsto\red{ \dfrac{3}{2}} \times \dfrac{2}{3} x = \red{\dfrac{3}{2} } \times \dfrac{5}{2}[/tex]

[tex]\bf On \: Simplification:[/tex]

[tex]\sf \longmapsto1 \times \dfrac{15}{4} [/tex]

[tex]\sf \longmapsto \: \dfrac{15}{4} [/tex]

[tex]\underline{\bf Answer\: In \: mixed\: fraction:}[/tex]

[tex]\sf \longmapsto \: 3\dfrac{3}{4} [/tex]

______________________________________

[tex]\underline{ \bf \: Henceforth,The\: value\: of\: x \: is:}[/tex]

[tex] \boxed{\huge\boxed{ \tt x = 3\dfrac{3}{4} }}[/tex]

Answer:

No solution

Step-by-step explanation:

Since both x's are positive, there's no way to put to x on either side, because when you transfer sides, you add/subtract the opposite, so there can't be a value for x