is √64 a rational or irrational?

Answer:

70/9

Step-by-step explanation:

We have the quadratic:

[tex]3x^2+4x-9[/tex]

So, let’s find the roots of the quadratic. We will set the expression equal to 0:

[tex]3x^2+4x-9=0[/tex]

Testing for factors, we can see that our quadratic isn’t factorable.

So, we can use the Quadratic Formula. The quadratic formula is given by:

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

In this case:

[tex]a=3, b=4,\text{ and } c=-9[/tex]

Therefore, by substitution:

[tex]\displaystyle x=\frac{-(4)\pm\sqrt{(4)^2-4(3)(-9)}}{2(3)}[/tex]

Evaluate:

[tex]\displaystyle x=\frac{-4\pm\sqrt{124}}{6}[/tex]

Simplify the square root:

[tex]\sqrt{124}=\sqrt{4\cdot31}=2\sqrt{31}[/tex]

Hence:

[tex]\displaystyle x=\frac{-4\pm2\sqrt{31}}{6}[/tex]

Reduce:

[tex]\displaystyle x=\frac{-2\pm\sqrt{31}}{3}[/tex]

So, our roots are:

[tex]\displaystyle x_1=\frac{-2+\sqrt{31}}{3}, x_2=\frac{-2-\sqrt{31}}{3}[/tex]

We want to find the sum of the squares of our two roots. So, let’s square each term:

[tex]\displaystyle (x_1)^2=\Big(\frac{-2+\sqrt{31}}{3}\Big)^2[/tex]

Square. For the numerator, we can use the perfect square trinomial patten where:

[tex](a+b)^2=(a^2+2ab+b^2)[/tex]

Therefore:

[tex]\displaystyle (x_1)^2=\Big(\frac{(-2)^2+2(-2)(\sqrt{31})+(\sqrt{31})^2}{9}\Big)[/tex]

Simplify:

[tex]\displaystyle (x_1)^2=\frac{35-4\sqrt{31}}{9}[/tex]

Similarly, for the second root, we will have:

[tex]\displaystyle (x_2)^2=\Big(\frac{-2-\sqrt{31}}{3}\Big)^2[/tex]

So:

[tex]\displaystyle (x_2)^2=\Big(\frac{(-2)^2+2(-2)(-\sqrt{31})+(-\sqrt{31})^2}{9}\Big)[/tex]

Simplify:

[tex]\displaystyle (x_2)^2=\frac{35+4\sqrt{31}}{9}[/tex]

Therefore, our sum will be:

[tex]\displaystyle (x_1)^2+(x_2)^2\\\\ \begin{aligned} &=\frac{35-4\sqrt{31}}{9}+\frac{35+4\sqrt{31}}{9}\\&=\frac{35-4\sqrt{31}+35+4\sqrt{31}}{9}\\&=\frac{70}{9}\end{aligned}[/tex]

Therefore, our final answer is 70/9.

Answer:

A,C,D

Step-by-step explanation:

Answer:

x = 30

Step-by-step explanation:

We have to find x

Given that:

20% of x = 12 % of (x +20)

This can be written as:

0.2(x) = 0.12 (x + 20)

0.2x = 0.12x + 2.4

Subtracting 0.12x from both sides we get:

0.2x - 0.12x = 0.12x - 0.12x + 2.4

0.08x = 2.4

Dividing both sides by x we get:

0.08/0.08x = 2.4/0.08

x = 30

Answer:

x = 30

Step-by-step explanation:

Set up an equation:

0.2x = 0.12(x + 20)

Distribute 0.12 and solve for x:

0.2x = 0.12x + 2.4

0.08x = 2.4

x = 30

So, the answer is x = 30

Answer:

200

Step-by-step explanation:

10*20=200.

I am not positive what you are asking but that is the answer I am able to give at this moment.

I hope I at least helped you. :)

Answer:

y + (1/4)(x + 4)

Step-by-step explanation:

One point on the graph is (-4, 0); another is (4, 2).

The change in x from the first point to the second is 8; this is the 'run.'

The change in y is 2 (which is 2 - 0).  This is the 'rise.'

Thus, the slope of the line is m = rise / run = 2/8 = 1/4

Let's use the point-slope form of the equation of a straight line:

y  - k = m(x - h).  Substituting 0 for k and -4 for h, we get:

y - 0 = (1/4)(x + 4), or

y + (1/4)(x + 4)

Answer:

2.50 a cookie

Step-by-step explanation:

Because you divide 30/12 and it doesnt equal a whole number because its in dollars if that makes sense

Answer:

you would divide 30/12= 2.5 per cookie

Step-by-step explanation:

Answer:

365,000

Step-by-step explanation:

Three hundred sixty five ten thousands means 3 hundred and 65 thousands

The number will be written in figures as 365,000

The hundred defines the 300 and the sixty-five ten thousands define 65,000

ten thousands is added in the number to define the nature of sixty-five.

Answer: A

Step-by-step explanation:

Answer:

A. Rachel is correct; Graph S is nonproportional.

Step-by-step explanation:

Answer:

t=40

Step-by-step explanation:

The sum of all angles in a triangle will always equal 180°. This means that:

(2t-42)+(4t-49)+(2t-49) = 180°

Let's solve this equation!

(2t-42)+(4t-49)+(2t-49) = 180

First we simplify what's on the left side:

2t-42+4t-49+2t-49 = 180

2t+4t+2t-42-49-49 = 180

8t-140 = 180

*Add 140 to both sides

8t = 180+140

8t = 320

Divide both sides by 8 to know what t means:

t = 320/8

t = 40

Answer:

parallel lines never  intersect

perpendicular  lines intersect at a right angle

Step-by-step explanation:

Answer:

Natalie will have [tex]1\frac{43}{56}[/tex] jars of coins all together after receiving John's coins.

Step-by-step explanation:

Given that:

Coins Natalie have = [tex]1\frac{1}{8}[/tex] jars of coins

Coins John have = [tex]\frac{9}{14}[/tex] jars of coins

When John will give all his coins to Natalie.

Total coins Natalie have = Her coins + John's coins

Total coins Natalie have = [tex]1\frac{1}{8}+\frac{9}{14}[/tex]

Total coins = [tex]\frac{9}{8}+\frac{9}{14}[/tex]

Total coins =[tex]\frac{63+36}{56}=\frac{99}{56}[/tex]

Total coins = [tex]1\frac{43}{56}[/tex]

Hence,

Natalie will have [tex]1\frac{43}{56}[/tex] jars of coins all together after receiving John's coins.

Answer:

5

Step-by-step explanation:

2*5 = 10

Answer:

16:9

Step-by-step explanation:

Answer:

Add -3 and 7. 4

Step-by-step explanation:

Uh ur welcome

Answer:

4

Step-by-step explanation:

I do it this way whenever there is a  - and a - I just add them but add negative sign. IF like in this problem - and a + I subtract...

Hope this helps :3

Answer:

the answer is d

Step-by-step explanation:

For 55 you times the average by the time it took and you get 55 same with kick 2 so kick 3 would be 2 seconds because 15 times 2 is 30

Answer:

Y=2

Step-by-step explanation:

YW thanks!

Answer:

A 454545 is the correct answer

Answer:

its 241

Step-by-step explanation:

i did it on khan

Answer:13,7,8 but if there’s an answer choice go with 7,8

Step-by-step explanation: Assuming b is an integer, we first look at factors of 4, being 1 and 4 or 2 and 2. The factors of 3 are 1 and 3 only. So the factorisation possibilities are (x+3)(4x+1), (4x+3)(x+1) and (2x+1)(2x+3).

Expanding these we get: 4x²+13x+3, 4x²+7x+3 and 4x²+8x+3, giving values of b=13, 7 and 8

The possible values of b in the given polynomial are 7, 8 or 13.

In mathematics, a polynomial is an expression consisting of indeterminates (also called variables) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer powers of variables.

Given is a polynomial, 4x²+bx+3, we need to find all possible values of b such that 4x²+bx+3 can be factored.

4x²+bx+3

4×3=2×2×3

2×2×3 = 2×6 and 2+6 = 8

2×2×3 = 4×3 and 4+3 = 7

2×2×3 = 12×1 and 12+1 = 13

b=7, b=8, and b=13

4x²+7x+3 = (4x+3) (x+1)

4x²+8x+3 = (2x+1) (2x+3)

4x²+13x+3 = (4x+1) (x+3)

Hence, the possible values of b in the given polynomial are 7, 8 or 13.

Learn more about polynomial click;

https://brainly.com/question/11536910

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Answer:

it looks decent just give it make it more detailed otherwise it looks good

Answer:

your drawing is good but I can't understand your ques

Answer:

THANK YOU?

Step-by-step explanation:

DNSNJSMSNNFJD

Please, give me brainliest

Answer: 240 grams of flour and 40 grams of sugar.

Step-by-step explanation: I used the rule of three to calculate the values for the flour and sugar. The common ratio that these numbers have would

be 40.

Reasoning: If the ratio is 6:4:1, then you can apply it as a rule of three. If 160 relates to 4, then x (the value of flour) will relate to 6. 160/4 = x/6, cross multiply, and x = 240. The amount of flour is 240 grams. Using the same logic, you can set another rule for the amount of sugar (represented by variable s); 160/4 = s/1. Cross multiply, and s = 40. The amount of sugar is 40 grams.

Answer:

625%

Step-by-step explanation:

6.25 multipied by 100 equals 625.

Answer:

Ramon, 16 hours

Step-by-step explanation:

Answer:

HI

Step-by-step explanation:

WOW

Answer: d. 92

Step-by-step explanation: 150 time for equals 600. so all you gotta do is multiply 23 times 4

Answer: 108.1 g

Step-by-step explanation:

432.4/4 = 108.1

Answer:

. umm whats the question

Step-by-step explanation:

Answer:

Step-by-step explanation:So, if the graph is a straight line, it is the graph of a linear function. From a table, you can verify a linear function by examining the x and y values. The rate of change for y with respect to x remains constant for a linear function. This rate of change is called the slope.Mar 9, 2011

Answer:

Step-by-step explanation:

Constance C. asked • 03/06/17. An item on sale costs 60 % of the original price. If the original price was $ 85 , what is the sale price? An item on sale costs 60 %