Mathematics High School

The Nature of Roots Of a Quadratic Equation help me with these pls

if you answer correctly i'll mark you as brainliest answer

Answers

Answer 1

Problem 1

Answers:

Real = sqrt(49), 5/6, 12.5, 8/12, 225, sqrt(24)/16, sqrt(32)

Not real = sqrt(-20) and sqrt(-16)/9

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Explanation:

Anything involving a square root of a negative number will result in a non-real answer. Anything else is real.

Traditionally y = sqrt(x) has a domain of nonnegative numbers. If x >= 0, then y is some real number. If x < 0, then we'll need to use the imaginary number i = sqrt(-1).

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

Problem 2

Answers:

Rational = sqrt(49), 5/8, 12.5, 8/12, and 225

Irrational = sqrt(24)/16, sqrt(32)

---------------

Explanation:

Ignore the non-real numbers. Focus solely on the real values.

A rational number is where we can write it as a ratio of two integers. An example is 5/8 since 5 and 8 are integers. The denominator can never be zero.

Decimal values that terminate can be written as a fraction. For instance, 12.5 = 125/10.

Square roots of perfect squares are also rational. For example sqrt(49) = 7 = 7/1

Something like sqrt(32) is not rational because we can't write it in the form p/q with p,q being integers. We say it is irrational.

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

Problem 3

Answers:

Perfect Squares = 225

Non-perfect squares = everything else

---------------

Explanation:

A perfect square is of the form x^2, where x is a positive integer.

The only perfect square listed is 225 because 225 = 15^2. Here x = 15.

Note: a perfect square is an integer itself.

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

Problem 4

As discussed earlier, rational numbers are fractions of integers. So we have something of the form p/q where p,q are integers and q is nonzero. An example of a rational number is p/q = 7/8 with p = 7 and q = 8.

Irrational numbers are ones that cannot be written as p/q. A famous example of an irrational number is pi = 3.14, but we could do something like sqrt(17) for instance as well. The stuff under the square root must be a non-perfect square.

Perfect squares are integers in the form x^2, with x being an integer also. A visual way to think of perfect squares is to think of a square with side length x, so its area is x^2. If x = 9, then its area is x^2 = 9^2 = 81, so 81 is a perfect square. We only consider whole number side lengths.

Related Questions

The radius of a circle is 8 meters. What is the diameter?

Answers

Answer:

16 meters

Step-by-step explanation:

r=8m

8*2=16

d=16m

Answer:

Step-by-step explanation:

The diameter is the radius times 2.

1/3 - 2/9 find the solution

Answers

Answer:

1/9

Step-by-step explanation:

1/3 - 2/9

Get a common denominator of 9

1/3 *3/3 = 3/9

3/9 - 2/9

1/9

i need help with 1/2x+13=9
im in the 8th grade btw

Answers

Answer:

-8

Step-by-step explanation:

You are wanting to solve for x

First you want to subtract 13 on both sides-

1/2x = -4

Now you want to divide on both sides-

x = -8

Answer:

1/-8

To find:

Step-by-step explanation:

1/2x+13=9

take 13 to the LHS. when you take 13 to the LHS it becomes negative

1/2x=9-13

1/2x=-4

by cross multiplying,

2x × -4=1

-8x=1

x=1/-8

hope it helps you!!

Evaluate. 5/8−(14)2= ________

Answers

Answer:

exact form -219/8

Decimal form - -27.375

Mixed number form - -27 3/8

(3y-1)^5 written in standard form please help!!!!

Answers

Answer:

Step-by-step explanation:

[tex](3y-1)[/tex]

[tex](3y-1)*(3y-1)*(3y-1)*(3y-1)*(3y-1)[/tex]

[tex]243y^5-405y^4+270y^3-90y^2+15y-1[/tex]

Which value must be added to the expressionx2+16x to make it a perfect-square trinomial?

Answers

Answer:

Step-by-step explanation:

Please write x^2+16x or x²+16x to indicate the exponentiation.

To rewrite x²+16x as a perfect square trinomial:

1) Take half of the coefficient of x, that is, half of 16, which is 8

2) Square this result: 8² or 64

3) Starting with x²+16x again, add 64 and then subtract 64 to get a trinomial expression equivalent to x²+16x:

x²+16x + 64 - 64

4) Rewrite the first three terms as the square of the binomial x + 8:

(x + 8)² - 64

Here (x + 8)² is a perfect square trinomial.

Answer:

The answer is C.) 64 on edge.

Solve for the variable in the following proportion

m/1/3 = 10/1 2/3

50
2
5
3/5

please help?

Answers

Answer:

the answer is 5

Step-by-step explanation:

HELP ASAP . You the real one if you do.

Answers

Answer:

x=1

Step-by-step explanation:

hope this helps and hope its correct

Find the measure of DCH.

Answers

Answer: angle DCH = 129 degrees

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

Work Shown:

Angles DCH and PCF are congruent because they are vertical angles.

angle DCH = angle PCF

5h+94 = 7h+80

94-80 = 7h-5h

14 = 2h

2h = 14

h = 14/2

h = 7

angle DCH = 5h+94

angle DCH = 5*7+94

angle DCH = 35+94

angle DCH = 129 degrees

angle PCF = 7h+80

angle PCF = 7*7+80

angle PCF = 49+80

angle PCF = 129

We get the same result for both angles, which confirms the correct h value.

Is 2.01 less than 2.2

Answers

Answer:

Yes, 2.01< 2.20

Step-by-step explanation:

Yes, because 2.01 is equal to 2 and 1/100 while 2.2 is equal to 2 and 20/100

Hope this makes sense. In short, yes 2.01 is less than 2.2

HELPPPP PLEASSEEEEEE!!!

Answers

Answer:

Answer:

b2 = 2A/h - b1

Step-by-step explanation:

write an equation for each quadratic function whose graph is shown

Answers

Answer:

9. y=5[tex]x^{2}[/tex]

10. y=2/3[tex]x^{2}[/tex]

11. y=1/10[tex]x^{2}[/tex]

12. y=-1/4[tex]x^{2}[/tex]

Step-by-step explanation:

9. Use vertex form (y=a(x-h)^2+k) and insert the vertex (0,0) as (h, k).

y=a(x-0)^2 +0

Substitute the x and y values for the given point on the graph, (-1, 5)

5=a(-1-0)^2+0

Solve for a.

5=a(-1)^2

5=a

Substitute a in vertex form and solve for general form (ax^2 +bx+c)

y=5[tex]x^{2}[/tex]

Use this method to find the rest of the equations.

does the table below show a proportional relationship

Answers

Answer:yes

Step-by-step explanation:

How can you tell if there will be more than one solution for the geometric means?

Answers

Answer: because there are different methods to it and different solutions.

Step-by-step explanation:

Which of the equations shown have infinitely many solutions?
Select all that apply
A 3x - 1 = 3x + 1
B. 2x - 1 = 1 - 2x
C3x - 2 = 2x - 3
D. 3(x - 1) = 3x - 3
E. 2x + 2 = 2(x + 1)
E 3(x - 2) = 2(x-3)

Answers

Answer:

D. 3(x-1) = 3x-3

Step-by-step explanation:

I'm sure that's the answer

Answer:

D and E

Step-by-step explanation:

Which is a rational number?
-15/4
-7/9
4 with a rational sign?
pi

Answers

Answer:

All are rational numbers I guess

Step-by-step explanation:

NoTE : I'm not sure

Answer:

For the first one its 7/9 ig

simplify and expand (X+3)(x-3)(3x+3)

Answers

Answer:

3x^3 + 3x^2 - 27x - 27

Step-by-step explanation:

Answer: 3x^3 + 3x^2 - 27x - 27

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

Work Shown:

(x+3)(x-3)(3x+3)

(x^2-9)(3x+3) .... difference of squares rule

y(3x+3) .... let y = x^2-9

y*3x + y*3 .... distribute

3x( y ) + 3( y )

3x( x^2 - 9 ) + 3(x^2 - 9) .... plug in y = x^2-9

3x*x^2 + 3x*(-9) + 3*x^2 + 3*(-9) .... distribute

3x^3 - 27x + 3x^2 - 27

3x^3 + 3x^2 - 27x - 27

Solve the system of equations using any method. 2X – Y + Z = – 2, 6X + 3Y – 4Z = 8, – 3X + 2Y +3Z = – 6

Answers

Answer:

Z = - 2, Y = 0, X = 0

Step-by-step explanation:

2X – Y + Z = – 2

6X + 3Y – 4Z = 8

– 3X + 2Y +3Z = – 6

isolate "X" in the first equation

2X - Y + Z = - 2 => isolate "2X"

2X = - 2 - Z + Y => divide either side by 2

X = - 1 - Z/2 + Y/2

substitute this value of X in the second two equations (applying the substitution method here)

6(- 1 - Z/2 + Y/2) + 3Y - 4Z = 8,

6Y - 7Z - 6 = 8

- 3(- 1 - Z/2 + Y/2) + 2Y +3Z = - 6,

Y + 9Z + 6/2 = - 6

isolate Y in the second equation (6Y - 7Z - 6 = 8) and substitute in the third equation (Y + 9Z + 6/2 = - 6)

6Y - 7Z - 6 = 8 => isolate 6Y

6Y = 14 + 7Z => divide either side by 6

Y = 7Z + 14/6 => substitute in second equation

7Z + 14/6 + 9Z + 6/2 = - 6 => solve for Z

61Z + 50/12 = - 6, Z = - 2

substitute the value of Z into the equations "Y = 7Z + 14/6" and using the value of Y and Z, substitute into "X = - 1 - Z/2 + Y/2"

Y = (7(- 2) + 14)/6 = 0 / 6

= 0

X = - 1 - (- 2)/2 + 0/2 = - 1 - (-1) + 0

= - 1 + 1 + 0 = 0

Anita is making headbands for her softball team. She needs a total of 3/4 yard of fabric. Select all types of fabric that cost less than $8 per yard. Total cost for 3/4 of cotton: 5.54 Total cost of 3/4 of Flannel: 2.62 Total cost of 3/4 of Fleece: 4.27 Total cost of 3/4 of Terry cloth: 6.52

Answers

Answer:

All except the Terry Cloth

Step-by-step explanation:

The fabrics that cost less than $8 per yard are cotton, flannel and fleece.

In order to determine the cost of a yard of each material, divide the total cost of 3/4 yards of that fabric by 3/4

cost of a yard = total cost ÷ [tex]\frac{3}{4}[/tex]

Cost of a yard of cotton = 5.54 ÷ [tex]\frac{3}{4}[/tex] = 6.85

Cost of a yard of Flannel = 2.62 ÷[tex]\frac{3}{4}[/tex] = 3.49

Cost per yard of Fleece = 4.27 ÷ [tex]\frac{3}{4}[/tex] = 5.69

Cost per yard of Terry Cloth = 6.52 ÷[tex]\frac{3}{4}[/tex] = 8.69

Based on the above calculations, all but Terry cloth cost less than $8 per yard

A similar question was solved here: https://brainly.com/question/2244723?referrer=searchResults

give me an example of irrational between 4 and 5

Answers

Answer:

√17, √18,√19,√20,√21,√22,√23 ,√24

Step-by-step explanation:

-8(1 + 4p) + 7p = – 25 – 8p

Answers

The answer for the is

p=1

evaluate the expression x+9, if x=8

Answers

Answer:

Step-by-step explanation:

x+9

if x=8 you would substitute x for 8 making the equation

8+9 = 17

therefore, the answer is 17.

Can someone please help me ASAP I’ll mark brainlist!!!!?!?

Answers

It might be D. I’m not positive sorry if it’s wrong

Hi, i need help quickly. I need the solution for
Estimate the value of
[tex] \sqrt{97.5 \div 1.96} [/tex]
Please make it quick

Answers

Answer:

7.05

Step-by-step explanation:

Answer:

7.053

Step-by-step explanation:

97.5/1.96=49.745

√49.745=7.053

Wage per hour $11.13.

3 hours per day of work.

Takes 44.93 (45) hours of work to get $500.

For your birthday, you received $50 in gifts from family and friends. Write an equation and solve, letting h represent hours, to find how many hours you will have to work to save the $500 with the $50 in gifts based on your hourly wage. How many weeks is that?

Answers

Answer:

It will be about fourteen days or two weeks to save that much while only working 3 hours each day for every day of the week

Step-by-step explanation:

Can you please help me with this please.... I’ve been posting these questions over and over and nothing...

Snorkel, mask, and flippers
Slope:

Snorkel, mask, and flippers
y-intercept:

Snorkel, mask, and flippers
Slope intercept form:

Answers

Answer:

Step-by-step explanation:

Snorkel, mask, and flippers Slope: 2 (so in the equation, it would look like 2x).

Snorkel, mask, and flippers Y-intercept: 10 (12 - 2 = 10, which is 0 hours, possibly the initial amount)

Snorkel, mask, and flippers Slope intercept form: y = 2x + 10

Three times a number increased by 7 is 100. Find the number.

Answers

Answer:

Step-by-step explanation:

100-7= 93

93÷3=31

Answer:

the number is 31

Step-by-step explanation:

the number is the variable x

3 times the number is 3x

increased by 7 is +7

is 100 is =100

3x +7 =100

subtract 7 from both sides

3x =93

divide by 3 on both sides

x = 31

Jubal wrote the four equations below. He examined them, without solving them, to determine which equation has no solution. 7 x + 1 = 7 x+ 1. 3 x + 2 = 3 x minus 2. 4 x + 1 = 3 x + 8. Negative 2 x minus 1 = negative 2 x minus 1. Which of Jubal's equations has no solution? 7 x + 1 = 7 x+ 1 3 x + 2 = 3 x minus 2 4 x + 1 = 3 x + 8 negative 2 x minus 1 = negative 2 x minus 1

Answers

Given:

Four equations are

[tex] 7 x + 1 = 7 x+ 1[/tex]

[tex]3 x + 2 = 3 x-2[/tex]

[tex]4 x + 1 = 3 x + 8[/tex]

[tex]-2x-1 = -2 x-1[/tex]

To find:

Without solving which equation has no solution.

Solution:

We know that, in an equation

1. No solution : When variable terms are same but constants are different.

2. Unique solution : When variable terms are different.

3. infinitely many solution : When variable terms and constants are same.

In first and fourth equations, terms on left sides are equal to the terms on the right side. So, LHS = RHS for any value of x.

Therefore, these two equations (first and fourth) have infinitely many solutions.

In second equation, variable terms are same on both sides, but the constants are difference. So, LHS ≠ RHS for any value of x.

Therefore, the second has no solutions.

In third equation, coefficient of x are difference on both sides.

So, this equation has unique solution.

Therefore, Jubal's equations [tex]3 x + 2 = 3 x-2[/tex] has no solution. Hence, the correct option is B.

Answer:

Step-by-step explanation:

Triangle A has side lengths 2, 3, and 4. Triangle B has side lengths 4, 5, and 6. Is Triangle A similar to Triangle B?

Answers

Answer:

No, you would need it to have the same multiples: for example, Triangle A has 2,3,4 so Triangle B would have 4,6,8

Step-by-step explanation:

I hope that makes sense!

Solve for the indicated variable.

2a + 2b = c for b

B = ?/?

Answers

Answer:

b = c − 2a

------------

Step-by-step explanation:

2a + 2b = c

2b = c − 2a

b = c − 2a

------------

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The Nature of Roots Of a Quadratic Equation help me with these pls​if you answer correctly i'll mark you as brainliest answer​

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The Nature of Roots Of a Quadratic Equation help me with these pls

if you answer correctly i'll mark you as brainliest answer