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Answer:

[tex]x = 2[/tex]

Step-by-step explanation:

Given

Conjecture: [tex]x + 3 < x^2[/tex] --- (Missing)

Required

Which value of x prove the conjecture otherwise

To do this , we simply substitute the values of x in the options

[tex]1.\ x = -\frac{1}{3}[/tex]

This is negative;

So, there is no need to check

[tex]2.\ x = -3[/tex]

This is also negative;

So, there is no need to check

[tex]3.\ x = 2[/tex]

[tex]x + 3 < x^2[/tex]

[tex]2 + 3 < 2^2[/tex]

[tex]5 < 4[/tex]

This value of x is false because 5 is not less than 4

[tex]4.\ x = 3[/tex]

[tex]x + 3 < x^2[/tex]

[tex]3 + 3 < 3^2[/tex]

[tex]6 < 9[/tex]

Answer:

480

Step-by-step explanation:

12*4=48 then add a zero to the end of it

hope that helps!

happy new year!

Answer:

Lance has 480 comic books.

Step-by-step explanation:

Multiply 12 by 40:)

Answer:

The values of p and q such that 2·x² - 4·x + 3 = 2·(x - p)² + q, are;

p = 1, q = 1

Step-by-step explanation:

The given equation are;

2·x² - 4·x + 3 = 2·(x - p)² + q

By expanding the right hand side of the equation, we have;

2·x² - 4·x + 3 = 2·(x - p)² + q = 2·x² - 4·p·x + 2·p² + q

2·x² - 4·x + 3  = 2·x² - 4·p·x + 2·p² + q

Comparing the coefficient of x in both equations, gives;

2·x² + (- 4)·x + 3  = 2·x² + (- 4·p)·x + 2·p² + q

-4 = -4·p

∴ p = -4/(-4) = 1

p = 1

Comparing only the constant terms (terms not multiplied by "x" or "x²"), we get;

3 = 2·p² + q

Substituting the value for "p" obtained above (p = 1 ) in the previous equation, we get;

3 = 2 × 1² + q  = 2 + q

∴ q = 3 - 2 = 1

q = 1.

Answer:

-18

Step-by-step explanation:

Step 1 - divide the numerator and denominator by 18

-324÷18 / 18÷18

Step 2 - divide the numbers

-18 / 18÷18  

-18/1

any expression divided by 1 remains the same

-18

Answer:

2 k 3 − 3 k 2 − 2 k

Step-by-step explanation:

Answer: ...

2k^3−3k^2−2k

Answer:

Step-by-step explanation:

The answer would be 5 because 14/7=2 and 6/3=2 and 10/ 2 =5 so 5

Answer:

length, width, and height are (b+2), (b-2), (b+3)

Step-by-step explanation:

Doing what the problem statement tells you to do, you get ...

 (b^3 +3b^2) -(4b +12)

 = b^2(b +3) -4(b +3) . . . factor each pair of terms

 = (b^2 -4)(b +3) . . .  write as a product

 = (b -2)(b +2)(b +3) . . . use the factoring of the difference of squares

The three factors are (b-2) , (b+2) , and (b+3). We have no clue as to how to associate those with length, width, and height. We just know these are the dimensions of the box.

The possible dimensions of the prism are:

Length: 9x, 5x + 7, or x + 3

Width: 5x + 7, x + 3, or 9x

Height: x + 3, 9x, or 5x + 7

A prism is a three-dimensional object.

There are triangular prism and rectangular prism.

We have,

To find the possible dimensions of the prism, we need to factor the given volume expression into three factors, each representing the length, width, and height of the box.

We start by looking for common factors among the coefficients of the three terms:

45x³ + 198x² + 189x

= 9x (5x² + 22x + 21)

Now we can factor the quadratic expression inside the parentheses:

5x² + 22x + 21

= 5x² + 15x + 7x + 21

= 5x(x + 3) + 7(x + 3)

= (5x + 7) (x + 3)

The volume expression can be factored as:

45x³ + 198x² + 189x

= 9x (5x + 7) (x + 3)

Thus,

The possible dimensions of the prism are:

Length: 9x, 5x + 7, or x + 3

Width: 5x + 7, x + 3, or 9x

Height: x + 3, 9x, or 5x + 7

Learn more about prism here:

https://brainly.com/question/12649592

#SPJ2

Answer:

b

Step-by-step explanation:

Answer:

x-5y

Step-by-step explanation:

Answer:

[tex]x-5y[/tex]

Step-by-step explanation:

[tex]6x-8y-5x+3y[/tex]

[tex]6x-5x-8y+3y[/tex]

[tex]x-5y[/tex]

Answer:

D

Step-by-step explanation:

ΔCBA ≅ Δ BCD

∠A = ∠D = 90°

BC = CB                  {hypotenuse and reflexive property}

BA = CD

Answer:

1/6

Step-by-step explanation: in a rate you need to make it a one so you double the 1/2 gallon to make it one gallon then since you doubled that you have to double the days to 6. So they drink 1 gallon per 6 days.

Answer:

[tex]\frac{dy}{dx}[/tex] = 8(2x + 3)³

Step-by-step explanation:

Differentiate using the chain rule

Given

y = f(g(x)) , then

[tex]\frac{dy}{dx}[/tex] = f'(g(x)) × g'(x)

Here

f(x) = [tex](2x+3)^{4}[/tex] ⇒ f'(x) = 4(2x + 3)³

g(x) = 2x + 3 ⇒ g'(x) = 2

Thus

[tex]\frac{dy}{dx}[/tex] = 4(2x + 3)³ × 2

    = 8(2x + 3)³

Answer:

median is 3.9

Step-by-step explanation:

You arrange them all from the smallest to the biggest, then cross out pairs from each side till you get the one in the middle

0.8, 2.6, 2.8, 3.5, 3.9, 4.6, 6.8, 8.5, 8.6

Answer:

12

Step-by-step explanation:

(5+2)^2 - 40 + 3

= 7^2 - 40 + 3

= 49 - 40 + 3

= 49 - 40

= 9+3

= 12

Answer:

+2 each year. 40+(2+y), y being years.

Answer:

Step-by-step explanation:

7

Answer:

7

Step-by-step explanation:

3.5 divided by .5

Answer:

Positive, Upward Slope.

Step-by-step explanation:

Answer:

the slope of a line shows how steep a straight line is, or the direction of a straight line

Answer:

912 divided byt he square root of AB to 5^2

Step-by-step explanation:

Answer:

AB to 5^2

Step-by-step explanation:

Flattykawa -_-

Answer:

D:7, -5 AND 4p,p

Step-by-step explanation:

B/c like terms are terms with the same variable and exponent.

If it's helpful ❤❤

THANK YOU.

Answer:

n can be a number less than 3

Step-by-step explanation:

Hope this helps!

Answer:

N<3

Step-by-step explanation:

Answer: a. Lin's tank hold 20 cups and Elena's tank hold 20 gallons; I know this because gallons are greater than cups.

Step-by-step explanation:

Gallons are greater than cups so the fish tank that will hold 20 gallons would have to be the bigger one which in this case is Elena's.

With cups being lesser in quantity than gallons, the fish tank that will hold 20 cups of water will definitely have to be the smaller one which in the case is Lina's.

Answer:

x=2

Step-by-step explanation:

First you put the equations in the form of y = mx + b

Then once they are like that it would look like:

y = -2x + 6

y = 3x - 4

So then you can set them equal to each other and it will look like this:

-2x + 6 = 3x - 4

Then you add 2x to both sides and get:

6 = 5x - 4

Next, add 4 to both sides and get:

10 = 5x

So then you will simplify by dividing both sides by 5 and getting:

2 = x

Answer:

If Norma performed 178 haircuts in a month, she would pay $534 to either salon

Step-by-step explanation:

Saloon 1:

Cost of saloon 1 = $534

Saloon 2:

Cost of saloon 2 = 3h

Where,

h = number of haircut

Equate the cost of renting either saloon

534 = 3h

h = 534 / 3

h = 178 hair cut

If Norma performed 178 haircuts in a month, she would pay $534 to either salon.

Answer:

50,373 feet

Step-by-step explanation:

tan 15° = 13500 / x

.268 = 13500 / x

x = 50,373

Answer:

9

Step-by-step explanation:

if you have two negatives next to eachother, the equation now adds like 5+4. 5+4=9

Answer:

-7/3

General Formulas and Concepts:

Algebra I

Slope-Intercept Form: y = mx + b

Step-by-step explanation:

Step 1: Define

y = -7/3x + 5

Step 2: Break Function

Identify Parts

Slope m = -7/3

y-intercept b = 5