Find all real solutions to (x^2+4)(x^3-4x^2-3x+12)=0

Answer:

(3,8)

Step-by-step explanation:

THIS IS AN EXAMPLE FOR ANY PROBLEM!!

Get the equation in the form y = ax2 + bx + c.

Calculate -b / 2a. This is the x-coordinate of the vertex.

To find the y-coordinate of the vertex, simply plug the value of -b / 2a into the equation for x and solve for y. This is the y-coordinate of the vertex.

- Good luck!

Add them both up and divided by 2, 52+45=97. 97/2 =48.5

Step-by-step explanation:

Answer:

78

Step-by-step explanation:

The range is the difference between the highest and lowest number:

4, 5, 8, 18, 21, 43, 82

The highest number is 82 and the lowest is 4

82 - 4 = 78

The range is 78

Answer:1. Use substitution to solve the system of equations:

   -x + 2y=7

    x - 3y = 3

2. Solve the system of equations by the elimination method

a.  2x+ y = -17

   x - y = 2

b. 3x + y = -15

  x + 2y = -10

Answer:

(0, 1)

Step-by-step explanation:

You can solve this by using the substitution or elimination method. For this problem, I'm going to use the substitution method. First, rewrite -4x-2y=-2 in slope-intercept form, which would be y=-2x+1. Substitute the y value in -9x+3y=3 (which would be -9x+3(-2x+1)=3) and solve.

-9x+3(-2x+1)=3

-9x-6x+3=3

-15x=0

x=0

Now, substitute the x value in for the x in any equation. You can do -4(0)-2y=-2 or -9(0)+3y=3. I'm going to use -9(0)+3y=3.

-9(0)+3y=3

3y=3

y=1

Use math-way to solve and check, it gives you all the answers, with a small explanation.

Answer:

y=35

Step-by-step explanation:

3(2y - 5) = 5(y + 4)

6y - 15 = 5y +20

6y - 5y = 20 + 15

y = 35

Answer:

Step-by-step explanation:

[tex]\text{Given that:}[/tex]

[tex]y = 1+ sec(x) \ \ y =3[/tex]

[tex]\text{we draw the graph and the curves intersect at:}[/tex]

[tex]x = - \dfrac{\pi}{3} \ and \ x = \dfrac{\pi}{3}[/tex]

[tex]\text{Applying washer method;}[/tex]

[tex]f(x) _{outer} - g(x) _{inner} --- (1)[/tex]

[tex]V= \int ^b_a A(x) \ dx --- (2)[/tex]

[tex]\text{outer radius = 3 - 1 = 2}[/tex]

[tex]\text{inner radius =}[/tex] [tex]( 1 + sec(x) ) - 1 = sec (x)[/tex]

[tex]A(x) = \pi ((2)^2 -(sec(x)^2) \\ \\ A(x) = \pi (4 - sec^2 (x)) ---- (3)[/tex]

[tex]\text{The volume V =}\int ^{\dfrac{\pi}{3}}_{-\dfrac{\pi}{3}} \ \ A(x) \ dx[/tex]

[tex]V = \int ^{\dfrac{\pi}{3}}_{-\dfrac{\pi}{3}} \ \ \pi (4- sec^2 (x) ) \ dx[/tex]

[tex]V = 2 \pi \int ^{\dfrac{\pi}{3}}_{0}( 4 - sec^2 (x)) \ dx[/tex]

[tex]V = 2 \pi \int ^{\pi/3}_{0} 4 . \ dx - 2 \pi \int ^{\pi/3}_{0} sec^2 (x) \ dx[/tex]

[tex]V = 2 \pi(4) \int ^{\pi/3}_{0} 1 . \ dx - 2 \pi \Big( tan (x)\Big )^{\dfrac{\pi}{3}}_{0}[/tex]

[tex]V = 8 \pi(x)^{\dfrac{\pi}{3}}_{0} - 2 \pi \Big( tan \dfrac{\pi}{3} -tan (0)\Big )[/tex]

[tex]V = 8 \pi({\dfrac{\pi}{3}}-{0}) - 2 \pi \Big( tan \sqrt{3}-(0)\Big )[/tex]

[tex]V = 8 \pi({\dfrac{\pi}{3}}) - 2 \pi \Big( \sqrt{3}\Big )[/tex]

[tex]\mathbf{V = 2 \pi \Big(\dfrac{4\pi}{3}- \sqrt{3} \Big)}[/tex]

Answer:

[tex]Total = 104\ hrs[/tex]

Step-by-step explanation:

Given

[tex]Monday = 15\ hrs[/tex]

[tex]Tuesday = 13\ hrs[/tex]

[tex]Wednesday = 24\ hrs[/tex]

Required

Determine the hours of practice over 6 days

First, we calculate the hours for the given 3 days.

[tex]Hours = Monday + Tuesday + Wednesday[/tex]

[tex]Hours = 15\ hrs + 13\ hrs + 24\ hrs[/tex]

[tex]Hours = 52\ hrs[/tex]

The hours of practice for the other three days is also 52 hours.

So, the total is:

[tex]Total = 52\ hrs + 52\ hrs[/tex]

[tex]Total = 104\ hrs[/tex]

Answer:

104

Step-by-step explanation:

Step-by-step explanation:

The power can come to the front according to logarithm rule.

Question:

You are making sandwiches for a large party. Each sandwich has two slices of bread, one slice of turkey, two slices of cheese, three slices of tomato and 5 slices of cucumber. How many sandwiches will you get from 10 slices of bread and 20 slices of cucumber? assuming you have plenty of everything

Answer:

4 sandwiches

Step-by-step explanation:

Given

1 Sandwich contains:

[tex]Bread = 2\ slices[/tex]

[tex]Turkey = 1\ slice[/tex]

[tex]Cheese = 2\ slices[/tex]

[tex]Tomato = 3\ slices[/tex]

[tex]Cucumber = 5\ slices[/tex]

Required

Number of sandwiches from 10 slices of bread and 20 slices of cucumber?

Since we are to assume that every other thing is in abundance, we will only consider the unit amount of bread and cucumber

[tex]Bread = 2\ slices[/tex]

[tex]Cucumber = 5\ slices[/tex]

Express as ratio

[tex]Bread : Cucumber = 2 : 5[/tex]

When the ratio is multiplied by 5, the slice of cucumber (25) will exceed the available slices (20).

So, we multiply by 4

[tex]Bread : Cucumber = 2*4 : 5*4[/tex]

[tex]Bread : Cucumber = 8 : 20[/tex]

This implies that:

8 slices of bread and 20 slices of cucumber are used

Hence:

4 sandwiches can be made

Answer:

Quadratic and Trinomial

Step-by-step explanation:

It has a degree of 2, making it a quadratic. It has 3 terms, so it's a trinomial.

Answer:

DE

Step-by-step explanation:

Answer:

[tex]\displaystyle f'(1) = \frac{3}{2}[/tex]

[tex]\displaystyle f''(1) = \frac{3}{4}[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to Right

Algebra II

Exponential Rule [Rewrite]:                                                                            [tex]\displaystyle b^{-m} = \frac{1}{b^m}[/tex]Exponential Rule [Root Rewrite]:                                                                   [tex]\displaystyle \sqrt[n]{x} = x^{\frac{1}{n}}[/tex]

Calculus

Derivatives

Derivative Notation

Basic Power Rule:

f(x) = cxⁿf’(x) = c·nxⁿ⁻¹

Derivative Property [Addition/Subtraction]: [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]

Derivative Rule [Product Rule]:                                                                             [tex]\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)[/tex]

Derivative Rule [Quotient Rule]:                                                                           [tex]\displaystyle \frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}[/tex]

Step-by-step explanation:

Step 1: Define

f(x) = x√x

f'(1) is x = 1 for 1st derivative

f''(1) is x = 1 for 2nd derivative

Step 2: Differentiate

[1st Derivative] Product Rule:                                                                       [tex]\displaystyle f'(x) = \frac{d}{dx}[x]\sqrt{x} + x\frac{d}{dx}[\sqrt{x}][/tex][1st Derivative] Rewrite [Exponential Rule - Root Rewrite]:                         [tex]\displaystyle f'(x) = \frac{d}{dx}[x]\sqrt{x} + x\frac{d}{dx}[x^{\frac{1}{2}}][/tex][1st Derivative] Basic Power Rule:                                                                 [tex]\displaystyle f'(x) = (1 \cdot x^{1 - 1})\sqrt{x} + x(\frac{1}{2}x^{\frac{1}{2}-1})[/tex][1st Derivative] Simply Exponents:                                                               [tex]\displaystyle f'(x) = (1 \cdot x^0)\sqrt{x} + x(\frac{1}{2}x^{\frac{-1}{2}})[/tex][1st Derivative] Simplify:                                                                                 [tex]\displaystyle f'(x) = \sqrt{x} + x(\frac{1}{2}x^{\frac{-1}{2}})[/tex][1st Derivative] Rewrite [Exponential Rule - Rewrite]:                                 [tex]\displaystyle f'(x) = \sqrt{x} + x(\frac{1}{2x^{\frac{1}{2}}})[/tex][1st Derivative] Rewrite [Exponential Rule - Root Rewrite]:                         [tex]\displaystyle f'(x) = \sqrt{x} + x(\frac{1}{2\sqrt{x}})[/tex][1st Derivative] Multiply:                                                                                 [tex]\displaystyle f'(x) = \sqrt{x} + \frac{x}{2\sqrt{x}}[/tex][2nd Derivative] Rewrite [Exponential Rule - Root Rewrite]:                     [tex]\displaystyle f'(x) = x^{\frac{1}{2}} + \frac{x}{2x^{\frac{1}{2}}}[/tex][2nd Derivative] Basic Power Rule/Quotient Rule [Derivative Property]: [tex]\displaystyle f''(x) = \frac{1}{2}x^{\frac{1}{2} - 1} + \frac{\frac{d}{dx}[x](2x^{\frac{1}{2}}) - x\frac{d}{dx}[2x^{\frac{1}{2}}]}{(2x^{\frac{1}{2}})^2}[/tex][2nd Derivative] Simplify/Evaluate Exponents:                                           [tex]\displaystyle f''(x) = \frac{1}{2}x^{\frac{-1}{2}} + \frac{\frac{d}{dx}[x](2x^{\frac{1}{2}}) - x\frac{d}{dx}[2x^{\frac{1}{2}}]}{4x}[/tex][2nd Derivative] Rewrite [Exponential Rule - Rewrite]:                               [tex]\displaystyle f''(x) = \frac{1}{2x^{\frac{1}{2}}} + \frac{\frac{d}{dx}[x](2x^{\frac{1}{2}}) - x\frac{d}{dx}[2x^{\frac{1}{2}}]}{4x}[/tex][2nd Derivative] Basic Power Rule:                                                             [tex]\displaystyle f''(x) = \frac{1}{2x^{\frac{1}{2}}} + \frac{(1 \cdot x^{1 - 1})(2x^{\frac{1}{2}}) - x(\frac{1}{2} \cdot 2x^{\frac{1}{2} - 1})}{4x}[/tex][2nd Derivative] Simply Exponents:                                                             [tex]\displaystyle f''(x) = \frac{1}{2x^{\frac{1}{2}}} + \frac{(1 \cdot x^0)(2x^{\frac{1}{2}}) - x(\frac{1}{2} \cdot 2x^{\frac{-1}{2}})}{4x}[/tex][2nd Derivative] Simplify:                                                                             [tex]\displaystyle f''(x) = \frac{1}{2x^{\frac{1}{2}}} + \frac{2x^{\frac{1}{2}} - x(\frac{1}{2} \cdot 2x^{\frac{-1}{2}})}{4x}[/tex][2nd Derivative] Multiply:                                                                             [tex]\displaystyle f''(x) = \frac{1}{2x^{\frac{1}{2}}} + \frac{2x^{\frac{1}{2}} - x(x^{\frac{-1}{2}})}{4x}[/tex][2nd Derivative] Rewrite [Exponential Rule - Rewrite]:                               [tex]\displaystyle f''(x) = \frac{1}{2x^{\frac{1}{2}}} + \frac{2x^{\frac{1}{2}} - x(\frac{1}{x^{\frac{1}{2}}})}{4x}[/tex][2nd Derivative] Multiply:                                                                             [tex]\displaystyle f''(x) = \frac{1}{2x^{\frac{1}{2}}} + \frac{2x^{\frac{1}{2}} - \frac{x}{x^{\frac{1}{2}}}}{4x}[/tex][2nd Derivative] Simplify:                                                                             [tex]\displaystyle f''(x) = \frac{1}{2x^{\frac{1}{2}}} + \frac{x^{\frac{1}{2}}}{4x}[/tex][2nd Derivative] Rewrite [Exponential Rule  - Root Rewrite]:                     [tex]\displaystyle f''(x) = \frac{1}{2\sqrt{x}} + \frac{\sqrt{x}}{4x}[/tex]

Step 3: Evaluate

[1st Derivative] Substitute in x:                                                                     [tex]\displaystyle f'(1) = \sqrt{1} + \frac{1}{2\sqrt{1}}[/tex][1st Derivative] Evaluate Roots:                                                                     [tex]\displaystyle f'(1) = 1 + \frac{1}{2(1)}[/tex][1st Derivative] Multiply:                                                                                 [tex]\displaystyle f'(1) = 1 + \frac{1}{2}[/tex][1st Derivative] Add:                                                                                       [tex]\displaystyle f'(1) = \frac{3}{2}[/tex][2nd Derivative] Substitute in x:                                                                   [tex]\displaystyle f''(1) = \frac{1}{2\sqrt{1}} + \frac{\sqrt{1}}{4(1)}[/tex][2nd Derivative] Evaluate Roots:                                                                 [tex]\displaystyle f''(1) = \frac{1}{2(1)} + \frac{1}{4(1)}[/tex][2nd Derivative] Multiply:                                                                             [tex]\displaystyle f''(1) = \frac{1}{2} + \frac{1}{4}[/tex][2nd Derivative] Add:                                                                                     [tex]\displaystyle f''(1) = \frac{3}{4}[/tex]

Answer:

The Answer should be Quadrant III

Step-by-step explanation:

Hope this helped!

Answer:

Your question is in what base please?

Step 1 Eliminate fractions by multiplying all terms by the least common denominator of all fractions.

Step 2 Simplify by combining like terms on each side of the inequality.

Step 3 Add or subtract quantities to obtain the unknown on one side and the numbers on the other.

hope this help you... :) and have a good day

Answer:equal to y

x is equal to y. Where as in an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥. x>y. x is greater than y.

Step-by-step explanation:

Ok so I’m going to try my best:
I’m guessing you would do $960 times 6.1 but you move the decimal point twice to the left which would be: .061
This is how we find out each month
58.56
So, we start out with $960 we keep adding 58.56 or to do faster we can multiply
Adding 58.56:
1 = 1018.56
2 = 1077.12

Multiplying 58.56 by 13:
KEEP IN MIND THAT WE START FROM $960 and we need TO GET TO $1,720
58.56 times 13 equals 761.28
Then we add
960 + 761.28
1721.28

So it would have to be 12 months since it needs to be less or “to the nearest year”
Therefore, the answer would be a year

I hope this helps! :) good luck

It’s 12 months I think I’m sorry if it’s wrong.

Answer:

$81.95

Step-by-step explanation:

0.07 * 55 = 3.85

(3.85 * 7) + 55

26.95 + 55

81.95

Answer:

D. 1/8

Step-by-step explanation:

A unit fraction is a fraction with numerator of 1.

Answer:

D 1/8 Because unit factions always have a one as the numarator

Sides of the triangle = 3, 4, 5

Here, one thing to remember is, you have to put 5 as the "Hypotenuse" (Longest side) & smaller one's as Base & Perpendicular.

Hope this helps!

Answer:The square root of 4 is 2 . The square root of 49 is 7 .Apr 19, 2015

Step-by-step explanation:

Answer:

416,000

Step-by-step explanation:

per hour 9*100=900

per week 900*40=36,000

per year 36,000*52=1,872,000

with raise

11*100=1,100

1,100*40=44,000

44,000*52=2,288,000

difference equals

416,000

Answer:

C

Step-by-step explanation:

7 - 2 = 5

11 - 3(2)

11 - 6 = 5

4(2) - 3

8 - 3 = 5

C is the only one that doesn't equal 5

Answer: 7 degrees of freedom.

Step-by-step explanation:

Answer:

The United States of America mostly and maybe Canada

I’m sorry I didn’t know that you were going to be in there until about it later this week and then he came back and forth

Answer:

D.324

Step-by-step explanation:

Answer:

D. 324 Sq in

Step-by-step explanation:

Painted area = area of rectangle + Area of square + Area of triangle

[tex] = 60 \times 4 + {8}^{2} + \frac{1}{2} \times 8 \times 5 \\ \\ = 240 + 64 + 20 \\ \\ = 324 \: {in}^{2} [/tex]

Answer:

(4,18); (6,22); (8,26)

Step-by-step explanation:

Plug in the numbers 4, 6, and 8, in for d using the equation.

c=2d+10

c=2(4)+10

c=8+10

c=18

(4,18)

c=2d+10

c=2(6)+10

c=12+10

c=22

(6,22)

c=2d+10

c=2(8)+10

c=16+10

c=26

(8,26)

Answer:

14

18

22

26

Step-by-step explanation:

c = 2d + 10

1st one: substitute 2 for d

c = 2 x 2 + 10

c = 14

2nd one: substitute 4 for d

c = 2 x 4 + 10

c = 18

3rd one: substitute 6 for d

c = 2 x 6 + 10

c = 22

4th one: substitute 8 for d

c = 2 x 8 + 10

c = 26

Answer:

-6

Step-by-step explanation:

2 x -3 = -6

1 positive and a negative integer multiplied will get a negative answer

The answer is -6 ! Good luck!

Answer:

6:8 and 8:14

Step-by-step explanation:

Answer:

The answer is 2.6

Hope this Helps!!!

10.6-3(4.5)
10.6-13.5
=-2.9