If the roots of ax² + bx + c = 0 differ by 3. Show that b² =9a² + 4ac​

Answer:

Diverges

General Formulas and Concepts:

Algebra I

Calculus

Limits

Series Convergence Tests

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle \sum^{\infty}_{n = 19} \frac{8n^3 - 2n^2 + 19}{6 + 3n^4}[/tex]

Step 2: Apply DCT

∴ the sum  [tex]\displaystyle \sum^{\infty}_{n = 19} \frac{8n^3 - 2n^2 + 19}{6 + 3n^4}[/tex]  is divergent by DCT.

Step 3: Apply LCT

∴ Because  [tex]\displaystyle \lim_{n \to \infty} \frac{a_n}{b_n} \neq 0[/tex]  and the sum  [tex]\displaystyle \sum^{\infty}_{n = 19} a_n[/tex]  diverges by DCT,  [tex]\displaystyle \sum^{\infty}_{n = 19} \frac{8n^3 - 2n^2 + 19}{6 + 3n^4}[/tex]   also diverges by LCT.

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Convergence Tests (BC Only)

Book: College Calculus 10e

Answer:

[tex](\frac{f}{g})(x) = \frac{x- 3}{2x + 1}[/tex]

Step-by-step explanation:

Given

[tex]f(x) =x^2 -x - 6[/tex]

[tex]g(x) = 2x^2 + 5x + 2[/tex]

Required

[tex](\frac{f}{g})(x)[/tex]

This is calculated as:

[tex](\frac{f}{g})(x) = \frac{f(x)}{g(x)}[/tex]

So, we have:

[tex](\frac{f}{g})(x) = \frac{x^2 - x - 6}{2x^2 + 5x + 2}[/tex]

Expand

[tex](\frac{f}{g})(x) = \frac{x^2 +2x - 3x - 6}{2x^2 + 4x+x + 2}[/tex]

Factorize

[tex](\frac{f}{g})(x) = \frac{x(x +2) - 3(x + 2)}{2x(x + 2)+1(x + 2)}[/tex]

Factor out x + 2

[tex](\frac{f}{g})(x) = \frac{(x- 3)(x + 2)}{(2x + 1)(x + 2)}[/tex]

Cancel out x + 2

[tex](\frac{f}{g})(x) = \frac{x- 3}{2x + 1}[/tex]

Answer:

a.) 16

b.) 8

Step-by-step explanation:

a. how much lower was the 6am temperature in Nome than in Wyoming

Essentially this question is asking us to find the difference of the temperatures of Nome and Wyoming at 6am

Temperature of Nome at 6am: -31

Temperature of Wyoming at 6am: -15

Difference between two temperatures: -31 - (-15)

The two negative signs cancel out and the sign changes to +

-31 + 15 = -16

The temperature in Nome was 16 degrees lower then in Wyoming

b. At noon the temperature of Boston had risen by 14 degrees. what was the temperature of boston at noon.

All we have to do for this one is add 14 to the temperature of Boston at 6am. ( This is because the question tells us the temperature has risen 14 degrees by noon )

-6 + 14 = 8

At noon the temperature would be 8 degrees in Boston.

Answer:

Low-value method

Step-by-step explanation:

consumers group

Answer:

96.72

Step-by-step explanation:

Answer:

96.77

Step-by-step explanation:

pi is 3.142

radius = 15.4ft

c = 2*3.142*15.4

Answer:

the

Step-by-step explanation:

it's fairly easy actually. You just have to use sin

66 because you have to solve the problem next time

Answer:

1/8

Step-by-step explanation:

Using the factor tree, we see that there is 8 possible outcomes ( right hand side)

There is only 1 way to go from left to right and have 3 wins

P(3 wins) = good outcomes / total

               =1/8

9514 1404 393

Answer:

  4. True

  5. False

Step-by-step explanation:

4. The number of x-intercepts produced by the quadratic formula may be 0, 1, or 2. It will be 0 if the two roots are complex. It will be 1 if the two roots lie in the same place (one root with multiplicity 2). It is true that there may be only one x-intercept.

__

5. The value of 'b' in the quadratic formula is the coefficient of the linear term. In the given quadratic, it is -5, not 5.

Answer:

D, 4√7

Step-by-step explanation:

Answer:

Step-by-step explanation:

c = 16

a = 12

b = ?

a^2 + b^2 = c^2

12^2 + b^2 = 16^2

144 + b^2 = 256

b^2 = 256 - 144

b^2 = 112

b^2 = 16 * 7

sqrt(b^2) = sqrt(16)*sqrt(7)

b = 4 * sqrt(7)

Step-by-step explanation:

153∕4 + 8i is the correct answer

[I'm supposing that you have to find the value of (1/ 2 + 4i)²]

Answer:

[tex] = \frac{ - 63}{4} + 4i[/tex]

Step-by-step explanation:

we must know that

[tex] {( \frac{1}{2} + 4i) }^{2} = { (\frac{1}{2} })^{2} + {(4i)}^{2} + 2 . \frac{1}{2} . 4i[/tex]

[tex] = \frac{1}{4} + 16 {i}^{2} + 4i[/tex]

[tex] = \frac{1}{4} - 16 + 4i[/tex]

[tex] = \frac{1 - 64}{4} + 4i[/tex]

[tex] = \underline{ \frac{ - 63}{4} + 4i} [/tex]

[I'm also assuming that instead of -153/4 + 4i option A says -63/ 4 + 4i.]

so the answer is option A.

Answer:

-6

Step-by-step explanation:

2 - [6 ÷ 2 + {6 × 1/2 + (7/2 - 3/2)}] =

Follow the correct order of operations.

Do one step at a time and copy everything else each time, so you don't lose track of any operation.

= ​2 - [6 ÷ 2 + {6 × 1/2 + 4/2}]

= 2 - [6 ÷ 2 + {6 × 1/2 + 2}]

= 2 - [6 ÷ 2 + {3 + 2}]

= 2 - [6 ÷ 2 + 5]

= 2 - [3 + 5]

= 2 - 8

= -6

Answer:

-6

hope this helps

Step-by-step explanation:

2_(6÷2+(6*1/2+(7/2-3/2))) solve the ones in bracket first

(7/2-3/2)=2

2-(6÷2+(6×1/2+2))

6×1/2+2

6×1/2=3

3+2=5

2-(6÷2+5)

6÷2=3

3+5=8

2-8

=-6

Answer:

[tex]{ \tt{y = 2x}}[/tex]

Answer:

2y=x

Step-by-step explanation:

Answer:

Exact heights of the next 100 babies born in a region.

Step-by-step explanation:

A discrete random variable involves two key factors ; discrete and randomness ; Hence, a discrete random variable should have a finite or countable Number of outputs or values. It should also stem from a random procedure. Here, the height of the next hundred babies is a random procedure as the next 100 babies in the region are unknown until Given birth too and as such all pregnant women have the chance of having their babies among. Since, we are dealing with exact height values which are countable (100), then we this is a discrete random variable.

Answer:

Selena's annual intake home salary is $ 26,640.

Step-by-step explanation:

Since Selena's gross annual salary as the content editor of a fashion Magazine is $ 40,000, and she contributes 10% of her salary before she pays taxes to a retirement account, and 25% of her remaining salary is then consumed in state and federal taxes, To determine what is Selena's annual intake home salary if she also has to pay $ 30 for health Insurance each month, the following calculation must be performed:

40,000 - (40,000 x 0.1) - (40,000 x 0.9 x 0.25) - (30 x 12) = X

40,000 - 4,000 - 9,000 - 360 = X

26.640 = X

Therefore, Selena's annual intake home salary is $ 26,640.

Answer:

Step-by-step explanation:

If you need the equation:

point slope form is:

y-y1 = m(x-x1)

m is the slope and (x1,y1) is a point on the line.

y- (-1) = 6(x-4)

If you want standard form:

y= 6x -24 -1

y=6x-25

Answer:

72

Step-by-step explanation:

To be divisible by 4, the number must be even, so we can eliminate 63 and 73  (There are other restrictions for 4, we just want to eliminate answers that cannot be true)

We have only 2 answers left

64 and 72

To be divisible by 3, the sum of the digits must be divisible by 3

6+4 = 10 which is not divisible by 3

7+2 = 9   9/3 =3  

Answer:

The linear equation that relates the cost C, in dollars, of renting the truck to the number x of miles driven is 0.05*x + 20 and the cost of renting the truck if the truck is driven 107 miles is 25.35.

Step-by-step explanation:

A linear function is a polynomial function of the first degree that has the form:

f (x) = y = m*x + b

where m is the slope of the function and b is the y-intercept.

The graph of a linear function is always a line.

A truck rental company rents a moving truck for one day by charging $20 plus $0.05 per mile. So, the number of miles travel is represented by "x"  and the cost per mile is represented by "c". The y-intercept is the starting cost at zero miles or $20.  The slope is the rate per mile or $0.05. Then:

c= 0.05*x + 20

If the truck is driven 107 miles, then:

c= 0.05* 107 + 20

Solving:

c= 25.35

So, the linear equation that relates the cost C, in dollars, of renting the truck to the number x of miles driven is 0.05*x + 20 and the cost of renting the truck if the truck is driven 107 miles is 25.35.

Answer:

= c^4 d^8 a^2

Step-by-step explanation:

Apply exponent rule: aa= a^2

= c^3 da^2 cd^7

= c^4 da^2 d^7

= c^4 d^8 a^2

Answer:

✓ x gal of 25% 20-x gal of 5% pure alcohol is x(.25)+(20-x)(.05)=20*.16=3.2 so .25x+1-.05x=3.2 gallons of 25% .20x=2.2 gallons of 5% x=11 gallons of 25%.

Step-by-step explanation:

Hope this helps~ ;D

Answer:

1. What is a recursive formula?

A recursive formula is a formula that defines each term of a sequence using preceding terms of the sequence.

2. What is a factorial?

factorial the product of all positive integers less than or equal to n:

3. What is the relationship between sequences, series and sigma notation?

A series can be represented in a sigma notation.

A series can be represented in a sigma notation.A series is a sum of a sequence of terms.

Step-by-step explanation:

d=20 J.

E=2,N,J

this is your answer

42-x=58

or, -x=58-42

with change in side sign also chamges we change sides to make like terms in one side and unlike in amother side.

or, -x= 16

or,x=-16.

therefore x=-16...

Hope this helps you.

Answer:

3500.416

Step-by-step explanation:

Compound interest formula

A = A0(1 + r/n)^nt

3200(1 + 0.6%)^15

3200(1 + 0.006)^15

3200(1.006)^15

Answer:

deflation ,,,,

Step-by-step explanation:

Deflation must have existed during the second 9-year period.

Deflation is a decrease in the general price level of goods and services in an economy over a period of time. This means that the purchasing power of money increases, as the same amount of money can buy more goods and services.

The opposite of inflation, which is an overall rise in the cost of goods and services over time, is deflation. Money loses value due to inflation, whereas it gains value due to deflation. Deflation can reduce demand for goods and services, though, if it lasts for a long time. This is because customers may put off purchases in expectation of cheaper costs. A downturn in economic activity may follow, which would be bad for the economy.

Given data ,

Deflation is a decrease in the general price level of goods and services in an economy over a period of time. A decrease in the Consumer Price Index (CPI) is a measure of deflation.

In the first 9-year period, the CPI decreased by 45%, which indicates a significant deflationary period. In the next 9-year period, the CPI decreased by only 5%, which still indicates a deflationary period, but not as severe as the previous one.

Hence , the process is deflation in the second year

To learn more about deflation click :

https://brainly.com/question/30060490

#SPJ7

C. Dilation.

Dilation can resize the image.

Translation will shift the imagine's position but won't change its actual size.

Rotation will mangle with image's orientation but also won't change its size.

Reflection is just a type of rotation which as established, also won't change its size.

Hope this helps.

Answer:

3/8

Step-by-step explanation:

We can write the entire book with the number 1. Now we can write this operation

3/8 + 1/4 + x = 1

3 + 2 + 8x = 8

5 + 8x = 8

8x = 3

x = 3/8

Answer:

y=1/4x  

Step-by-step explanation:

Just did the math ;D

Answer:

The y-coordinate of point A is [tex]\sqrt{3}[/tex].  

Step-by-step explanation:

The equation of the circle is represented by the following expression:

[tex](x-h)^{2}+(y-k)^{2} = r^{2}[/tex] (1)

Where:

[tex]x[/tex] - Independent variable.

[tex]y[/tex] - Dependent variable.

[tex]h[/tex], [tex]k[/tex] - Coordinates of the center of the circle.

[tex]r[/tex] - Radius of the circle.

If we know that [tex]h = 0[/tex], [tex]k = 0[/tex] and [tex]r = 2[/tex], then the equation of the circle is:

[tex]x^{2} + y^{2} = 4[/tex] (1b)

Then, we clear [tex]y[/tex] within (1b):

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

[tex]y = \pm \sqrt{4-x^{2}}[/tex] (2)

If we know that [tex]x = 1[/tex], then the y-coordinate of point A is:

[tex]y = \sqrt{4-1^{2}}[/tex]

[tex]y = \sqrt{3}[/tex]

The y-coordinate of point A is [tex]\sqrt{3}[/tex].