Solve the quadratic equation by using either a numeric or a graphic approach.
x^2-11x-121= 0

The expression (x+1)(x+3)(x+5) can be expanded to the form ax^3+bx^2+cx+d with a, b, and c as positive integers and d as negative by first multiplying (x+1) and (x+3) to get x^2+4x+3, which is then multiplied by (x+5) to obtain x^3+9x^2+23x+15.

To show that

(x+1)(x+3)(x+5)

can be written in the form

ax^3+bx^2+cx+d  where a,b and c are all positive integers, and d is a negative integer, perform multiplication for the given factors as follows:

Firstly, multiply (x+1) and (x+3) which yields x^2+4x+3.

Then, multiply this result by (x+5) which gives the final form: x^3+9x^2+23x+15.

So, a=1, b=9, c=23, and d=15 proving the original expression can be written in the stated form.

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The future value of $82,100 invested at a 4.3% annual interest rate compounded continuously for 2 years using the formula V = Pe^{rt}, will be approximately $90,137.30.

Your question involves the calculation of the future value of an investment using the formula for continuous compound interest, in this case $82,100 invested at an annual rate of 4.3%, over 2 years. This scenario relies on the mathematical concept of compound interest, which means the interest earned on the initial investment is added to the principal, and this combined amount earns interest as well.

Using the formula V = Pe^{rt}. where:
P = principal amount (initial investment) = $82,100,
r = annual nominal interest rate (decimal) = 4.3/100 = .043,
t = time the money is invested for = 2 years,
e = Euler's number (approx. 2.71828).

The calculation then becomes: V = $82,100 * e^(0.043 * 2) = $82,100 * e^(0.086). Using a calculator to do the exponentiation and the multiplication, the balance in the account after 2 years would approximately be $90,137.30.

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Answer:

2 Pieces

Mostly depends how much slices are there

Step-by-step explanation:

Every element is called half the whole by all equal sections. Similarly, the half fraction is defined as the whole half component of both of the two equivalent sections of the rectangle.

Hope this helps

Answer:

1 expression) 477 - 6s

2 equation) s = 75

Step-by-step explanation:

Also, the first expression is simplified

Answer:

Variance = 78.5

Standard Deviation = 8.86

Step-by-step explanation:

Given

Mean = 81

Required

Find the variance and standard deviation of the given set of data.

Provided that we already know the mean; to calculate the variance, follow the steps below.

1. Subtract the mean from each data.

76 - 81 = -5

87 - 81 = 6

65 - 81 = -16

88 - 81 = 7

67 - 81 = -14

84 - 81 = 3

77 - 81 = -4

82 - 81 = 1

91 - 81 = 10

85 - 81 = 4

90 - 81 = 9

2. Square these results

-5² = 25

6² = 36

-16² = 256

7² = 49

-14² = 196

3² = 9

-4² = 16

1² = 1

10² = 100

4² = 16

9² = 81

3. Sum these results

Sum = 25+36+256+49+196+9+16+1+100+16+81

Sum = 785

4. Calculate variance by dividing the sum by n - 1 where n = 11

So, n - 1 = 11 - 1 = 10

Variance = 785/10

Variance = 78.50

5. Calculate standard deviation by finding the square root of variance

S.D = √78.50

S.D = 8.86 (Approximated)

Answer:

71.36 and 8.45

Step-by-step explanation:

Answer:

C

Source:

Trust me

Answer:

(5x + 1) • (5x - 1)

Step-by-step explanation:

Step 1:

Equation at the end of step 1:

5^2x^2 - 1

Step 2:

Trying to factor as a Difference of Squares :

Factoring: 25x^2-1

Theory :

A difference of two perfect squares,

A difference of two perfect squares, A^2 - B^2 can be factored into (A+B) • (A-B)

Proof : (A+B) • (A-B)

= A^2 - AB + BA - B^2

= A^2 - AB + AB - B^2

= A^2 - B^2

Note : AB = BA is the commutative property of multiplication.

Note : - AB + AB equals zero and is therefore eliminated from the expression.

Check : 25 is the square of 5

Check : 1 is the square of 1

Check : x^2 is the square of x^1

Factorization is :

(5x + 1) • (5x - 1)

Final result :

(5x + 1) • (5x - 1)

Answer:

Step-by-step explanation:

(5x-1) (5x+1)

Answer:

Greater ; Greater

Smaller ; Greater

Step-by-step explanation:

Slopes

First row

A: 15/2

B: (25-12.5)/(4-2) = 12.5/2

A has a greater slope than B

-4x + 2y = 8

2y = 4x + 8

y = 2x + 4

A: 2

B: 3/2

A has a greater slope than B

Second Row

A: (2.6-2)/(3-0) = 0.6/3 = 0.1

B: (5-4)/(4-0) = 1/4 = 0.25

A has a smaller slope than B

A: 60

B: (325-50)/5-0) = 275/5 = 55

A has a greater slope than B

Answer:

The area I believe.

Step-by-step explanation:

The Length of a two-dimensional figure can be any side.

length is the measure of some distance from one end to another end.

The side is a distance between two vertexes joined with another part of the figure.

We can measure that distance which means it could be a length.

Thus, The Length of a two-dimensional figure can be any side.

Learn more about length;

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Answer:

The domain is all real numbers

Step-by-step explanation:

if y = 3x and x can be any number

you can do 3 times -29 or 3 times 1/3

Answer:

3/10

Step-by-step explanation:

there are 10 letters in substitute

there are 3 t's

3/10

The probability of choosing the letter 't' will be 3 / 10.

Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

Given that:-

The probability will be calculated as:-

There are 10 letters in the word SUBSTITUTE.

Out of these 10 letters, t is three times in the word

So probability will be:-

P  =  3  /  10

Therefore the probability of choosing the letter 't' will be 3 / 10.

To know more about probability follow

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Answer:

y decreases by half everytime

Step-by-step explanation:

Radius of the hemisphere and the cone base:  R = 2 in

Height of the cone:   H = 6 - 2 = 4 in

π ≈ 3,14

Ice inside cone:

                           [tex]V_1=\frac13\pi R^2\cdot H=\frac13\pi\cdot2^2\cdot 4=\frac{16}3\pi[/tex]

Ice outside cone:

                            [tex]V_2=\frac12\cdot\frac43\pi R^3=\frac23\pi\cdot2^3=\frac{16}3\pi[/tex]

Total of ice:

[tex]V=V_1+V_2=\frac{16}3\pi+\frac{16}3\pi=\frac{32}3\pi\approx\frac{32}3\cdot3,14=33,49(3)\approx33,5[/tex]

There are 33,5 cubic inches of ice in the cone.

Answer: 6

Step-by-step explanation:

Answer:

mean = 0

Step-by-step explanation:

-3 -2 -1

0

1

2

3

if your set is  -3, -2, -1, 0, 1, 2, 3  the your mean = 0

Answer:

2/5

Step-by-step explanation:

Defining x the weight of each quarter grades (4x for the 4 quarter grades), then the weight of the mid-term exam grade is 2x, and the weight of the final exam is 4x. The addition of all grades is 4x + 2x + 4x = 10x (this represents the combination of grades that makes the final course grade).

So, the final exam grade represents 4x/10x = 2/5 of the final course grade.

Answer:

2/5

Step-by-step explanation:

just did the test

Answer:

Step-by-step explanation:

The question is not properly structured and the equation is also incorrect. Here is the correct question.

You and some friends went to a haunted house on Halloween. The mummy scared one friend so much that she jumped into the air! The equation h= -4t²+ 2t models her jump where h is her jumps height in feet t seconds after the mummy scares her. When did she reach her maximum.

Give the equation h= -4t²+ 2t that models my friend jump where h is her jumps height in feet t seconds, At maximum height, her velocity will be zero i.e

Vmax = 0m/s

Velocity is the rate of change in distance of a body i.e V = dh/dt

Given  h= -4t²+ 2t

V = dh/dt = -8t+2

Since v = 0m/s

0 = -8t+2

-8t = -2

t = -2/-8

t = 0.25 secs

She reaches her maximum height after 0.25 seconds

Answer:

15

Step-by-step explanation:

Since a square has 4 sides, that means that each side is equal to the other three sides because it is a square. If so, we do 60/4 to get is 15. To check the answer 15x4 is equal to 60.

Answer:

each side will be 15

Step-by-step explanation:

because if its a square and all the sides are the same lengh and one of the sides are 15 then all of the other sides will also be 15,so that will equal 60.

Answer:

He has 29 crayons left

Step-by-step explanation:

56-27=29

All you have to do is subtract since fewer means less and to find less you need to subtract

Answer:

  A) 21.02°

  B) 26.74°

  C) 22.79°

  D) DNE

Step-by-step explanation:

We can solve the equation for the angle:

  D = 672·sin(2θ)

  D/672 = sin(2θ)

  arcsin(D/672) = 2θ

  θ = arcsin(D/672)/2

A) For D = 450, θ = arcsin(450/672)/2 = 21.0198° ≈ 21.02°

B) For D = 540, θ = arcsin(540/672)/2 = 26.7363° ≈ 26.74°

C) For D = 480, θ = arcsin(480/672)/2 = 22.7923° ≈ 22.79°

D) For D = 720, θ = arcsin(720/672)/2 = DNE

Answer:

the balance after 5 years is: 26540.744

Step-by-step explanation:

Given the information:

We have the compound interest function ta model the situation is:

[tex]A=P(1+\frac{r}{n} )^{nt}[/tex]

<=> A = [tex]20000(1+\frac{0.05}{4} )^{4*5}[/tex]

<=> A = $26540.744

Hence, the balance after 5 years is: $26540.744

Answer:

$25,640.74

Step-by-step explanation:

The total compound interest is $5,640.74.

The final balance is $25,640.74.

with zero additional deposits

hope this helps:)

Answer:

A

Step-by-step explanation:

Answer:

476.25 hertz

Step-by-step explanation:

Since the speed of a wave is the wave length multiplied by the frequency, the frequency can be written as the speed divided by the wave length. 3810/8=476.25 hZ. Hope this helps!

Answer:

150%  change

Step-by-step explanation:

Formula for Percent change =  C =[ (new - old)/ old ]* 100%

C =  [ (25 in. - 10 in.) / 10 in. ] = [15/10 ] * 100% = 150 %

Answer:

0.5

Step-by-step explanation:

hypotenuse/adjacent=r

7/14=0.5

Answer: 12

Step-by-step explanation:

12 times 12 is 144 so 12.in each row

Helen will use 12 glass tiles in one row of her plate, as the square plate has a total area of 144 square centimeters and each tile measures one square centimeter.

The student's question involves calculating the number of glass tiles Helen would use in one row of a square plate, given that she has 144 square centimeters of glass tiles and each tile measures one square centimeter. To determine the number of tiles in one row, we need to remember that the area of a square is equal to the side length squared. Since the total area is 144 square centimeters, we take the square root of 144 to find the length of one side, which is 12 centimeters. Therefore, Helen will use 12 glass tiles in one row of her plate, as there would be 12 tiles lengthwise and 12 tiles widthwise to make up the total area of 144 square centimeters.

We have been given that a parabola has vertex [tex](-8,-7)[/tex] and also passes through the point [tex](-7,-4)[/tex]. We are asked to write the equation of the parabola in vertex form.

We know that vertex form of parabola in format [tex]y=a(x-h)^2+k[/tex], with a vertex at point (h,k).

Let us write equation of parabola using our given information as:

[tex]y=a(x-(-8))^2-7[/tex]

[tex]y=a(x+8)^2-7[/tex]

Now we will substitute the coordinates of point [tex](-7,-4)[/tex] to solve for a as:

[tex]-4=a(-7+8)^2-7[/tex]

[tex]-4=a(1)^2-7[/tex]

[tex]-4+7=a-7+7[/tex]

[tex]3=a[/tex]

Therefore, our required equation would be [tex]y=3(x+8)^2-7[/tex].

Answer:

17×1= 17, and 8×1= 8

17 and 8 is ur answer

i hope its right...

Step-by-step explanation:

1 7/8 into an improper fraction is 15/8

You can say that

3      5

---- x ----

2      4

The answer option which can have a negative impact on your credit score is: 3) applying for multiple credit cards in a short period of time (e.g., a week).

A credit score refers to a numerical expression between 300 to 850, that typically represents an individual's financial history and credit worthiness.

This ultimately implies that, the higher your credit score, the higher and better it is to obtain a credit (money) from a potential lender.

Generally, the ratings of a credit score by FICO include the following;

Generally, the best ways to improve your credit score are;

1. You should ensure you don't pay less than the minimum amount due.

2. You should ensure you pay your bills on time or as at when due.

3. You shouldn't move credit card debt around.

4. You should pay down balances on your credit card accounts.

However, when you apply for multiple credit cards in a short period of time (e.g., a week), it is most likely to have a negative impact on your credit score.

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Answer:

15.42477796

Step-by-step explanation:

1/2π x 6 + 6

- sorry if its wrong

Answer:

3pi

Step-by-step explanation:

refer to the picture for steps.