Write the prime factorization of 30. Use exponents when appropriate and order the factors from least to greatest (for example, 2235).

In exercise 1:

Situation: The account holder saves $30 each month

The first three terms of the sequence are: $120, $150, $180.

In exercise 2:

Situation: The account earns 25% interest each month.

The first three terms of the sequence are: $120, $150, $187.50.

A sequence in mathematics is described as an enumerated collection of objects in which repetitions are allowed and order matters.

Explaining  exercise 1:

In this exercise, the account balance for each month should form an arithmetic sequence with a common difference of $30

February 1 balance: $150

March 1 balance: $180

Hence, we have the first three terms of the sequence as:  $120, $150, $180.

Explaining exercise 2:

In this exercise, the account balance for each month should form a geometric sequence with a common ratio of 1.25.

The account earns 25% interest each month is the situation here.

February 1 balance: $150

March 1 balance: $187.50

The first three terms of the sequence are: $120, $150, $187.50.

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The first five term of the sequence are -12, -24, -36, -48 and -60.

A sequence is an enumerated collection of objects that follows are particular pattern.

The explicit formula of the sequence is aₙ = -12n

where

Therefore, let's find the first five terms of the sequence as follows:

a₁ = -12(1) = -12

a₂ = -12(2) = - 24

a₃  = -12(3) = -36

a₄  = -12(4) = -48

a₅  = -12(5) = - 60

Therefore, the sequence are -12, -24, -36, -48 and -60.

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Answer:

A

Step-by-step explanation:

simply divide each ter by -7x ..

Answer:

0, -3.

Step-by-step explanation:

12x(x+3)=0

Either 12x = 0 or (x + 3) = 0

x = 0/12 or x = -3

So, x = 0 or x = -3

Answer:

p = 6

Step-by-step explanation:

5. The quadratic function for the height of the rock, h = -16·t² + 79·t + 50, indicates;

a. The height of the rock will be 125 feet above the beach at 1.28 seconds and 3.66 seconds after it is thrown

b. The maximum height reached is about 147.5 feet

The time it takes the rock to reach the maximum height is about 2.47 seconds

A quadratic function is a function of the form; f(x) = a·x² + b·x + c, where, a, b, and c are numbers, and a ≠ 0.

The initial velocity of the rock = 79 ft/s

Height of the cliff above the beach from which the rock is thrown = 50 feet

The function for the height of the rock above the beach is; h = -16·t² + 79·t + 50

Please find attached the graph of the height of the rock as a function of time, created with MS Excel.

Required; When the height of the rock will be 125 feet above the beach

When the height of the rock is 125 feet, we get;

h = 125 = -16·t² + 79·t + 50

-16·t² + 79·t + 50 - 125 = 0

-16·t² + 79·t - 75 = 0

The value of t obtained using an online tool are;

t = (79 + √(1441))/32 ≈ 3.66 and t = (79 - √(1441))/32 ≈ 1.28

The times at which the height of the rock will be 125 feet above the beach are; 1.28 seconds and 3.66 seconds after the rock is thrown

b. The maximum height of the rock can be obtained from the formula for finding the maximum height of a quadratic equation of the form; f(x) = a·x² + b·x + c, which is;

At the maximum point, x = -b/(2·a)

The function for the height; h = -16·t² + 79·t + 50, indicates that we get;

a = -16, b = 79, and c = 50

Therefore;

The time it takes the rock to reach the maximum height, t(max), is therefore;

t(max) = -79/(2 × (-16)) ≈ 2.47

It takes about 2.47 seconds for the rock to reach the maximum height

The maximum height, h(max) = -16 × 2.46875² + 79×2.46875 + 50 ≈ 147.5

The maximum height reached by the rock is about 147.5 feet

Possible part of the question, obtained from a similar online question, includes;

a. The time it takes the rock to reach a height of 125 feet above the beach
b. The maximum height reached by the rock and the duration it takes the rock to reach the maximum height.

Please find attached the possible graph in the question, created with MS Excel, using the function for the height of the rock.

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Answer:

11205 is correct answer

Step-by-step explanation:

that makes ORQ a right-angled triangle, and we can use Pythagoras

c² = a² + b²

c being the Hypotenuse (the side opposite of the 90° angle), a and b are the legs.

OQ is the radius of the circle = OM = LM/2 = 20/2 = 10 cm.

RQ = PQ/2 = 16/2 = 8 cm.

so, our Pythagoras equation looks like :

OQ² = RQ² + OR²

10² = 8² + OR²

100 = 64 + OR²

36 = OR²

OR = 6 cm

RM = OM - OR = 10 - 6 = 4 cm

The area of the region bounded by the curves y = x² + 6x + 9 and y = 4 is 16  ² / ₃ square units.

First, we need to find the points of intersection between the two curves. Set y = x² + 6x + 9 equal to y = 4:

x² + 6x + 9 = 4

Now, solve for x:

x² + 6x + 5 = 0

Factor the quadratic equation:

(x + 5)(x + 1) = 0

This gives us the solutions x = -5 and x = -1. These are the x-coordinates of the points of intersection.

Now, to find the area of the region bounded by the curves, we'll integrate the difference between the two functions with respect to x, from x = -5 to x = -1:

Area = ∫[4 - (x² + 6x + 9)]dx from -5 to -1

Area = ∫[5 - x² - 6x]dx from -5 to -1

Now, integrate:

Area = [5x - (x³/3) - 3x²] from -5 to -1

Plug in the limits:

Area = (5(-1) - (-1)³/3 - 3(-1)²) - (5(-5) - (-5)³/3 - 3(-5)²)

Area = (-5 - 1/3 - 3) - (-25 + 125/3 - 75)

Area = (-8 1/3) - (- 25/3)

Area = 16  ² / ₃ square units

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Answer:

6 times

Step-by-step explanation:

24/4 = 6

Answer:

Step-by-step explanation:

The possible rational zeros of a polynomial function are all the possible values of x, where x is a factor of the constant term of the function divided by a factor of the leading coefficient of the function.

For the polynomial function f(x) = x^4 - 5x^3 + 8x^2 - 20x + 16, the constant term is 16 and the leading coefficient is 1. Therefore, the possible rational zeros are all the possible values of x, where x is a factor of 16 divided by a factor of 1. That is, the possible rational zeros are:

±1, ±2, ±4, ±8, ±16

To check if any of these possible zeros are actually zeros of the function, we can use synthetic division or long division to test each one.

Answer:

  C.  m = 1440d

Step-by-step explanation:

You want to know the equation that represents the relationship between days (d) and minutes (m) given the table of values (d, m) = (4, 5760), (7, 10080), or (11, 15840).

On the off chance you don't already know that the number of days must be multiplied by minutes per day to find the number of minutes (m = 1440d), you can always try the table values in the response choices to see what works:

  A.  5760 = 4/1440 . . . . . . nope

  B.  5760 = 4 + 1440 . . . . . nope

  C.  5760 = 1440·4 . . . . . . . yep

  D.  4 = 1440·5760 . . . . . . . nope

The equation that works is m = 1440d.

__

Additional comment

Fractions work the same way with units that they do with numbers. Common factors in numerator and denominator cancel.

  [tex]\dfrac{2}{3}\times 3=2\\\\\dfrac{\text{minutes}}{\text{day}}\times \text{days}=\text{minutes}[/tex]

The values of the variables and the side lengths are

From the question, we have the following parameters that can be used in our computation:

AB = AC

Perimeter = 27.3

Using the attached figure, we have

6x - 2y = x + 5

Evaluate

5x = 2y + 5

For the perimeter, we have

AC + AB + BC = 27.3

So, we have

6x - 2y + x + 5 + y + 6.3 = 27.3

Simplify

7x = y + 16

Multiply by 2

14x = 2y + 32

Subtract from 5x = 2y + 5

9x = 27

So, we have

x = 3

This means that

2y + 32 = 14 * 3

2y + 32 = 42

Evaluate

2y = 10

y = 5

For the side lengths, we have

AC + AB + BC = 27.3

So, we have

AC = 6(3) - 2(5) = 8

AB = 3 + 5 = 8

BC = 5 + 6.3 = 11.3

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Answer:

Step-by-step explanation:

4x + 6 + 24 - 2x =

2x + 30

Answer: A. Nikko by 2 inches

Step-by-step explanation: Because 82 inches = 6ft 10in, which is 2 inches taller than Ricco.

Answer:

the value of (4m-n)/(n+2p) is 3/7.

Step-by-step explanation:

Let's substitute the given ratio in terms of a common multiplier, k:

m = 3k

n = 6k

p = 4k

Now we can substitute these values in the expression:

(4m-n)/(n+2p) = (4(3k) - 6k)/(6k + 2(4k)) = (12k - 6k)/(6k + 8k) = 6k/14k = 3/7

Therefore, the value of (4m-n)/(n+2p) is 3/7.

Answer:

5+x+3 simplified is x+8

Step-by-step explanation:

when you simplify something, you combine terms and write it in the simplest way you can. So combine 5 and 3 to get 8, and then the final answer of x+8

Answer: x+8

Step-by-step explanation:

"5 + x + 3" can be simplified by combining the numerical terms, which are 5 and 3, to get 8.

Then, just rewrite the expression as "x + 8." Therefore, "5 + x + 3" simplified is just "x + 8".

The total contribution to Sharon's account over the 25-year period is $64,800.

To find the total contribution to Sharon's account, we need to consider both her contribution and her employer's contribution.

Social Security taxes are generally split evenly between the employee and the employer, with each paying half of the tax.

Sharon paid $32,400 in Social Security taxes over the 25-year period, which represents her share (half) of the total Social Security taxes paid.

To find the total contribution to her account, we simply need to double her share to include the employer's contribution:

Total contribution = Sharon's contribution + Employer's contribution

Total contribution = $32,400 + $32,400

Total contribution = $64,800

The total contribution to Sharon's account over the 25-year period is $64,800.

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The interest earned by Sarah in four (4) years is approximately $62.16.

The formula accrued amount in a compounded interest is expressed as;

A = P( 1 + r/n )^( n × t )

Where A is accrued amount, P is principal, r is interest rate and t is time.

Given that;

First, we convert R as a percent to r as a decimal

r = R/100

r = 7/100

r = 0.07

Now, the the values into the above formula and solve for accrued amount (A).

A = P( 1 + r/n )^( n × t )

A = $200( 1 + 0.07/1 )^( 1 × 4 )

A = $200( 1 + 0.07 )^( 4 )

A = $200( 1.07 )^( 4 )

A = $262.16

Now, we know that;

Accrued amount (A) = Principal (P) + Interest (I)

Solve for Interest (I)

$262.16 = $200 + I

I = $262.16 - $200

I = $62.16

Therefore, the interest earned is $62.16.

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Answer:

69

Step-by-step explanation:

69

Answer:

Line DB and AC intersect at point E.

∠AEB = ∠DEC because they are vertical angles.

∠EAB and ∠ECD are alternate interior angles because AB and CD are parallel lines and line AC crosses through both parallel lines.

m∠EAB = m∠ECD because they are alternate interior angles.

ΔABE ≅ ΔCDE because there are two sets of congruent angles.

Using inequality, x < 63.33, Student take 62 and adult take 68.

By utilizing the "equal tο" symbοl in mathematics, equatiοns are nοt necessarily balanced οn bοth sides. Sοmetimes it can be abοut a "nοt equal tο" relatiοnship, which denοtes that οne thing is better than οr wοrse than anοther.

A relatiοnship between twο numbers οr οther mathematical expressiοns that yields an unfair cοmparisοn is referred tο as an inequality in mathematics. Certain algebraic mathematical expressiοns are referred tο as inequalities.

The student's ticket sells fοr $5,

adult ticket sells fοr $950,

Tοtal auditοrium = 130,

If x represents the number οf student, then adult = 130 - x,

∴ 5x + 9.5y > 950

insert y = 130 - x5x + 9.5(130 - x) > 950,

5x + 1235 - 9.5 x > 950

x < 63.33

∴ Student take 62 and adult take 68.

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The volume of the building is approximately 18,840 cubic feet.

So the answer is (B) 18,840 ft³

What is volume of cone ?

The volume of a cone is a measure of the amount of space that the cone occupies and can be calculated using the formula:

[tex]V = (1/3)\pi r^2h[/tex]

where V is the volume of the cone, r is the radius of the base of the cone, h is the height of the cone, and π is a mathematical constant approximately equal to 3.14.

According to the question:
The volume V of a cone can be calculated using the formula:

[tex]V = (1/3)\pi r^2h[/tex]

where r is the radius of the base of the cone, h is the height of the cone, and π is a constant approximately equal to 3.14.

In this case, the radius r is 30 feet and the height h is 20 feet. Substituting these values into the formula, we get:

[tex]V = (1/3)\pi (30)^2(20)[/tex]

[tex]V = (1/3)\pi (900)(20)[/tex]

[tex]V = (1/3)(56,520)[/tex]

[tex]V = 18,840[/tex]

Therefore, the volume of the building is approximately 18,840 cubic feet.

So the answer is (B) 18,840 ft³.

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Answer:

The answer is D

Step-by-step explanation:

Function A

f(x)  =  1 / ( x - 3)

The  vertical asymptote is  the value of x that makes x - 3 = 0 ⇒   x = 3

The vertical asymptote of B   is  x = 4

So....

Function A has a vertical asymptote at x = 3.

Function B has a vertical asymptote at x = 4.

The area of the figure is obtained to be approximately 74.1 units².

What is area?

An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure.

The rectangle has the length of 6 units.

The rectangle has the breadth of 10 units.

The semicircle has a diameter of 6 units.

The semicircle has the radius of 3 units.

The formula for area of rectangle is -

Area (r) = l × b

Substitute the values into the equation -

Area (r) = 6 × 10

Area (r) = 60 units²

The formula for area of semicircle is -

Area (r) = πr² / 2

Substitute the values into the equation -

Area (s) = [3.14 × (3)²] / 2

Area (s) = 28.26 / 2

Area (s) = 14.13 units²

The total area of the diagram is -

Total Area = Area (r) + Area (s)

Substitute the values into the equation -

Total Area = 60 + 14.13

Total Area = 74.13 units²

Therefore, the area of the figure is 74.1 units².

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The jeweler made 4 bracelets and 6 necklaces using 172 grams of gold.

An equation is a mathematical statement that shows that two expressions are equal. It contains variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. Equations are used to solve problems by finding the values of the variables that make the equation true.

Let x be the number of bracelets made, and y be the number of necklaces made.

Then, we can create the following system of equations:

Equation 1: 7x + 24y = 172 (the total amount of gold used is 172 grams)

Equation 2: y = x + 2 (the number of necklaces made is 2 more than the number of bracelets made)

So, the variables are x (the number of bracelets made) and y (the number of necklaces made).

We can solve this system of equations to find the values of x and y. We can use substitution or elimination to solve for one variable and then plug it into the other equation.

Substitution method:

From Equation 2, we have y = x + 2. Substituting this into Equation 1, we get:

7x + 24(x+2) = 172

7x + 24x + 48 = 172

31x = 124

x = 4

So, the jeweler made 4 bracelets.

Plugging this into Equation 2, we get:

y = x + 2 = 4 + 2 = 6

So, the jeweler made 6 necklaces.

Therefore, the jeweler made 4 bracelets and 6 necklaces using 172 grams of gold.

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Answer:

CF =  12
DE  = 23
CD =  23
DF = 23.9

Step-by-step explanation:

We can see that there are 2 right-angled triangles: DEF and CDF with common side FD.

They are right angled triangles because the EF and CF are radii of the circle and these segments intersect the tangents at 90°

The common side DF is the hypotenuse for both triangles

The sides EF and CF are radii of the circle so EF = CF

We have two triangles which have two sides equal and one of the angles equal to the corresponding angle of the other

By the SSA theorem, the two triangles are similar

SSA Theorem

if two sides and an angle not included between them are respectively equal to two sides and an angle of the other then the two triangles are equal

Therefore by the law of similar triangles,

CD  = EF

Plugging in the expressions we get
13x - 16 = 4x + 11

Subtract 4x from both sides:
13x - 4x - 16 = 11
9x - 16 = 11

Add 16 to both sides:
9x - 16 + 16 = 11 + 16

9x = 27

x = 27/9 = 3

Therefore
ED = 4x + 11 = 4(3) + 11 = 12 + 11 = 23

and this is equal to CD

Using the Pythagorean theorem for right triangles,

For ΔDEF,

DF² = EF² + DE²

DF² = 12² + 23²

= 144 + 529

= 673

DF = √673

= 25.9422

= 25.9 rounded to the nearest tenth

So the measures of the segments are
CF = 12
DE = 23
CD = 23
DF = 23.9

"Problem:

Jenny earns a base pay of $1000 per month plus a 5% commission on all sales. Last month she sold $8000 worth of products. What was her total earnings for the month?

Solution:

Jenny's commission for the month is 5% of $8000, which can be calculated as:

Commission = 5% of $8000 = (5/100) * $8000 = $400

Her total earnings for the month can be found by adding her base pay and commission:

Total Earnings = Base Pay + Commission

Total Earnings = $1000 + $400

Total Earnings = $1400

Therefore, Jenny's total earnings for the month were $1400." (ChatGPT, 2023)

Answer:

Write the whole number as a fraction by placing it over 1. For example, if you want to multiply 2/5 by 3, you can write 3 as 3/1.

Multiply the numerators of the two fractions together. For example, 2/5 x 3/1 = (2 x 3) / 5 = 6/5.

Simplify the resulting fraction, if necessary, by reducing it to its lowest terms. For example, 6/5 can be simplified to 1 1/5 (or 1.2 as a decimal).

Therefore, when you multiply a fraction by a whole number, you multiply the numerator of the fraction by the whole number and keep the denominator the same.

Step-by-step explanation: