Identify the quotient and the remainder

(24x^3 - 14x^2 + 20x +6)÷(4x^2 - 3x +5)

Answers

Answer 1

The quotient is (6x + 1) and the remainder is (-7x + 1).

What is a factor of a polynomial?

We know that if x = a is one of the roots of a given polynomial x - a = 0 is a factor of the given polynomial.

To confirm if x - a = 0 is a factor of a polynomial we replace f(x) with f(a) and if the remainder is zero then it is confirmed that x - a = 0 is a factor.

Given A cubic polynomial 24x³ - 14x² + 20x + 6 divided by 4x² - 3x + 5.

So, (24x³ - 14x² + 20x + 6)/(4x² - 3x + 5).

= (4x² - 3x + 5)(6x + 1) + (-7x + 1)/(4x² - 3x + 5) in rhe form N = DQ + R.

The same applies to the division of polynomials.

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Related Questions

guys please help its due today!​

Answers

a) Let x be the number of games played and let y be the total price.

What in mathematics is a linear equation?

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

(b)

Pin Lanes: y = 10 + 3x

Strike Lanes: y = 4 + 6x

(c) To find the number of games at which the total price is the same at both places, we can set the two equations equal to each other and solve for x:

10 + 3x = 4 + 6x

6x = 6

x = 1

So the total price would be the same if you played 1 game at both Pin Lanes and Strike Lanes.

(d) Since you want to play 4 games, you can substitute x = 4 into the equation for each place:

Pin Lanes: y = 10 + 3(4) = 22

Strike Lanes: y = 4 + 6(4) = 28

Since 4 games at Pin Lanes costs $22 and 4 games at Strike Lanes costs $28, it would be cheaper to play at Pin Lanes.

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If you shift the cubic parent function, F(x)=x^3, down 9 units, what is the equation of the new function

Answers

Therefore the table values of which represents a linear function are table 2 and table 3

What is linear equation?

A linear equation is a first-order (linear) term and a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. A "linear equation of two variables" is what is sometimes referred to here, where y and x are the variables.

Here,

The values shown in table 2 have same constant rate of change of 3 units.

where as,

The values shown in table 3 have same constant rate of change of 5 units.

Therefore the table values of which represents a linear function are table 2 and table 3

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draw and divide a rectangle to show each product use a distributive property to find the product 5×14

Answers

The product of 5 and 14 using the distributive property is 70.

What is Multiplication?

Multiplication of two numbers is defined as the addition of one of the number repeatedly until the times of the other number.

a × b means that a is added to itself b times or b is added to itself a times.

For three numbers a, b and c, Distributive property states that,

a (b + c) = a b + a c

We have to find the product 5 × 14 using distributive property.

5 × 14 = 5 (12 + 2)

Using distributive property,

5 × 14 = (5 × 12) + (5 × 2)

          = 60 + 10

          = 70

Hence using distributive property, we can find the product of 5 and 14 as 70.

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Here is a graph of the function h.
Use the graph to find the following
If there is more than one answer, separate them with commas
(a)
All local minimum values of
h
(b) All values at which h has a local minimum:

Answers

The graph also shows two other local maxima, at x=0.5 and x=1.5.

The local minimum(a) -4, -2, 0, 2 (b) The local minimum values of h occur at x = -4, -2, 0, and 2.These values can be seen on the graph as points at which the graph of h changes from decreasing to increasing.At each of these points, the value of h is at a minimum compared to the values of h on either side of the point.All values at which h has a local maximum: 0.5, 1.5All local maximum values of h: 2.5, 4.5.The graph of the function h is a parabola that opens upwards, with a turning point at x=1.This indicates that the function has a local maximum at this point.The local maximum values of h at these points can be determined by looking at the y-values at these points, which are 2.5 and 4.5 respectively.

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Consider the line whose equation is y=x+3.
Fill in the table below and then plot the line.

Answers

For the given line whose equation is [tex]y=x+3[/tex] :

x   y    (x,y)

0 3     (0,3)

1 4     (1,4)

2 5     (2,5)

3      6      (3,6)

What is equation?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

Define expression.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator)

A line in slope-intercept form, y = mx + b, where m is the slope of the line and b is the y-intercept .

Given the equation y = x + 3, the slope (m) is 1 and the y-intercept (b) is 3.

So, we can fill the table like this:

For the given line whose equation is [tex]y=x+3[/tex] :

x   y    (x,y)

0 3     (0,3)

1 4     (1,4)

2 5     (2,5)

3      6     (3,6)

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The measures of the angles of a triangle are shown in the figure below. Solve for x.
(5x-17)®
(7x-3)
56°

Answers

The measurement of three angles in the triangle are 43°, 81°, 56°.

What are the angles of a triangle?

A triangle's interior angles always add up to 180°, whereas its exterior angles are equal to the sum of the two interior angles that are not adjacent to it.

Given three angles,

∠A = (5x - 17)°

∠B = (7x - 3)°

∠C = 56°

We know that in a triangle ∠A + ∠B + ∠C = 180°

By substituting values,

(5x - 17) + (7x - 3) + 56 = 180

12x -20 + 56 = 180

12 x + 36 = 180

12x = 180 - 36

12x = 144

x = 144/12

x = 12

By substituting values of x we get,

∠A = (5x - 17)°

     = 5 x 12 - 17

     = 60 - 17

     = 43

∠A = 43°

∠B = (7x - 3)°

     = 7 x 12 - 3

     = 84 - 3

     = 81

∠B = 81°

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The design of a digital box camera maximizes the volume while keeping the sum of the dimensions at 4.5 inches. If the length must be 1.5 times the height, what should each dimension be?

Answers

6.75!!! You either times 4.5 and 1.5 or divide!

i need to solve this so can you pls hlp

Answers

Answer: D

Step-by-step explanation: x is a variable, and so is the number of tractors he sells. he is going to get paid $1000 for sure each month.

So 150x(the number of tractors) + 1000(his pay each month)

value of y please help me

Answers

Answer is y= 22

Step by step

We know the triangle dum is equal to 180

One angle is 40, so 180 - 40 = 140

The two angles labeled x are congruent, so 140 / 2 = 70.

X = 70

Now the supplement angle of x and 5y = 180 degrees.

70 + 5y = 180

Subtract 70 from both sides to isolate y

70 - 70 + 5y = 180 - 70
Simplify

5y = 110

Divide both sides by 5 to solve for y

5/5 y = 110/5

y = 22

Which of the following points best represents the location of -1;
15.
ос
OD
Ов
ОА
+
-2
в с
0
on the number line?
D
2 +
2

Answers

A because u start from the -1 going backwards and where point A is just makes sense

If the equation of a circle is (x + 5)2+(y-7)2=36, its radius is
06
016
0 36

Answers

Therefore , the solution is circle Part 1: The central idea ( -5 , 7 ). 2nd part: Radius is 6 in part 2,3rd part: FALSE and Parts 4. There are 10 miles between A and B.

What is circle?

A circular shape called a circle is created by following a moving point in a plane so that its distance from a particular point remains constant. The Greek word kirkos, which means hoop or ring, distance is the source of the English word circle.

Here,

The common circle equation is,

( x - h )² + ( y - k ) ( y - k )

6² = r²

where the circle's radius is r and the center's coordinates are (h, k).

Part 1.

Using the common circle equation, we obtain,

Circle's circumference's coordinate is ( -5 , 7 )

Consequently, the second choice is the right one.

Part 2.

Using the common circle equation, we obtain,

circle radius is six.

Consequently, the first choice is the right one.

Part 3.

Using the common circle equation, we obtain,

Circle's circumference's coordinate is ( 2 , 3 )

Therefore False.

Part 1.

In comparison to the common circle equation, we obtain,

Circle's center's coordinates are: ( -5 , 7 )

As a result, the second choice is the right one.

Part 2.

In comparison to the common circle equation, we obtain,

circle's diameter is six.

As a result, the first choice is right.

Part 3.

In comparison to the common circle equation, we obtain,

Circle's center's coordinates are: ( 2 , 3 )

So, False.

Part 1.

Giving the distance between two points,

Distance between A(-5, 3) and B (5, 3), expressed as:

=> [tex]\sqrt{(x2-x1)^{2} + (y2-y1)^{2} )}[/tex]

= >  [tex]\sqrt{(-5-5)^{2} + (3-3)^{2} )}[/tex]

=> 10

Thus, 3rd Option is correct.

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100 POINTS!!! Please help.

Answers

Answer:

[tex]\dfrac{1}{a^{20}c^2d^2e^{6}}[/tex]

Step-by-step explanation:

Given expression:

[tex](a^{10}b^{0}cde^{3})^{-2}[/tex]

[tex]\textsf{Apply the exponent rule} \quad a^{-n}=\dfrac{1}{a^n}:[/tex]

[tex]\implies \dfrac{1}{(a^{10}b^{0}cde^{3})^{2}}[/tex]

[tex]\textsf{Apply the exponent rule} \quad (a^b)^c=a^{bc}:[/tex]

[tex]\implies \dfrac{1}{a^{(10 \times 2)}b^{(0 \times 2)}c^2d^2e^{(3 \times 2)}}[/tex]

Simplify:

[tex]\implies \dfrac{1}{a^{20}b^{0}c^2d^2e^{6}}[/tex]

[tex]\textsf{Apply the exponent rule} \quad a^0=1:[/tex]

[tex]\implies \dfrac{1}{a^{20}(1)c^2d^2e^{6}}[/tex]

[tex]\implies \dfrac{1}{a^{20}c^2d^2e^{6}}[/tex]

You are going to run at a constant speed of 6.5 miles per hour for 30 minutes. You calculate the distance you will run. What mistake did you make in your calculation? [Use the formula S = dt.]

Answers

Answer:

Below

Step-by-step explanation:

S = dt        S = distance    d = rate = 6.5 m/ hr    t = time = 30 min = 1/2 hr

S = (6.5 m/hr) *(1/2 hr) = 3.25 miles

The value of distance you will run will be;

⇒ Distance = 3.25 miles

What is Division method?

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

You are going to run at a constant speed of 6.5 miles per hour for 30 minutes.

Here,

Speed = 6.5 miles per hour

Time = 30 minutes

        = 30/60 hour

        = 1/2 hour

We know that;

⇒ Speed = Distance / Time

Substitute all the values we get;

⇒ 6.5 = Distance / (1/2)

⇒ 6.5 × 1/2 = Distance

⇒ Distance = 3.25 miles

Thus, We get;

⇒ Distance = 3.25 miles

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-20 POINTS- only answer If you know dont guess again.

Answers

Using the Pythagoras theorem, the value of y is [tex]6\sqrt{7}[/tex], and the value that goes in the green box is 6.

What is Pythagoras Theorem?

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse. Due to its position opposite the 90° angle, the hypotenuse in this case is the longest side.

Mark the intersections as A, B, C, and D.

It is given that BC=12 and CD=9.

The relationship between the height on the hypotenuse of a right triangle and the two line segments it generates on the hypotenuse is described by the right triangle altitude theorem, also known as the geometric mean theorem. It claims that the altitude is equal to the geometric mean of the two segments.

Apply the geometric mean theorem -

(AC)^2 = BC x CD

(AC)^2 = 12 x 9

(AC)^2 = 108

AC = [tex]\sqrt{108}[/tex]

AC = [tex]6\sqrt{3}[/tex]

Triangle ABC is a right-angled triangle, so apply Pythagoras theorem -

(AB)^2=(BC)^2+(AC)^2

(AB)^2=(12)^2+([tex]6\sqrt{3}[/tex])^2

(AB)^2=144+108

(AB)^2=252

AB=[tex]\sqrt{252}[/tex]

AB=[tex]6\sqrt{7}[/tex]

Therefore, the value of y is obtained as [tex]6\sqrt{7}[/tex].

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Which expression is equivalent to -3(x+4)(x-6)-(x^2+8x-10)?

Answers

Answer:-4x^2-2x+46.

Step-by-step explanation:

To simplify this expression, you can start by distributing the negative sign to the first set of parentheses:

(-3)(x+4)(x-6)-(x^2+8x-10)

Then, you can distribute the -3 to the terms inside the first set of parentheses:

(-3x-12)(x-6)-(x^2+8x-10)

Then, you can combine like terms:

-3x^2+6x+36-x^2-8x+10

This simplifies to:

-4x^2-2x+46

Therefore, the expression that is equivalent to -3(x+4)(x-6)-(x^2+8x-10) is -4x^2-2x+46.

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Find the value of x that makes the quadrilateral a parallelogram?

Answers

Answer:

5

Step-by-step explanation:

since the sides of parallelogram are parallel

then 3X+3 = 4X-2 (they are equal because they are alternating angles )

3X+3 = 4X-2 subtract 3X from both sides

3 = X-2. add 2 to both sides

X= 5

Answer:

x = 5

Step-by-step explanation:

As the diagonals of a parallelogram bisect each other (divide into two equal parts):

[tex]\implies 2x+1=x+6[/tex]

[tex]\implies 4x-2=3x+3[/tex]

Solve the first equation for x:

[tex]\implies 2x+1-1=x+6-1[/tex]

[tex]\implies 2x=x+5[/tex]

[tex]\implies 2x-x=x+5-x[/tex]

[tex]\implies x=5[/tex]

Solve the second equation for x:

[tex]\implies 4x-2+2=3x+3+2[/tex]

[tex]\implies 4x=3x+5[/tex]

[tex]\implies 4x-3x=3x+5-3x[/tex]

[tex]\implies x=5[/tex]

Therefore, the value of x that makes the quadrilateral a parallelogram is:

x = 5

hello i need help with ym math today please and thanks

Answers

The annual cost if she chooses to make monthly payment is $1920 and money saved is $170

How to determine the incomes?

The given parameters that will help us to determine the incomes are

Mindley switching to insurance comapnyAnnual premium $1750/ yearMonthly premium $160*12 = $1920

a)  Annual cost if she chooses to make one annual monthly installment is $1920

b) Money saved is she makes one annual payment is $(1920-1750)= $170

3) Volume of gas = 60 L

Efficiency rating = 10.2km/L

Average drive = Volume / Efficiency = 60/10.2 = 5.9km/L

b) Cost of gas = 149.9⊄⊄/L

Number of liters =60

= 60*149.9

=$8994

c) Constant gas price = $149.9⊄/L

Number of weeks /year = 52

=52*149.9

= $7795

4) Morgan pay $15/hr

Number of hours per week = 40

Gross monthly income = 40*15*4

=$2400

b)   Monthly income $2400

Amount left after deduction = 85%

=0.85*2400

Net income = $2040

In conclusion Mindley receives $1920 monthly and saves $170

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A line passes through the origin (−1, 1) and (4, n). Find the value of n.

Answers

The line y = - x has a coordinate value of (4, - 4) passing through the origin.

What are lines and their slopes?

We know lines have various types of equations, the general type is

Ax + By + c = 0, and equation of a line in slope-intercept form is

y = mx + b.

Where slope = m and b = y-intercept.

the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.

Given, A line passes through the origin, (−1, 1) and (4, n).

So, The slope of the line is,

m = (1 - 0)/(- 1 - 0).

m = - 1.

Now,

1 = -1(-1) + b.

b = 0.

y = - x.

At x = 4,

y = - 4.

So, The point (4, n) is (4, - 4).

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Graph the linear equation.

4x+6y=−12

Plot two points on the line to graph the line.

Answers

Answer: (-3,0) and (0,-2)

Step-by-step explanation:

Please help I was sick and missed out on class thank you.

Answers

On solving the value of provided question we can say that - the value of the slope intercept y = -3.

what is slope intercept?

The point on the y-axis where the slope of the line passes is known as the intersection point in mathematics. the location on a line or curve where the y-axis crosses that point. This is demonstrated by putting y = mx+c as the equation for the straight line, where m denotes the slope and c the y-intercept. In the intercept form of the equation, the slope (m) and y-intercept (b) of the line are highlighted. The slope is m, and the y-intercept is b for equations in the intercept form (y=mx+b). Additionally, certain equations may be recast to seem like slope intercepts. For instance, if y=x is rewritten as y=1x+0, the slope becomes 1 and the y-intercept becomes 0.

as we can see from graph that,

line passes through origin, so x= 0

the, y = -5x - 3

y = -3

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Select all the relations which represent a function.
- (1,3), (2,5), (2,7), (4,9) (1,3), (1,5), (1,7), (4,9) 0 (1,2), (2,5), (2,1), (4,5)
(1,3), (2,5), (3,7), (4,9) (1,3), (2,3), (3,3), (4,3)

Answers

Therefore , (1, 3), (2, 5), (3, 7) (4, 9) and (1, 3), (2, 3), (3, 3) (4, 3) are the relations that represent a function.  

Function is what?

According to a function's rule, every x value in the domain has one and only one range of y values. Definition. A one-to-one function exists when there is just one and only one value of x such that f(x) = y.

Here,

The relationship is (1, 3), (2, 5), and (2, 7) (4, 9)

Given that 2 is repeated, the connection is not a function.

The relationship is (1, 3), (2, 5), and (3, 7) (4, 9)

Since there are no repeating numbers, the relation is a function.

The relationship stated is (1, 3), (1, 5), and (1, 7). (4, 9)

The relationship is not a 1 repeated function.

The relationships are (1, 3), (2, 3), and (3, 3). (4, 3)

Since there are no repeating numbers, the relation is a function.

The relationship stated is (1, 2), (2, 5), and (2, 1) (4, 5)

As 2 repeated, the relationship is not a function.

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Find the value of x.
30°
105°
xo

Answers

Exterior angle of triangle x has a value of 135 in this sentence.

What is the simplest technique to measure angles?

A protractor can be used to measure angles precisely. Angles are measured in degrees, hence the term "degree measure." Since one full revolution is equivalent to 360 degrees, it is divided into 360 segments.

What exactly is the triangle rule?

According to the "sides of a triangle rule," any two sides of a triangle must add up to be longer than the third side.

By extending one side of the triangle, an external angle is formed. An exterior angle is the angle formed by the stretched side and the side that is immediately adjacent.

Practice. Triangle Angle Measurement

via the triangle's external angle characteristic, x = 105 + 30 = 135.

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I don’t understand this ssshh

Answers

After evaluating the given expressions the results could be 245 / 89 , 43/6, 33/4 .

What is expression ?

expression can be defined as with the minimum of two variables or numbers and at least one math operation.

Given that ,

7/ 8  * 14  / (3/8 * 6 ) + 2  1/5

= (7/8 * 14 )/ ((18 / 8) + 11/5)

= (98/ 8 ) / (90 + 88) / 40

= (98/ 8 ) /  (178/ 40)

= (98 * 40) / (8* 78)

= 245/89

Hence the final value could be 245/53.

7/ 8  + (6*7/8 - 4 * 3/16 ) / (3/4 )

(7/8 + (21/4 - 3/4 ) )  / (3/4)

(7/8 + 18/4)  / (3/4)

(43/8) / (3/4)

43/6

Hence the final value could be 43/6.

3  1/7  * (3 1/3 * (2/3 + 1/6 ) - 5/18 ) / 2 (3/7)

11/7 * (10/6 - 5/18) / (17/7)

(11/7 )* (27/ 18) /( 17/7)

(11* 27/18 )/ (17)

33/34.

Hence the final value could be 33/34.

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(5 x 7) + (n x 4) = 5 x (7+ 4) write each missing number

Answers

The missing number in the expression (5 x 7) + (n x 4) = 5 x (7+ 4) is 5.

What are GCF and distributive property?

The GCF of two or more than two numbers is the highest number that divides the given two numbers completely.

We also know that distributive property states a(b + c) = ab + ac.

Given, An expression (5 × 7) + (n × 4) = 5 × (7 + 4).

Now, If we expand the RHS we have,

5×(7 + 4).

= (5 × 7) + (5 × 4).

Now, Writing the obtained RHS with LHS we have,

(5 × 7) + (n × 4) =  (5 × 7) + (5 × 4).

So, The missing number is 5.

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3 Dylan needs to buy new contact lenses. His ophthalmologist sells 8-lens boxes in
packs of 2 for $52 and 10-lens boxes in packs of 4 for $120. Which option is the
better deal?

Answers

Answer:

Dylan should purchase the 10-lens boxes in packs of 4 for $120, as this is the better deal. This option provides 40 lenses for $120, which works out to be $3 per lens. The 8-lens boxes in packs of 2 for $52 only provides 16 lenses for $52, which works out to be $3.25 per lens Therefore, the 10-lens boxes in packs of 4 is the better deal.

Step-by-step explanation:

Answer:

he should buy the 10-lens boxes in packs of 4 for $120

Step-by-step explanation:

Is the set of rational expressions closed under division

Answers

Answer:

Step-by-step

Closure property is true for division except for zero.

Hannah simplified the radical below and wants someone to check the work (view image)

Answers

Answer:

4|x|y²√(3yz)

She forgot the absolute value sign on x, and she left out the exponent on y.

Step-by-step explanation:

Step 1 is correct.

x may be positive, zero, or negative.

√x is always non-negative. To assure that √x² is non-negative, √x² = |x|.

√16 = 4

√3 = √3

√x² = |x|

√y² × √y² = √y^4 = y²

Since y² is always non-negative, there is no need for absolute value sign.

√y^4 = y²

Answer should be

4|x|y²√(3yz)

A new homeowner is purchasing a living room set for $2,975 and must decide between two financing offers.

Offer 1: $250 down payment, 24.90% interest rate, compounded monthly, for 3 years, with no payments due for 6 months and then fixed payments of $139.05 for the remainder of the loan term

Offer 2: $400 down payment, 22.90% interest rate, compounded monthly, for 3 years, with no payments due for 12 months and then fixed payments of $165.76 for the remainder of the loan term

Part A: What is the total cost of offer 1? Explain which technology you used to solve and each step of your process. (3 points)

Part B: What is the total cost of offer 2? Explain which technology you used to solve and each step of your process. (3 points)

Part C: Which financing offer should the new homeowner choose? Explain your reasoning. (4 points)

Answers

Answer:

To compare the two financing offers, we need to calculate the total cost of each offer.

Part A: What is the total cost of offer 1?

To calculate the total cost of offer 1, we need to first calculate the total amount of interest that will be paid over the course of the loan. We can do this using the following formula:

Total interest = (interest rate/12) * loan amount * number of payments

In this case, the loan amount is $2,975, the interest rate is 24.90%, and the number of payments is 36 (3 years * 12 months/year). Plugging these values into the formula, we have:

Total interest = (0.2490/12) * $2,975 * 36

Calculating, we find that the total interest is approximately $1,534.89.

To calculate the total cost of the loan, we need to add the total interest to the original loan amount. In this case, the total cost is $2,975 + $1,534.89 = $4,509.89.

Therefore, the total cost of offer 1 is $4,509.89.

Part B: What is the total cost of offer 2?

To calculate the total cost of offer 2, we need to first calculate the total amount of interest that will be paid over the course of the loan. We can do this using the following formula:

Total interest = (interest rate/12) * loan amount * number of payments

In this case, the loan amount is $2,975, the interest rate is 22.90%, and the number of payments is 36 (3 years * 12 months/year). Plugging these values into the formula, we have:

Total interest = (0.2290/12) * $2,

To continue the calculation of the total cost of offer 2, we need to calculate the total interest using the formula:

Total interest = (interest rate/12) * loan amount * number of payments

In this case, the loan amount is $2,975, the interest rate is 22.90%, and the number of payments is 36 (3 years * 12 months/year). Plugging these values into the formula, we have:

Total interest = (0.2290/12) * $2,975 * 36

Calculating, we find that the total interest is approximately $1,405.70.

To calculate the total cost of the loan, we need to add the total interest to the original loan amount. In this case, the total cost is $2,975 + $1,405.70 = $4,381.70.

Therefore, the total cost of offer 2 is $4,381.70.

Part C: Which financing offer should the new homeowner choose?

Based on the total cost of the two financing offers, it is more cost-effective for the new homeowner to choose offer 2. Offer 2 has a lower total cost ($4,381.70) compared to offer 1 ($4,509.89), so it would be the better choice for the new homeowner.

Step-by-step explanation:

To calculate the total cost of Offer 1, we can use the formula for the present value of an ordinary annuity:

PV = PMT * (1 - (1 + r)^-n) / r

Where PV is the present value (in this case, the total cost of the loan), PMT is the fixed payment amount, r is the monthly interest rate (in decimal form), and n is the number of payments.

Plugging in the values from Offer 1, we get:

PV = $139.05 * (1 - (1 + 0.2490)^-36) / 0.2490

Using a calculator or spreadsheet to compute the exponent and division, we find that the total cost of Offer 1 is $4,941.51.

To calculate the total cost of Offer 2, we can use the same formula:

PV = $165.76 * (1 - (1 + 0.2290)^-36) / 0.2290

Using a calculator or spreadsheet to compute the exponent and division, we find that the total cost of Offer 2 is $4,847.93.

Based on these calculations, the new homeowner should choose Offer 2, as it has a lower total cost. This decision is based on the fact that Offer 2 has a lower interest rate and a longer period of time with no payments due, which results in a lower present value (total cost) of the loan.

To solve these problems, I used the present value of an ordinary annuity formula and a calculator or spreadsheet to compute the exponent and division.

D. Maria collects postcards. The table gives the
number of each type of postcard she has in her
collection. Use the data to write each ratio in
three different ways.
A. U.S. Landmarks to European Landmarks:

Answers

Answer: A. U.S. Landmarks to European Landmarks

Maria has 25 U.S. landmark postcards and 20 European landmark postcards. The ratio of U.S. landmarks to European landmarks can be written as 25:20 or as 25/20.

Alternatively, we can express the ratio as a fraction. If we divide the number of U.S. landmark postcards by the total number of U.S. and European landmark postcards, we get 25/(25+20)=25/45

The last way we can express the ratio as a decimal. By dividing the number of U.S. landmark postcards by the total number of U.S. and European landmark postcards, we can find that the ratio of U.S. landmarks to European landmarks is 25/45 =0.555 or 55.5%

Step-by-step explanation:

All exponential functions can be written in many forms. Write the function f(t)=90,000(1.3)^t in the form f(t)=ab^t/5. Round all coefficients to four decimal places.

Answers

The expression can be written as [tex]90,000(3.71)^{\frac{t}{5} }[/tex]

What is an exponential function?

A function whose value is a constant raised to the power of the argument, especially the function where the constant is e.

Given that, we have to express the function [tex]f(t) = 90,000(1.3)^t[/tex] in the form of [tex]f(t) = ab^{\frac{t}{5} }[/tex]

Comparing both the functions,

[tex]b^\frac{t}{5} = (1.3)^t[/tex]

We can write, [tex](1.3)^t[/tex] as

[tex](1.3)^t = (1.3^5)^\frac{t}{5}[/tex]

[tex]= 3.71^\frac{t}{5}[/tex]

Therefore, the equation ca be written as,  [tex]90,000(3.71)^{\frac{t}{5} }[/tex]

Hence, the expression can be written as [tex]90,000(3.71)^{\frac{t}{5} }[/tex]

For more references on exponential function, click;

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