Question 3
Melissa wants to check the accuracy of the finance charge on her promissory note.
She has a $2,000, two-year loan at a APR of 6%.
What is her monthly payment?
$
What is the total of her monthly payments?
$
What is the finance charge?
6 pts
$

When a transversal crosses a pair of parallel lines same side interior angle pair are supplementary.

What is parallel lines?
Two lines in same plane that are equally spaced apart and never cross each other are said to be parallel lines in geometry. Both lateral and vertical shapes are possible. Examples of parallel lines can be found everywhere, including zebra crossings, rows of notebooks, and the nearby railroad tracks. Different shapes' sides run parallel to one another. The single arrow lines in the rectangle below are parallel to one another, and the double arrow lines also are parallel to one another.

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Answer: 2z+2

Step-by-step explanation:

The geometric relationship sum of ∠A+∠B = 90° as they are complementary.

What is are complementary?

The territory included by a triangle's sides is referred to as its area. Depending on the length of the sides and the internal angles, a triangle's area changes from one triangle to another. Square units like m2, cm2, and in2 are used to express the area of a triangle.

They are referred to as complementary angles when the sum of two angles is 90 degrees. For instance, the angles of 30 degrees and 60 degrees complement one another.

It is given that angle A and angle B are complementary.

Hence, The geometric relationship sum of ∠A+∠B = 90°

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Answer: There are 151200 permutations

Answer:

In the word "bookkeeping" there are approximately 151,200 permutations.

Step-by-step explanation:

Permutations:

Is a way, especially one of several possible variations, in which a set or number of things can be ordered or arranged.

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The area of the circle is 25.12 unit² and the circumference is 17.75 units.

The space a circle takes up on a two-dimensional plane is known as the area of the circle. The region included by the circle's radius or perimeter is another way to define the circle's area.

A circle's perimeter is known as its circumference. It is the circumference of the circle as a whole. A circle's circumference is calculated by multiplying its diameter by the constant π.

The given points of radius are

(x₁, y₁) = (2, 3)

(x₂, y₂) = (4, 1)

The formula for the distance between the specified points is

r = [tex]\sqrt{(y_{2}-y_{1})^{2} + (x_{2}-x_{1})^{2} }[/tex]

r = [tex]\sqrt{(1-3)^{2} + (4-2)^{2} }[/tex]

r =  [tex]\sqrt{4+4}[/tex]

r = 2[tex]\sqrt{2}[/tex] units

The area of the given circle will be given by the formula A = πr²

A = 3.14 × (2√2)²

= 3.14 × 8

= 25.12 unit²

The circumference of the given circle will be given as

C = 2πr

C = 2 × 3.14 ×2√2

C = 12.56√2

C = 12.56 × 1.414

C = 17.75 unit

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If we make r the subject formula, then the formula would be r = log_h(V/π) + (h/3)

In this question, we have been given a formula V=πh^(r-h/3)

We need to make r the subject formula

This means we need to rewrite formula for r.

V = πh^(r-h/3)

h^(r-h/3) = V/ π

r - h/3 = log_h(V/π)

r = log_h(V/π) + (h/3)

Therefore, if we make r the subject formula, then the formula would be r = log_h(V/π) + (h/3)

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Grape Juice (cups) 6 8 10 Rainbow Sherbet (cups) 0.75 1 1.25 represents the correct relationship.

A ratio is a comparison between two similar quantities in simplest form.

Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.

In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.

Given, The proportional relationship for 6 cups of grape juice for every three-fourths cup of rainbow sherbet.

So, the ratio of grape to rainbow sherbet is 3/4 : 6 = 3 : 24.

Which is (24/3) = 8 times.

Now checking the options Grape Juice (cups) 6 8 10 Rainbow Sherbet (cups) 0.75 1 1.25 is the correct relationship.

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Answer:

x=7y+x

Step-by-step explanation:

Isolate x on one side

x-7y=8

 +7y.  +7y

x=7y+8

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Answer:

y=-3/2x +2

Step-by-step explanation:

Answer:

y = 1.50x +2

Step-by-step explanation:

First, we must find two points.

Equation of a straight line:

y = mx + b ------(i)

Step 1: Calculating Slope (m).

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\frac{2-0.500}{1-0}[/tex]

[tex]m=\frac{1.50}{1}[/tex]

[tex]m=1.50[/tex]

Now putting value of m in equation (i)

                             y = 1.50x + b -----(ii)

Step 2: Calculating Y-intercept (b).

Lets choose the first point, (0,2) for calculating y-intercept:

2 = 1.50(0) + b

2 = 0 + b

2 = b

b = 2

Now putting value of b in equation (ii)

y = 1.50x + 2

Using metric units, the cost of rice in London is ₤0.85 per pound

To solve this problem, we need to convert the price per kilogram to price per pound.

We can use the conversion factor of

1 pound = 0.454kg

And

$1 = ₤1.18

Let's proceed to convert from kilogram to pounds since the currency is already in the desired unit.

1lb = 0.454kg

x = 1kg

x = 1 / 0.454

x = 2.2lb

This implies that

₤1.88 = 2.2lb

x = 1lb

x = (1.88 * 1) / 2.2

x = 0.85

This becomes ₤0.85 per pound

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Answer:

Im not sure but I think the answer is 6, but only if the total amount is for sure 17

Step-by-step explanation:

This is because we know that whatever the number is is five more than the unknown number and equals 17. This can be written as n + (5 + n) = 17, which can be simplified to x = 6.

The independent variable in this situation is C. area of the prism.

In mathematical modeling, statistical modeling, and experimental sciences, dependent and independent variables are variables. Dependent variables are so named because their values are studied in an experiment under the assumption or demand that they are dependent, by some law or rule, on the values of other variables.

The term "independent variable" means exactly what it sounds like. It is a variable that is independent of the other variables you are attempting to measure. For example, age could be an independent variable.

In this case, the area doesn't change in relation to others. It's independent.

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The ratio 5 to 2 is written in other notations as

Mathematicians use the term "ratio" to compare two or more numbers.

It serves as a comparison tool to show how big or small an amount is in relation to another.

In a ratio, division is used to compare two amounts.

The ratio 5 is to 2 can be represented as a fraction to 5 / 2

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The velocity experimented by the car is equal to - 1 feet per second.

Herein we have the graph of the position of the car (y), in feet, versus time (t), in seconds. The graph shows a linear equation, that is, the position is described by a polynomial of the form:

y = m · t + b

Then, the functions for the velocity and acceleration are shown below:

Velocity

dy / dt = m

The slope represents the velocity of the car.

Acceleration

d²y / dt² = 0

Then, the velocity of the car is found by means of the secant line formula:

dy / dt = (0 ft - 10 ft) / (10 s - 0 s)

dy / dt = - 1 ft / s

The velocity of the car is - 1 feet per second.

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Answer:

It costs 32.75 for five pounds. and the expression would be p7.25-3.50

Step-by-step explanation:

5*7.25 = 36. 25. 36.25-3.50=32.75

c=p7.25-3.50 would be the expression. :)

A) Y = [tex]-2^{x}+4[/tex] is the equation which have real zero(s) corresponding to the x-intercept(s) of the graph below

What does a mathematical coordinate mean?

a set of numbers used to represent the horizontal and vertical divisions of the positions of two reference axes in a coordinate plane. often shown as the combination of x-values and y-values (x,y).

What is the Slope Intercept Form Equation?

The slope intercept equation can be used to find the general equation of a straight line using its slope and the point of its y-axis junction. The equation in slope intercept form is Y = mx + b.

You must enter y=0 for the x intercept.

in equation A we can see that at x=2 , y=0

so hence answer is option A) Y =[tex]-2^{x}+4\\[/tex]

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Two planes that are orthogonal to one another are parallel. This is untrue. Although they might not be parallel, two planes can be orthogonal to a third plane.

Parallel lines in geometry are coplanar, straight lines that don't cross at any point. In the same three-dimensional space, parallel planes are any planes that never cross. Curves with a predetermined minimum distance between them and no contact or intersection are said to be parallel.

Given,

Two planes intersected by a third plane are parallel.

Two planes that are orthogonal to one another are parallel. This is untrue. Although they might not be parallel, two planes can be orthogonal to a third plane.

A line is formed by the intersection of two planes. The planes are parallel if they do not intersect. Due to the endless nature of planes, they cannot meet at a single place. Stack a hardcover book on your desk and open the two hard covers at any random angle. The coverings' planes are not parallel to one another but are individually perpendicular to the desk top (or necessarily perpendicular to each other).

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The missing terms of the arithmetic sequence -13, - 6,  1 , 8 , 15,  22.

an = a1, a2, a3, a4, a5, a6

formula for nth term is :

an = a + (n - 1)d

where

an = last term

a = a1 = first term

n = number of terms

d = difference between two terms

here

a2 = a + d

- 6 = a + d    ....(1)

a5 = a + 4d

15 = a + 4d      .......(2)

on solving equation we get :

- 6 = a   +    d    ....(1)

15 =  a    +    4d      .......(2)

(-)    (-)      (-)

- 21 =  - 3d

d = 21/3

d = 7

using the value of d in equation the value of a is :

- 6 = a + d  

-6  = a + 7

a = -6 -7 = -13

then

a1 = a = -13

a2 = a + d  = -13 + 7 = -6

a3 = a + 2d  = -13 +2 x 7 = 1

a4 = a + 3d =  -13 + 3 x 7 = 8

a5 = a + 4d =  -13 +4 x 7 = 15

a6 = a + 5d = -13 +5 x 7 = 22

The missing terms of the arithmetic sequence -13, - 6,  1 , 8 , 15,  22.

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Answer: -13.35

Step-by-step explanation:

Trust the process

Answer:

0.3115264797507,0.1610305958132,0.7,1.4

The area in square feet is 180.

Given:

There is a rectangular floor is 5 yd long and 4 yd wide.

Required:

Jessica wants to tile the floor with tile sold by the square foot

Now, According to the question:

First of all we need to convert the given data in foot from yd.

We know that:

1 yd = 3feet

4 yd = 12 feet

5 yd = 15 feet

Now find the area of rectangular floor

Length of the floor = 5 yd = 15 feet

Breadth of the floor = 4 yd = 12 feet

Area = l x b

Area of the rectangular floor is :

15 x 12 = 180 feet sq.

Hence, The area in square feet is 180.

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By reviewing Damon's work, the true statement is, Damon used the subtraction property of equality.

what is true statement?

A statement is true if the assertion it makes is true, and it is false if the assertion it makes is untrue. For example, the statement "The trains are always late" is only accurate if the situation it describes—that is, if the trains are indeed always late—actually exists.

As given, Damon is saving for a vacation.

He estimates that he’ll need about $2,500 for the trip.

He created an equation last week to model his savings plan to determine how many more months of saving it will take to reach his goal.

In the equation Damon created, x represents the number of months since last week and y represents the total amount he’s saved for the vacation.

The statements are,

Step 1: y = 500 + 400x

Step 2: y - 500 = 500 + 400x - 500

Step 3: y - 500 = 400x

Step 4: y - 500/400 = 400x/400

Step 5: y - 500/400 = x

Step 6: 2500 - 500/400 = x

Step 7: 5 = x

Therefore, the true statement is Damon used the subtraction property of equality in step 3.

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Answer:

6 x 10^18

Step-by-step explanation:

3  x 2 = 6

10^9 * 10^9 = 10^(9+9) = 10^18

The given function is linear and constant because your equation is represented by the standard form for the linear equation.

A linear function can be represented by an equation. The standard form for the linear equation is: y= mx+b , for example, y=6x+4. Where:

m= the slope.

b= the constant term that represents the y-intercept

For the given example: m=6 and b=4.

An equation is classified as nonlinear when it is not represented by the standard form for the linear equation. For example, 2x²+x+10, x², x³, x³ +2, etc.

The given equation is  4y=24. Firstly, you should rewrite it  to the standard form for the linear equation is: y= mx+b. Therefore,

4y=24

y=24/4

y=6

If the standard form for the linear equation is y= mx+b, for the given equation m=0 and b=6. Thus, the given equations is linear and constant. It can be classified for constant because for any value of x, the value of y always be equal to 6.

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The gas bill exceeded $87 from last month to this month.

We know simple interest (SI) is given by SI = (p×r×t)/100, where

p = principle, r = rate in percentage, and t = time in years.

Given, The Haddad expected the automatic withdrawal of their gas bill to

be more than last month's bill of $215.85 but did not know by how much.

Their account showed a previous balance of $417.80, $350.00 in deposited checks, and an automatic deposit of $150.00.

∴ Their current balance is (417.80 + 250 + 150) = $817.8 and $5.25 in interest which is (105/100)×$817.7 = $858.69.

Haddads' present balance is $555.82,

∴ The gas bill is $(858.69 - 555.82) = $302.87.

So the gas bill s exceeded by $(302.87 - 215.85) = $87.

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Answer: 72.5%

Step-by-step explanation: Since you want the percent of the paid amount of the received amount this will be your equation: paid/received. So if you do 412/567.89, you get ≈ .725 or 72.5%.

The height of the two trees will be same after 13 years and the height of the trees will be 24 feet.

According to the question,

We have the following information:

One tree, a ficus, was 6 feet tall when it. was planted and has grown 1.5 feet per year. The other tree, an oak, was grown from an acorn on the ground and has grown 2 feet per year.

So, for first tree, we have:

6, 7.5, 9, ...

Now, this is an arithmetic progression.

So, for the second tree, we have:

0,2,4, ...

Now, this is again an arithmetic progression.

Formula to find nth term of an A.P.:

an = a+(n-1)d where a is the first term and d is the common difference

6+(n-1)1.5 = 0+(n-1)2

6+1.5n-1.5 = 0+2n-2

4.5 = 2n-1.5n-2

6.5 = 0.5n

n = 13 years

Now, we have the height of the trees after 13 years:

an = 0+(13-1)2

an = 12*2

an = 24 feet

Hence, the height of the two trees will be same after 13 years and the height of the trees will be 24 feet.

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The trigonometric expression tan² x + 1 = sec² x is proved by using the fundamental trigonometric formula and the definition of tangent and secant.

In this problem we must prove the existence of a trigonometric formula by means of definitions of trigonometric functions and the fundamental trigonometric formula.

Step 1 - Introduce the fundamental trigonometric formula and the definitions of tangent and secant:

sin² x + cos² x = 1, tan x = sin x / cos x, sec x = 1 / cos x

Step 2 - Divide each side of the formula by cos² x:

sin² x / cos² x + cos² x / cos² x = 1 / cos² x

(sin x / cos x)² + 1 = (1 / cos x)²

Step 3 - Use the definition of the two trigonometric functions:

tan² x + 1 = sec² x

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