Alison wants to borrow $18,000 for a new car. If annual interest rate for a 60-month loan is 3.6% , set up the equation to calculate Alison’s monthly payment.

The process of plotting the graph a quadratic equation using the vertex and intercepts is explained below.

The term quadratic equation is defined as a polynomial equation of a second degree, which implies that it comprises a minimum of one term that is squared.

Here we have given the vertex and intercepts.

And now we have to explain the process of plotting the graph through this.

As we all know that when you graph a quadratic then there are a couple of things you need to consider that will make your life easier.

The first thing that you need to find the vertex .

And that one is derived through  vertex form by using the equation y=a(x−h)² + k here the point (h,k) defines the vertex.

Where as it can be either the highest or lowest point on your graph and it is the first thing you need to graph.

Then the next steps is use the intercept that can be obtained by plug in 0 for y in the equation and then we have to solve is  for x then you will find the coordinates of the two intercepts.

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The coordinates of the image after a rotation 270° clockwise about the origin.

A'(-4,-4)

B'(-2,6)

C'(-1,1)

D(-3,-5)

What is rotation?

A rotation is a transformation that turns the figure in either a clockwise or counterclockwise direction. You can turn a figure 90°, a quarter turn, either clockwise or counterclockwise. When you spin the figure exactly halfway, you have rotated it 180°. Turning it all the way around rotates the figure 360°.

This question is solved by applying a 270° clockwise about the origin, which has the following rule:

(x, y) = (-y, x)

Coordinate Q:

At the Figure, coordinate Q is Q(-4, 5). Applying the rule:

(-4, 5) = (-5, -4)

So the image of Q is Q'(-5, -4).

Coordinate R:

In Figure, the coordinate R is R(-2, 5). Applying the rule:

(-2, 5) = (-5, -2)

So the image of R is R'(-5, -2).

Coordinate S:

At the Figure, coordinate S is S(-2, 9). Applying the rule:

(-2, 9) = (-9, -2)

So the image of S is S' (-9, -2)

Coordinate T:

At the Figure, coordinate T is T(-4, 9). Applying the rule:

(-4, 9) = (-9, -4)

So the image of T is T'(-9,-4).

The coordinates of the image after a rotation 270° clockwise about the origin.

A'(-4,-4)

B'(-2,6)

C'(-1,1)

D(-3,-5)

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The smallest value of x for which the following inequality holds true is 7.

We are given

1/2 + 1/3 +...+ 1/x > 3/2

Here we will keep on assuming values of x till we get the first value of x for which LHS > RHS

manipulating the inequality we get

1/3 +... + 1/x > 1

or, 1/4 + ... + 1/x > 2/3

or, 1/5 + .... + 1/x > 5/12

or, 1/6 + ... > 13/60

or, 1/7 + ... > 3/60

or, 1/7 +... > 1/20

We know that when the numerator is the same, the denominator with the smaller value is the larger fraction.

Hence with the addition of the series till 1/7, we get a value larger than 3/2

Hence the smallest value of x is 7.

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Correct Question

suppose 1/2 + 1/3 +...+ 1/x > 3/2. what is the smallest possible value for x?

No, the graph of a function does not contain every straight line. Due to the fact that they satisfy the vertical line test, nearly all linear equations are functions.

Relationships that fail the vertical line test are the exceptions. All linear equations, when graphed, result in straight lines, but not all linear equations result in linear functions. A graph must be both linear (a straight line) and a function in order to be a linear function (matching each x-value to only one y-value).

A vertical line has an equation of the form x = a, where an is any real number, and is the only instance in which a linear equation is not a function.

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The equation of  the parabola is = [tex]x^{2}-10x-2y+32[/tex]

Let us assume (x,y) be a point on the parabola then the distance of this point from focus is equal to the distance from the directrix.

Distance of a point from focus =[tex]sqrt{((x-5)^2 + (y-4)^2)}[/tex]

Distance of point from directrix =|y-3|/[tex]\sqrt{1^2 + 0^2}[/tex]

squaring both sides we get,

(x-5)^2 + (y-4)^2 =(y-3)^2

= [tex]x^{2}-10x-2y+32[/tex]

The equation of  the parabola is = [tex]x^{2}-10x-2y+32[/tex]

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Answer: 13/1560 (The distance flown in 13 hours is 1560 miles)

Step-by-step explanation: Rate X Time = distance

Therefore:

    r (rate) X 5 (hours) = 600 (distance)

    r = 600/5

    r = 120 miles per hour

    The rate of speed of the jet is 120 mph.

Then, to find out the distance flown in 13 hours:

    120 (rate) X 13 (time) = d (distance)

    120 X 13 = d

    1560 = d

    The distance flown in 13 hours is 1560 miles.

The value of an acute triangle is 180°. All three interior angles of an acute triangle measure less than 90°. The value of angles of an acute triangle adds up to 180°.

A triangle is a fundamental polygon with three sides and three vertices. As the triangle has three sides, it also has three interior angles. An angle which measures between 0° to 90° is called an acute angle. An acute triangle is a kind of triangle in which all three internal angles of the triangle are less than 90°.

Acute triangles are also called acute-angled triangles. Even though the length of the sides of acute triangles varies, the interior angles are never more than 90°.

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The thing that should be done for the game to be fair is 2. Add 2 cards with stars.

Probability simply means the chance that a particular thing or event will happen. It is the occurence of likely events. It is simply the area of mathematics that deals with the numerical estimates of the chance that an event will occur.

Since Four of the cards have stars on them and the other 6 are blank and you win if you draw a card with a star, it's important to add 2 cards with stars.

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On solving the provided question, we can say that by unitary method 1 week = $500 => 52 weeks = $ 52 * 500 = $26,000

The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.

here,

we know that

1 year = 52 weeks

by unitary method

1 week = $500

52 weeks = $ 52 * 500 = $26,000

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The graph of x − 2 is a vertical line.

The graph of x − 2  is a straight line that is perfectly vertical, with no slope or angle. This line has an x-intercept of -2, meaning that the line crosses the x-axis at a point where x is equal to -2.

All points on the line have the same y-value, which is -2. This line extends infinitely in both directions and is a key example of a linear equation.

x − 2 is a linear equation, so its graph will be a straight line. In this case, the graph of x − 2 will be a vertical line that passes through the point (2, 0).

This is because when x is equal to 2, the equation will equal 0. As the x-value increases, the y-value will increase in a linear fashion, resulting in a vertical line.

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The answer of 5 more than 5 is 10.

The answer of 5 more than 5 is 10 which can be derived using simple mathematical calculations.

To find 5 more than 5, you can add 5 to the original number 5.

5 + 5 = 10

It's a simple arithmetic operation where you add a specific number, in this case 5, to the original number.

An arithmetic operation is a mathematical process that combines two or more numbers to produce a new number. The most basic arithmetic operations are addition, subtraction, multiplication, and division.

Addition: It is the process of combining two or more numbers to find their sum. For example, 2 + 3 = 5 is an addition operation.

Subtraction: It is the process of finding the difference between two numbers. For example, 5 - 3 = 2 is a subtraction operation.

Multiplication: It is the process of finding the product of two or more numbers. For example, 3 x 4 = 12 is a multiplication operation.

Division: It is the process of finding the quotient of two numbers. For example, 12 ÷ 3 = 4 is a division operation.

Therefore, The answer of 5 more than 5 is 10.

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The missing numbers for the respective rows are:

row 1: -0.5

row 2: -0.3 and -0.1

row 3: -0.2

The 3rd column to the right have a total of:

0 + 0.1 + (-0.4) = -0.3

Missing number for row 1(top row):

-0.2 - 0 - 0.3 = -0.5

Missing number for the diagonal from top left:

0.4 - 0.2 - 0.3 = -0.1

Missing number for row 2 (2nd number for 1st column):

0.1 - 0.1 - 0.3 = -0.3

Missing number for row 3 (bottom row):

0.4 - 0.3 - 0.3 = -0.2.

Therefore, row 1 have the missing number; -0.5. Row 2 missing numbers from left; -0.3 and -0.1. Row 3 missing number is -0.2.

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Answer:

52.393

the square root of 2745 is 52.393

On solving the provided question we can say that from the graphs  y=e^-x+x => y = -3

Mathematicians use graphs to logically convey facts or values using visual representations or charts. A graph point will typically reflect a relationship between two or more things. Nodes, or vertices, and edges make form a graph, a non-linear data structure. Glue together the nodes, often referred to as vertices. This graph has vertices V=1, 2, 3, 5, and edges E=1, 2, 1, 3, 2, 4, and (2.5), (3.5). (4.5). Statistical charts (bar charts, pie charts, line charts, etc.) graphical representations of exponential growth. a logarithmic graph in the shape of a triangle

here,

from the graphs

y=e^-x+x

for(-3,6)

y = e^-3 -3

y = -3

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Answer:

the loss of other alternatives when one alternative is chosen.

example: if you have to choose between buying a shoe or a coat and you choose to buy the coat, the shoe is the opportunity cost.

Step-by-step explanation:

The derivatives of b(t) with respect to t will be d(b(t))/dt = - ωacos(kx - ωt)

We have been given b(t) = asin(kx - ωt)

Hence, we need to find db(t)/dt

We will treat a, k, x, and ω as constants since no information is provided.

We will be using the chain rule to find the derivative

First, we consider sin as an individual term to get-

a______

Next, we know that the derivative of sin is cos Hence we get

acos(kx - ωt)______

Now we will move on to the terms in the brackets

Here kx is a constant so the derivative of this will be 0.

Hence we get left with - ωt

here the differentiation will clearly be - ω

Hence we get the final derivative

d(b(t))/dt = - ωacos(kx - ωt)

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Correct Question

what is the derivative of b(t) with respect to t for b(t) = asin(kx - ωt)

Since the Pennsylvania lottery was rigged, the probability of drawing a 666 in the April 24th, 1980 drawing is 100%. The probability of drawing a 666 in the September 19th, 1980 Connecticut lottery, however, is extremely low, as it was not rigged and the odds of picking a specific 6-digit combination are 1 in 1 million.

To calculate this probability, you would take 1 divided by 1 million, which would be 0.000001. This means that the probability of drawing a 666 in the Connecticut lottery is 0.000001.   In conclusion, the probability of drawing a 666 in the April 24th, 1980 Pennsylvania lottery is 100%, while the probability of drawing a 666 in the September 19th, 1980 Connecticut lottery is 0.000001.

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Answer: g [tex]\geq[/tex] -4

Step-by-step explanation:

[tex]3\leq7+g[/tex]

Subtract 7 from both sides:

-4 [tex]\leq[/tex] g, so

g [tex]\geq[/tex] -4

Answer:

g ≥ -4

Step-by-step explanation:

3≤7+g

We rewrite g on the left side

g + 7  ≥ 3

g  ≥ -4

Answer:

For 1st both both a and b lies on the graph but for 2nd only a lies on the graph

Step-by-step explanation:

The number of trees on each acre of land, given that the trees are evenly spaced out, is 101 trees per acre

To find out how many trees are on each acre of land, we need to divide the total number of trees by the number of acres. This is given that the trees are spread out evenly as is the case here.

The number of trees per acre of land is therefore:

= Number of trees in total / Number of acres

= 3, 434 / 34

= 101 trees per acre

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Answer:

third graph

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = [tex]\frac{1}{3}[/tex] x + 12 ← is in slope- intercept form

with slope m = [tex]\frac{1}{3}[/tex] and y- intercept c = 12

y = 3x + 4 ← is in slope- intercept form

with slope m = 3 and y- intercept c = 4

• If m > 0 , then graph slopes upwards from left to right

Both equations have a positive slope, thus both slope upwards from left to right.

the first equation has a y- intercept of 12

the second equation has a y- intercept of 4

Theses lines are represented in the third graph

Amelia drove a total of 8.4 miles on her birthday.

Miles are a unit of distance or length measurement. They are commonly used to measure the distance between two points on a map, or the length of a journey. The term 'mile' is derived from the Latin word for 'thousand', and is equal to 1.609 kilometers. Miles are a preferred unit of measurement in the United States, UK, Canada, and some other countries.

The 3 miles from her house to her parents’ house and 1 mile from her parents’ house to her grandparents' house make up 4 miles of her total journey. She then drove the same distance of 4 miles back home, totaling 8.4 miles.

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The correct statement regarding the sign of the reciprocal function is given as follows:

C. The function is positive when x > 0.

The intervals for which a function is positive are the intervals for which the function graph lies above the x-axis.

The intervals for which a function is negative are the intervals for which the function graph lies below the x-axis.

Hence the positive and negative intervals for this problem are given as follows:

Meaning that the correct option is given by option c.

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If volleyball team purchased 15 jackets, 12 pairs of sweatpants for $348 and basketball team purchases 8 jackets , 8 pairs of sweatpants for $200, the the system of equations that represent the situation is (b)  [tex]15x+12y = 348[/tex] and [tex]8x+8y = 200[/tex] .

let the number of jackets purchased be = x ;

let the number of pairs of sweatshirts purchased be = y ;

the volley ball team purchased 15 jackets and 12 pairs of sweatpants for $348 ,

that means the equation that represents the situation is :

[tex]15x+12y = 348[/tex] .

Also given that , the basketball team purchased 8 jackets and 8 pairs of sweatpants for $200 ,

that means the equation that represents the situation is :

[tex]8x+8y = 200[/tex] .

Therefore , the system of equations are [tex]15x+12y = 348[/tex] and [tex]8x+8y = 200[/tex] .

The given question is incomplete , the complete question is

A sports apparel supplier offers teams the option of purchasing extra apparel for players. A volleyball team purchases 15 jackets and 12 pairs of sweatpants for $348. A basketball team purchases 8 jackets and 8 pairs of sweatpants for $200. Let x represent the price of a jacket and let y represent the price of a pair of sweatpants. Which system of equations can be used to find the price of each item ?

(a) 8x + 8y = 200  ;  12x + 15y = 348   ;

(b) 8x + 8y = 200  ; 15x + 12y = 348 ;  

(c) 8x + 8y = 348  ;  12x + 15y = 200 ;  

(d) 8x + 8y = 348 ;  15x + 12y = 200 .

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The polynomial functions f(x) = x³-2x²-3x+6

To solve this question, we use the factor theorem, and using it, the polynomial function is: f(x) = x³-2x²-3x+6

The factor theorem means that if k is a root of f(x), f(k) = 0.

Thus, applying the factor theorem for this question, we have to choose the function for which:

f(2) =0, f(√3) =0, f(-√3) = 0

Function 1:

f(x) = x³-2x²-3x+6

Testing the values:

f(2( = 2³-2(2)²-3(2) +6

= 8--6+9 = 0

f(√3) = √3³-2(√3)²-3√3 +6

=3√3-3√3 = 0

f(-√3) = -√3³-2(-√3)²-3(-√3) +6

= -3√3-√3 = 0

Thus, since all three conditions are satisfied,  is the polynomial function.

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Complete question:

Using the Factor Theorem, which of the polynomial functions has the zeros 2, radical 3 , and negative radical 3 ? f (x) = x3 – 2x2 – 3x + 6, f (x)= x3 – 2x2 + 3x + 6, f (x) = x3 + 2x2 – 3x + 6, f (x) = x3 + 2x2 – 3x – 6

C) 6p³ – 23p² + 9p + 28 is the product obtained when Iliana multiplied

3p – 7 and 2p² – 3p – 4.

A mathematical equation is a statement of equality between two expressions that can contain numbers, variables, and mathematical operators. Equations are often used to describe relationships between different quantities, and can be used to solve problems and make predictions. They can also be represented graphically. Equations can be simple or complex, with one or multiple variables. They are used in various fields like physics, chemistry, engineering, economics etc.

In order to find the result we multiply both mathematical equation together

(3p – 7)*(2p² – 3p – 4).

=> 6p³ - 9 p²  - 12p - 14p² + 21p +28

=> 6p³ - 23 p² + 9p + 28

so the product of both mathematical equation is 6p³ - 23 p² + 9p + 28

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Complete question:

Iliana multiplied 3p – 7 and 2p² – 3p – 4. Her work is shown in the table.

Which is the product?

A) 6p³ + 23p² + 9p + 28

B) 6p³ – 23p² – 9p + 28

C) 6p³ – 23p² + 9p + 28

D) 6p³ + 23p² – 9p + 28p-

The slope of the given equation is -1/5 and the y - intercept is -1.

What is slope and y - intercept?

This procedure determines how quickly the value of the function's dependent variable, y, changes in relation to the independent variable, x. (independent variable). The slope itself identifies the slope and direction of the line.

the y-coordinate of a point on a surface, curve, or line where they cross the y-axis.

Consider, the given equation

p(x) = -1 - 1/5x

We have to find the slope and y - intercept of the given equation.

Rewrite the equation as,

y = -1/5x - 1

Compare this equation with

y = mx + c

where

m is the slope and

c is the y - intercept

So, from above equation, we get

m = -1/5 and c = -1

Hence, the slope of the given equation is -1/5 and the y - intercept is -1.

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Graph each inequality onto the same Cartesian Coordinate axes. Where the inequality shadings overlap is the solution.

How to solve each system of inequalities by graphing?

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Answer:

It will be located in the explanation

Step-by-step explanation:

The value of X² will always be positive, whether the value of "X" is positive or negative.

X² will always be positive because the square of any number, whether positive or negative, will always be positive.

For example, (-1)² = 1, which is a positive number. Therefore, regardless of the sign of X, X² will always be positive. Then we can conclude The value of X² will always be positive, regardless of the sign of X.

A quadratic equation is an equation of the form ax2 + bx + c = 0, where a, b, and c are constants, and a ≠ 0. It can be solved using the quadratic formula, which is: x = [-b ± √(b2 - 4ac)] / 2a. This formula gives the two solutions to the equation.

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