you borrow $90 from your grandmother. you pay back $15 each week.
a. write an equation in standard for that represents the amount owed y after x weeks.
b. find the y intercept of the graph. what does this represent?
c. find the x intercept of the graph. what does this represent?

The correct answer is [tex]\sum_{n=1}^{20} (-8 + 5(n-1))[/tex]

The sum using summation notation, assuming the suggested pattern continues, can be written as:

[tex]\sum_{n=1}^{20} (-8 + 5(n-1))[/tex]

[tex]-8 - 3 + 2 + 7 + \ldots + 67 = \sum_{n=1}^{20} (-8 + 5(n-1))[/tex]

Explanation:

- The pattern appears to be an arithmetic progression with a common difference of 5.

- The first term is -8, and the common difference is 5.

- The nth term of an arithmetic progression can be expressed as [tex]a_n = a_1 + (n-1)d[/tex], where [tex]a_1[/tex] is the first term, and [tex]d[/tex] is the common difference.

- Substituting [tex]a_1 = -8[/tex] and [tex]d = 5[/tex], we get [tex]a_n = -8 + 5(n-1)[/tex].

- The sum of the first 20 terms of this arithmetic progression can be represented using the summation notation, with the index [tex]n[/tex] ranging from 1 to 20.

Therefore, the sum using summation notation is [tex]\sum_{n=1}^{20} (-8 + 5(n-1))[/tex].

Complete question:

Write the sum using summation notation, assuming the suggested pattern continues.

-8 - 3 + 2 + 7 + ... + 67

summation of the quantity negative eight plus five n from n equals zero to fifteen

summation of negative forty times n from n equals zero to infinity

summation of negative forty times n from n equals zero to fifteen

summation of the quantity negative eight plus five n from n equals zero to infinity

Answer:

The correct option is C.

Step-by-step explanation:

It is given that line segment AB has a length of 3 units. It is translated 2 units to the right on a coordinate plane to obtain line segment A'B'.

Translation is a rigid transformation. It means the shape and size of preimage and image are same. In other words we can say that the preimage and image are congruent.

Corresponding sides of congruent figures are congruent.

[tex]AB\cong A'B'[/tex]

[tex]AB=A'B'[/tex]            (Definition of concurrent segment)

[tex]3=A'B'[/tex]                (AB=3 units)

The length of A'B' is 3 units. Therefore the correct option is C.

The solution to the system of linear equations graphed is (-2.5, -2). So, the correct answer is option D.

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

The ordered pair that is a solution to both equations is the system's solution. We graph both equations in the same coordinate system in order to visually solve a system of linear equations. The intersection of the two lines is where the system's answer will be found.

In the given graph, the intersection point is (-2.5, -2).

Therefore, option D is the correct answer.

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[tex]\bf c(\stackrel{x_1}{3}~,~\stackrel{y_1}{8})\qquad d(\stackrel{x_2}{-2}~,~\stackrel{y_2}{5}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{5-8}{-2-3}\implies \cfrac{-3}{-5}\implies \cfrac{3}{5}[/tex]

Answer:

3/5

Step-by-step explanation:

To find the slope, we use the formula

m = (y2-y1)/(x2-x1)

   = (5-8)/(-2-3)

   = -3/-5

   =3/5

The slope is 3/5

A. Sigma notation

The formula for finding the nth value of the geometric series is given as:

an = a1 * r^n

Where,

an = nth value of the series

a1 = 1st value in the geometric series = 940

r = common ratio = 1/5

n = nth order

The sigma notation for the sum of this infinite geometric series is therefore,

                     (see attached photo)

B. Sum of the infinite geometric series

The formula for calculating the sum of an infinite geometric series is given as:

S = a1  / (1 – r)

Substituting the given values:

S = 940 / (1 – 1/5)

S = 1,175

Answer:

[tex]x=-2,x=2[/tex]

Step-by-step explanation:

we have

[tex]x^{2}+2=6[/tex]

we know that

The solution of the function is equivalent to solve the following system of equations

[tex]y=x^{2}+2[/tex] ------> equation A

[tex]y=6[/tex] ------> equation B

The x-coordinate of the intersection point both graphs is the solution of the given function

Using a graphing tool

see the attached figure

The intersection points are [tex](-2,6)[/tex] and [tex](2,6)[/tex]

therefore

The solution of the given function are

[tex]x=-2,x=2[/tex]

The diagonals are 3 cms long each. The area of the kite in the given figure is 9 [tex]cm^2[/tex].

Mathematically, a quadrilateral with two pairs of adjacent sides that are congruent (have equal length) is termed a "kite". Note that not all quadrilaterals with congruent adjacent sides are kites. Kites have numerous applications in geometry, including the study of polygons, symmetry, and angles. They can be used to solve geometric problems and to analyze relationships between sides, angles, and diagonals within the quadrilateral.

Given that the length of the diagonals = 3 cm.

It is known that

Area of a quadrilateral with equal diagonals = product of the diagonals.

Area = 3 [tex]\times[/tex] 3.

Area = 9 [tex]cm^2[/tex].

The area of the kite is 9 [tex]cm^2[/tex].

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Given the constraints, the total number of ways Mr. Smith can distribute pets to his children is calculated as 216 ways. This involves the concept of combinations and permutations from combinatorics in mathematics.

The problem posed is a typical combinatorics or probability question found in mathematics. Given the constraints, the number of ways Mr. Smith can distribute pets is calculated as follows:

Since these scenarios are independent, we multiply these results. Hence, the total number of ways Mr. Smith can distribute pets to his children is 6 x 6 x 6 = 216.

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Considering the preferences of each child, there are 2160 different possible ways Mr. Smith can distribute the 7 pets to his 7 children.

The question posed is a classic problem of combinatorics. We have Anna, Betty, Charlie, Danny, and three other unnamed children who will be receiving pets. Anna and Betty do not want the goldfish, and Charlie and Danny want only cats. Therefore, options for Anna and Betty include the 4 cats and 2 dogs (6 choices total). For each choice Anna makes, Betty has one less choice (5). We can multiply these together, which will give us 30 possible assignments for Anna and Betty. For Charlie and Danny, who just want cats, there are 4 available. Charlie can have one of 4, then Danny can have one of the remaining 3, yielding 12 possibilities.

With Anna, Betty, Charlie, and Danny assigned pets, there are 3 children and 3 pets (2 dogs and 1 goldfish) remaining. Three children can be given 3 pets in 3! = 3*2*1 = 6 ways.

Finally, multiplying these together gives us 30 * 12 * 6 = 2160 possible ways Mr. Smith can distribute the pets among his children.

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To write the equation in point-slope form, plug in the given values of the point and slope into the formula and simplify.

To write an equation in point-slope form for a line, we use the formula: y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line. In this case, the given point is (8, -3) and the slope is -1/4. Plugging in these values into the formula, we get:

y - (-3) = (-1/4)(x - 8)

Simplifying the equation, we have:

y + 3 = (-1/4)x + 2

Therefore, the equation in point-slope form for the line through the point (8, -3) with slope -1/4 is y + 3 = (-1/4)x + 2.

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The weight of Anna is: 115 pounds

and the weight of Janet is: 135 pounds.

It is given that:

Janet weighs 20 pounds more than Anna.

This means if the weight of Anna is: x pounds

Then the age of Janet is: (x+20) pounds.

Also,

The sum of their weights is 250 pounds.

i.e.

x+x+20=250

i.e.

2x+20=250

On subtracting both side by 20 we have:

2x=250-20

i.e.

2x=230

On dividing both side by 2 we have:

x=115

Hence, the weight of Anna is:115 pounds.

and the weight of Janet is: 115+20=135 pounds.

Answer:

The solution is x = 2 or x = 3  

Step-by-step explanation:

we have to find the solution of the equation

[tex] x=2+\sqrt{(x-2)}[/tex]

[tex]x=2+\sqrt{(x-2)}\\ \\x-2=\sqrt{x-2}\\\\\text{Squaring on both sides }\\\\(x-2)^2=x-2\\\\x^2+4-4x=x-2\\\\x^2-5x+6=0\\\\x^2-2x-3x+6=0\\\\x(x-2)-3(x-2)=0\\\\(x-2)(x-3)=0\\\\x=2\text{ or }x=3[/tex]

Hence, correct option is x = 2 or x = 3

Answer:

C) x = 2 or x = 3

Step-by-step explanation:

Edge 2021

The probability that Vicky takes out a blue chip in both draws is 5/25 x 5/25 = 25/625.

Probability determines how likely it is that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

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replace y with -3

2y + 7 becomes 2(-3) + 7 = -6 +7 =1

-4(-3)-10 = 12-10 = 2

The correct answer is X=-3+or-rad33/6

The roots of the quadratic equation 3x^2+3x-2=0 as provided by the quadratic formula are x1 = (3 + sqrt(33))/6 and x2 = (3 - sqrt(33))/6.

The quadratic equation in question is 3x^2+3x-2=0. Here, a=3, b=3, and c=-2. We can solve this equation using the quadratic formula, which, in general terms, is given as: x = [-b ± sqrt(b² - 4ac)] / 2a.

Plugging the coefficients into the quadratic formula, we get:

x = [-3 ± sqrt((3)² - 4*3*(-2))] / 2*3

= [-3 ± sqrt(9 + 24)] / 6

= [-3 ± sqrt(33)] / 6

That gives us two roots: x1 = (3 + sqrt(33))/6 and x2 = (3 - sqrt(33))/6. These are the solutions for the quadratic equation given.

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Final answer:

To convert the chances of a '1 in 19' win into a probability value, you divide 1 by 19 to get 0.05263 and then round to 0.053. Therefore, the lottery win probability is 0.053.

Explanation:

To express the likelihood of a win in a lottery game as a probability value between 0 and 1, when the chances of a win are stated as "1 in 19", you follow these steps:

Understand that "1 in 19" means there is one chance to win for every 19 trials, so the total number of possible outcomes is 19 (18 losses + 1 win).

Express the chance to win as a fraction with the number of wins (1) over the total number of potential outcomes (19).

Convert the fraction into a decimal by dividing the numerator (1) by the denominator (19), which gives you approximately 0.05263.

Round the result to three decimal places, as requested, which gives you a probability value of 0.053.

Therefore, the probability of winning the lottery game is 0.053.

Answer:

Dilation by a scale factor of 2 followed by reflection about the x-axis

Step-by-step explanation:

To answer it and view it properly let's do it by parts.

1) A closer look at the Triangle ABC shows us the coordinate points A(-2,-1) B(0,0) and C(1,-3).

2) Reflection across the x-axis gives us this triangle: A'(-2,1) B'(0,0) and C'(1,3). Notice that all y-coordinates have an opposite sign. This is a natural characteristic of a Reflection: an opposed sign of one Coordinate.

3) Finally, To Dilate a Triangle is to transform it so that it gets bigger than its original size.

If we compare the triangle with points  A''(-4,2) B"(0,0) and C"(2,6) to A'(-2,1) B'(0,0) C'(1,3). Each coordinate is multiplied by 2.

Dilation by a scale factor of 2 followed by reflection about the x-axis

The complex solutions of x^2+5x-5=0 are (-5 + √45)/(2) and (-5 - √45)/(2).

To find the complex solutions of x2+5x-5=0, we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac))/(2a)

Substituting the values a=1, b=5, and c=-5 into the formula, we get:

x = (-5 ± √(5^2 - 4(1)(-5)))/(2(1))

Simplifying further,

x = (-5 ± √(25 + 20))/(2)

x = (-5 ± √(45))/(2)

Since the square root of 45 cannot be simplified, we can write the solutions as:

x = (-5 ± √45)/(2)

Therefore, the complex solutions to the equation x2+5x-5=0 are:

x = (-5 + √45)/(2), (-5 - √45)/(2)

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