To isolate the variable in the equation -3x - 9 = -27, the first step is to add 9 to both sides. This gives you -3x = -18. What is the next step to isolate the variable?

 A.+ 18  B.18  C. -3  D.+ 3x

Answers

Answer 1
-3x-9=-27
Add 9 to both side
-3x-9+9=-27+9
-3x=-18
divided -3 to each side
-3x/-3=-18/-3
x=6
Check:
-3x-9=-27
substitute x with 6
-3(6)-9=-27
-18-9=-27
-27=-27. As a result, the next step to isolate the variable is divided -3 to both side. Hope it help!
Answer 2

Next step to isolate the variable is to divide by -3 .

Given,

-3x-9=-27

Firstly,

Add 9 to both side of the equation,

-3x-9+9=-27+9

-3x=-18

Now,

Divide -3 to each side

-3x/-3=-18/-3

x=6

Now,

Check:

-3x-9=-27

Substitute x with 6

-3(6)-9=-27

-18-9=-2

Thus, the next step to isolate the variable is to divide -3 to both side of equation.

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Related Questions

Identify the function that best models the data.

Answers

The answer you are  looking for is A, I'm a little rusts at these but that should your answer have a good day!
Using a graphing calculator with a quadratic regression function, the answer is letter A.

Line segment AB has a length of 4 units. It is translated 1 unit to the right on a coordinate plane to obtain line segment A prime B prime. What is the length of A prime B prime?

Answers

Line segment A'B' still has a length of 4 units.  When you perform the translation, all you do is move the line segment, without altering its length.

Answer:

4

Step-by-step explanation:

Mia's perents said that she can use a space in the yard that measures. 13 feet long by 9 feet wide for her wildflower garden. What is the area of the garden

Answers

A = L * W
A = 13 * 9
A = 117 square ft <==

The area of 13 feet long by 9 feet wide wildflower garden is 117 square feet.

Use the concept of a rectangle defined as:

Rectangles are four-sided polygons with all internal angles equal to 90 degrees. At each corner or vertex, two sides meet at right angles. The rectangle differs from a square in that its opposite sides are equal in length.

To find the area of her garden,

Multiply the length and width of the space.

In this case,

the length is 13 feet and the width is 9 feet.

So, the area of Mia's garden would be,

13 feet x 9 feet = 117 square feet.

Hence,

The area of the garden is 117 square feet.

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What is the mean salary of a salesperson at the company

Answers

a fixed regular payment, typically paid on a monthly or biweekly basis but often expressed as an annual sum, made by an employer to an employee, especially a professional or white-collar worker.

Square sandbox with sides 3 feet long. She wants to put sand 0.85 feet deep in the box. What is the exact measure, in cubic feet of sand, tat Maija needs?

Answers

3 * 3 = 9 * 0.85 = 7.65 cubic feet of sand
Final answer:

To find the volume of sand needed for Maija's sandbox, multiply the length, width, and depth. As the sandbox is a square, both the length and width are 3 feet. The depth is 0.85 feet. Thus, Maija needs 7.65 cubic feet of sand.

Explanation:

This question is about calculating volume, specifically the volume of sand that Maija needs for her sandbox. The volume of a box is calculated by the formula: volume = length x width x height. Since the sandbox is square, the length and width are both 3 feet. The height, or in this case, the depth of the sand, is 0.85 feet.

Therefore, the volume of sand needed is calculated as follows: Volume = 3 ft x 3 ft x 0.85 ft = 7.65 cubic feet. So, Maija needs exactly 7.65 cubic feet of sand for her sandbox.

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Where does the normal line to the parabola y = x − x2 at the point (1, 0) intersect the parabola a second time?

Answers

find the line that is normal to the parabola at the given point
remember that normal means perpendicular
perpendicular lines have slopes that multiply to -1
we can use point slope form to write the equation of the line since we are given the point (1,0)

we just need the slope

take derivitive
y'=1-2x
at x=1
y'=1-2(1)
y'=1-2
y'=-1

the slope is -1
the perpendicular of that slope is what number we can multiply to get -1
-1 times what=-1?
what=1
duh
so
point (1,0) and slope 1
y-0=1(x-1)
y=x-1 is da equation

solve for where y=x-1 and y=x-x² intersect

set equatl to each other since equal y
x-1=x-x²
x²-1=0
factor difference of 2 perfect squares
(x-1)(x+1)=0
set to zero

x-1=0
x=1
we got this point already

x+1=0
x=-1
sub back
y=-1-(-1)²
y=-1-(1)
y=-1-1
y=-2

it intersects at (-1,-2)

The normal line to the parabola [tex]y=x-x^2[/tex] at the point [tex](1,0)[/tex] intersect it second time at the point [tex](-1,-2)[/tex].

The given equation is:

[tex]y = x-x^2[/tex]

at point,

[tex](1,0)[/tex]

then,

→ [tex]y' = 1-2x[/tex]

So, at (1,0),

→ [tex]y' = 1-2\times 1[/tex]

      [tex]= -1[/tex]

Since,

This is the slope of the tangent, we take its negative reciprocal to get the slope of normal:

= [tex]-\frac{1}{(-1)}[/tex]

= [tex]1[/tex]

The normal line has slope 1 and goes through (1,0):

→ [tex]y-0=1(x-1)[/tex]

→       [tex]y = x-1[/tex]

We want to know where this intersects [tex]y = x-x^2[/tex], we get

→ [tex]x-1=x-x^2[/tex]

→ [tex]x^2=1[/tex]

→ [tex]x = \pm 1[/tex]

hence,

The point corresponding to (1,0) is the one we started with, so we want x=-1:  

→ [tex]x = -1[/tex]

→ [tex]y = x-x^2[/tex]

By substituting the value of "x", we get

→    [tex]= -1-1[/tex]

→    [tex]= -1[/tex]

Thus the answer above is right.

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A bird's nest is on top of a power pole that is 30 feet tall. The bird is above the nest and the angle formed from the nest to the bird is 25°. The horizontal distance from the bird to the pole is 100 feet. Approximately how far is the bird above the ground?

Answers

check the picture below

the bird is y + 30 above the ground.

make sure your calculator is in Degree mode.
Ah! I thought it was the distance from the base of the pole to the bird.

Okay. The height of the bird:

With the tangent:  height/length = tan(angle)

tan(25) = height/100---> height= 100*tan(25)= 46.63 ft (make sure the calculator is in degree)


But this is the height from the nest, from the ground is +30:

76.63

Evaluate the expression below when y = -3.

2y + 7

-4y − 10

i need help#awnser

Answers

Start with the given equation:
[tex]2y+7[/tex]
Substitute known values:
[tex]2(-3)+7[/tex]
Evaluate:
[tex]-6+7=1[/tex]


Similarly:
[tex]-4y-10[/tex]
[tex]-4(-3)-10[/tex]
[tex]12-10=2[/tex]

replace y with -3

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

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

The table below shows the number of students in a school who like tacos and/or pizza:


Like Tacos Do Not Like Tacos Total
Like Pizza 57 13 70
Do Not Like Pizza 12 15 27
Total 69 28 97

What is the relative frequency, by row, of students who like both tacos and pizza?
0.18
0.46
0.81
0.83

Answers

                           like tacos........no tacos.....total
like pizza               57                    13            70
no pizza                12                    15            27
----------------------------------------------------------------
total                       69                    28            97

relative frequency who both like tacos and pizzas = 57/70 = 0.81

Answer:

Relative frequency, by row, of students who like both tacos and pizza is:

0.81

Step-by-step explanation:

                                  Like Tacos Do Not Like Tacos      Total

Like Pizza                    57                 13                       70

Do Not Like Pizza            12                  15                       27

Total                            69          28                       97

The relative frequency by row is calculated as the ratio of the frequency of the required field to the total frequency of that row

Hence, relative frequency, by row, of students who like both tacos and pizza is:

57/70

=0.81

Find all complex solutions of x^2+5x-5=0.

(If there is more than one solution, separate them with commas.)

Answers

we use quadratic formula for that one
remember that √-1=i

so

for
ax^2+bx+c=0
[tex]x=\frac{-b+/-\sqrt{b^2-4ac}}{2a}[/tex]
so
given
1x^2+5x-5=0
a=1
b=5
c=-5

[tex]x=\frac{-5+/-\sqrt{5^2-4(1)(-5)}}{2(1)}[/tex]
[tex]x=\frac{-5+/-\sqrt{25+20}}{2}[/tex]
[tex]x=\frac{-5+/-\sqrt{45}}{2}[/tex]
[tex]x=\frac{-5+/-3\sqrt{5}}{2}[/tex]

solutions:
[tex]x=\frac{-5+3\sqrt{5}}{2}, \frac{-5-3\sqrt{5}}{2}[/tex]
Final answer:

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

Explanation:

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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WILL GIVE BRAINLIEST!! PPLEASE HELP!!

The graph of which function does not contain the point (0, 1)?

A.
y=(3/4)^x
B.
y=-2^x
C.
y=3^x
D.
y=(1/2)^x

Answers

Simplest way: sub in the coordinate into the equation.

Since they are all exponential functions, so all of them should pass through (0,1)

However, B has the minus sign, which flips the function vertically, so it passes through (0,-1)

Answer is B

How do I find the linear equation for y=4x-5

Answers

This is simple as all you have to learn is what slope intercept form is and how it works. In SIF, the number paired with the x is the slope, which should always be put over 1 if it is not already put over another number. The slope is the "rise over the run" which means that it is a proportion. For every 4 that you go up in this case, you should be moving over 1 on the x axis. The other number (-5) is the y-intercept, which means that the line you draw at the slope should go through that number. 

In the attached image, the y-intercept (-5) is highlighted and the blue dots shows that the line goes up 4 and over 1 (slope) between each point. 

Help identify!!!! ADB

Answers

The value of angle ADB in the triangle ADB is determined as m∠ ADB = 95⁰. (Option A).

How to calculate angle ADB?

The value of angle ADB is calculated by applying intersecting chord theorem and principle of sum of angles in a triangle.

The intersecting chord theorem states that the angle at tangent is half of the arc angle of the two intersecting chords.

So the value of angle A is calculated as follows;

m ∠ BAC = ¹/₂ x arc BC

m ∠ BAC = ¹/₂ x 110

m ∠ BAC  = 55

The value of angle ADB is calculated as follows;

m ∠ ABD + m ∠ ADB + m ∠ BAD = 180 (sum of angles in a triangle)

30 + m ∠ ADB + 55 = 180

m ∠ ADB + 85 = 180

m ∠ ADB = 180 - 85

m ∠ ADB = 95⁰

The number of chips of different colors in vicky's bag is shown below: 5 blue chips 11 pink chips 9 white chips vicky takes out a chip from the bag randomly without looking. she replaces the chip and then takes out another chip from the bag. what is the probability that vicky takes out a blue chip in both draws? 5 over 25 multiplied by 5 over 25 equals 25 over 625 5 over 25 plus 5 over 25 equals 10 over 25 5 over 25 multiplied by 4 over 24 equals 20 over 600 5 over 25 plus 4 over 24 equals 220 over 600

Answers

P( blue on first draw) =  5/25
P( blue on second draw) = 5/25

These events are independent so the probabilities are multiplied

answer is 5/25 * 5/25   = 25/625  = 1/25

The first choice is correct

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

What is the probability that vicky takes out a blue chip in both draws?

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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represent each of the fractions below both with a diagram and with words. A.2/3. B.1 1/8. C.6/9.

Answers

The diagram for each fraction is shown below

2/3 in words is 'two third'
11/8 in words is 'eleven-eighth'
6/9 in words is 'six-ninth'

Kit folds a bandana diagonally before tying it around her head. The side length of the bandana is 16 in. About how long is the diagonal?

Answers

Folding it diagonally forms a 45-45-90 right isosceles triangle. This type of triangle has lengths of x, x, and x [tex] \sqrt{2} [/tex] The longest side being the hypotenuse, this makes the diagonal 16 [tex] \sqrt{2} [/tex] inches or approx. 22.63 inches

The length of the diagonal of Kit's bandana tied around her head is approximately 22.63 inches long.

Kit folds a bandana diagonally.

To find the length of the diagonal (hypotenuse of a right triangle), we can use the Pythagorean theorem.

The bandana side length (a) is 16 in.

Let x be the length of the diagonal.

Using a^2 + a^2 = x^2, we get 16^2 + 16^2 = x^2. Solving this gives x ≈ 22.63 in.

Probability help please? In a certain instant lottery game, the chances of a win are stated as "1 in 19." Express the indicated degree of likelihood as a probability value between 0 and 1 inclusive. (round to three decimal places) I am confused and need a step by step instructions. Please help

Answers

The question is basically asking to find the chances in percentage. It is first given in fraction form, which is 1/19. This is approximately 0.053, once divided.

1/19 (One divided by 19)=0.0526

0.0526 rounded is about 0.053 (to three decimal places).

Answer: About 0.053

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.

Solve x2 + 2 = 6 by graphing the related function.

Answers

Solve x2 + 2 = 6 by graphing the related function. x^2 + 2 is a parabola with a vertex at the point (0, 2). When x = -1 or x = 1, then x^2 + 2 = 3, so we should put the points (-1,3) and (1,3) on the graph. When x = -2 or x = 2, then x^2 + 2 = 6, so we should put the points (-2,6) and (2,6) on the graph. We could continue adding points to the graph if we want, but we already have our two solutions. x^2 + 2 = 6 when x = -2 or x = 2. Therefore, x = -2, and x = 2 are the two solutions to this equation.

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]

A test consists of 20 problems and students are told to answer any 15 of these questions. In how many different ways can they choose the 15 questions?

Answers

1 - 15
2 - 17
3 - 18
4 - 19
5 - 20
Since order is not important, we are looking for unique combinations. For this type of problem you use the "n choose k" equation.

n!/(k!(n-k)!), where n=total amount of choices, k=number of choices made.

In this case:

20!/(15!(20-15)!)

20!/(15!*5!)

15504

Can you guys help me with 3-8 please thank you <3

Answers

For number 3 The rest are all the same just with different numbers):

[tex]R_{ave}=\frac{f(b)-f(a)}{b-a}[/tex]
[tex]R_{ave}=\frac{f(3)-f(1)}{3-1}[/tex]
[tex]R_{ave}=\frac{(2(3^{2})-20(3))-(2(1^{2})-20(1))}{2}[/tex]
[tex]R_{ave}=\frac{(2(9)-60)-(2(1)-20)}{2}[/tex]
[tex]R_{ave}=\frac{(18-60)-(2-20)}{2}[/tex]
[tex]R_{ave}=\frac{(-42)-(-18)}{2}[/tex]
[tex]R_{ave}=\frac{-24}{2}[/tex]
[tex]R_{ave}=-12[/tex]

Can someone please help me solve 91

Answers

[tex]3x^3+7x^2-20x=0\\ x(3x^2+7x-20)=0\\ x(3x^2-5x+12x-20)=0\\ x(x(3x-5)+4(3x-5))=0\\ x(x+4)(3x-5)=0\\ x=0 \vee x=-4 \vee x=\dfrac{5}{3}[/tex]
3x^3+7x^2-20x=0  factor out x first

x(3x^2+7x-20)=0

x(3x^2+12x-5x-20)=0

x(3x(x+4)-5(x+4))=0

x(3x-5)(x+4)=0

x={-4, 0, 5/3}

Given the Arithmetic sequence A1,A2,A3,A4 A1,A2,A3,A4 45, 58, 71, 84 What is the value of A43 A43 ?

Answers

The rule for the Arithmetic sequence is adding 13

The formula is given in the form
[tex]n_{th} [/tex] term = [tex]dn- 0^{th} [/tex] term. where [tex]d[/tex] is the difference between consecutive terms

We have [tex]d=13[/tex] and the [tex]0^{th} [/tex] term = 45 - 13 = 32

The formula for the sequence in question is given by
[tex]n_{th} [/tex] term = 13n + 32

Hence, the [tex]43^{th} [/tex]term is given = 13(43) + 32 = 591

Need some help on geometry practice problems!

Answers

[tex]\bf \textit{middle point of 2 points }\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ -1}}\quad ,&{{2}})\quad % (c,d) &({{ 7}}\quad ,&{{ 3}}) \end{array}\qquad % coordinates of midpoint \left(\cfrac{{{ x_2}} + {{ x_1}}}{2}\quad ,\quad \cfrac{{{ y_2}} + {{ y_1}}}{2} \right) \\\\\\ \left(\cfrac{{{ 7-1}} }{2}\quad ,\quad \cfrac{3+2}{2} \right)[/tex]
A(-1, 2)  and B(7, 3)

[tex]x_m= \cfrac{x_a+x_b}{2}= \cfrac{-1+7}{2}= \cfrac{6}{2}=3 \\ \\ y_m= \cfrac{y_a+y_b}{2}= \cfrac{2+3}{2}= \cfrac{5}{2} \\ \\ \text{midpoint is} \ (3, \frac{5}{2} )[/tex]

how do you know when to rewrite square trinomials and difference of squares as separate factors

Answers

Recognizing the specific forms of square trinomials and the difference of squares allows you to rewrite them as separate factors, simplifying algebraic expressions and facilitating further mathematical operations.

Knowing when to rewrite square trinomials and the difference of squares as separate factors depends on the algebraic expression you are dealing with. Let's consider each case separately.

1. Square Trinomials:

  - Square trinomials have the form [tex]\(a^2 + 2ab + b^2\) or \(a^2 - 2ab + b^2\)[/tex], where(a) and (b) are algebraic expressions.

  - These trinomials can be factored into the square of a binomial: [tex]\((a + b)^2\) or \((a - b)^2\).[/tex]

  - You should rewrite a square trinomial as separate factors when you encounter an expression that matches the form of a perfect square trinomial. Recognizing this pattern allows you to simplify the expression.

2. Difference of Squares:

  - The difference of squares has the form [tex]\(a^2 - b^2\),[/tex] where (a) and (b) are algebraic expressions.

  - This expression can be factored into the product of conjugates: [tex]\((a + b)(a - b)\).[/tex]

  - You should rewrite a difference of squares as separate factors when you have an expression in the form [tex]\(a^2 - b^2\)[/tex]. Recognizing this pattern helps you simplify and factor the expression efficiently.

I need help with number 17

Answers

To find f(x)-g(x), find (3x-21)-(3x+21)

(3x-21)-(3x+21)

Flip the signs in the second binomial
(3x-21)-3x-21

Combine like terms
3x-3x-21-21
-21-21
-42

The final answer is -42. X is irrelevant because whatever you plug in will always equal -42.

77+14 is the same as blank +11

Answers

77 + 14 = 91
91 - 11 = 80

Therefore, 80 + 11 = 90
The answer is 80. Hope I helped!
77 + 14 = x + 11
        91 = x + 11
        80 = x

Therefore the blank is 80.

80 + 11 = 91
77 + 14 = 91

91 = 91

Find the slope of the line that contains the points named c (3,8),d (-2,5)

Answers

[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

find the area of the kite

Answers

I think it would be A... 

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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Formula for volume and surface area of a cylinder and explain why

Answers

V = πr² * h (where r is the radius and h the height)
Total SA = Lateral Area + 2Base Area

LA = 2πr * h
BA = πr²

Why?

The cylinder is made by rotating a rectangle for 360°. Two sides make the top and bottom faces, that are circles. The radius is the dimension of the widht/lenght that generated the circles. The other sides form the lateral face (the cylinder has only one lateral face).

Of course to find the lateral area you multiply the radius for 2, to find the diameter of the circle and multiply for π since the rectangle rotates.

For the circles, the base area is just the formula to find the area of a circumference.

You sum the two areas (two times the base area, since it has a circle on the top and one on the bottom) to find the total area.

For the volume, that is the profondity, the capacity of the cylinder, you find the base area (so you know all the capacity) and multiply for the height.

Write the sum using summation notation, assuming the suggested pattern continues. -8 - 3 + 2 + 7 + ... + 67

Answers

[tex]a_1=-8\\ r=5\\ a_n=67\\\\ a_n=a_1+(n-1)r\\ 67=-8+(n-1)\cdot5\\ 67=-8+5n-5\\ 5n=80\\ n=16\\\\ \displaystyle \sum_{i=1}^{16}(-8+(n-1)\cdot5)=\sum_{i=1}^{16}(-8+5n-5)=\boxed{\sum_{i=1}^{16}(5n-13)}[/tex]

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

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