In an arithmetic sequence, consecutive terms differ by a fixed number d :
[tex]a_8=a_7+d[/tex]
[tex]a_9=a_8+d=a_7+2d[/tex]
[tex]a_{10}=a_9+d=a_7+3d[/tex]
and so on up to
[tex]a_{19}=a_7+12d[/tex]
Solve for d :
[tex]140=32+12d\implies12d=108\implies d=9[/tex]
Work backwards to find the first term in the sequence, and hence the n-th term:
[tex]a_6=a_7-d[/tex]
[tex]a_5=a_6-d=a_7-2d[/tex]
and so on down to
[tex]a_1=a_7-6d[/tex]
So the first term is
[tex]a_1=32-6\cdot9=-22[/tex]
which means the n-th term is
[tex]a_n=a_1+(n-1)d=-22+9(n-1)=9n-31[/tex]
[tex]S_n[/tex] denotes the n-th partial sum of the sequence, i.e. the sum of the first n terms. We want to find the number of terms such that this sum is 511:
[tex]\displaystyle S_n=\sum_{i=1}^na_i=\sum_{i=1}^n(9i-31)=511[/tex]
Distribute the summation and recall the formulas,
[tex]\displaystyle\sum_{i=1}^n1=n[/tex]
[tex]\displaystyle\sum_{i=1}^ni=\frac{n(n+1)}2[/tex]
[tex]\implies S_n=\displaystyle9\sum_{i=1}^ni-31\sum_{i=1}^n1[/tex]
[tex]\implies511=9\cdot\dfrac{n(n+1)}2-31n[/tex]
[tex]\implies1022=9n^2-53n[/tex]
[tex]\implies9n^2-53n-1022=0[/tex]
[tex]\implies(n-14)(9n+73)=0[/tex]
[tex]\implies n=14\text{ or }n=-\dfrac{73}9[/tex]
n must be a positive integer, so we the sum is obtained from the first n = 14 terms.
PLEASE I REALLY NEED HELP What differences are there on the graph of f(x)=2x to the graph of h(x)=2x-3?
Answer:
The graph if h(x) =2x-3 will have the same slope, but placed lower on the graph, because it's y intercept is -3, while the y-int of f(x) is 0, which is higher up on the y axis
A rectangle with an area of x2 – 4x – 12 square units is represented by the model. What side lengths should be used to model the rectangle? (x + 2) and (x – 6) (x + 6) and (x – 2) (x + 2) and (x – 10) (x + 10) and (x – 2)
Answer: (x+2) and (x-6) represents the side lengths.
Step-by-step explanation:
The area of the rectangle is [tex]x^{2} -4x -12[/tex] so in this case to find the side lengths we need to factor out the area.
To factor [tex]x^{2} -4x-12[/tex] We need to find two numbers that if we multiply together we will have -12 and if we add those two number we will get -4.
-6 and 2 works out
Because -6 * 2 = -12 and -6 +2 = -4
Now we will rewrite the area as
[tex]x^{2}[/tex] +2x - 6x -12 Group them
([tex]x^{2}[/tex] +2x) (-6x -12) factor them
x (x +2) -6(x+2) factor out x+2
(x+2)(x-6) Done!
Answer: The correct answer is A (x+2)(x-6) on Edg 2020;)
Do 26 and if u want to do 27 too I’ll give Brainlynest
Answer:
26) translation: (x - 4, y + 3)
27) see down below
Step-by-step explanation:
26) Its a translation since the shape isn't reflected nor rotated. To find the translation, you can see that the shape would move 4 to the left (- 4), and up 3 ( + 3), which gives you (x - 4, y + 3) (x determines left/right and y determines up/down).
27)
<1 = 135
<2 = 45
<3 = 45
<4 = x = 20
<5 = 135
<6 = 45
<8 = 135
You can do one or both if u do both I’ll give Brainlynest
Answer:
18) a. X
19) d. 69°
Step-by-step explanation:
18) A reflection is a transformation where an image is flipped over a line. So V will still be in the same place, it will just be flipped over line B. The only answer that makes sense in X.
19) All the angles in the picture are vertical angles. Vertical angles are angles that are across from each other when two lines cross and they are always equal.
The angle opposite the angle that is 78° is also 78°.
The angle opposite the angle that is 33° is also 33°.
The three angles form a straight line so:
78° + 33° + x = 180°
111° + x = 180°
x = 69°
Since the angle is a vertical angle and is opposite angle a, angle a will also be 69°.
Hope this helps. :)
Please answer it now in two minutes
Answer:
Triangle E, F, G and Triangle T, U, V.
Step-by-step explanation:
They both are congruent because have the same shape, same size, and they both mirror each other.
Answer:
Triangle EFG and triangle TVU
Step-by-step explanation:
You must use congruent segments and keep track of the corresponding sides and vertices.
Triangle EFG and triangle TVU
what are the points of intersection of -x^2+9x-3 and y=3x
Answer:
Easiest and fastest way is to graph both equations into a graphing calc and trace the graph to where they intersect.
Alternatively, you can use substitution to solve for your answer.
Step-by-step explanation:
1) Point M divides line segment AB, in the direction from A to B. in a ratio of 4 to 9. What value on the number line
would indicate the location of point M?
Answer:
Point M will be located between 0 and 1 at [tex]\frac{1}{13}[/tex].
Step-by-step explanation:
Two points A and B have been given on a number line.
Point A is at -3 and point B at 7.
Distance between these points AB = 7 - (-3)
= 7 + 3
= 10 units
Another point M divides the given segment AB in the ratio of 4 : 9.
Therefore, length of segment AM will be = [tex]\frac{4\times 10}{(4+9)}[/tex]
= [tex]\frac{40}{13}[/tex]
= [tex]3\frac{1}{13}[/tex] units
Now the position of point M will be at [tex](-3+3\frac{1}{13})[/tex] = [tex]\frac{1}{13}[/tex]
Therefore, point M will be located between 0 and 1 at [tex]\frac{1}{13}[/tex].
Consider triangle ABC. Triangle A B C. Angle C is 80 degrees and angles B and A are y degrees. What is the value of y in the triangle? Angle y = °
Answer:
y is equal to 50 degrees.
Step-by-step explanation:
The sum of the angles of a triangle is always 180 degrees. To find what y is, subtract 80 from 180 and divide the difference by 2. This will give you 50 degrees.
Answer:
y= 50°
Step-by-step explanation:
∠A =∠B = y. So, ΔABC is an isosceles triangle.
Sum of angles of triangle = 180
∠A + ∠B + ∠C = 180
y + y + 80 = 180 {add like terms}
2y + 80 = 180 {Subtract 80 from both sides}
2y + 80 - 80 = 180 - 80
2y = 100 {divide both sides by 2}
2y/2 = 100/2
y= 50°
explain the differences between an equation and an equality. how do those differences affect solutions.
Answer:. An equation is a mathematical statement that shows the equal value of two expressions while an inequality is a mathematical statement that shows that an expression is lesser than or more than the other. 2. An equation shows the equality of two variables while an inequality shows the inequality of two variables.
Step-by-step explanation:
What value of n makes the equation true?
-1/5n + 7=2
n=
Answer:
n = 25
Step-by-step explanation:
Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.
PEMDAS is the order of operation, and is:
Parenthesis
Exponents & roots
Multiplication
Division
Addition
Subtraction
~
First, subtract 7 from both sides:
(-1/5)n + 7 (-7) = 2 (-7)
(-1/5)n = 2 - 7
(-1/5)n = -5
Next, multiply -5 from both sides:
(-1/5)(-5)n = (-5)(-5)
n = -5 * -5
n = 25
25 is your answer for n.
~
Answer: n = 25
Step-by-step explanation: In this equation, our first step is to isolate the n term by subtracting 7 from both sides.
On the left, +7 -7 cancels and we're left with -1/5n.
On the right, 2 - 7 simplifies to -5.
So we have -1/5n = -5.
In order to get n by itself, since it's being multiplied by a fraction,
we multiply both sides of the equation by the reciprocal of that fraction.
The reciprocal of -1/5 is -5/1.
So we multiply both sides of the equation by -5/1.
So we have (-5/1)(-1/5n) = -5(-5/1).
On the left, our 1's cancel and our 1's cancel.
Also, remember that a negative times a negative is a positive.
So on the left we are left with n.
On the right, -5(-5/1) is 25.
So n = 25.
The ant repeats the two steps 7 times going around the polygon until it reaches its starting position .the ant makes one complete revolution (360 degree) to draw this regular 7 sided polygon. The value of A correct to 1 decimal place is ____________
Answer:
(C)51.4 degrees
Step-by-step explanation:
The sum of the exterior angle of a polygon is 360 degrees. (one complete revolution).
Given a regular polygon, the sum of each exterior angle is calculated using the formula:
[tex]\dfrac{360^\circ}{n}[/tex] where n is the number of sides.
The regular polygon shown made by the ant has 7 sides.
Therefore:
Each exterior angle [tex]=\dfrac{360^\circ}{7}=51.43^\circ[/tex]
Therefore:
The value of A correct to 1 decimal place is 51.4 degrees.
The correct option is C.
Answer:
The correct value of A to 1 decimal place is [tex]51.4^o[/tex].
Step-by-step explanation:
Given information:
The ant repeats the two steps 7 times going around the polygon
The sum of the exterior angle of polygon is [tex]360^o[/tex]
The formula for the exterior angle is
[tex]= 360/n[/tex]
Here,
[tex]n=7[/tex]
Hence, the Value of A will be
[tex]A=360/7\\A=51.4^o[/tex]
The correct value of A to 1 decimal place is [tex]51.4^o[/tex].
For more information visit:
https://brainly.com/question/21212890
An interior angle of a regular convex polygon is 140°. How many sides does the polygon have?
Answer:
hope it will help uh.....
Which equation has no solution?
1. 4(x+3)+2x=6(x+2)
2. 5+2(3+2x)=x+3(x+1)
3. 5(x+3)+x=4(x+3)+3
4. 4+6(2+x)=2(3x+8)
Answer:
Number 3 does not have a solution
Step-by-step explanation:
Does anyone know the answer to the table below?
Hey there! :)
Answer:
16 minutes.
Step-by-step explanation:
Create an equation in the form y = mx + b to solve this problem. Begin by solving for the rate of change of the table using the slope formula:
[tex]m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Plug in values from the table into the equation:
[tex]m = \frac{64 - 40}{9 - 5}[/tex]
Simplify:
[tex]m = \frac{24}{4}[/tex]
m = 6.
Plug in the slope and a point from the table into the equation
y = mx + b
40 = 6(5) + b
40 = 30 + b
40 - 30 = b
b = 10.
Rewrite the equation:
y = 6x + 10
To solve for how long it took her to ride 1 km, plug 1 into the equation:
y = 6(1) + 10
y = 6 + 10
y = 16 minutes.
4x - 1
2.
= x + 7
Can someone help please?
Answer:
6[tex]\frac{1}{3}[/tex]
Step-by-step explanation:
4x-12 = x+7
4x-12+12 = x+7+12
4x = x+19
4x-x = x+19-x
3x=19
x = 6[tex]\frac{1}{3}[/tex]
And if we substitute the value of x into the equation 4x-12 = x+7,
we will get 13[tex]\frac{1}{3}[/tex] = 13[tex]\frac{1}{3}[/tex] in the end.
Hope this helps :)
HELP ME PLEASE ~ Thanks :)
Answer:
A
Step-by-step explanation:
99/479
formula: girls in action divided by everyone
Two mechanics were working on your car. One can complete the given job in six hours, but the new guy takes eight hours. They worked together for the first two hours, but then the first guy left to help another mechanic on a different job. How long will it take the new guy to finish your car?
Answer:
3 1/3 hours
Step-by-step explanation:
In 2 hours, the first guy did 2/6 = 1/3 of the job. Meanwhile, the new guy did 2/8 = 1/4 of the job. When the first guy left, the remaining amount of the job was ...
1 - 1/3 - 1/4 = 12/12 -4/12 -3/12 = 5/12 . . . . . fraction of job remaining
So, completion of the remaining 5/12 of the job will take the new guy ...
(5/12)(8 hours) = 10/3 hours = 3 1/3 hours
The temperature each hour in Elma, Texas on October 1 is modelled by the equation
t(h) = 10 cos(15h - 10)° + 30 where his hour of the day with 0 meaning midnight, and t is the
temperature in degrees Celsius. How hot did it get in Elma on October 1?
Answer:
[tex]39.8^{\circ} C[/tex]
Step-by-step explanation:
We are given that the temperature each hour in Elma Texas on October 1 is modelled by the equation
[tex]t(h)=10cos(15h-10)^{\circ}+30[/tex]
Where h=Hour of the day with 0 meaning midnight
t=Temperature in degree Celsius
We have to find the temperature on October 1.
Substitute h=0
[tex]t(0)=10cos(15(0)-10)+30[/tex]
[tex]t(0)=10cos(-10)+30[/tex]
[tex]t(0)=39.8^{\circ} C[/tex]
Hence, the temperature in Elma on October 1=[tex]39.8^{\circ} C[/tex]
A bowl has 85 pieces of candy. Nineteen children empty the bowl of candy. Some children take 3 pieces, some children take 5 pieces, and 1 child takes 7 pieces of candy. How many children take 3 pieces of candy?
Answer:
children take 3 pieces of candy are 6
Step-by-step explanation:
x+y=19-1 x+y=18
3x+5y=85-7 3x+5y=78
eliminate x by multiplying the first equation by 3:
3x+3y=54
3x+5y=85 subtract
(3x+3y)-(3x+6y)=54-78
3x-3y-3x-5y=-24
-2y=-24 y=-24/-2=12
y=12 , substitute for y:
x+y=18
x=18-12
x=6
check: 3x+5y=78
3(6)+5(12)=78
18+60=78 correct
I'm kind of unsure of my answer, please help me. I appreciate your answers.
Find two consecutive integers whose sum is 113. Which of the following equations could be used to solve the problem?
choices:
2 x + 1 = 113
[tex]x^{2}[/tex] + 1= 113
2 x = 113
2 x + 2 = 113
Answer:
We can call the numbers x and x + 1. Then we can write:
x + x + 1 = 113 which simplifies to 2x + 1 = 113.
Answer:
Hey there!
The correct answer would be x+x+1=113, or 2x+1=113.
Let the smaller number be x, then the larger number would be x+1
Thus, the sum of x and x+1 would be 2x+1.
We have that 2x+1=113.
Now, this is just a simple linear equation we have to solve.
Start by subtracting 1 to get 2x=112
Then, divide by 2 to get x=56
Since x=56, x+1 would be 57.
Thus, you would have the two numbers be 56 and 57, and use 2x+1 to solve.
Hope this helps :)
Please answer! I will mark brainliest for best answer :)
Answer:
5
Step-by-step explanation:
Number of players injured in a game count the other side
Linear Equations HELP ASAP
Answer: D) y = -1/4x + 6
Step-by-step explanation:
First turn the equation into slope-intercept form: y = 4x + 6
For a line to be perpendicular to another line, it's slope must be the opposite reciprocal of the other perpendicular line. Thus, the slope of the perpendicular line is -1/4. As the y-intercept of the line is (0,6), the lines must intersect as (0,6). Thus, the other line must also have a y-intercept of 6. Thus, the answer is D.
Hope this helps <3
Triangle X Y Z is shown. If m∠X = 34° and m∠Z = 26°, what is m∠Y?
Answer:
given, triangle XYZ in which m of angle X=34°
angle Z= 26°
now,angle Y =?
we have,
AngleX + angle Y+ angle Z = 180°
or, 34°+angle Y +26°=180°
or, angle Y= 180°-60°
therefore, angle Y =120°.
hope it helped..
Answer:
Triangle X Y Z is shown.
If m∠X = 34° and m∠Z = 26°, what is m∠Y?
Answer:
m∠Y = 120°
Step-by-step explanation:
I just took the test and got 100% on Edge2021
2a + 5a x 4a - a simplify
Answer:
20a² + a
= a(20a + 1)
Step-by-step explanation:
2a + 5a × 4a - a
= 2a + 20a² - a
= 20a² + a
find the 7th term of the geometric progression which begins with -6250,1250,-250
Answer:
a₇ = - 0.4
Step-by-step explanation:
The n th term of a geometric progression is
[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]
where a₁ is the first term and r the common ratio
Here a₁ = - 6250 and r = [tex]\frac{1250}{-6250}[/tex] = - [tex]\frac{1}{5}[/tex] , thus
a₇ = - 6250 × [tex](-\frac{1}{5}) ^{6}[/tex]
= - 6250 × [tex]\frac{1}{15625}[/tex] = - [tex]\frac{6250}{15625}[/tex] = - 0.4
What is the range of the function shown on the graph above?
Answer:
A.
Step-by-step explanation:
Since range is y-axis based, we are looking at the y-values. We see that the endpoints of the graphed segment are closed points, so they are included in the range. That eliminates B (exludes values) and C (Not infinity, it's a segment, not a line). Choice A is the best answer because when you identify the y-values, you get -8 to -3 included.
Plz write it for me how u got it ❤️On paper then send it to me
Answer:
See below in bold.
Step-by-step explanation:
1. x^2 - 13x - 30
We need 2 numbers whose product is -30 and whose sum = -13.
They are -15 and + 2:
Answer is (x - 15)(x + 2).
2. 2x^2 + 4x - 126
First we can take 2 out to give:
2(x^2 + 2x - 63)
Now we need 2 numbers whose product is - 63 and sum = +2.
These are +9 and - 7 so
Answer is 2(x - 7)(x + 9).
3. -30x^3 + 3x^2 + 9x
First we can take out -3x to give
-3x(10x^2 - x - 3)
Now we want 2 numbers whose product is 10*-3 = -30 and whose sum is -1. They are -6 and +5 so we write the above as:
-3x(10x^2 + 5x - 6x - 3)
Now we factor the parentheses by grouping:
= -3x( 5x(2x + 1) - 3(2x + 1)
= -3x(2x + 1)(5x - 3) Answer.
The answer to the second part is 12x^2 - 13x - 21.
Part 3
1, 18.
2. 6.
3. = 5(2(-3)^2 - 3*3*4 + 4^2) - 3)) - 2(-3)(-3 + 7(4) - 1) - 3*4^2
= 5*(67) - 2(72) - 48
= 143.
4. (11m^2 - 7) - (6m^2 + 3m - 11) + (3m^2 - m - 9)
= 11m^2 - 7 - 6m^2 - 3m + 11 + 3m^2 - m - 9
= 8m^2 - 4m - 5
A = 8, B = 4 and C = 5.
Find the probability that a student earns a grade D or F
Answer:
P=.14 or 1/7
Step-by-step explanation:
P(d)=3/35
P(f)=2/35
P( D or F) = 3/35 + 2/35=
1/7 or .14
Maryann's friends loved her bulletin board , and 4 of them asked her to make one for their homes. She offered to make each of her friends a replica of her bulletin board that measures 2 meters by 3 meters . How many kilograms of burlap should Maryann collect to complete the bulletin boards for her friends?
Complete Question:
To create a bulletin board, Maryann is planning to stretch fabric from burlap sacks over cardstock. She collects 6 kg of burlap sacks. The area density of the burlap is 0.4 kg/m².
Maryann's friends loved her bulletin board , and 4 of them asked her to make one for their homes. She offered to make each of her friends a replica of her bulletin board that measures 2 meters by 3 meters . How many kilograms of burlap should Maryann collect to complete the bulletin boards for her friends?
Answer:
To complete the bulletin boards for her friends, Maryanne should collect 6 kg of burlap more
Step-by-step explanation:
Mass of burlap sacks that Maryann collects = 6 kg
Area density of burlap = 0.4 kg/m²
Area Density = Mass / Area........(1)
The Area of bulletin board that can be made with the 6 kg of burlap sand can be calculated by using equation (1)
0.4 = 6 / Area
Area = 6/0.4
Area of bulletin board that can be made from 6 kg= 15 m² of bulletin board
The area of bulletin board that Maryann made for herself = 2 * 3 = 6m²
To make similar bulletin boards for her four friends, the total area of bulletin board made for her 4 friends = 6 * 4 = 24m²
To calculate the mass of burlap required to make a 24m² bulletin board, use equation (1)
0.4 = Mass / 24
Mass = 0.4 * 24
Mass = 9.6 kg
The mass of burlap used to make Maryann's bulletin board alone:
0.4 = Mass/6
Mass = 2.4 kg
Out of the 6kg that she got, she has used 2.4 kg for herself
The remaining mass of burlap = 6 - 2.4 = 3.6 kg
Therefore, to complete the bulletin board for her friend, she should collect (9.6 - 3.6) = 6 kg of bulletin more
2.2 units to the right of 0 horizontal number line
Answer:
2.2
Step-by-step explanation:
2.2 units to the right of zero indicates that the integer is positive on a horizontal number line.
0 + 2.2 = 2.2