Step-by-step explanation:
-4x-6=-4x-4-2
-4x+4x=6-4-2
x=1
Message instructor about this question
-Match each part of the explicit formula relating the term values and term positions in an arithmetic sequence with the best description of what it
represents.
Note that you might use some choices more than once and might not use all choices.
ar+d(n-1)
11
Submit
a. the change in the term value when the position changes from the first term to the nth term
b. the change in the term value when the position changes by 1
c. the value of the term a
d. the value of the term at position n
e, the value of the term 0-1
f. the position of the term an
g. the change in the term position from the first term to the nth
Using arithmetic sequence concepts, the matching terms are given as follows:
[tex]a_n[/tex]: d.[tex]a_1 + (n - 1)d[/tex]: a.n: f.d: b.d(n - 1): e.n - 1: g.What is an arithmetic sequence?In an arithmetic sequence, the difference between consecutive terms is always the same, called common difference d.
The nth term of an arithmetic sequence is given by:
[tex]a_n = a_1 + (n - 1)d[/tex]
In which [tex]a_1[/tex] is the first term.
Hence, in this problem, the terms are classified as follows:
[tex]a_n[/tex]: value of the term at position n, hence it matches with item d.[tex]a_1 + (n - 1)d[/tex]: change in the term value when the position changes from the first term to the nth term, hence item a.n: position of the term [tex]a_n[/tex], hence item f.d: common ratio, which is the change in the term value when the position changes by 1, hence item b.d(n - 1): value at the position n - 1, hence item e.n - 1: the change in the term position from the first term to the nth, hence item g.More can be learned about arithmetic sequence concepts at https://brainly.com/question/6561461
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The garden and a walkway around its perimeter have an area of 378. Find the width of the walkway if the garden measures 12 feet wide 15 feet long
The width of walkway is 3 feet.
What is rectangle ?
A rectangle has 2 congruent diagonals, that is the two diagonals are equal to each other. The diagonals of a rectangle bisects each other into equal segments.
We have been given that the garden and the walkway around its perimeter have an area of 378 square feet.
Let us suppose the width of the walkway is x feet.
the length of garden and the walkway will be = 15+2x
and, the breadth of garden and the walkway will be = 12+2x
Now, area of the garden and the walkway around its perimeter is given by :
A = (15+2x)(12+2x)
A = 4x^2 + 54x + 180
Now, the area is given is given as 378 square feet. Hence, we have
4x^2 + 54x + 180 = 378
4x^2 + 54x -198 = 0
Using quadratic formula to find the roots of above equation we get :
x = 3, -33/2
Taking positive value of x that is 3 as area cannot be negative.
Therefore, the width of walkway is 3 feet.
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Half the difference of k and 18
Answer:
k and 16
Step-by-step explanation:
I will cry
Nan
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Nan
uppose a person who is 81 inches tall casts a shadow that is 94.5 inches long. Another person in the same place casts a shadow that is 84 inches long. Determine the height of the second person.
The height of the second person is 72 inches .
The quantitative relation is outlined because the comparison of 2 quantities of constant units that indicates what proportion} of 1 amount is gift within the alternative quantity .Let the height of the second person be "x"
We need to line up a relationship between 2 sets of numbers.
We are told that the connection could be a direct proportion as it is given that "a person 81 inches tall casts a shadow 94.5 inches long". therefore we will setup a magnitude relation that relates those 2 which is given by 81/94.5.
Since 81 and 94.5 are unit each in inches and that we will categorical the peak of the tree within the same units, feet, because the shadow of the tree, we do not got to worry concerning conversion of units.
81 is to 94.5 as x is to 84 is given by
81/94.5 = x / 84
0.8571 × 84 = x
72 = x
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Evaluate the expression when a= -6 and c=4
-c +6a
Answer:
x=3: 2(3) = 6.
Step-by-step explanation:
Given two terms of each arithmetic sequence, find a₁ and d .a₄=-2.4 and a₆ = 2
The common difference d is 2.2 and the first term a1 is -9.
How to find the a1 and d?The difference between any two consecutive integers in an arithmetic progression (AP) sequence of numbers is always the same value.
The formula of Arithmetic progression is
a(n) = a1 + (n - 1)d
given that the two terms of arithmetic sequence,
a4 = -2.4 and a6 = 2.
now, find the common difference d.
a(n) = a1 + (n - 1)d
Let take a(n) = a6 and a1 = a4.
a6 = a4 + (6 - 4)d
a6 = a4 + 2d
now substitute the values of a6 and a4
2 = -2.4 + 2d
2 + 2.4 = 2d
d = 4.4/2
d = 2.2
so, the common difference d is 2.2.
then, find the term a1.
take the formula
a(n) = a1 + (n - 1)d
now, substitute a(n) = a4 and d = 2.2.
-2.4 = a1 + (4-1)d
-2.4 = a1 + 3d
-2.4 = a1 + 3(2.2)
-2.4 = a1 + 6.6
a1 = -6.6-2.4
a1 = -9.
so, the first term a1 is -9.
Hence, the common difference d is 2.2 and the first term a1 is -9.
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I need help please with this problem
Answer:
Step-by-step explanation:
4.5 in
Divide the area of the triangle by the height.
What is the GCF of 24 and 42?
Answer:
6
Step-by-step explanation:
To find the GCF by factoring, list out all of the factors of each number and select the largest that both have in common.
PLEASE HELP !!!!!!!!!!
ASAP THIS IS IMPORTANT
The size of the segment in the scale drawing using a drawing scale factor of 5 meters to one box is 30 meters.
What are scale factors?A scale factor is a value with which the dimensions of an original two dimensional geometric figure or a three dimensional solid can be multiplied to obtain an image.
Scale factors are used in maps and drawings to represent a large geographic area, or a life sized object on paper, such that the relative sizes of the sides of the original figure are maintained
Solution;
Using the height of the arc in the drawing as the reference, we have;
50 m is equivalent to 10 boxes
Therefore;
The length of one box = (50 m)/10 = 5 m
The scale of the drawing is therefore;
One box = 5 metersThe length of the given segment = 6 box length
The length, L, of the segment is too therefore;
L = 6 box × 5 m/box = 30 m
The length of the segment is L = 30 meters
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Find the value of each variable and the measure of each labeled angle
assuming 2x= 3x-42,
x=42
2x= 84
and 3x-42= 84
In right AABC with mzC-90°, mzB-75°, and AB = 12 cm. Find the area
of AABC.
The area of triangle ΔABC with ∠C = 90°, ∠B = 75° an AB = 12 cm will be 18.16 square centimeters.
We have a right - angled triangle ΔABC.
We have to find the area of ΔABC.
What is Pythagoras theorem ?Pythagoras theorem states - In a right - angled triangle ΔABC, the square of the hypotenuse is equal to the sum of the squares of the base and perpendicular. Mathematically -
h² = b² + p²
According to the question -
(Refer to the image attached)
∠C = 90°
∠B = 75°
AB = 12 cm
Now -
sin 75° = AC/AB
AC = AB sin(75°) = 12 sin(75°) = 12 x 0.97 = 11.64 cm
and
tan 75° = AC/BC
BC = AC/tan(75°) = 11.64/3.73 = 3.12 cm
Therefore, the area of triangle ΔABC -
A = 1/2 (AC x BC) = 0.5 x 3.12 x 11.64 = 18.16 cm²
Hence, the area of triangle ΔABC will be 18.16 cm².
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The black marble is farther from the target than the yellow marble but closer to the target than the pink marble. Which marble is farthest from the target?
O the black marble
O the pink marble
O the yellow marble
Answer:The marble that is farthest from the target is the pink marble.
Step-by-step explanation:
1. Find a rule for the following table. Write your rule as a
sentence relating the input and the output.
Rule:
C
Input
O
Output
59
29
39
119
No output
39
Step-by-step explanation:
The attached image should be what you're looking for.
-2.45 as a fraction form
A room has an area of 32 square feet. How many square inches is that? How many square
yards?
Answer:
In bold below.
Step-by-step explanation:
There are 12*12 = 144 square inches in a square foot.
So, there are 144 in^2 per 1 ft^2
So, we have:
144 in^2
32 ft^2 ----------- = 4608 in^2.
1 ft^2
For yards it is 1 yd^2 per 9 ft^2 :-
1 yd^2
32 ft^2 = ------------ = 3.56 yd^2.
9 ft^2
PLEASE HELP SOLVEEEEE
Answer:
10 24 32 are the answers
Step-by-step explanation:
My mom is a teacher lol
How do I write a percent problem for which the percent is greater than 100 and the part is known???
Percentages greater than 100% can be expressed as x% where x is any real number
How to express a percentage greater than 100%?As a general rule, percentages are represented by %
Take for instance
x% is pronounced x percentage
Where x is any real number
Whether x is greater than 100 or not, the format of the expression remains the same
i.e. 150 percent is written as 150% and 25 percent is written as 25%
Hence, percentages greater than 100% can be expressed as x% where x is any real number
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Write an algebraic proof.
Given: Δ XYZ with medians XR , YS, ZQ
Prove: XP/PR=2
According to the centroid theorem, the centroid is 23 times the distance from each vertex to the midpoint of the opposite side.
What is meant by Centroid Theorem?The triangle's centroid is the point where the three medians intersect. According to the centroid theorem, the centroid is 23 times the distance from each vertex to the midpoint of the opposite side.
Consider the algebraic relationships that exist for triangle medians.
The centroid of a triangle is 2/3 the distance from one vertex to the midpoint of the opposite side, according to the Centroid Theorem.
Given: [tex]$\triangle XYZ[/tex] with medians [tex]$\overline{X R}[/tex], [tex]\overline{Y S}$[/tex], and [tex]$\overline{Z Q}$[/tex].
By using Centroid Theorem, we get
1. XP = 2/3 XR
2. XR = XP + PR( Segment Addition Postulate)
3. XP = 2/3(XR+PR) (Substitution Property)
4. XP = 2/3 XP + 2/3 PR (Distributive Property)
5. 1/3 XP = 2/3 PR(Subtraction Property)
6. XP = 2PR (Multiplication Property)
7. XP/PR = 2 (Division Property)
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A company makes desks, coffee tables, and corner tables. Each item uses units of wood, fabric, and stuffing.
Desks use 50 units of wood, 40 units of fabric, and 45 units of stuffing.
Coffee tables use 30 units of wood, 15 units of fabric, and 10 units of stuffing.
Corner tables use 5 units of wood, 5 units of fabric, and 5 units of stuffing.
There are 690 units of wood, 620 units of fabric, and 510 units of stuffing available to make the items.
Which three equations are needed to find the largest number of x desks, y coffee tables, and z corner tables that can be made?
Drag and drop the correct equations into the box.
Answer: 50x+30y+5z= 690
40x+15y+5z= 620
45x+10y+5z= 510
Step-by-step explanation: The first equation to find units of wood, the second is for the units of fabric, and the third is for the units of stuffing.
6. Fudge There are 99 calories in an ounce of cream cheese,
12 calories in a teaspoon of vanilla extract, 389 calories in
a cup of powdered sugar, and 145 calories in a square of
chocolate. Salt has 0 calories. (See Example 2.)
a. How many calories are in the fudge recipe?
b.
This recipe uses an 8-inch by 8-inch dish. How many
calories are in a 1-inch by 1-inch piece of fudge?
Using proportions, it is found that:
a. There are 2736 calories in the fudge recipe.
b. There are 42.75 calories in a 1-inch by 1-inch piece of fudge.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.
For this problem, the recipe is composed by:
6 ounces of cream cheese: 99 calories per ounce.1/8 of a teaspoon of salt: 0 calories.1/2 of a teaspoon of vanilla extract: 12 calories in a teaspoon.4 cups of sugar: 389 calories per cup.4 squares of chocolate: 145 calories per square.Hence the number of calories in the recipe is given by:
6 x 99 + 0.5 x 12 + 4 x 389 + 4 x 145 = 2736.
There are 2736 calories in the fudge recipe.
For item b, the areas are given as follows:
Dish: 8 x 8 = 64 inches².Piece: 1 x 1 = 1 inch².Hence the piece of fugde is 1/64 of the recipe, thus:
1/64 x 2736 = 42.75 calories.
There are 42.75 calories in a 1-inch by 1-inch piece of fudge.
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Determine whether the equation below has a one solution no solution or an infinite number of solutions afterwords determine two values of X I support your conclusion X -2 equals -2+ X
The given equation is an identity, so it is true for any value of x, and x can take infinite values, thus, the linear equation has infinite solutions.
How many solutions has the given equation?Here we have the linear equation:
x - 2 = -2 + x
And we want to see how many solutions it has, so let's solve it.
IF we add 2 in both sides we will get:
x - 2 + 2 = -2 + x + 2
x + (-2 + 2) = x + (-2 + 2)
x = x
Now, that is an identity, so it is true for any value of x, and x can take infinite values, thus, the linear equation has infinite solutions.
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Why do you think that it is important to learn about points, lines, and planes?
Points lines and plane together are the undefined teerms that provide the base for geometry . the definition must be a word whose meaning is accepted as intiutively clear as that meaning is accepted without definition this words are called undefined terms . Although these terms are not defined in a broad way it is used for defining other terms but a small description is needed .
POINTS is the most fundamental object in geometry just like cell is the basic unit of life . A point just looks like a dot and is named by a variable the objecive of the point is to represent a position only .It has zero size .
LINES A straight line can be a medium connecting a set of infinetly many points . it extends infinitely in opposite direction . It has infinte lenght , no widht , no height .The symbol ↔ denotes that line , a line can also be denoted with a smaller letter .
PLANES It is considered as a set of infinite points joining to form a flat surface extending in all directions infinetly it has undefined lenght widht and no height . A single capital letter is used to denote a plane .
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Determine the slope of the line that contains the given points.
J(7,-3), K(-8,-3)
The slope of the line containing (7,-3) and (-8,-3) is Zero(0).
The slope of a straight line can be written as follows,
m = [tex](y_{2} - y_{1} )/(x_{2} - x_{1} )[/tex] equation1
The line is containing the points (-3,3) and (4,3). So, we can write
[tex]y_{2}[/tex] = -3 , [tex]y_{1}[/tex] = -3 , [tex]x_{2}[/tex] = -8 , and [tex]x_{1}[/tex] = 7 .
On substituting the values of variables in equation1, we will get
m = ( (-3)-(-3) ) / ( (-8)-(7) ) = (0/(-15)) = 0.
As the slope of a line is Zero(0), so we can conclude that the given line is a straight line.
Here:
m = the slope of the line
( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] ) are the first coordinates.
( [tex]x_{2}[/tex] , [tex]y_{2}[/tex] )are the second coordinates.
The slope of the line containing (7,-3) and (-8,-3) is Zero(0).
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Find the percent change. Andy's bank account went from $99 to $70.
The percentage of $99 to $70 is -29.29.The percentage change of $99 to $70 is decreases.
How to find the percentage change of Andy's bank account?given that
the Andy's bank account went from $99 to $70.
The previous value is $99.
The new value is $70.
A percentage is a figure or ratio stated as a fraction of 100 in mathematics. It is generally represents by the percent sign, "%."
The most reliable indicator of percent change is the percent of growth or decrease. Calculations are frequently used to determine how much something has changed,
so the
change = original - new = $99 - $70 = -29
[tex]percentage = \frac{ - 29}{99} \times 100[/tex]
percentage = -29.29.
Hence,The percentage change of $99 to $70 is decreases.
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Membership at the Lose for Less Gym requires new members to pay an
enrollment fee of $79.95 and purchase a key card for $19.95, in addition to
the regular monthly fee of $24.95.
Write an equation that represents the cost C for membership for m months.
What is the cost of a 2-year membership?
$1,157.55
$698.70
$678.75
$2,422.55
The equation that represents the cost C for membership for m months is:99.90+24.95m
The cost of a 2-year membership is $698.70
What makes up the total cost for membership for m months?
The fact that each member has to pay an enrollment fee and purchase key card for $79.95 and $19.95 respectively, means that the total fixed charge which is sum of both amounts is computed as shown below:
fixed charge=$79.95+$19.95
fixed charge=$99.90
variable cost per month=$24.95
total variable cost of m months=24.95m
C=99.90+24.95m
m=24(24 months=2 years)
cost of a 2-year membership=99.90+(24.95*24)
cost of a 2-year membership=$698.70
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Marc wants to qualify for the 200-meter dash at the school championship.
In order to qualify, his mean running time for 5 races must be no greater than 22.8 seconds.
A list of Marc's running times, in seconds, for his first 4 races is shown.
23.1, 23.2. 22.8, 21.9
What is the maximum running time, in seconds, Marc can have in his last race in order to qualify for the championship? Round the answer to
the nearest tenth.
______ seconds
the maximum time that he can have in his last race is 23 seconds.
What is the maximum running time, in seconds?
We know that the average can not be greater than 22.8 seconds, then if x represents the time of the last race, the maximum value that x can take is given by the equation:
(23.1 + 23.2 + 22.8 + 21.9 + x)/5 = 22.8
(That is the equation for the mean of the 5 times)
Solving that for x we will get:
(23.1 + 23.2 + 22.8 + 21.9 + x) = 5*22.8
91 + x = 114
x = 114 - 91 = 23
So the maximum time that he can have in his last race is 23 seconds.
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Please help 1 through 3
i) cost of oil change = $29.99
ii) Balance on December 1 = $252.009
iii) Difference between the two balance = $85.79
According to the question we have been that
Total balance on November 1 = $337.88
i) We need to find how much did the oil change cost.
For that we will first calculate how much balance was left after depositing after pay check.
Balance after spending in groceries= $337.88 - $ 42.59 = $295.29
Balance after depositing from savings account = $295.29 + $125.00 = $420.29
Balance after spending in electric bill = $420.29 - $35.67 = $384.62
Balance after depositing from paycheck = $415.00 + $384.62 = $799.62
Therefore, Cost of oil changing = $799.62 - $769.63 = $29.99
ii) For the balance on December 1 after rent had paid, we will first calculate the balance after spending for birthday present.
Balance after spending for birthday present = $769.63 - $17.54 = $752.09
Therefore the balance on December 1 = $752.09 - $500.00 = $252.09
iii) Difference in the two balance is
= balance on November 1 - Balance on December 1
= $337.88 - $252.09
= $85.79
Hence the difference in the two balances is $85.79
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Please solve this! Show steps too, please.
Answer:
y=2x-7
Step-by-step explanation:
[tex]2x-y=6 \\ \\ -2x+y=-6 \\ \\ y=2x-6[/tex]
Parallel lines have the same slope, so we want the line with a slope of 2 through (3, -1).
This line is y=2x-7.
please, can anyone solve this integral?
Write an equation of the line with the given slope and y -intercept. Use slope-intercept form. Then rewrite the equation in standard form. m=-6, b=9
The slope-intercept form is y = mx + b.
If the value of m = -6 and b = 9 then 6x + y = 9 be the standard form.
What is meant by slope intercept form?Y = mx + b is the general formula for the slope-intercept form, where m stands for the line's slope and b for the y-value of the line's y-intercept. We may more easily determine a line's slope and its y-axis intersection using the slope-intercept form of a linear equation.
Let the value of m = -6(slope)
b = 9 (y -intercept)
The slope-intercept form is given by,
y = mx + b
y = -6x + 9
Therefore, y = -6x + 9 is the slope-intercept form
Standard form is given by, Ax + By = C
Since, slope-intercept form is y = -6x + 9
⇒ 6x + y = 9
Therefore, 6x + y = 9 is the standard form.
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