which of the following is an arithmetic sequence with common difference 2
A. 1, -3, 5, -7, 9
B. 2, 4, 8, 16, 32
C. 10, 8, 6, 4, 2
D. 13, 15, 17, 19, 21
Answer:
C is the answer.
C has a common difference of "2"
Step-by-step explanation:
You could say that the word "difference" also means Subtraction, so in a simpler way of saying "The common difference of 2" you could say, "Which one of the following is subtracting by 2?"
PLEASE MARK BRAINLIEST
Solve for x. -6 = x – 35
Answer:
The answer is x=29
Step-by-step explanation:
-6 = x – 35
=-6+35=x-35+35
x=29
Answer:
41
Step-by-step explanation:
35- -6= 41
41-35=6
35-41=6
Marsha recorded the time it took seven children of different ages to run one lap around the track.
Using the line of best fit, which is closest to the length of time it should take Marsha's 6 year old niece to
run one lap?
A. 190
B. 200
C. 205
D. 210
Given: 3x + 2y + 7 = 5x +3y +10
Prove: m = -2
please help im very confused :)
also make sure to include the statements and reasonings as shown in the screenshot!
Answer:
See Below.
Step-by-step explanation:
1) Given:
[tex]3x+2y+7=5x+3y+10[/tex]
2) Subtraction Property of Equality (subtract 2y from both sides):
[tex]3x+7=5x+y+10[/tex]
3) Subtraction Property of Equality (subtract 5x from both sides):
[tex]-2x+7=y+10[/tex]
4) Subtraction Property of Equality (subtract 10 from both sides):
[tex]-2x-3=y[/tex]
5) Symmetric Property:
[tex]y=-2x-3[/tex]
6) Slope-intercept form:
[tex]y=mx+b\text{, where $m$ is slope and $b$ is y-intercept.}[/tex]
7) Substitution:
[tex]m=-2[/tex]
WILL GIVE BRAINLIEST!!!!! Use the system of equations to answer the questions. 2x + 3y = 3 y = 8 – 3x The value of y from the second equation is substituted back into the first equation. What is the resulting equation? What is the value of x? What is the value of y?
Answer:
x=3 y=-1
Step-by-step explanation:
2x+3y=3;y=8−3x
Rewrite
y=−3x+8 2x+3y=3
Step: Solvey=−3x+8 for y:
y=−3x+8
Step: Substitute−3x+8foryin2x+3y=3:
2x+3y=3
2x+3(−3x+8)=3
−7x+24=3(Simplify both sides of the equation)
−7x+24+−24=3+−24(Add -24 to both sides)
−7x=−21
−7 - 7
x=3 (Divide both sides by -7)
x=3
Step: Substitute3forxiny=−3x+8:
y=−3x+8
y=(−3)(3)+8
y=−1(Simplify both sides of the equation)
this might be confusing but you gotta study :)
What is the slope of the linear function?
Answer:
the slope is [tex]\frac{7}{4}[/tex]
Step-by-step explanation:
Given: 4y - 7x = 10; solve y
4y - 7x = 10; add 7x to both sides to isolate the 4y variable
4y = 7x + 10; now divide by 4
y = [tex]\frac{7}{4}[/tex]x + [tex]\frac{10}{4}[/tex]; reduce the fraction
y = [tex]\frac{7}{4}[/tex]x + [tex]\frac{5}{2}[/tex]; the slope is
Answer:
m= 7/4
Step-by-step explanation:
a restaurant starts with 10 dozen pieces of cornbread.every order receives 2 piece of cornbread.At the end of their lunch rush,there are 28 pieces of cornbread left.How many orders did the restaurant take?
Twelve less than two-thirds a number is 48.What is the number?
Can you please help me with those two questions and don’t only do 1 if you don’t know the answer dont comment
Answer:
32 ordersStep-by-step explanation:
10 dozen = 120120 - 28x2=28x2=56120 - 56=6464 divided by 2= 3218 + 19x = 10x + 54
can someone help me with this
Answer:
The answer is X= 4.
The Green Lawns Company uses the equation C=82.75a+56 to determine the amount to charge for mowing a city park, where a is the number of acres in the park and C is the cost in dollars. What is the significance of the number 82.75 in the equation?
Answer: The significance of the number 82.75 in the equation = amount charged per acre in the park.
Step-by-step explanation:
Given: The Green Lawns Company uses the equation C=82.75a+56 to determine the amount to charge for mowing a city park, where a is the number of acres in the park and C is the cost in dollars.
In linear equation y=mx+c, = rate of change of y with respect to x.
Here Coefficient of a = rate of change of C with respect to a.
i.e. Coefficient of a =amount charged per acre in the park.
Hence, The significance of the number 82.75 in the equation = amount charged per acre in the park.
GEW has angle measures given by m<=5x+6 m<=3x and m
Answer:
(D) 24°
Step-by-step explanation:
(5x + 6)° + (3x)° + (142 - 4x)° = 180°
5x + 6 + 3x + 142 - 4x = 180
4x + 148 = 180
4x = 32
x° = 8°
m∠E = 3×8° = 24°
When translating the point (3,5) 5 units up and 3 units to the left, we should get:
Answer:
(0, 10 )
Step-by-step explanation:
5 units up means add 5 to the y- coordinate
3 units left means subtract 3 from the x- coordinate
Translation rule is
(x, y ) → (x - 3, y + 5 ) , thus
(3, 5 ) → (3 - 3, 5 + 5 ) → (0, 10 )
Angie and Kenny play online video games. Angie buys 1 software package and 1month of gameplay. Kenny buys 1 software package and 2 months of game play. Each software package costs $30. If their total cost is $90, what is the cost of one month of gameplay?
Answer: $10
Step-by-step explanation:
Angie buys = 1 software package and 1month of gameplay.
Kenny buys = 1 software package and 2 months of game play.
Cost of each software package = $30. Total cost = $90
The total cost is the addition of what Kenny and Angie bought. This will be:
(1 SF + 1 G) + (1 SF + 2 G) = 90
where,
SF = software package = 30
G = game
(1 SF + 1 G) + (1 SF + 2 G) = 90
30 + 1G + 30 + 2G = 90
60 + 3G = 90
3G = 90 - 60
3G = 30
G = 30/3
G = 10
One month of game play cost $10
Help please I will give Brainliest!!!!
Josiah invested $96,000 in an account paying an interest rate of 3.5% compounded continuously. Assuming no deposits or withdrawals are made, how long would it take, to the nearest year, for the value of the account to reach $153,400?
The number of years it will take for the value of the money in the account to reach $153,400 would be = 17 years.
What is simple interest?Simple interest is defined as the amount of money that is received as an extra cash based on an investment made in an account.
The principal amount of money invested= $96,000
The rate of interest = 3.5%
The total interest on the principal amount = $153,400- $96,000 = $57,400
The time for this investment= ?
Using the formula for simple interest= p×T×R/100
57,400 = 96,000 ×T× 3.5 /100
Make T the subject of formula;
T = 57,400×100/96,000×3.5
T = 5740000/336000
T = 17 years (approximately)
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Congruent Triangle Combination
Answer:
1) ΔABC ≅ ΔDBC by Side-Angle-Side (SAS)
2) ΔABC ≅ ΔCDB by Side-Side-Side (SSS)
3) ΔABC ≅ ΔDBE by Angle-Angle-Side (AAS)
4) m∠Y = 53°
5) y = 3
6) ΔABC ≅ ΔEDC by Side-Angle-Side (SAS)
7) ΔABC ≅ ΔADC by Angle-Angle-Side (AAS)
8) ΔABC ≅ ΔADC by Side-Angle-Side (SSS)
Step-by-step explanation:
1) Side AC ≅ Side BD [tex]{}[/tex] given
Side BC ≅ Side BC [tex]{}[/tex] reflexive property
∠DBC ≅ ∠ACB [tex]{}[/tex] given
Therefore ΔABC ≅ ΔDBC by Side-Angle-Side (SAS)
2) Side AC ≅ Side BD [tex]{}[/tex] given
Side DC ≅ Side BA [tex]{}[/tex] given
Side BC ≅ Side BC [tex]{}[/tex] reflexive property
Therefore, ΔABC ≅ ΔCDB by Side-Side-Side (SSS)
3) ∠BAC ≅ ∠DEB [tex]{}[/tex] given
Side BC ≅ Side BD [tex]{}[/tex] given
∠ABC ≅ ∠DBE [tex]{}[/tex] vertically opposite angles
Therefore, ΔABC ≅ ΔDBE by Angle-Angle-Side (AAS)
4) ΔXYZ ≅ ΔABC [tex]{}[/tex] given
m∠A = 44°, and m∠C = 83°
m∠B = 180 - (44 + 83) = 53° [tex]{}[/tex] Sum of angles in a triangle
m∠Y = m∠B = 53° [tex]{}[/tex] Corresponding Parts of Congruent Triangles are Congruent (CPCTC)
5) Given that Triangle GHK is congruent to Triangle TZK
GH ≅ XT, KG ≅ KT, and HK ≅ ZK by the definition of congruency
Therefore, GH = 4 = XT = 3y - 2
4 = 3y - 2
3y - 2 = 4
3y = 4 + 2 = 6
y = 6/2 = 3
y = 3
6) Side BC ≅ Side EC [tex]{}[/tex] given
Side AC ≅ Side DC [tex]{}[/tex] given
∠ACB ≅ ∠DCE [tex]{}[/tex] vertically opposite angles
Therefore, ΔABC ≅ ΔEDC by Side-Angle-Side (SAS)
7) ∠BAC ≅ ∠DAC [tex]{}[/tex] given
∠ADC ≅ ∠ABC [tex]{}[/tex] given
Side AC ≅ Side AC [tex]{}[/tex] reflexive property
Therefore, ΔABC ≅ ΔADC by Angle-Angle-Side (AAS)
8) Side AD ≅ Side BC [tex]{}[/tex] given
Side AC ≅ Side AC [tex]{}[/tex] reflexive property
Side AB ≅ Side DC [tex]{}[/tex] given that the included angle between the two legs side AD and side AC and side AC and side BC are both acute, the third sides side AB and side DC are equal
Therefore, ΔABC ≅ ΔADC by Side-Angle-Side (SSS)
Which graph represents a proportional relationship?
Answer:
If the relationship between two quantities is a proportional relationship, this relationship can be represented by the graph of a straight line through the origin with a slope equal to the unit rate. For each point (x, y) on the graph, ž is equal to k, where k is the unit rate. The point (1, k) is a point on the graph.
2 cartons of juice in the month of January. In the month of February, she drank twice as many cartons of juice as in
January. How many cartons of juice did she drink in February?
Answer:
She drank 4 cartons in February.
Step-by-step explanation:You multiply 2x2 because it doubles.
Which physical property do the two rocks share?
A. Shininess
B. Color
C. State
D. Texture
Answer:
Step-by-step explanation:
State promise
The two rocks share the option C. State.
What are Physical Properties?Physical properties are properties of a substance which does not involve any chemical composition or changes in the substance.
Examples are color, density, hardness, and so on.
Given are two rocks.
Clearly, from the picture, we can say that shininess is different. The first rock is more shining.
Clearly colors are also not same.
Regarding the state of both rocks, both rocks are solid. So they share the property of state.
Texture is also different for both. Second one is harder texture.
Hence the physical property that both rocks share is state.
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Mr. Bearfield deposited $3,500 in a new investment account. -The investment pays 8% interest compounded annually on this account. -Mr. Bearfield did not make any additional deposits or withdrawals. What is the balance of the account at the end of three years?
Answer:
In 3 years, you will have $4,408.99
Step-by-step explanation:
The formula used in the compound interest calculator is A = P(1+r/n)^(nt)
A = the future value of the investment
P = the principal investment amount
r = the interest rate (decimal)
n = the number of times that interest is compounded per period
t = the number of periods the money is invested for
There are between 24 and 40 students in a class,
The ratio of boys to girls is 4:7
How many students are in the class?
Answer:answer is 387
Step-by-step explanation:ok got it
Answer:
There are 33 students in the class.
Step-by-step explanation:
The table shows the results of a survey of 200 randomly selected people on whether they like watermelon,
cantaloupe, or both.
Which is the marginal relative frequency for the people who do not like cantaloupe?
A. 25/91
B. 66/200
C. 91/200
D. 66/91
Answer:
C
Step-by-step explanation:
Marginal relative frequency for the people who do not like cantaloupe is 0.455
or
91/100
Answer:
C is correct
Step-by-step explanation:
NEED HELP ASAP
Given: (DE) is a midsegment of triangle ABC.
Find the value of x and y.
What is the length of (AC)?
Answer:
X=13. y=5 AC=20
Step-by-step explanation:
To do this we first have to find the value of x... giving the fact that DE is a mid segment, We know that the length of BC is double the length of DE this means that the length of BC equals 16. So, to equal 16 x will have to equal 13 so 13 + 3 = 16. Now we will find the value of y. We do this by looking at the length of ae and ec. AE equals EC so now that we know x equals 13 we can do 13 minus 3 equals 10 for AE. since EC has to equal 10 we can do 10 minus 5 which equals 5. We now know that y equals 5. We can now add this all up to find the length of AC. We would do 10 + 10 = 20. Hope this helps!
The length of AC from the diagram is 25
To get the value of x and y, we will use the similarity theorem of a triangle
BC = 2DE
x + 3 = 2(8)
x + 3 = 16
x = 16 - 3
x = 13
Hence BC = 16
From the given figure;
AE/DE = AC/BC
x-3/8 = (x-3+y+5)/x+3
10/8 = 15+y/13
130 = 8(15+y)
130 = 120 + y
y = 10
Get the length of AC
AC = 13-3+10+5
AC = 25
Hence the length of AC from the diagram is 25
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1. Label the Type of Slope
Answer:
positive slope
Step-by-step explanation:
Sean adds up all the even integers from 2 to 500, inclusive. Julie adds up all the integers from 1 to 250, inclusive. What is Sean's sum divided by Julie's sum?
Answer:
Sean's sum divided by Julie's sum is 2.
Step-by-step explanation:
The sum of an arithmetic sequence is:
[tex]\frac{n}{2}(2a+(n-1)d)[/tex]
In Sean's sequence, a = 2, n = 250, and d = 2
In Julie's sequence, a = 1, n = 250, and d = 2
[tex]\frac{\frac{250}{2}(2(2)+(250-1)2)}{\frac{250}{2}(2(1)+(250-1)1)}\\= 2[/tex]
The Sean's sum divided by Julie's sum gives the 2.
What is arithmetic sequence?An arithmetic sequence is sequence of integers with its adjacent terms differing with one common difference.
If the initial term of a sequence is 'a' and the common difference is of 'd', then we have the arithmetic sequence as:
a, a + d, a + 2d, ... , a + (n+1)d, ...
Its nth term is ; T_n = a + (n-1)d
(for all positive integer values of n)
And thus, the common difference is T_{n+1} - T_n for all positive integer values of n
The sum of an arithmetic sequence is;
[tex]= \dfrac{n}{2}[2a + (n-1)d ][/tex]
In Sean's sequence, a = 2, n = 250, and d = 2
[tex]= \dfrac{250}{2}[2(2) + (250-1)2 ]\\[/tex]
In Julie's sequence, a = 1, n = 250, and d = 2 then;
[tex]= \dfrac{250}{2}[2(1) + (250-1)2 ]\\[/tex]
Therefore, the Sean's sum divided by Julie's sum gives the 2.
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Write an equation of the line that passes through the points ( 4, 2), (0, -6) *
9514 1404 393
Answer:
y = 2x -6
Step-by-step explanation:
One form you can use for this purpose is ...
(x2 -x1)(y -y1) = (y2 -y1)(x -x1)
Filling in the given point values, this is ...
(0 -4)(y -2) = (-6 -2)(x -4)
-4y +8 = -8x +32
Generally, we like the equation to have coefficients with no common factors. All of these coefficients can be divided by -4.
y -2 = 2x -8
This can be rearranged to any form you may like--or left as is.
y = 2x -6 . . . . . slope-intercept form
explain what it means to solve a system of equations
Answer:
um hope this helps :D
Step-by-step explanation:
A system of equations is a collection of two or more equations with a same set of unknowns. In solving a system of equations, we try to find values for each of the unknowns that will satisfy every equation in the system. The problem can be expressed in narrative form or the problem can be expressed in algebraic form.
A collection of two or more equations with the same set of unknowns is referred to as a system of equations. I
What is a system of equations?A system of equations is a collection of two or more equations with the same set of unknowns. In solving a system of equations, we try to find values for each of the unknowns that will satisfy every equation in the system. The problem can be expressed in narrative form or the problem can be expressed in algebraic form.
If the lines intersect, we identify the point of intersection. This is the solution to the system. The solutions of a system of equations are the values of the variables that make all the equations true.
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Use substitution to show that 9+6(10-7x) is equivalent to 69-42x.
.
Answer:
hope this helps
Step-by-step explanation:
9+6(10-7x)
9+60-42x
69-42x
I will give Brainlyest to the first person
A family gathered 12 seashells from the beach bringing the total number of seashells in their collection to 86
Which equation can be used to find, x, the number of seashells in the collection before the 12 were added?
Answer:
The first selection is the answer.
Step-by-step explanation:
x+12=86
The equation that can be used to find x is x + 12 = 86
A linear equation is of the form:
y = mx + b;
where y, x are variables, m is the slope of the line and b is the y intercept.
Let x represent the number of seashells in the collection before the 12 were added. Hence to find x, we use the equation:
x + 12 = 86
The equation that can be used to find x is x + 12 = 86
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On your last math quiz, you got 15
out of 20 questions correct. What is
your percentage of correct answers?
Answer: 75%
Step-by-step explanation: So 15/20 simplified is 3/4 and 3 divided by 4 equals 0.75. To convert a decimal to a percentage, you multiply 0.75 by 100 to get 75%.
Which of the following results in the expression 0.22 x 86?
Answer:
18.92
Step-by-step explanation:
Im preatty sure this is right
Answer:
18.92
I multiplied 0.22 and 86
What is the factorization of x^2-4x+3?
Answer:
D. (x - 3)(x - 1)
Step-by-step explanation:
Factor the following:
[tex] \longrightarrow [/tex] x² - 4x + 3
The factors of 3 that sum to -4 are -1 and -3.
So,
[tex] \longrightarrow [/tex] x² - x - 3x + 3
[tex] \longrightarrow [/tex] x(x - 1) - 3(x - 1)
[tex] \longrightarrow [/tex] (x - 3)(x - 1)