Answer:
yes
Step-by-step explanation
the common difference is -30
Final answer:
The sequence -38, -68, -98, -128,... is an arithmetic sequence because the common difference between consecutive terms is consistent, which is -30.
Explanation:
The student has asked whether the sequence -38, -68, -98, -128,... is arithmetic. To determine if a sequence is arithmetic, we need to check if the difference between any two consecutive terms (also known as the common difference) is the same.
Let's calculate the difference between the first two terms:
-68 - (-38) = -68 + 38 = -30
Now, let's calculate the difference between the second and the third terms:
-98 - (-68) = -98 + 68 = -30
Similarly, the difference between the third and the fourth terms is:
-128 - (-98) = -128 + 98 = -30
Since the common difference is the same (-30) for all consecutive terms mentioned, the sequence is indeed an arithmetic sequence.
In 2000, the average price of a football ticket for a Minnesota Vikings game was $48.28. During the next 20 years, the price increased an average of 6% each year. Write a model giving the annual price p (in dollars) of a ticket t in years after 2000.
[tex]y = 48.28(1.06)^t[/tex] is the model giving the annual price p (in dollars) of a ticket t in years after 2000 is found
Solution:
Given that,
In 2000, the average price of a football ticket for a Minnesota Vikings game was $48.28
During the next 20 years, the price increased an average of 6% each year
The increasing function is given by:
[tex]y = a(1+r)^t[/tex]
Where,
y is the value after t years
t is the number of years
a is the initial value
r is rate of increase in decimal
From given,
a = 48.28
[tex]r = 6 \% = \frac{6}{100} = 0.06[/tex]
Substituting the values we get,
[tex]y = 48.28(1+0.06)^t\\\\y = 48.28(1.06)^t[/tex]
Thus the model giving the annual price p (in dollars) of a ticket t in years after 2000 is found
What number decreased by 77 equals negative 18
Answer:
59
Step-by-step explanation:
77+(-18)=59
Check:
59-77=(-18)
Hoped this helped !
Cheers, Z.
Answer:
59
Step-by-step explanation:
59-77=-18
77+-18=59
The sum of two numbers is 50. The first number is 43 less than twice the second number. Write and solve a system of equations to find the two numbers.
Answer: 19 and 31
Step-by-step explanation: Make the first number x, the second number y.
The sum of x and y is 50: x+y=50
x is 43 less than 2y: x=2y-43
replace x in equation x+y=50 with x=2y-43: 2y-43+y=50
combine like terms: 3y-43=50
add 43 to both sides: 3y=93
divide both sides by 3: y=31
replace y in equation x+y=50 with y=31: x+31=50
subtract 43 31 from both sides: x=19
the solution to the question is the first number is 19, the second number is 31
The two numbers that sum up to 50 with one being 43 less than twice the other, we set up a system of equations, solve for one variable, and then substitute it back into the other equation, resulting in the numbers 19 and 31.
The question asks us to find two numbers whose sum is 50 and where the first number is 43 less than twice the second number. To solve this, we can create a system of equations to represent the given conditions. Let the first number be x and the second number be y.
According to the question, the sum of the two numbers is 50, which gives us our first equation:
x + y = 50 (Equation 1)
The first number x is 43 less than twice the second number y. This provides the second equation:
x = 2y - 43 (Equation 2)
We now have a simple system of two linear equations:
x + y = 50
x = 2y - 43
We can substitute the second equation into the first to solve for y:
(2y - 43) + y = 50
3y - 43 = 50
Add 43 to both sides:
3y = 93
Divide both sides by 3:
y = 31
We can now substitute y = 31 back into Equation 2 to find x:
x = 2(31) - 43
x = 62 - 43
x = 19
Therefore, the two numbers are 19 and 31.
jake rode his bike from 2:30 to 3:30. then he took a shower.he finished his shower 30 minutes after the bike ride ended what time was it when he finished his shower? how would you show this time on a clock face
Answer:
4
Step-by-step explanation:
PLEASE HURRY WILL GIVE YOU MY ACCOUNT AND BRAINLIEST IF YOU ANSWER CORRECTLY
The box plots show the weights, in pounds, of the dogs in two different animal shelters.
Which is true of the data in the box plots? Select three choices.
1 The median weight for shelter A is greater than that for shelter B.
2 The median weight for shelter B is greater than that for shelter A.
3 The data for shelter A are a symmetric data set.
4 The data for shelter B are a symmetric data set.
5 The interquartile range of shelter A is greater than the interquartile range of shelter B
WILL REPORT IF WRONG
Answer:
A, D, E
Step-by-step explanation:
Who knows this answer
Answer:
Step-by-step explanation:
∠ABC = ∠ DEF {GIVEN}
= ∠GHI { ∠DEF = ∠GHI - given}
∠ ABC = ∠GHI
solve for x. step by step please show the work
x+(-4) =10
x + (-4) = 10.
We can use the positive - negative rule.
x + (-4) = 10.
x - 4 = 10.
x = 10 + 4
x = 14.
Which value is an output of the function? -6,-2,4,7
Without knowing the function itself, it's impossible to definitively say which of the values (-6,-2,4,7) is an output. Any of these numbers could potentially be an output depending on the function.
Explanation:In the context of this question, an output of a function refers to the result you get after substituting an input (or value from the domain) into the function. For example, if we have a function f(x) = x+2, and we input the value 3 (from our domain), our output (or range) will be 5. Unless we know the actual function, it's difficult to determine which of the listed values (-6,-2,4,7) is an output because any of these could potentially be an output depending on the function. Thus, without additional context, the statement 'Which value is an output of the function?' cannot be definitively answered.
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The output of a function is -6.
The output of a function is the value that the function produces when a certain input is given. In the table above, the function is f(x). We are given that x can be any of the values -6, -2, 4, or 7. We want to know which of the values -6, -2, 4, 7, or 12 is an output of the function.
To find out, we can look at the table. We see that the only value in the table that is an output of the function is -6. This is because when we plug in x = -6 into the function, we get f(x) = -6.
Therefore, the answer is -6.
For such more question on function
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Lin's father is paying for a $20 meal. He has a 15%-off for the meal. After the discount, a 7% sales tax is applied. What does Lin's father pay for the meal?
Answer:
18.19
Step-by-step explanation:
$20-15%=$17
$17+7%=18.19
Lin's father pays $18.19 for the meal after the 15% discount and 7% sales tax.
Explanation:To find out what Lin's father pays for the meal after the discount and sales tax, we need to follow these steps:
Calculate the amount of the discount by multiplying the original price by the discount rate.Subtract the discount amount from the original price to find the discounted price.Calculate the amount of the sales tax by multiplying the discounted price by the sales tax rate.Add the sales tax amount to the discounted price to find the total amount paid for the meal.Let's apply these steps to the given information:
Discount rate: 15%Sales tax rate: 7%Original price: $20Step 1: Discount amount = $20 x 15% = $3
Step 2: Discounted price = $20 - $3 = $17
Step 3: Sales tax amount = $17 x 7% = $1.19
Step 4: Total amount paid = $17 + $1.19 = $18.19
Therefore, Lin's father pays $18.19 for the meal after the discount and sales tax.
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The farmer's market opens for 2 1/5 hours in the
morning and3 2/3 hours in the afternoon How long is
the farmer's market open in a day
Triangle LAQ has side lengths of 9, 20, and 15. Classify the triangle by its sides.
scalene triangle
equilateral triangle
isosceles triangle
scalar triangle
Answer:
Scalene triangle
Step-by-step explanation:
It is a scalene triangle because none of the sides are equal .equilateral triangle have the three sides equal. isosceles triangle have only two equal sides
What is -4 divided by -0.2?
Answer:
20
Step-by-step explanation:
-4/-0.2
When dividing numbers with the same sign, the result is always positive. In this case, -4 divided by -0.2 is equal to 20.
Explanation:When dividing numbers with the same sign, the result is always positive. In this case, -4 divided by -0.2 is equal to 20.
PLEASE HELP
Examine the system of equations.
-3x + y = 4,
-9x + 5y = -1
What is the solution?
Answer:
x= - 3.5
y= - 6.5
Step-by-step explanation:
-3x+y = 4 equation 1
-9x + 5y = -1 equation 2
and
equation 1 can be written as
y = 4+ 3x
so put this in equation 2
-9x + 5 ( 4+ 3x) = -1
-9x +20 +15x = -1
6x = -21
X= -21 ÷ 6
X = - 3.5
so put this value of x in equation 1 to find value of y
-3 ( -3.5) + y = 4
10.5 + y = 4
y = 4 - 10.5
Y = - 6.5
Answer:
x= - 3.5
y= - 6.5-
The sales tax for an item was $29.60 and it cost $370 before tax. Find the sales tax rate. Write your answer as a percentage
Answer: 8%
Step-by-step explanation: 370 * 8% = 29.60
Answer: 8% sales tax rate
Step-by-step explanation:
First, you need to find what percentage 29.60 is from 370, so you divide 29.60 by 370 and you get 0.08 then you multiply that by 100 to get your answer in percent. 100 multiplied by 0.08 would be 8%.
What is the binomial expansion of (x + 2y)7?
2x7 + 14x6y + 42x5y2 + 70x4y3 + 70x3y4 + 42x2y5 + 14xy6 + 2y7
x7 + 14x6y + 42x5y2 + 70x4y3 + 70x3y4 + 42x2y5 + 14xy6 + y7
x7 + 7x6y + 21x5y2 + 35x4y3 + 35x3y4 + 21x2y5 + 7xy6 + y7
x7 + 14x6y + 84x5y2 + 280x4y3 + 560x3y4 + 672x2y5 + 448xy6 + 128y7
Step-by-step explanation:
We find,
[tex](x+2y)^7[/tex]
To find, the binomial expansion of of [tex](x+2y)^7[/tex] = ?
We know that,
[tex](x+y)^{n} =^nC_0x^n+^nC_1x^{n-1}y+nC_2x^{n-2}y^2+nC_3x^{n-3}y^3+...+^nC_ny^n[/tex]
∴ [tex](x+2y)^7[/tex]
Here, n = 7, x = x and y = 2y
[tex](x+2y)^7[/tex]= [tex]^7C_0x^7+^7C_1x^{7-1}(2y)+^7C_2x^{7-2}(2y)^2+^7C_3x^{7-3}(2y)^3+^7C_4x^{7-4}(2y)^4+^7C_5x^{7-5}(2y)^5+^7C_6x(2y)^6+(2y)^7[/tex][tex]=x^7+7x^{6(2y)+21x^{5}4y^2+35x^{4}8y^3+^35x^{3}16y^4+21x^{2}32y^5+7x64y^6+128y^7[/tex]
[tex]=x^7+14x^{6}y+84x^{5}y^2+280x^{4}y^3+560x^{3}y^4+672x^{2}y^5+448xy^6+128y^7[/tex]
∴ The binomial expansion of of [tex](x+2y)^7[/tex]
[tex]=x^7+14x^{6}y+84x^{5}y^2+280x^{4}y^3+560x^{3}y^4+672x^{2}y^5+448xy^6+128y^7[/tex]
Thus, the required "option 4)" is correct.
Answer:
D. x7 + 14x6y + 84x5y2 + 280x4y3 + 560x3y4 + 672x2y5 + 448xy6 + 128y7
Step-by-step explanation:
Is 8in 15in and 17in a right triangle
Answer:
YesStep-by-step explanation:
Since 8^2+15^2 = 289 and 17^2 = 289 then 8^2+15^2 = 17^2
8^2+15^2 = 17^2 Then according to the reciprocal of the Pythagorean theorem
it’s a right triangle
36x - 8y2 when x=3 an y= -6
Hey there!
First off, I’m going to assume that the 2 in the second term is an exponent. If it isn’t, let me know and I’ll fix the answer.
Anyways, let’s start by plugging the values for the variables into the equation.
36(3)-8(-6)^2
Square -6
108-8(36)
Multiply.
108-288
Subtract.
-180
Your answer is -180.
Hope this helps!
Is y=-3x^2 +10 a function
Answer:
YES
Step-by-step explanation:
Simplify the expression: 2/3 divided by - {1/6 - 8/6}
Answer:
4/7
Step-by-step explanation:
1/6-8/6=-7/6
-[1/6-8/6]=7/6
---------------------
(2/3)/(7/6)=(2/3)(6/7)=12/21=4/7
4x-4y=0
Y=2x+6
Solve by substitution
Answer: x = -6, and y = -6 (-6, -6)
Step-by-step explanation: What we have here is a pair of simultaneous equations. Since we have been instructed to solve by substitution, we shall begin with the one which has one of the variables as having a coefficient of 1. We shall start with equation 2 which is,
y = 2x + 6
Having taken note of this, we can now go on to the other equation and substitute for the value of y.
Hence, from equation 1,
4x - 4y = 0 (substitute for the value of y)
4x - 4(2x + 6) = 0
4x - 8x - 24 = 0
-4x -24 = 0
Add 24 to both sides of the equation
-4x = 24
Divide both sides of the equation by -4
x = -6
Having calculated the value of x, we can now go on to substitute for the value of x in equation 2.
Therefore,
y = 2x + 6
y = 2(-6) + 6
y = -12 + 6
y = -6.
So, x = -6 and y = -6
A motorboat traveling with a current can go 120 km in 4 hours. Against the current, it takes 6 hours to go the same distance. Find the speed of the motorboat and speed of the current.
180 is the speed of the motorboat. I don't know the speed of the current.
........................................
120÷4=30
30×6=180
how many triangles can be drawn with side lengths of 3 inches, 5 inches, and 6 inches
Answer:
One triangle
Step-by-step explanation:
we know that
The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side
Verify the length sides of triangle
Applying the triangle inequality theorem
1) 3+5 > 6 ---> is true
2) 3+6 > 5 ---> is true
3) 5+6> 3----> is true
therefore
One triangle can be drawn with the given lengths
With side lengths of 3 inches, 5 inches, and 6 inches, only one triangle can be drawn as these dimensions meet the triangle inequality theorem, allowing for the creation of one unique triangle.
Explanation:The question is about determining if a triangle can be constructed with given side lengths. According to the triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the third side. In this case, the side lengths are 3 inches, 5 inches, and 6 inches.
Adding the lengths of the two shorter sides, 3 inches + 5 inches = 8 inches, which is greater than the length of the longest side, 6 inches. This means a triangle with these side lengths can be drawn. However, it is important to note that the lengths provided can only create one unique triangle, since the lengths are fixed and there can't be another triangle with different angles with the same side lengths.
Therefore, with side lengths of 3 inches, 5 inches, and 6 inches, exactly one triangle can be drawn.
Need help..Can't understand this..
Answer:
E
Step-by-step explanation:
Given the system of two equations:
[tex]\left\{\begin{array}{l}\dfrac{2}{3}x-\dfrac{1}{2}y=1\\ \\-\dfrac{4}{3}x+y=-3\end{array}\right.[/tex]
Multiply the first equation by 6 and the second equation by 3 to eliminate fractions:
[tex]\left\{\begin{array}{l}4}x-3y=6\\ \\-4x+3y=-9\end{array}\right.[/tex]
Add these two equations:
[tex]4x-3y-4x+3y=6-9\\ \\0=-3[/tex]
You get false equality [tex](0\neq -9)[/tex], so the system of two equations has no solution (two equations represent parallel lines)
Roland has 180 coins in his collection. Approximately 67% of the coins are quarters. About how many quarters does he have?
Answer:
120.6
Step-by-step explanation:
Since we know that 67 percent of coins are quarters.
Total coins = 180
67% of 180= 180 * 67/100
120.6.
So he has about 120.6 quarters.
Answer:
126 quarters
Step-by-step explanation:
67% ≈ 70%
70% = 70/100
70% = 7/10
180 * 7/10 = 126 quarters
write the fraction as a sum of fractions three different ways 7/10
easy problem plz help find area of triangle
Answer:
49.5
Step-by-step explanation: 11x9=99/2
Zeros: -1, 1, 8; degree: 3
Answer:
y=(x+1)(x-1)(x+8)
Step-by-step explanation:
When creating a factor with a known zero, use (x-ZERO)
For instance: a zero of -1 would be reprsented as (x+1)
Every Halloween, trick-or-treaters love going to Erica's house to see her spooky decorations and get some of her delicious caramel chews.
There is a proportional relationship between the number of kids in a group, x, and the total number of caramel chews Erica gives to that group, y.
x (kids) y (caramel chews)
2 6
4 12
5 15
6 18
Write an equation for the relationship between x and y.
y=
Answer:
[tex]y=3x[/tex]
Step-by-step explanation:
Let
x ----> the number of kids in a group
y ----> the total number of caramel chews Erica gives to that group
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]k=\frac{y}{x}[/tex] or [tex]y=kx[/tex]
Find the value of the constant of proportionality k
take a ordered pair from the data in the table and determine the value of k
For x=2, y=6 ----> [tex]k=\frac{y}{x}[/tex] ----> [tex]k=\frac{6}{2}=3\ caramels/kid[/tex]
therefore
[tex]y=3x[/tex]
Subtract. Express your answer in lowest terms 10 2/5 - 3 4/5
6 3/11 that well be the answer
Answer:6 3/5
Step-by-step explanation: 10 2/5 - 3 4/5 = 33
5
= 63
5
= 6.6
(9x3 - 18x²+2x+2) / (3x-1)
Answer:
Quotient =(3x²-5x-1) and reminder = 1
Step-by-step explanation:
[tex]\frac{9x^3-18x^2+2x+2}{3x-1}[/tex]
3x-1)9x³-18x²+2x+2(3x²-5x-1
9x³-3x²
------------------------
-15x²+2x+2
-15x²+5x
------------------
-3x+2
-3x+1
--------
1
Therefore 9x³-18x²+2x+2=(3x²-5x-1)(3x-1)+1
Quotient =(3x²-5x-1) and reminder = 1