Answer:
The 71st term is 428.
Step-by-step explanation:
Use Arithmetic Explicit formula:
f(n) = f(1) + (n - 1) d
Solve:
f(71) = 8 + (71 - 1) 6
f(71) = 8 + (70) 6
f(71) = 8 + 420
f(71) = 428
Determine if the leading coefficient of the following function is positive or negative and whether the function has a minimum or maximum vertex point.
Answer:
The leading coefficient of the function shown is negative and the function shown has a maximum vertex point.
Step-by-step explanation:
The leading coefficient is the term with the highest degree in a polynomial.
For example in 4x² + 3x + 1 the leading coefficient would be 4x² as 4x² is the term with the highest degree.
The leading coefficient tells us whether the equation, when graphed, will rise or fall.
If the leading coefficient is negative then the equation will fall when graphed, in contrast if the leading coefficient is positive the equation will rise when graphed.
Looking at the graph, it appears that the equation is falling, meaning that the leading coefficient must be negative.
If the equation falls then it has a maximum point, if it rises then it has a minimum point.
Because the equation shown falls it will have a maximum point.
Write an equation for the graph shown in the form y=ax+b.
Answer:
y=0.2x+1
Step-by-step explanation:
2=5a+b
1.2=1a+b
0=-5a+b
we get that a=0.2, b=1
The required equation will be y = -0.5x + 27.5 passes through the points (-5, 0) and (5, 2).
What is the Linear equation?A linear equation is defined as an equation in which the highest power of the variable is always one.
According to the given graph,
We can see two points are (-5, 0) and (5, 2)
The linear equation will be: y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]
Here
x₁ = -5, y₁ = 0
x₂ = 5, y₂ = 2
⇒ y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₂]
Substitute values in the equation, we get
⇒ y - 0 = (2 - 0)/(8-4)(x-(-5))
⇒ y - 30 = (2)/(-4)(x + 5)
⇒ y - 30 = -1/2(x + 5)
⇒ y = (-1/2)x - 5/2 + 30
⇒ y = -0.5x + 27.5
Thus, the required equation will be y = -0.5x + 27.5 passes through the points (-5, 0) and (5, 2).
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Need help with number 4 only
Answer: The filled out chart is shown below.
===========================================================
Explanation:
For each row, we divide the number of locations over the population count. Treat the population values in millions. Something like 35.2 million means 35,200,000 which is the same as writing 35.2*10^6 when using scientific notation. I prefer to stick to scientific notation.
In the first row, they computed 1460/(35.2*10^6) = 0.0000415 = 4.15*10^(-5); the last entry of 4.15 for this row represents having 4.15 stores for 100,000 people. In other words, we chop off the 10^(-5) portion in 4.15*10^(-5). This is because the 10^(-5) portion represents "1 out of 100,000".
The other remaining rows are handled the same way. I'll show the steps for the second row
per capita as a decimal = 6530/(325.7*10^6) = 0.00002per capita as sci notation = 2 * 10^(-5)Starbucks per 100,000 = 2Like the previous row, each value is approximate.
Check out the table below. The stuff in gray represents the new entries that were previously blank.
what is the area of the trapizeum
(first base + second base)x height ÷ 2
DWhen rolling a cube with faces numbered 1-6 and flipping a far coin, what is the probability of rolling a number 5, and the coin landing heads up?
Answer:
0.6 recurring or 2/3
Step-by-step explanation:
1/6 plus 1/2 = 2/3
(-9,6) and (-3,2) help pls
(-9,6) and (-3,2) help pls
Answer : -12.8
Find the value of x that makes lines u and y parallel.
Answer:
x = 7
Step-by-step explanation:
If u // v, then
19x - 3 = 130 {Corresponding angles are congruent}
19x = 130 + 3
19x = 133
x = 133/19
x = 7
Please help with freshmen math
Answer:
7375
24
Step-by-step explanation:
c=5500+125(15)
c=7375
8500=5500+125n
Solve each equation for y.
a. (y-10)=-3(x-2)
y=
c. (y-2) = 1/3 (x-3)
y=
Answer:
a. [tex]\boxed{y=-3x+16}[/tex]
b.[tex]\boxed{y=\frac{1}{3}x+1}[/tex]
Step-by-step explanation:
a.[tex]y-10=-3(x-2)[/tex]
[tex]\rightarrow y=-3x+6+10\\\rightarrow \boxed{y=-3x+16}[/tex]
b. [tex]y-2=\frac{1}{3}(x-3)\\\rightarrow y=\frac{1}{3}x-1+2\\\rightarrow \boxed{y=\frac{1}{3}x+1}[/tex]
The table below represents a linear function. Identify the rate of change of the function.
(0,4) (4,-3) (8,-10) (12,-17)
Step-by-step explanation:
the rate of change is the slope of the line y/x. it is always the factor of x in the equation.
it indicates how many units y changes, when x changes a certain amount of units when going from one point to another.
we only need to look at 2 points.
to go from (0, 4) to (4, -3)
x changes by +4 (from 0 to 4),
y changes by -7 (from 4 to -3).
so the rate of change is -7/3
Which integer can you multiply by itself to get 400 as the square number?.
Answer:
20x20=400 so 20 is your integer
Step-by-step explanation:
20 × 20 = 400.
Step-by-step explanation:
-2z+3-z=□-4z+2
please give me the answer
Step-by-step explanation:
[tex]\displaystyle \rm -2z+3-z=-4z+2 \\\\ -3z+3=-4z+2 \\\\ 4z-3z=-3+2 \\\\ \underline{z=-1 \ \ \ \ } \\\\[/tex]
[tex]\large{\rm{\underline{\underline{Answer:}}}}[/tex]
Given to solve: -2z+3-z = -4z+2
⇛ -3z + 3 = -4z + 2
⇛ -3z + 4z = 2 - 3
⇛ z = -1
Required value of z is -1. The steps we followed are: We shifted z to a single side and other numbers to other side. Then we equated to get the result.
Rehan proved by mathematical Induction that for all the positive Integers, n^3+ 2n is divisible by 3. Can you find an integer counterexample to show that this statement is not true? Explain.
Reproduce the proof. When n = 1, we have
n³ + 2n = 1³ + 2 = 3
which is clearly divisible by 3.
Assume n³ + 2n is divisible by 3. Then for the next natural number n + 1, we have
(n + 1)³ + 2 (n + 1) = n³ + 3n² + 3n + 1 + 2n + 2
= n³ + 2n + 3 (n² + n + 1)
The first two terms n³ + 2n are divisible by 3 according to our assumption, and 3 (n² + n + 1) is clearly a multiple of, and therefore divisible by, 3 as well.
So the claim that 3 divides n³ + 2n is true for all natural numbers n.
HELPP YALL! I WILL MARK BRAINIEST!! LOOK AT THE PICTURE!!
Answer:
Slope of the parrelel line: -2/3x
Slope of the perpendicular line: 3/2x
Step-by-step explanation:
Lets first put this into slope intercept form:
y = mx + b
9y = -6x - 1
y = -2/3x = 1/9
So our slope is -2/3x
If we have a line parrelel to this, it means it has the exact same slope, but a different b value.
So the slope of this parellel line would also be -2/3x
Next we need to find the slope of the perpendicular line.
This is the exact opposite of our slope.
To find this, lets first understand our slope.
Our slope is the change in y over the change in x:
Δy/Δx
A perpendicular line is going to be the flipped, and negative of this.
You can think of a perpendicular line being:
-Δx/Δy
Since our slope is -2/3x
Our perpendicular line would be 3/2x
So our answer for the second question is 3/2x
Useful things to remember:
Slope of a line: Δy/ΔxSlope of a parrelel line: Δy/ΔxSlope of a perpendicular line: -Δx/ΔyHope this helps!
Helpppppppppppppppppppp
Answer:
B and C
Step-by-step explanation:
I hope you find this helpful
GENERALIZATION:
1.) What is the sign of the product if two numbers is multiplied with like signs?
_______________________________
_______________________________
2.) What is the sign of the product if two numbers are multiplied with unlike signs?
_______________________________
_______________________________
Step-by-step explanation:
Complete detail of explanation is given.PLEASE HELP ASAP!!!!!
Answer:
x = 7
Step-by-step explanation:
The sum of exterior angles in a polygon is 360°.
( 11x - 5 )° + ( 4x + 29 )° + ( 6x + 13 )° + ( 9x - 15 )° + 67° + 61° = 360°
30x + 22 + 128 = 360
30x = 210
x = 7
The size of an insect population doubles every week. If there are 25 insects initially present, how many insects will there be in eight weeks?
Answer:
tence there will be 6,00 insects abter 8 weeks.
Step-by-step explanation:
what is the best estimate for the volume of a kitchen sink?
PLS HELPPP
FIND X
I will mark braniliest
Answer:
x = 11
Step-by-step explanation:
∠ EAB = ∠ AED = 4x ( alternate angles )
∠ AEB and ∠ GEB are adjacent angles on a straight line and sum to 180° , so
∠ AEB + 125° = 180° ( subtract 125° from both sides )
∠ AEB = 55°
The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.
∠ EBC is an exterior angle of the triangle , then
∠ EBC = ∠ AEB + ∠EAB , that is
9x = 55 + 4x ( subtract 4x from both sides )
5x = 55 ( divide both sides by 5 )
x = 11
in 12 minutes max made 35 paper airplanes at the same rate how long would it take him to make 140 airplanes?
Answer:
Step-by-step explanation:
It will take 48 minutes to make 140 airplanes. 35 × 4 = 140 airplanes. So take 12 × 4 = 48 minutes.
Bran Crunch regularly costs $3.00 a bos and is now on sale $2.25.Fruit and Oat Cereal is regularly $5.00 and is on sale for $4.00.Which cereal is giving the better percentage saving?.
Answer:
The three dollar
Step-by-step explanation:
for the three dollar one its 25% off and the 5 dollar one is 20% off
(Please Help) (50 Points) Write the equation for the transformations of the graph of y = x^2
Use the form: y = a (x-h)^2 +k
Translated 2 units left and 7 units down.
A is the scale or vertical stretch
H is what makes it move right or left.
K is what makes it move up or down.
a = 1
h = -2
k = -7
y = (1) (x-(-2))² + (-7)
y= (x + 2)² -7
(Also, you will learn b in the equation. The equation would be a(b(x-h))² + k. B would be about horizontal compression.)
Enter the greatest common factor of 6 and 4
Answer: 2
Step-by-step explanation:
find the value of y when x = 16.
y=9 when x=8
Answer:When x=16 , y=36 . Explanation: If y varies directly as x , then if y increases, x increases, and if y decreases, x decreases.
Step-by-step explanation: because
A larger kind of bacteria is about 0.00039 in. long. Write this length using
scientific notation
Answer:
3.9X10^-4
Step-by-step explanation:
The value is increasing so your exponent increases
2. The product of 0.4 and a number is 8.
(a) Represent the statement as an equation. Use n for the variable.
(b) Determine the solution set using the replacement set .
Answer:n = 20
Step-by-step explanatio
0.4 * n = 8
n = 8 / 0.4
n = 20
The equation represents 0.4n = 8 and the solution will be n = 20.
What is a number system?The number system is a way to represent or express numbers.
A decimal number is a very common number that we use frequently.
Any of the multiple sets of symbols and the guidelines for utilizing them to represent numbers are included in the Number System.
As per the given,
Product of 0.4 and n is 8.
0.4n = 8
n = 8/0.4
n = 80/4 = 20
Hence "The answer will be n = 20 because the equation says that 0.4n = 8".
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Solve by drawing an area model and then use the standard algorithm: 432 x 620
The students in Mrs. Brown's class were asked how many minutes it takes them to get to school in the morning. Here is what they answered:
10, 14, 7, 7, 6, 12, 6
Find the mean and median travel times for these students.
If necessary, round your answers to the nearest tenth.
mean:
median:
Answer:
it takes me 14 minutes to go to class
In how many distinct ways can the digits in the number 7,511,111 be arranged?
The number of distinct ways in which the digits of the number 7,511,111 can be arranged is of:
42.
How to obtain the number of arrangements?The total number of arrangements of n elements is given by the factorial of n, as follows:
A(n) = n!
When a few of the elements repeat, the number of arrangements with repetition is given by the equation presented as follows, also involving factorials.
[tex]A_n^{n_1, n_2, \cdots n_n} = \frac{n!}{n_1!n_2! \cdots n_n!}[/tex]
In which [tex]n_1, n_2, \cdots n_n[/tex] is the number of times that each element repeats.
For the number 7,511,111, we have that:
There are seven digits.The digit one repeats five times.Hence the number of distinct arrangements of the number 7,511,111 is given as follows:
7!/5! = 7 x 6 = 42 distinct arrangements.
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