========================================================
Explanation:
The first term is 4 because of the notation [tex]a_1 = 4[/tex]
To get the second term, we'll use the recursive equation [tex]a_n = 5(a_{n-1})-1[/tex] which basically says [tex]\text{nth term} = 5*(\text{previous term})-1[/tex]. To get the second term, we'll multiply the first term by 5, then subtract off 1.
2nd term = 5*(1st term) - 1
2nd term = 5*4 - 1
2nd term = 19
This means [tex]a_2 = 19[/tex]
We repeat this process again to find the third term [tex]a_3[/tex]
[tex]a_n = 5*(a_{n-1})-1\\\\a_3 = 5*(a_{3-1})-1\\\\a_3 = 5*(a_{2})-1\\\\a_3 = 5*(19)-1\\\\a_3 = 95-1\\\\a_3 = \boldsymbol{94}\\\\[/tex]
The third term is 94
Lyndon got a new job which pays $24.25 per hour. He works 40 hours per week. He pays 5% state income tax on his earnings. How much does Lyndon have remaining after state income tax is deducted from 4 weeks of pay?
Answer:
$3686 remaining after tax
Step-by-step explanation:
Bran walked a total of 16 kilometers by making 4 trips to his grandfather's place. How many trips will Bran have to make in all to walk a total of 28 kilometers?
Bran has to make in all to walk a total of 28 kilometers : 4 x 2 = 8 ( trips )
ok done. thank to me :>
Two tins are geometrically similar, if the ratio of there volume is 27:64, find the ratio of the curved surface areas
Answer:
9:16.
Step-by-step explanation
The scale factor is ∛27:∛64
= 3:4.
So the ratio of the curved areas = 3^2:4^2
= 9:16.
Use the solutions below to write the quadratic expression in standard form.
x=-6 x=2
Graph the following
1. f(x) = 2x² + 2
2. f(x) = 5x²+ 20x-1
Answer:
Step-by-step explanation:
Use DESMOS. See attached.
In 1993, the moose population in a park was measured to be 4650. By 1998, the population was measured
again to be 4100. If the population continues to change linearly:
A.) Find a formula for the moose population, P, in terms of t, the years since 1990.
P(t) =
B.) What does your model predict the moose population to be in 2006?
Answer:
Here plz give brainliest not easy to explain in detail like this
Step-by-step explanation:
We will consider x on the graph to be years since 1990 and y on the graph to be the number of Moose.
We have two points on the graph: (4, 4290) and (8, 3850)
Using the slope formula (m = [y2 - y1]/[x2 - x1]), we can find the slope of this line:
m = (y2 - y1)/(x2 - x1) Slope formula
m = (3850 - 4290)/(8 - 4) Substitution
m = -440/4 Solve the subtraction problems in the parenthesis
m = -110 Reduce the fraction
Now that we have the slope of the line, we can use the point-slope formula (y - y1 = m[x - x1]) to find the equation for the line. I will use the first point, but either point will produce the same answer.
y - y1 = m(x - x1) Point-slop e formula
y - 4290 = -110(x - 4) Substitution
y - 4290 = -110x + 440 Distribute the -110
y - 4290 + 4290 = -110x + 440 + 4290 Add 4290 to each side
y = -110x + 4730 Simplify
Since the formula that is being sought is supposed to be interms of P and t, I will replace y with P and x with t.
P(t) = -110t + 4730
To predict the population in 2006, we need to determine the years from 1990 to 2006.
2006 - 1990 = 16
P(16) = -110 (16) + 4730
P(16) = -1760 + 4730
P(16) = 2970
graph the f(x)=(x+2)^2+3
Answer:
am also not sure
Step-by-step explanation:
Suppose the voltage in an electrical circuit varies with time according to the formula V(t) = 40 sin(t) for t in the interval [0,].
The numerical value of the mean voltage in the circuit is
The numerical value of the mean voltage is 25.47 V
To find the numerical value of the mean voltage, V of V(t) = 40 sin(t), we integrate V(t) with respect to t over the interval [0.π]
So,
[tex]V = \frac{1}{\pi } \int\limits^\pi _0 {V(t)} \, dt \\V = \frac{1}{\pi } \int\limits^\pi _0 {40sint} \, dt \\V = \frac{1}{\pi } [-40cost]_{0}{\pi } \\V = \frac{1}{\pi } -[40cos\pi - 40cos0]\\\\V = \frac{1}{\pi } (-[40 X (-1) - 40 X 1})\\V = -\frac{1}{\pi } [-40 - 40]\\V = \frac{80}{\pi } \\V = 25.465 V[/tex]
V ≅ 25.47 V
So, the numerical value of the mean voltage is 25.47 V
Learn more about mean volatage here:
https://brainly.com/question/17928028
Write in point slope form the equation for the line that goes through the point (-1,-6) and has a slope of 16
Answer:
y+6 = 16 (x+1)
Step-by-step explanation:
Point slope form of an equation is
y-y1 = m(x-x1)
where m is the slope and (x1,y1) is a point on the line
y- -6 = 16 (x- -1)
y+6 = 16 (x+1)
Manny has 48 feet of wood. He wants to use all of it to create a border around a garden. The equation 2 l plus 2 w equals 48 can be used to find the length and width of the garden, where l is the length and w is the width of the garden. If Manny makes the garden 15 feet long, how wide should the garden be?
9 feet
18 feet
30 feet
33 feet
Answer:
Step-by-step explanation:
The Width of the garden will be 9 feet.
Step-by-step explanation:
Given:
Manny has wood =48 feet
Length of the garden = 15 feet
The equation which can be used .
We need to find the width of the garden.
Solution :
Now Length of the garden is given we will substitute in the given equation to find the width.
Now Using Subtraction property we will subtract both side by 30 we get;
Now Using Division Property we will divide both side by 2 we get;
Hence the Width of the garden will be 9 feet.
(04.01 LC)
The equations y = −3x + 1 and y = 2x − 4 are shown in the graph.
graph of y equals 2 times x minus 4 and y equals negative 3 times x plus 1
Which is the solution to the system of equations? (1 point)
Group of answer choices
(−2, −1)
(−2, 1)
(−1, −2)
(1, −2)
Answer:
(1, −2)
Step-by-step explanation:
−3x + 1 = 2x − 4
−5x + 1 = − 4........subtract 2x from both sides
-5x = -5.................subtract 4 from both sides
x = 1.......................divide both sides by - 5
now that you have x value find y by plugging in the x value in either one of the equations (I'll be using y = -3 +1)
y = -3(1)+1
y = -3+1.............multiply
y = -2................add
jerry has 3,572 live chickens in his poultry farm.if there are 38 boxes , how many chickens must go in each box?
Answer: 94 live chickens go in each box.
Step-by-step explanation: 3,572 divided by 38 = 94 so 94 live chickens go in each box.
hope this helps :)
1) 6p + 12 - 2 = 8p + 4
6p + 12 - 2 = 8p + 4
6p + 10 = 8p + 4
6p - 8p = 4 - 10
-2p = -6
2p = 6
p = 3
Answer:
p = 3
Step-by-step explanation:
First, simplify. Combine like terms. Like terms are terms with the same variable as well as same amount of said variable:
6p + (12 - 2) = 8p + 4
6p + (10) = 8p + 4
Isolate the variable, p. 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 operations, and stands for:
Parenthesis
Exponents (& roots)
Multiplications
Divisions
Addition
Subtraction
First, subtract 8p and 10 from both sides of the equation:
6p (-8p) + 10 (-10) = 8p (-8p) + 4 (-10)
6p - 8p = 4 - 10
-2p = -6
Next, isolate the variable, p, by dividing -2 from both sides of the equations:
(-2p)/-2 = (-6)/-2
p = -6/-2
p = 3
3 is your answer.
~
There are 30 coins in 5 rows.
How many coins in each row?
Answer:
It is 30 divide by 5
Step-by-step explanation:
is 3/4 greater than 1? i need help please
Answer:
No.
Step-by-step explanation:
3/4 = 0.75.
=> 0.75 < 1
Hoped this helped.
Ayushi wanted to paint a wall of a room of dimensions 6 m × 5 m. It has a window of dimensions 2 m × 0.5 m and a door of dimensions 3 m × 1.5 m. What area of the wall is required to be painted by Ayushi?
Can you guys plz answer this???
Answer:
Required wall to be painted: 24.5 m²Step-by-step explanation:
Wall dimensions: 6 m x 5 m
=> Wall dimensions: 30 m²
Area of window: 0.5 x 2
=> Area of window: 1 m²
Area of door: 3 m × 1.5 m
=> 4.5 m²
Required wall to be painted: 30 - 1 - 4.5
=> Required wall to be painted: 24.5 m²
Therefore, the required paint for the wall to be fully painted is 24.5 m². Hoped this helped.
On a certain hot summer's day, 294 people used the public swimming pool. The daily prices are for $1.75 children and for $2.25 adults. The receipts for admission totaled $635.50 How many children and how many adults swam at the public pool that day?
Answer:
a = 242 adult and c = 52 children
Step-by-step explanation:
Solving as a system of equations.
a = adult
c = children
The adult and the children equal 294 people
a + c = 294
adult cost is 2.25 per adult
Total amount of adult is 2.25a because the number of adult are not given.
children cost is 1.75 per children
Total amount children is 1.75c because the number of children are not given
Total receipts $635.50.
a + c = 294 multiply by -1.75 -1.75a - 1.75c = - 514.50
2.25a + 1.75c = 635.50 does not change 2.25a + 1.75c = 635.50
Add these equations together
-1.75a - 1.75c = - 514.50
2.25a + 1.75c = 635.50
.50a = 121.00
a = 121.00/.50a
a = 242 adult
a + c = 294
242 + c = 294
c = 294 - 242
c = 52 children
Check: $2.25(242) + $1.75( 52) = $635 .50
$544.50 + $91.00 = $635.50
$635.50 = $635.50
If f(1) = 5 and f(n) = 4f(n − 1) - 2 then find the value of f(5).
Hi,
This is the same situation as a sequence case.
You have two informations :
[tex]\left \{ {{f(1)=5} \atop {f(n)=4f(n-1)-2}} \right.[/tex]
You need to solve this rank by rank for n = 1, 2, 3, 4 and 5.
We already have f(n) for n = 1 : it is f(1) = 5.
n = 2 :
f(2) = 4 * f(2-1) - 2 = 4 * f(1) - 2 = 4 * 5 - 2 = 20 - 2 = 18 because f(1) = 5
n=3 :
f(3) = 4 * f(3-1) -2 = 4 * f(2) -2 = 4 * 18 -2 = 72 - 2 = 70
n = 4 :
f(4) = 4 * f(4-1) -2 = 4* f(3) - 2 = 4* 70 - 2 = 280 - 2 = 278
n = 5 :
f(5) = 4 * f(5-1) - 2 = 4*f(4) - 2 = 4 * 278 - 2 = 1112 - 2 = 1110
so f(5) = 1110
Good Luck
plz help will mark as brainliest
Answer:
18⁰
Step-by-step explanation:
As AOB is a line so it's is 180 ⁰
Hence,
5y+3y+2y=180⁰
10y=180⁰
y=180⁰/10
y=18⁰
Red At Santa's workshop, Jingles
the Elf sampled candy canes. He found
that 18 candy canes were broken. This
number represented 15% of the total
number of candy canes he inspected.
What was the total number of candy
canes Jingles sampled?
Based on the total number of candy canes damaged and the proportion of the total it was, the total inspected was 120 candy canes.
Assuming the total number of candy canes inspected is x, the relevant formula would be:
18 = x × 15%
Solving for x would give us:
18 = 0.15x
x = 18 / 0.15
= 120 candy canes
In conclusion, 120 canes were sampled.
Find out more at https://brainly.com/question/529563.
Consider the graph shown below.
What are the coordinates of point C after a dilation with a scale factor of 5,centered at the origin
Answer:
10,5
Step-by-step explanation:
After a dilation of 5, it should become 10 and 5 because it was 2,1 before.
oletha rapples from the top of a cliff at a rate of -6 inches per second. It takes oletha 4 minutes to reach the bottom of the cliff. What is the height of the cliff in feet?
Answer:-120
Step-by-step explanation:multiply -6 by 60 seconds which it will give you -360 in inch’s and then multiply -360 into 4 and that’s -1440 and then combert them into -120
5. What is the correct word form of 9.602?
A nine and sixty-two hundredths
B nine and six hundred two hundredths
C nine and sixty-two thousandths
D nine and six hundred two thousandths
Answer:
D is the correct answer
Step-by-step explanation:
your welcome
Answer:
nine and six hundred two thousandthsStep-by-step explanation:
x2-4x+6=0
Someone help with solve this
Answer:
0 is the answer..(•‿•)(. (•‿•)(•‿•)(•‿•)
PLS HELP ME 20 points total
Answer:
b and f
Step-by-step explanation:
maths
Answer:
A) The point (1, 0.60) means that one pound of potatoes cost $0.60.
F) The point (40, 24) means that 40 pounds of potatoes cost $24.00.
Step-by-step explanation:
The given graph shows the linear relationship between the total cost and the number of pounds of potatoes.
In order to determine the total cost of potatoes per pound, use the following points on the graph:
Let (x₁, y₁) = (20, 12)
(x₂, y₂) = (25, 15)
Substitute these values into the following slope formula:
m = (y₂ - y₁)/(x₂ - x₁)
m = (15 - 12) / (25, 20)
m = 3/5
Therefore, the slope of the line is 3/5 or 0.60. This means that the total cost increases by $0.60 for every pound of potatoes.
Option A: Since we determined that the slope represents the change in total cost increases by $0.60 for every pound of potatoes. Multiplying the number of pounds by the cost per pound, $0.60, will give you the total cost of the potatoes. Thus, 1 pound of potatoes × $0.60 per pound = $0.60.
This matches the points described in Option A, thereby making it as one of the valid answers.
Option B) is incorrect because the total cost of 12 pounds of potatoes is $7.20. The given option states that $7.20 is the cost per pound of potatoes, which is false. The cost per pound of potatoes is $0.60.
Option C) Similar to Option B, 12 pounds of potatoes doesn't cost $20 per pound.
Option D) The descriptions of the coordinates, (25, 15) were mixed up: it should have been "25 pounds of potatoes cost $15." Hence, Option D is incorrect.
Option E) Similar to Option D, the descriptions of the coordinates, (30, 18) were mixed up: it should have been "30 pounds of potatoes cost $18." Hence, Option D is incorrect.
Option F) The point, (40, 24) appropriately represents the total cost of $24 for the 40 pounds of potatoes. Therefore, Option F is correct.
Please help asap!! Thanks:) and please don’t answer just for points
Answer:
68 ft^2
Step-by-step explanation:
Find the area of the large rectangle as if the piece were there
A = l*w
A = 6 * 14
A =84
Subtract the area of the square that is missing
A = 4*4 = 16
84 - 16 =68
The area of the figure is 68 ft^2
I actually don’t understand this can someone please help?
Answer:
It's proportional when you have a straight line that goes through the origin, meaning (0,0), meaning x = 0 and y = 0, meaning: when x = 0, then y has to be = 0 too! That's obviously not the case here. You can see that the line hit the y axis way above 0. So this graph is not directly proportional to x.
Step-by-step explanation:
What is the answer of this question please reply!
0.00536 by 25
Answer:
0.134
Step-by-step explanation:
"By" means multiplied by, so the question is, what's 0.00536 multiplied by 25?
In the first step, we multiply all the numbers in the decimal by 5, and we get 0.02680. In the second, we multiply all the numbers in the decimal by 20, and we get 0.10720. Then we add the two together and get 0.134.
I hope that helped :)
plz help I need answer asap!
Answer:
x=2.4
Step-by-step explanation:
for this one we find the scale factor you can pick any two similar points i picked 3 and 1.8 i did 1.8/3 and found the scale factor is .6 so x= ML or 4 * .6 (our scale factor) which gives x=2.4
Answer:
x=2.4
Step-by-step explanation:
This is simple! If you know how to find scale factor then then problem is a breeze.
Look at side JK and side PQ. To find the scale divide 3 by 1.8 This gives you 1.66666666667. We don’t want this long number but we can work with it :3
Now to find that missing side= x
4 / 1.66666666667= 2.4
x=2.4
( pssstt! This “/“ means division ;-)
hope this helped :D
f(x)=3/5x-4/3 What x value makes f(x)=0
(will give brainliest to whoever answers first)
Answer:
3
Step-by-step explanation: