The value of f(1) is 31
Solution:
Given that the sequence is defined by formula:
[tex]f(n+1) = f(n) - 3[/tex]
To find: f( 1 )
Also given that,
[tex]f(4) = 22[/tex]
So, we can say,
[tex]f(4) = f(3+1) = 22[/tex]
Substitute n = 3 in given formula
[tex]f(3+1) = f(3) - 3\\\\f(4) = f(3) - 3\\\\Substitute\ f(4) = 22\\\\22 = f(3) -3\\\\f(3) = 25[/tex]
Now we got, f(3) = 25
Use the similar steps to find for f(2)
Substitute n = 2 in given function
[tex]f(2+1) = f(2) - 3 \\\\f(3) = f(2) -3\\\\25 = f(2) - 3\\\\f(2) = 28[/tex]
Use the similar steps to find for f(1)
Substitute n = 1 in given function
[tex]f(1+1) = f(1) - 3\\\\f(2) = f(1) - 3\\\\28 = f(1) - 3\\\\f(1) = 28+3\\\\f(1) = 31[/tex]
Thus value of f(1) is 31
Jenna and Callie collect stamps. Jenna has 20 less than twice the number of stamps that Callie has. Write an expression that represents the number of stamps that Jenna has.
The expression that represents the number of stamps that Jenna has is 2x - 20
Step-by-step explanation:
Let us revise some algebraic expressions
a is 5 more than b ⇒ a = b + 5a is 3 less than b ⇒ a = b - 3a is twice b ⇒ a = 2 bThe sum of a and b ⇒ a + bThe difference of a and b ⇒ a - bThe quotient of a and b ⇒ a ÷ bThe product of a and b ⇒ a × b∵ Jenna and Callie collect stamps
∵ Jenna has 20 less than twice the number of stamps that Callie has
- Assume that Callie has x stamps, that means to find the number
of stamps of Jenna multiply x by 2 and subtract 20 from the product
∵ Callie has x stamps
∵ Twice means × 2
∴ Jenna has = 2(x) - 20
∴ Jenna has = 2x - 20
The expression that represents the number of stamps that Jenna has is 2x - 20
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2. Find the missing side length of the right triangle
shown below.
26 cm
10 cm
A. 18 cm
B. 20 cm
C. 22 cm
D. 24 cm
Using the Pythagorean Theorem with a hypotenuse of 26 cm and one side of 10 cm, the length of the other side is found to be 24 cm. Thus, the correct answer is (D) 24 cm.
In a right-angled triangle, you can use the Pythagorean Theorem to find the length of the missing side.
The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse c is equal to the sum of the squares of the lengths of the other two sides a and b:
[tex]\[c^2 = a^2 + b^2\][/tex]
Given that the hypotenuse c is 26 cm and one side a is 10 cm:
[tex]\[26^2 = 10^2 + b^2\]\[676 = 100 + b^2\]\[b^2 = 576\]\[b = 24\][/tex]
Therefore, the length of the other side is 24 cm, and the correct answer is (D) 24 cm.
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The complete question is:
The hypotenuse of a right triangle is 26 cm long. If one of the remaining two sides is 10 cm long. Find the length of the other side.
A. 18 cm
B. 20 cm
C. 22 cm
D. 24 cm
What is the simplified expression for 6 (2 (y + x))?
6 y + 12 x
12 y + 12 x
12 y + 8 x
8 y + 8 x
Step-by-step explanation:
6(2(y+x))=6(2x+2y)=12x+12y
Answer:
12y + 12x
Step-by-step explanation:
You're welcome.
John is selling tickets to an event. Attendees can either buy a general admission ticket, x, or a VIP ticket, y. The general admission tickets are $70 and the VIP tickets are $80. If he knows he sold a total of 29 tickets and made $2,130, how many of each type did he sell?
Step-by-step explanation:
x+y=29...because x and y means how many tickets they have
and if normal 1 ticket is 70...then x number of tickets are $70x.
and
1 VIP ticket is 80...then y number of tickets are $80y..got that?...sum of all earned by selling tickets equal to $2130
so...
70x+80y=2130
so...equations are
x+y=29
70x+80y=2130
solve these equations.i did the hard part...you will get the answer...if u dont know hot to solve this comment me...
What fraction is located at Point AAA on the number line?
Answer:
i don't see no number line
Step-by-step explanation:
Answer:
no pic
Step-by-step explanation:
A bicycle manufacturing company makes a particular type of bike. Each child bike requires 4 hours to build and 4 hours to test c e que tous
build and 4 hours to test. With the number of workers, the company is able to have up to 120 hours of building time and 100 hours of testing in the
represents child bikes and a represents adult bikes, determine which system of inequality best explans whether the company and tes and 150
bikes in the week
No, because the bike order does not meet the restrictions of 40 + 6a s 120 and 4C + 4a s 100
No, because the bike order does not meet the restrictions of 40 + 4a s 120 and 6C + 4a 5 100
Yes, because the bike order meets the restrictions of 40 + 6a s 120 and 4C + 4a s 100
Yes, because the bike order meets the restrictions of 40 + 4a s 120 and 6c + 4a 5 100
As the question is unable to be understood/incomplete hence let's discuss the complete question (most probable question) and the answer for that.
Updated Question:
"A bicycle manufacturing company makes a particular type of bike. Each child bike requires 4 hours to build and 4 hours to test. Each adult bike requires 6 hours to build and 4 hours to test. With the number of workers, the company is able to have up to 120 hours of building time and 100 hours of testing time for a week. If c represents child bikes and a represents adult bikes, determine which system of inequality best explains whether the company can build 20 child bikes and 6 adult bikes in the week. No, because the bike order does not meet the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100 No, because the bike order does not meet the restrictions of 4c + 4a ≤ 120 and 6c + 4a ≤ 100 Yes, because the bike order meets the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100 Yes, because the bike order meets the restrictions of 4c + 4a ≤ 120 and 6c + 4a ≤ 100"
Answer:
Correct answer for this question is first option because it satisfies the first inequality but not the second one.
Step by Step Explanation:
[tex]NO,\\4c+6a\leq 120\\ and\\4c+4a\leq 100[/tex]
First Inequality:
4(20)+6(6)≤120
80+36≤120
116≤120 ⇒ TRUE
Second Inequality:
4(20)+4(6)≤100
80+24≤100
104≤100 ⇒ FALSE
Use the formula d=rt to find the average speed of a car if the car traveled 320 miles in 8 hours.
Answer:
320 miles = (8 hours)(r)
r = 40 mph
in 2014 there were about 126 million women in the United States, and women were about 51.4% of the total population. what was the total population in 2014?
Answer:
Step-by-step explanation
51.4% of the total population is 126 million
let x be the total population
turn ur percent to a decimal
0.514x = 126,000,000
x = 126 / 0.514
x = 245,136,186.77 <==
Answer:
245 millions
Step-by-step explanation:
51.4 > 126million
100 > X
X=100*126/51,4
X=245.1
Select the correct answer.
Which group settled in America to escape religious persecution?
O
A.
Puritans
O
B.
Quakers
O
c.
Baptists
O D. Methodists
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Answer:
A. Puritans
Remember, King James was Catholic (brought up presbyetirian) and later enforced Anglican
A) Puritans settled in America to escape religious persecution.
what is emigration?Emigration is the act of leaving one's country or region to live in another. It is a type of migration, which refers to the movement of people from one place to another. Emigration is different from immigration, which is the process of entering a new country or region to live there permanently.
The Puritans were a group of English Protestants in the 16th and 17th centuries who sought to "purify" the Church of England from what they saw as Roman Catholic practices.
They faced persecution and discrimination in England, which led many of them to emigrate to America in search of religious freedom.
The most well-known group of Puritan emigrants to America were the Pilgrims, who established the Plymouth Colony in Massachusetts in 1620.
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Complete question:
Which group settled in America to escape religious persecution?
A.) Puritans
B.) Quakers
C.) Baptists
D.) Methodists
Round 9.3959 to the nearest hundredth
Answer:
The answer is 9.396
Step-by-step explanation:
What is the exact value of cos (67.5° )?
The exact value of cos(67.5°) is found using half-angle identities in trigonometry, which leads to the solution √(2 - √2)/2.
Explanation:To find the exact value of cos (67.5°), we can use the half-angle identity for cosine which states that cos(θ/2) = ± √ ((1+cosθ)/2). In this case, to find the cosine of 67.5 degrees, we effectively need to calculate the half-angle of 135 degrees.
Thus, cos(67.5°) = cos(135°/2) = √ ((1+cos135°)/2) = √ ((1 - √2/2)/2). This further simplifies to √(2 - √2)/2.
This is because the cosine of 135 degrees equals -√2/2 (as it's in the second quadrant where cosine is negative).
Therefore, the exact value of cos(67.5°) is √(2 - √2)/2.
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Solve the equation -1/4x=7
Answer:
-1/4 x = 7
x4 x4
-x = 28
x = -28
Step-by-step explanation:
Answer: -1/4*-28=7
x=-28
Step-by-step explanation:
First, do -1/4 and you should get-0.25 as your answer .
Next, do 7/-0.25
Last, check your answer and to do so simply multiply -1/4*-28 and you should get 7 as your final answer.
78 divided by 2789 how would I do this in long division form
39 points!!!!! HURRY AND SHOW STEPS.... Point B is collinear with A and C and partitions AC in a 3:4 ratio. B is located at (4,1) and C is located at (12,5). Find the coordinates of endpoint A.
Answer:
(11,3)
Step-by-step explanation:
Which of the following inequalities could be the result of the first step in solving the inequality
3(x – 4) < 8x + 13 for x?
AX-45 x+13
B x-458x+10
(C3x – 4 5 8x+13
D
3x – 12 5 8x + 13
In the inequality 3(x – 4) < 8x + 13, the first step is to distribute the 3 on the left-hand side. That results in the inequality 3x – 12 < 8x + 13. Therefore, the correct answer from the options given is (D) 3x – 12 < 5 8x + 13.
Explanation:The question is asking for the inequality that could result after the first step when solving the given inequality 3(x – 4) < 8x + 13. The first step involves distributing the multiplication on the left side of the inequality. Therefore, 3 multiplied by x gives 3x and 3 multiplied by -4 gives -12. This leads to the inequality 3x – 12 < 8x + 13.
So, the correct answer from the options given is:
(D) 3x – 12 < 5 8x + 13.
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The area of a rectangle is 17 1/2 in and it’s shorter side is 3 1/2in.draw a diagram that shows this information. What is the length of the longer side
Answer: 5
Step-by-step explanation:
17 1/2 is equal to 17.5
3 1/2 is equal to 3.5
Since 17.5 is the area, you must divide by 3.5, which equals 5
To find the length of the longer side of a rectangle with an area of 17 1/2 square inches and a shorter side of 3 1/2 inches, divide the area by the width to get the length. The length of the longer side is 5 inches.
Explanation:The question is asking how to find the length of the longer side of a rectangle given that the area of the rectangle is 17 1/2 square inches and one of the shorter sides is 3 1/2 inches. To find the length of the other side, which we will call length, use the formula for the area of a rectangle which is area = length × width. Since the area and width (shorter side) are known, the equation can be set up as follows:
17 1/2 = length × 3 1/2To find the length, divide the area by the width:Length = (17 1/2) / (3 1/2)Convert mixed numbers to improper fractions:Length = (35/2) / (7/2)Multiply by the reciprocal of the divisor:Length = (35/2) × (2/7)Simplify the fractions:Length = 5Therefore, the length of the longer side of the rectangle is 5 inches.
(2,-1)
Is one of many solutions to the inequality:
X - 3y<1
True or false?
Answer:
False
Step-by-step explanation:
lets find out..
x - 3y < 1.....check (2,-1)....x = 2 and y = -1
now we sub
2 - 3(-1) < 1
2 + 3 < 1
5 < 1.......so is 5 less then 1 ? NO, it is not...so (2,-1) IS NOT a solution
Answer:false
Step-by-step explanation:
Ms. Ellis expected 50 families to attend parent teacher conference but 60 families attended. What is the percent error?
Answer:
20%.
Step-by-step explanation:
That is (60 - 50) / 50
= 10/50
= 1/5
To convert to a percent we multiply by 100:
= 20%.
I think it will be 10% because you invited 50 right? And 60 atended or was it 60 and 50 atended? Well either way I think it’s 10%
A two-column proof
O uses a visual representation of the logical flow of steps needed to reach a conclusion
o contains a table with a logical series of statements and reasons that reach a conclusion
O contains a set of sentences explaining the steps needed to reach a conclusion,
O uses inductive reasoning to prove a statement.
Answer:
B contains a table with a logical series of statements and reasons that reach a conclusion.
Step-by-step explanation:
A two-column proof
uses a visual representation of the logical flow of steps needed to reach a conclusion.
contains a table with a logical series of statements and reasons that reach a conclusion.
contains a set of sentences explaining the steps needed to reach a conclusion.
uses inductive reasoning to prove a statement.
-4x + y = 4
2x + 2y =13
Answer: What exactly are you asking??
Step-by-step explanation:
Problem 1 Answer: x = -1 + 0.25y
Show Work:
1) Solving
-4x + y = 4
2) Solving for variable 'x'.
3) Move all terms containing x to the left, all other terms to the right.
4) Add '-1y' to each side of the equation.
-4x + y + -1y = 4 + -1y
5) Combine like terms: y + -1y = 0
-4x + 0 = 4 + -1y
-4x = 4 + -1y
6) Divide each side by '-4'.
x = -1 + 0.25y
7) Simplifying
x = -1 + 0.25y
Problem 2 Answer: x = 6.5 + -1y
Show Work:
1) Solving
2x + 2y = 13
2) Solving for variable 'x'.
3) Move all terms containing x to the left, all other terms to the right.
4) Add '-2y' to each side of the equation.
2x + 2y + -2y = 13 + -2y
5) Combine like terms: 2y + -2y = 0
2x + 0 = 13 + -2y
2x = 13 + -2y
6) Divide each side by '2'.
x = 6.5 + -1y
7) Simplifying
x = 6.5 + -1y
simplify this expression
2[(13-1)^2+2]
Answer:
292
Step-by-step explanation:
2(12^2+2)
2(144+2)
2(146)
292
Answer:
292
Step-by-step explanation:
13-1=12
12×12=144
144+2=146
146×2= 292
Please help me with this math Question. I want to finish meh homework :((((
The original price of jacket was $180
Step-by-step explanation:
Markdown is the money that is reduced on an item on sale.
Given
Markdown = $63
Percentage = 35%
Let x be the price of the jacket
Then the percentage formula will be sued to find the price of the jacket
[tex]Markdown= 35\%\ of\ x\\63 = 0.35 * x\\x = \frac{63}{0.35}\\x = 180[/tex]
Hence,
The original price of jacket was $180
Keywords: Percentage, Mark up, mark down
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Which of the following lengths cannot be the lengths of the sides of a triangle?
A. 4,6,9
B. 3,4,2
C. 2,2,3
D. 1, 1, 2
Two cars are 190 miles apart and travel toward each other along the same road. They meet in 2 hours. One car travels 5 miles per hour faster than the other car. What is the average speed of each car?
The speed of slower car is 45 mph and faster car is 50 mph.
Step-by-step explanation:
Given,
Distance covered by both cars = 190 miles
Time taken by both of them = 2 hours
Let,
x be the speed of slower car.
Speed of faster car = x+5
Combined speed = x+x+5 = 2x+5
We know that;
Distance = Speed * Time
[tex]190=(2x+5)*2\\190=4x+10\\4x=190-10\\4x=180\\[/tex]
Dividing both sides by 4
[tex]\frac{4x}{4}=\frac{180}{4}\\x=45[/tex]
Speed of slower car = 45 miles per hour
Speed of faster car = 45+5 = 50 miles per hour
The speed of slower car is 45 mph and faster car is 50 mph.
Keywords: speed, distance
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The problem given is a relative speed problem in mathematics. By solving the equation, we find that the slower car travels at 45 mph and the faster car travels at 50 mph.
Explanation:This is a
problem of relative speed
in
mathematics
. Let's consider the speed of the slower car as 'x' miles per hour. The faster car is travelling 'x+5' miles per hour. Since they are moving towards each other, the sum of their speeds equals the total distance divided by the total time, that is (x + (x + 5)) = 190/2. Simplifying the equation, we get 2x + 5 = 95. Solving further, we get x = 45 miles per hour. Therefore, the slower car is travelling at 45 mph and the faster car is travelling at 50 mph.
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Evaluate each expression if d = 12 and e = 1/3 2d-5
Answer:
19
Step-by-step explanation:
Plug it in
Please help me with the question. You must solve for x.
Answer:
[tex]x= (3, \frac{3}{10} )[/tex]
Step-by-step explanation:
The figure is composed of two similar triangles; therefore,
[tex]\frac{7x}{19x-4} =\frac{7x+8}{(5x+5)+(19x-4)}[/tex] this says the ratio of the sides is same for the two triangles.
we simplify and a rearrange to get
[tex]7x(24x+1)=(7x+8)(19x-4)[/tex]
which we expand and get
[tex]168x^2+7x=133x^2+124x-32[/tex]
[tex]35x^2-117x+32=0[/tex]
this quadratic equation has solutions
[tex]x=3.04[/tex]
[tex]x=0.30[/tex]
As integers and simplified fractions these are
[tex]x= (3, \frac{3}{10} )[/tex]
Figure LMNO is a parallelogram. Parallelogram L M N O is shown. Angle M is (3 x) degrees and angle N is (8 x minus 40) degrees. What is the value of x? 8 10 13 20
Answer:
20
Step-by-step explanation:
we know that
In a parallelogram, opposite angles are congruent and consecutive angles are supplementary
In this problem
M and N are consecutive angles so
[tex]m\angle M+m\angle N=180^o[/tex]
substitute the given values
[tex]3x^o+(8x-40)^o=180^o[/tex]
solve for x
[tex]11x-40=180\\11x=220\\x=20[/tex]
Answer:
20
Step-by-step explanation:
If h(x) = 6 - X, what is the value of (h*h)(10)?
The value of [tex]\bold{ h(h(10))=10}[/tex]
Solution:
Given: [tex]h(x) = 6 - x[/tex]
To find: The value of (h*h)(10)
We know that, [tex](h*h)(x)=h(h(x))[/tex]
which is,
[tex]\Rightarrow h(h(x))=6-(6-x)=x[/tex]
On solving we get,
[tex]\Rightarrow6-6+x=x[/tex]
So, for x = 10 it will be,
[tex]h(h(10))=10[/tex]
Hence, the required value is 10.
Find the value of the y-intercept of the line whose equation is 5x - 3y = -12.
To find the y-intercept, rewrite the equation of the line in slope-intercept form:
Slope-intercept form: y = mx + b (b is the y-intercept)
This is how you get your equation in slope-intercept form:
5x -3y = -12
-3y = -5x - 12
-3y/-3 = (-5x -12)/-3
y = (5/3)x + 4
The answer is 4.
Please let me know if you understand in the comments!
1. A six-sided number cube is rolled and a card is drawn from a
standard deck. Find the total number of outcomes.
Answer:
it's 312
Step-by-step explanation:
1/6 is the total number of outcomes from the cube
1/52 is the total number of outcomes from the deck
multiply them and get 1/312
312 outcomes!
The question is an illustration of arrangement and selection.
The total number of outcomes is 312
The given parameters are:
Cube and Standard deck
A cube has 6 faces
A standard deck has 52 cards
So, the total number of outcome is:
[tex]\mathbf{Total = Cube \times Standard\ deck}[/tex]
Substitute known values
[tex]\mathbf{Total = 6 \times 52}[/tex]
[tex]\mathbf{Total = 312}[/tex]
Hence, the total number of outcomes is 312
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