Answer:
4th term = 28
5th term = 37
6th term = 45
Step-by-step explanation:
f(n + 1) = f(n) + 8
f(1) = 5
f(1 + 1) = f(1) + 8 = 5+8 = 13
f(2) = 13
f(2 + 1) = f(2) + 8 = 13+8 = 21
Thus, series is 5, 13, 21......
In arithmetic series
Nth term is given by
n th term = a + (n-1)d
where a is the first term
and d is the common difference.
common difference d = nth term - (n-1)th term
For this series
a = 5
lets take nth term as 2nd term and 1st term as (n-1)th term
d = 13-5 = 8
n th term = a + (n-1)d
using the formula for nth term
4th term = 5 + (4-1)8 = 29
5th term = 5 + (5-1) 8= 37
6th term = 5+ (6-1)8 = 45
Thus, 4th term = 28
5th term = 37
6th term = 45
Note this, problem can be solved using f(n + 1) = f(n) + 8 by putting n = 3,4,5 as well but for learning concept of arithmetic series, i have used above process. Hope it helps.
What is an equation of the line that passes through the points (-7, -6) and
(-1,0)?
Answer:
equation of line:
y = mx+c
1) find the gradient, m
[tex]m = \frac{y2 - y1}{x2 - x1} [/tex]
[tex]m = \frac{ - 6 - 0}{ - 7 - ( - 1)} [/tex]
[tex]m = 1[/tex]
2) find y-intercept, c using coordinate (-1,0)
y = mx + c
0 = 1(-1)+ c
-1 + c = 0
c = 1
the equation of line: y = x + 1
someone help plz, I'm stuck
Answer:
Original price reduced by 30%
Step-by-step explanation:
You want the deepest discount, which means you want the greatest percent/amount off. The first choice is 20%. The second is 30%. The third one is 25%, because you are paying for 75% (100-75). The second choice offers the deepest discount because it is 30% off.
In a cookie-eating contest, Luke ate 8 cookies in 1 minute and 30 seconds. At this rate, how many cookies will he eat in 3 minutes and 45 seconds?
Answer:
20 cookies
Step-by-step explanation:
Change from minutes and seconds to seconds
1 minute 30 seconds = 90 seconds
3 minutes 45 seconds = 3 *60 +45 = 180+45 = 225 seconds
Now we can use ratios to solve
8 cookies x cookies
------------- = -----------------
90 seconds 225 seconds
Using cross products
8 * 225 = 90x
Divide each side by 90
1800/90 = 90x/90
20 =x
Express 3*(4*5) as a common fraction given a*b= ab/a+b .
Answer:3 ⋅ ( 4 ⋅ 5 ) = 23 a ⋅ b = a ( b a ) + b = a = 2
Step-by-step explanation:
The common fraction for the given expression is 60/47.
What is a fraction?A fraction represents part of a whole. When something is broken up into a number of parts, the fraction shows how many of those parts you have.
Given that an expression, 3*(4*5) such that, a*b= ab/a+b
Solving the expression as per the given formula,
4*5 = 4×5/(4+5) = 20/9
Now,
3*(4*5) can be written as, 3*20/9
Therefore,
3*20/9 = 3×20/9/(3+20/9)
= 20/3×9/47
= 60/47
Hence, the common fraction for the given expression is 60/47.
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In the diagram, point D divides line segment AB in the ratio of 5:3. If line segment AC is vertical and line segment CD is horizontal, what are the coordinates of point C? A. (2, -1) B. (5, -3) C. (2, -3) D. (7, -1)
Answer:
A.
[tex]Point\ C = (2,-1)[/tex]
Step-by-step explanation:
Given
[tex]A = (2,-6)[/tex]
[tex]B = (10,2)[/tex]
[tex]m:n = 5:3[/tex]
Required
Determine the coordinates of C
Since, point D divides line AB in ratio, 5 : 3;
We start by calculating the coordinates of D;
This is done as follows;
[tex]D(x,y) = (\frac{mx_2 + nx_1}{m+n},\frac{my_2 + ny_1}{m+n})[/tex]
Where
[tex](x_1,y_1) = (2,6)[/tex]
[tex](x_2,y_2) = (10,2)[/tex]
[tex]m:n = 5:3[/tex]
[tex]D(x,y) = (\frac{5 * 10 + 3 * 2}{5+3},\frac{5 * 2 + 3 * -6}{5+3})[/tex]
[tex]D(x,y) = (\frac{50 + 6}{8},\frac{10 - 18}{8})[/tex]
[tex]D(x,y) = (\frac{56}{8},\frac{-8}{8})[/tex]
[tex]D(x,y) = (7},-1)[/tex]
Since AC is vertical
Then, Point C has the same x coordinate as A
[tex]x-coordinate = 2[/tex]
Similarly;
Since CD is horizontal
Then, Point C has the same y coordinate as D
[tex]y-coordinate = -1[/tex]
Hence,
[tex]Point\ C = (2,-1)[/tex]
Answer:
Option A
Step-by-step explanation:
A. (2, -1)
Help me please I need help
Answer:
4 to the power of 8
Step-by-step explanation:
if they have the same base number with a exponent u can add the exponenets together to simplify it but if they dont have the same base number you can not add the exponents together
Answer:
b.
[tex] {4}^{8} [/tex]
Step-by-step explanation:
With the same base you just add the exponents.
−5+(−5r)+10 answer plz
Answer:
-5r + 5
Step-by-step explanation:
We simply simplify by adding like terms. Only thing we can combine are the constants -5 and 10, which we get 5. So then our answer is -5r + 5.
Answer:
5(1-r)
Simplified expression 5-5r
Step-by-step explanation:
In the proportion 15/3 = v/7 , which number is equal to y in the proportion ?
Answer:
3
Step-by-step explanation:
Answer:
y=3
Step-by-step explanation:
Jade and Fred sit on opposite ends of a 16-foot seesaw. Jade weighs 45 pounds
and Fred weighs 50 pounds. Where would Cynthia have to sit to balance the
seesaw if she weighs 30 pounds? (The fulcrum is at the center.)
If Max is opening a bank account and he deposits $1500 and it has compound interest at a 9%, how much money will he have 8 years if the interest compounds semi-annually?
Answer:
$3,033.56
Step-by-step explanation:
(see attached for reference)
The formula for compound interest is given by
A = P [ 1 + (r/n) ]^(nt)
Where,
A = final amount (we are asked to find this)
P = principal = given as $1500
r = annual interest rate = 9% = 0.09
n = 2 (for compounding semi-annually)
t = time, given as 8 years
Substituting the above into the equation:
A = P [ 1 + (r/n) ]^(nt)
A = 1500 [ 1 + (0.09/2) ]^[(2)(8)]
A = 1500 [ 1.045) ]^[16]
A = $3,033.56
if -5 is a root of the quadratic equation 2x2+px-15=0 and the quadratic equation p(x^2+x)+k=0 has equal roots. find the value of k
Answer:
k= 7/4
Step-by-step explanation:
2x²+px-15=0
One of roots is -5, then:
2*(-5)²- 5p -15 =050 -5p - 15= 05p= 35p=7----
p(x²+x)+k=0
replacing value of p:
7(x²+x)+k=07x²+7x+k=0it has equal roots, then the discriminant is zero:
b² - 4ac=0
7²-4*7*k=07 -4k=04k=7k= 7/4How many 4-digit numbers can be formed using only the digits 9, 8 and 7?
Answer:
There are 81 numbers
Step-by-step explanation:
Imagine that you have 4 boxes (one for each digit). In each box, you only have 3 choices for what digit you will do. You have to multiply all of the options (3*3*3*3) and you get 81.
Which graph represents the solution to this system of inequalities? y 2x – 4 A. B. C. D.
Answer:
I mean you dont got no graph
Step-by-step explanation:
butttttt.....
The graph wit a straight line that intersects the y-axis at -4 and goes up by 2 and to tha right by 1.
Answer:
Theres no graph
Step-by-step explanation:
SOMEONE PLEASE HELP!!!!!!!!!
Solve 2 x - 1 < 7 and 5x + 3 < 3.
A. {x l x < 0}
B. {x l x < 4}
C. {x l 0 < x < 4}
Answer:
Step-by-step explanation:
2x - 1 < 7
Add 1 to both sides
2x - 1 + 1 < 7+1
2x < 8
Divide both sides by 2
2x/2 < 8/2
x < 4
5x + 3 < 3
Subtract 3 form both sides
5x + 3 - 3 < 3-3
5x < 0
x < 0
x <4 & x < 0
So, solution ,
{x / x< 0 }
Answer:
A. {x l x < 0}
Step-by-step explanation:
2 x - 1 < 7 and 5x + 3 < 3.
Solve one inequality at a time
2 x - 1 < 7
Add 1 to each side
2 x - 1+1 < 7 +1
2x <8
Divide by 2
2x/2 <8/4
x <4
Now solve the other
5x + 3 < 3
Subtract 3
5x +3-3 < 3-3
5x<0
x <0
Recombine
x<4 and x<0
We go with the more restrictive and merge the overlapping interval since we have an and
x<0
WILL MARK THE BRAINLIEST need answered asapThere are 25 trees on the Jackson’s property. Twenty percent of the trees are oak trees. Which equation can be used to find the number of oak trees on the property? StartFraction 25 divided by 1 Over 20 divided by 1 EndFraction = StartFraction 25 Over 20 EndFraction StartFraction 100 times 5 Over 20 times 5 EndFraction = StartFraction 500 Over 100 EndFraction StartFraction 20 times 4 Over 25 times 4 EndFraction = StartFraction 80 Over 100 EndFraction StartFraction 20 divided by 4 Over 100 divided by 4 EndFraction = StartFraction 5 Over 25 EndFraction
Answer:
20% of 25 trees=25*20/100=5 trees.
Step-by-step explanation: i hope this helps
C
:)hope this helps :)
WILL MARK BRAINLIEST! Identify and explain each example as Newton’s First, Second, or Third law of motion. I pull on the Earth because Earth pulls on me. Answer 1 Choose... The velocity of a falling object isn’t constant because Earth’s gravity exerts a force on it. Answer 2 Choose... If air resistance is ignored, the acceleration of a falling object is equal to the ratio of the force of gravity to mass. HELP PLZ!!!
Answer:
1.) Newton 3rd law
2.) Newton 1st law
3.) Newton 2nd law.
Step-by-step explanation:
1.) I pull on the Earth because Earth pulls on me. This can be identified as Newton 3rd law of motion. The law state that, in every action, there must be equal and opposite reaction.
As the earth pulls on you, the reaction to that action which is equal and opposite is you pulling back on earth.
2.) The velocity of a falling object isn’t constant because Earth’s gravity exerts a force on it. This can be identified by Newton 1st law of motion which state that: an object will continue to be at rest or in a linear motion except an external force act on it.
The velocity of a falling object suppose to be constant if there is no external force. But it isn’t constant because Earth’s gravity exerts a force on it.
3.) If air resistance is ignored, the acceleration of a falling object is equal to the ratio of the force of gravity to mass. This can be identified by Newton 2nd law of motion which state that: The rate of change in momentum is proportional to the applied force. Or
F = ma
Where F = applied force
M = mass of the object
a = acceleration
If air resistance is ignored,
F = mg
where g = acceleration due to gravity.
Answer:
1. Newton 3rd law
2. Newton 1st law
3. Newton 2nd law.
Step-by-step explanation:
For her birthday, Samantha received a gift card, with a value of $200, to a department store. She wants to purchase at least 5 articles of clothing for work. At the store, sweaters cost $24.49 each and dress pants cost $36.99 each. If Samantha does not spend more than the amount on the gift card, which system of inequalities could be used to determine the number of sweaters, s, and the number of dress pants, p, she can buy? A. s + p $200 B. s + p > 5 $24.49s + $36.99p 5 $36.99s + $24.49p < $200
Your answer choices are a bit jumbled and some symbols are missing. However, the answer will involve the two inequalities
[tex]s+p \ge 5 \ \text{ and } \ 24.49s+36.99p \le 200[/tex]
The first inequality is the idea where she wants to buy at least 5 articles of clothing. The expression s+p is the total amount of sweaters and pants purchased, and we want this quantity to be 5 or larger.
The second inequality has the total amount spent (24.49s+36.99p) to be at most 200 dollars. In other words, we want the amount spent to be $200 or less.
24.49s = amount spent on just the sweaters
36.99p = amount spent on just the pants
24.49s+36.99p = total amount spent
What is the value of the expression 1.3(x + 2)-(y - 6) when x = 4 and y = 2
A) 1.1
B) 11.8
C) 2.6
D) 26
Answer:
11.8Option B is the right option.
solution,
X=4
y=2
now,
[tex]1.3(x + 2) - (y - 6) \\ = 1.3(4 + 2) - (2 - 6) \\ = 1.3 \times 6 - ( - 4) \\ = 7.8 + 4 \\ = 11.8[/tex]
Hope this helps..
Good luck on your assignment
Answer:
It's 11.8
Step-by-step explanation:
What is the value of x in the equation? Two-thirds (x + 6) = negative 18 –36 –33 –24 Negative 18
Answer:
-33
Step-by-step explanation:
2/3 (x + 6) = - 18
Multiply by 3/2 on each side
3/2 *2/3 (x + 6) = - 18*3/2
x+6 = -27
Subtract 6 from each side
x+6-6 = -27-6
x = -33
Answer: C -33
Step-by-step explanation: I did a test
Which lines have a slope of 1/2?
Answer:
c and d
Step-by-step explanation:
rise/run
for every 2 that c and d progress positive on the x-axis, it only rises 1 on the y-axis
x + 6 = 2x -11 please show work
Answer:
x=17solution,
[tex]x + 6 = 2x - 11 \\ or \: x - 2x = - 11 - 6 \\ \: or \: - x = - 17 \\ x = 17[/tex]
Hope this helps..
Good luck on your assignment..
Find the distance between the points (–15, 3) and (–9, 8). A) units B) units C) units D) units
Answer:
√61
Step-by-step explanation:
d=√(x2 - x1)^2 + (y2 - y1)^2
√(-9-(-15))^2 + (8-3)^2
√61
The distance between points P(-15, 3) and Q(-9, 8) is √61 units.
What is algebra?Algebra is a study of mathematical expressions, in which numbers and quantities are represented in formulas and equations by letters and other universal symbols.
The given points are,
P(-15, 3) and Q(-9, 8).
The distance between two points A(x₁, y₁) and B(x₂, y₂)
Distance
= √(x₂ - x₁)² + (y₂ - y₁)²
To find the distance between points PQ,
Use formula
PQ = √(-9 - (-15))²+(8 - 3)²
= √(-9 + 15) ²+(5)²
= √(6) ²+(5)²
= √36 + 25
= √61
The required distance between given points is √61 units.
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suppose that y varies inversely with x. use the information to find k, and then choose the equation of variation. x = 28 when y = 2 A. k=56, y 56/2 B. k = 14 y = x/14 C. k = 56, y = 56x D. k = 14. y = 14/x
Answer: A
Step-by-step explanation:
Given that y varies inversely with x, that is,
y ∝ 1/xyou will introduce constant k when the proportionality constant sign is changed to equality sign.y = k(1/x)when x = 28, y = 2substitute x and y into the formula to get k2 = k(1/28)open the bracket and cross multiplyk = 56substituting k back into equation givesy = 56/xoption A should be the answer. but it wasn't written clearlyAre triangles DEF and LNM similar if LN equals 4, MN equals 3, DE equals 12, and FE equals 9? Yes, by the SAS Similarity Postulate Yes, by the SSS Similarity Postulate No, the corresponding sides are not proportional No, there is not enough info
Answer:
yes, sas
Step-by-step explanation:
12:4 and 9:3 are the same ratio so the sides are proportional. Since they have a congruent angle too, the answer is yes by the SAS Similarity Postulate.
Penny received an unexpected $5,000.00 gift from a distant relative. She invests it in a mutual fund that increases the value of the original investment by 8% each year. In 15 years, Penny hopes to have $40,000 available to make a down payment on a house. How much would she need to invest right now in order to have enough for her down payment in 15 years?
Answer:
Penny would need to put in ~ $18,181.82
Step-by-step explanation:
Using the equation [tex]A = P(1+rt)[/tex]
Where A = the total
P is equal to the starting amount
r is equal to the rate (percent)
and t is equal to the total time.
We can put in:
A = $40,000
r = 0.08 (8%)
t = 15
[tex]40,000 = P(1 +(0.08* 15))\\40,000 = P(1+1.2)\\40,000 = P(2.2)\\\frac{40,000}{2.2} = P\\ \frac{200,000}{11} = P\\P = $18181.8181818181...[/tex]
Round to the nearest whole cent
P = $18,181.82
Problem 3
Your cat had a litter of seven kittens of the kittens are female and white, and of the kittens are white. What is the
probability that your cousin will choose a female kitten given that it is a white?
Answer:
3/4
Step-by-step explanation:
From the above question, total number of cats in the litter = 7
We are told in the question that 4/7 of the kittens are white
This means
The number of kittens that are not white = 7 - 4/7 = 3/7
The number of kittens that are female and white = 3/7
This question is a conditional probability question
The probability that your cousin will choose a female kitten given that it is white is calculated as:
Probability that the kittens are female and white ÷ Probability that the kittens are white
= 3/7 ÷ 4/7
= 3/7 × 7/4
= 3/4
Therefore, probability that your cousin will choose a female kitten given that it is a white is 3/4
Solve for x by finding the missing side of the triangle. Round your answer to the nearest tenth.
Answer:
x≈14.28
Step-by-step explanation:
cos32° = 12/x
so : x= 12/cos32° = 12/0.84 = 14.28
Plz help me. Geometry
Answer:
B
Step-by-step explanation:
Since opposite angles in a parallelogram are congruent, ∠B = ∠D which means:
5y + 31 = 96
5y = 65
y = 13°
Additionally, opposite sides of a parallelogram are congruent, therefore AB = CD which means:
x² - 18 = 7x
x² - 7x - 18 = 0
(x - 9)(x + 2) = 0
x = 9° or -2°
Answer:
Step-by-step explanation:
SINCE IT IS A PARALLELOGRAM,
AB=CD
and B = D
therefore x= 9, y=13
hope it helps
Hey guys please help find the area
Answer: 120 inches
Step-by-step explanation: because 12 times 10 is 120
- Lawrence bends a wire of length 18 cm
into an equilateral triangle. He then
measures the sides of the triangle and
finds them to be 5.8 cm each.He uses
this measurement to calculate his
absolute error in the area obtained. What
is his answer?
Answer:
1.02 cm²
Step-by-step explanation:
An equilateral triangle is a triangle with all three sides of equal length.
The perimeter of the triangle made by Lawrence is 18 cm. Which is calculated as follows:
perimeter of equilateral triangle = 3*side
Therefore, each side is 18/3 = 6 cm long
Area of equilateral triangle = √3/4*side²
Area obtained by Lawrence = √3/4*5.8² = 14.57 cm²
Actual area of the triangle = √3/4*6² = 15.59 cm²
Absolute Error = | Measured Value - Actual Value |
Absolute Error = |14.57 - 15.59| = 1.02 cm²