a. n-(n - 1) = 1
b. n( n - 1) = n² - n
c. (n - 1) + n = 2n - 1
d. (n - 1) + n = 2n - 1
Solution:
General Rule for Equation Solving
Remove parentheses and combine like terms to simplify each side of the equation.To isolate the variable term on one side of the equation, use addition or subtraction.To find the variable, use multiplication or division.Given two consecutive numbers , (n - 1) , n
simplifying :
n - (n - 1)
= n -1(n - 1)
= n - n + 1
= 1
multiplying :
n( n -1)
= n² - n
simplifying :
(n-1) + n
= n - 1 + n
= 2n -1
by adding two numbers :
(n - 1) + n
= n -1 + n
= 2n - 1
To learn more about equations refer to :
https://brainly.com/question/22688504
#SPJ13
The area of a circle is 25 pi ft 2.
03 Fill in the Blank Text
Simplify the following expression:
14a + 3(a + 4b) - 2b
Answer:
17a+10b
Step-by-step explanation:
hope this work have a nice day
Determine the measure
Answer:
∠ D ≈ 31.0°
Step-by-step explanation:
using the tangent ratio in the right triangle
tan D = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{EF}{DE}[/tex] = [tex]\frac{9}{15}[/tex] , then
∠ D = [tex]tan^{-1}[/tex] ( [tex]\frac{9}{15}[/tex] ) ≈ 31.0° ( to the nearest tenth )
Solve for X -5x>2(x-14)
Hey there!
[tex]-5x > 2(x-14)[/tex]
Our first step is to simplify both sides of the inequality:
[tex]-5x > 2x-28[/tex]
Now, we need to subtract 2x from both sides:
[tex]-5x-2x > 2x-28-2x\\-7x < -28[/tex]
Our final step is to divide both sides by -7:
[tex]\frac{-7x}{-7} > \frac{-28}{-7}[/tex]
[tex]x < 4[/tex]
Hope this helps!
I am thinking of a number between one and one thousand if you get it right I will give you a hundred points.
also if you can solve this problem,
3+2(3x-1)=100/3(2-3)
Answer:
x= -103/18
Step-by-step explanation:
1.distribute, 3+2(3x-1)=100/3(2-3)
3+6x-2=100/3 (2-3)
2
Subtract the numbers
3
Rearrange terms
4
Subtract the numbers
5
Multiply the numbers
6
Subtract
1
from both sides
7
Simplify
8
Divide both sides by the same factor
9
Simplify
Scarlett sells designer ponchos. The revenue, RRR, she makes from selling a batch of nnn ponchos is given by the function R(n)=20nR(n)=20nR, left parenthesis, n, right parenthesis, equals, 20, n, and the expenses, EEE, that she incurs from producing a batch of nnn ponchos is given by the function E(n)=10\cdot \sqrt{n}E(n)=10⋅
n
E, left parenthesis, n, right parenthesis, equals, 10, dot, square root of, n, end square root.
Let PPP be the total profit Scarlett makes from producing and selling a batch of nnn ponchos.
Write a formula for P(n)P(n)P, left parenthesis, n, right parenthesis in terms of R(n)R(n)R, left parenthesis, n, right parenthesis and E(n)E(n)E, left parenthesis, n, right parenthesis.
P(n)=P(n)=P, left parenthesis, n, right parenthesis, equals
Write a formula for P(n)P(n)P, left parenthesis, n, right parenthesis in terms of nnn.
Scarlett should sell more than ¼ of batch of ponchos to make the profit.
Given,
The revenue made by Scarlett from selling batch of ponchos, R = 20n
The expenses she incurs from producing a batch of ponchos, E = 10√n
The total profit, P = R - E
= 20n - 10√n
Now,
Profit is earned when Revenue > Expenses
20n > 10√n
÷10 ÷10
2n > √n
(2n)² > (√n)²
4n² > n
4n² - n > 0
n(4n - 1)> 0
n > 0 and 4n - 1 > 0
n > 1/4
That is, Scarlett should sell more than ¼ of batch of ponchos to make the profit.
Learn more about profit here:
https://brainly.com/question/11851506
#SPJ1
annarose read 93.50 books in 8.5 months. Her favorite book is the outsiders. At that rate how many books does she expect to read annually?
number sentence 1:
number sentence 2:
At the unit rate of reading 93.5 books in 8.5 months, Annarose expects to read 132 books annually.
What is the unit rate?The unit rate is the ratio or speed that Annarose reads books.
From her established unit reading rate, she reads 11 books in a month.
The unit rate is computed by ensuring that the denominator becomes 1 after the division operation.
The number of books she read in 8.5 months = 93.5 books.
The number of books she can read in 1 month = 11 books (93.5/8.5).
The number of books she can read in 12 months = 132 books (11 x 12).
Thus, given Annarose's reading unit rate, she expects to read 132 books annually, at an average of 11 books every month.
Learn more about the unit rate at brainly.com/question/4895463
#SPJ1
Ryan deposits $775 in an account that pays 4.24% simple interest for four years. Brian deposits $775 in an account that pays 4.24% simple interest for one year.
The interest earned by Ryan is $131.44 and the interest earned by Brian is $32.86 .
In the question,
it is given that
amount deposited by Ryan = $775
time for which the amount is deposited = 4 years
rate at which the amount is deposited = 4.24%
So the simple interest = (p*r*t)/100
= (775 * 4.24*4 ) /100
= 13144/100
= 131.44
amount deposited by Brian = $775
time for which the amount is deposited = 1 years
rate at which the amount is deposited = 4.24%
So the simple interest = (p*r*t)/100
= (775 * 4.24 * 1 ) /100
= 3286/100
= 32.86
Therefore , the interest earned by Ryan is $131.44 and the interest earned by Brian is $32.86 .
The given question is incomplete , the complete question is
Ryan deposits $775 in an account that pays 4.24% simple interest for four years. Brian deposits $775 in an account that pays 4.24% simple interest for one year. Find the interest earned by both Ryan and Brian ?
Learn more about Interest here
https://brainly.com/question/19091875
#SPJ1
On the 1:1000 scale plan, the length and width of the house are drawn as 2 cm and 1.5 cm.
a. Find the actual size.
6. Find the ratio of the area of the foundation of the house to the area on the floor plan.
Answer:
a. Actual size: 20 m x 15m
b. 1,000,000 : 1
Step-by-step explanation:
(a) Since scale is 1:1000, multiply both length and width on the floor pan to get actual length and width of house
a. Actual size
= 2 x 1000 cm x 1.5 x 1000 cm
= 2000 cm x 1500 cm
= 20m x 15m (since 1 m = 100 cm
(b) Area on plan = 2 x 1.5 = 3 cm²
Actual area = 2000 x 1500 = 3,000,000 cm²
Ratio of actual area to floor plan area
= 3,000,000 / 3 = 1,000,000 : 1
Point-slope form: y minus y 1 = m (x minus x 1).
Use the point-slope form of a line to write the equation of a line that has a slope of 2 and passes through the point (–4, 3). Write the equation in slope-intercept form.
Choose the equation of the line.
y = 2x – 7
y = 2x + 11
y = –4x + 14
y = 3x +14
Help me please!!
what is the answer to -9+7x < 47
The solution of the inequality - 9 + 7x < 47 will be;
⇒ x < 8
What is mean by Inequality?
A relation by which we can compare two or more mathematical expression is called an inequality.
Given that;
The inequality is;
⇒ - 9 + 7x < 47
Now, Solve the expression as;
The inequality is;
⇒ - 9 + 7x < 47
Solve as;
⇒ - 9 + 7x < 47
Add 9 both side;
⇒ - 9 + 7x + 9 < 47 + 9
⇒ 7x < 56
Divide by 7, we get;
⇒ 7x/7 < 56/7
⇒ x < 8
Therefore, The solution of the inequality - 9 + 7x < 47 will be;
⇒ x < 8
Learn more about the inequality visit:
https://brainly.com/question/25275758
#SPJ1
aisha had 4 yards of fabric she used 3/5 of the fabric to make a backpack.Which fraction shows how many yards of fabric aisha used
Answer:
[tex] = \frac{3}{5} \\ [/tex]
The graph of function f is shown.
Which statement correctly compares the two functions?
A. They have the same x- and y-intercepts.
B. They have the same x-intercept and the same end behavior as x approaches ∞.
C. They have different x- and y-intercepts but the same end behavior as x approaches ∞.
D. They have the same y-intercept and the same end behavior as x approaches ∞.
In the picture, there is a graph and table. It displays the graph of the function f. Option C is correct, As x approaches, they have different x- intercept and y-intercepts but the same end behavior∞.
Given that,
In the picture, there is a graph and table.
It displays the graph of the function f.
Which of the two statements compares the two functions correctly.
A. Their x- and y-intercepts are identical.
B. As x gets closer to, they exhibit the same x-intercept and end behavior∞.
C. As x approaches, they have different x- and y-intercepts but the same end behavior∞.
D. As x gets closer to, they exhibit the same y-intercept and end behavior∞.
So, from the given table and graph we get
Option C is correct.
Therefore, Option C is correct.
To learn more about intercept visit: https://brainly.com/question/14180189
#SPJ1
I have a review work sheet that’s not Homework and I don’t get it
1)
white (w) marble
yellow (y) marble
green (g) marble
red (r) marble
Pw+Pw+Pg+Pr=1 (Eq. 1 )
w+y+g+r=12 (Eq. 2)
Answer: There are 12 marbles in the bag. SInce the question says the bag contains 12 marbles.
2)
a) Pw+Py = Pg
w + y = g (Eq. 3)
b) Pw = 10/40 = 1/4
If P = 1/4, if we have 12 marbles, P=3/12
Then, we know that we have 3 white marbles
Answer: There are 3 white marbles in the bag.
3) Pr = 1/5. Considering that 2 marbles were removed, we have 10 markles. The Pr=2/10.
Answer: Thus, we have 2 balls red.
4) From 12 marbles, we already know that 3 are white and 2 are red.
Then: 12-3-2= 7
Answer: 7 marbles are green or yellow.
5)
From question 4 , we know that;
y + g = 7
y = 7 - g (Eq. 4)
And from Eq. 3
w + y = g
3 + y = g
Substituing Eq. 4 in Eq. 3:
3 + 7 - g = g
10 = 2g
10/2 = g
g = 5
And:
y = 7 - g
y = 7-5
y = 2
The numeratiors are:
3 (Pw), 2 (Py), 5 (Pg)
5) 2 = yellow marbles
5 = green marbles
Seven cards are chosen from a well-shuffled deck of 52 playing cards. In how many selections do at least 3 jacks occur?.
In 193 selections at least 3 jacks occur.
Combination or permutation?To decide whether to use combination or permutation, we need to look at whether the order matters, as follows:
Order matters: permutation is used.Order does not matter: combination is used.In the context of this problem, the order in which the cards are chosen is not important, hence a combination is used.
The number of combinations of x elements from a set of n elements is given according to the formula presented below.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
There are two cases in which at least 3 jacks occur, as follows, considering that a standard deck has 4 jacks:
3 Jacks selected from a set of 4, and one non Jack card selected from a set of 48.4 Jacks cards from a set of 4.Hence the number of ways to choose the cards is calculated as follows:
[tex]C_{4,3}C_{48,1} + C_{4,4} = 4(48) + 1 = 193[/tex]
A similar problem, also involving combinations, is given at https://brainly.com/question/25821700
#SPJ1
. Constructed Response. Be sure to answer all parts of the constructed response.
Miles, Hayden, and Dubem are going to have a paint battle. Miles fills his wall at a rate of
12 wall in 9 minutes, Hayden can fill his wall at 15 wall in 313 minutes, and Dubem can cover 49 wall in 638 minutes.
Part A Place the students in order from fastest to slowest, in terms of who has the fastest water filling rate.
1.
2.
3.
Part B Explain how you determined the fastest rate.
Placing the students in order from fastest to slowest, in terms of who has the fastest water filling rate is;
1. Miles
2. Dubem
3. Hayden
The way the fastest rate is determined is by finding the unit rates
What is the unit rate of work done?A unit rate (or unit ratio) is a ratio that describes how many units of the first type of quantity corresponds to one unit of the second type of quantity.
Now, from the question, the rate would clearly be number of walls filled per minute.
1) Mills fills his wall at a rate of 12 wall in 9 minutes. Thus;
Mills unit rate = 12/9 = 4/3 walls filled per minute = 1.333 walls filled per minute
2) Hayden can fill his wall at 15 wall in 313 minutes. Thus;
Hayden's unit rate = 15/313 walls filled per minute = 0.0479 walls filled per minute
3) Dubem can cover 49 wall in 638 minutes. Thus;
Dubem's unit rate = 49/638 walls filled per minute = 0.0768 walls filled per minute
Looking at the decimal unit rates, we can see that fastest to slowest in order are;
1. Miles
2. Dubem
3. Hayden
The way I knew who was faster was to look at the decimal values of their unit rates and it is seen that Miles covered the most part of wall in one minute
Read more about Unit Rate of work at; https://brainly.com/question/19493296
#SPJ1
how much will Yoona charge to walk 8 dogs
Yoona will charge $20.75 to walk 8 dogs based on the trend of Yoona charges to walk dogs.
How to find the amount to be charged?First, find the pattern in the amount that Yoona charges to walk each additional dog.
Additional cost to walk 2 dogs:
= 40 - 37.25
= $2.75
Additional cost to walk 3 dogs:
= 37.25 - 34.50
= $2.75
Additional cost to walk 4 dogs:
= 34.50 - 31.75
= $2.75
Every extra dog therefore leads to a fall in price by $2.75. For eight dogs, Yoona would charge:
= 40 - (7 x 2.75)
= 40 - 19.25
= $20.75
Find out more on cost to walk dogs at https://brainly.com/question/24523218
#SPJ1
4. pls help will mark brainliest
Answer:
y = -16 + 4x
Step-by-step explanation:
The standard slope equation is y=mx+b. M is the slope and also the y intercept so if you look at the graph you can see that -16 is the y intercept, next you have to find the x intercept, why? I don't remember but then you do that in the equation, as you can also see on the graph, 4 is the x intercept so its 4x. put that into y intersect form at it's y = -16 + 4x
PLEASE HELP
Susan is mixing 4% butterfat milk with 1% butterfat milk to create 6 quarts of 2% butterfat milk. How many quarts of each will
she need?
O 1 of 4% and 5 of 1%
O 2 of 4% and 4 of 1%
Answer:
the first one took it on egde
Step-by-step explanation:
A side of the triangle below has been extended to form an exterior angle of 156°. Find
the value of x.
The value of x of angle ∠C is 66°.
What are angles?An angle is a figure formed by two rays or lines that have the same endpoint in plane geometry. The Latin word "angulus," which means "corner," is where the word "angle" originates. The common endpoint of the two rays—known as the vertex—is referred to as an angle's sides. Depending on the measurement, there are various angles in geometry. Basic angles are identified by their names: acute, obtuse, right, straight, reflex, and full rotation.So, the value of x:
As we can see that A is a straight angle. Then ∠BAC will be:
156 + ∠BAC = 180∠BAC = 180 - 156∠BAC = 24°Now, we know that in △ABC, ∠A = 24° and ∠B = 90° (Given), then ∠C will be:
x + ∠A + ∠B = 180x + 24 + 90 = 180x + 114 = 180x = 180 - 114x = 66Therefore, the value of x of angle ∠C is 66°.
Know more about angles here:
https://brainly.com/question/25716982
#SPJ9
Can someone help me with this?
m is perpendicular to l, s is perpendicular to t, and t is perpendicular to u. Based on the angle shown, these lines are parallel.
What is parallel?Parallel lines are lines that are always the same distance apart in a plane. Parallel lines never cross. Perpendicular lines are those that intersect at a right angle (90 degrees). If two lines in two-dimensional Euclidean space do not intersect, they are said to be parallel. Parallel lines in three-dimensional Euclidean space not only do not intersect, but also maintain a constant separation between points closest to each other on the two lines. Parallel lines in geometry are two lines in the same plane that are at equal distance from each other but never meet. They can be both horizontal and vertical in orientation.To learn more about parallel, refer to:
https://brainly.com/question/26961508
#SPJ13
Calculate rates (backwards)
If you pay $60 for bulk rice, at $4.00 / kg, how many kilograms can you buy?
Answer:
15kg
Step-by-step explanation:
$60 divide by $4 kg
60/4=15
Find the perimeter of ALMN. Round your answer to the nearest tenth if necessary.
Answer:
148
Step-by-step explanation:
The triangle are similar because the angle measurements are the same.
180-51-34 = 95
180-95-51 = 34
If we match up the corresponding sides we see that the side with 45 corresponds to the side with 36. Now we need to find the scale factor.
Let s = the scale factor
45s = 36 Divide both sides by 45
s = .8
This means that the corresponding length of the triangle on the right is .8 of the triangle on the left.
The corresponding side to x is 79, so 79 x .8 = 63.2. Now that we know the three sides we can add them together to find the perimeter.
63.2 + 36 + 48.8 = 148
Answer:
Perimeter = 147.9
hope this helps!
simplify the expression (0.25 to the power of 3)5 using a single whole-number exponent help me
Using exponent properties, we can rewrite the expression using a single whole-number exponent as:
(0.25³)⁵ = 0.25¹⁵
How to simplify the given expression?Here we have the numerical expression:
(0.25³)⁵
Here we need to use the exponent property:
(xᵃ)ᵇ = xᵃ*ᵇ
Using that in our expression, we will get:
(0.25³)⁵ = 0.25³*⁵ = 0.25¹⁵
So we already have a single whole-number exponent, we can also rewrite:
0.25¹⁵ = (1/4)¹⁵
Learn more about exponents:
https://brainly.com/question/11975096
#SPJ1
A contractor purchases 7 dozen pairs of padded work gloves for $99.96 . She incorrectly calculates the unit price as $14.28
per pair for the expense report. What is the correct unit price? What is the error?
The cost or unit price for purchasing each pair of work gloves is $1.19.
The cost of 7 dozen pairs of padded work gloves purchased by the contractor is $99.96.
The incorrect unit price calculated by the contractor is $14.28 per pair.
Now, we know 1 dozen is equal to 12 units.
Therefore,
The number of pairs of gloves purchased = 7 × 12 = 84
As the total cost is $99.96, the cost of each pair will be:
= $99.96 ÷ 84
= $1.19
The error by the contractor was that she didn't consider the word dozen in his calculation. She simply divided the total cost by 7 to calculate the price per pair.
The unit price of purchasing each pair of work gloves is $1.19.
Learn more about unit price here:
brainly.com/question/14286952
#SPJ1
The correlation coefficient (r) between the number of volunteers x and the number of bags of trash collected y is 0.964.
What percent of the variation in the number of bags of trash collected can be explained by differences in the number of volunteers?
The correlation coefficient between the number of volunteers x and the number of bags of trash collected y, so the percentage of variation in the number of bags of trash collected is 92.92 %.
What is the Correlation coefficient?You may gauge how closely two variables are related by looking at their correlation coefficients. Pearson's correlation coefficient is the most often used of the several correlation coefficient types. Often employed in linear regression, Pearson's correlation (also known as Pearson's R) is a correlation coefficient. It's likely that you'll learn about Pearson's R first if you're just getting started in statistics. Actually, Pearson's is typically mentioned when someone mentions the correlation coefficient.
According to the question,
The correlation coefficient i.e., r between x and y is 0.964.
r = 0.964
Squaring on both sides :
r² = 0.964²
r² = 0.9292
Now, convert this into percentage form by multiplying it will 100.
⇒0.9292 × 100
= 92.92 %.
Hence, the percentage of the variation will be 92.92 %.
To get more information about the correlation coefficient :
https://brainly.com/question/15577278
#SPJ1
Which types of dilation are the given scale factors? select expansion or contraction to correctly describe the type of dilation for each given scale factor.
This question is based on dilation. Therefore, the scale factor [tex]$-\mathbf{4}$[/tex] and [tex]$\mathbf{2 . 5}$[/tex] are for expansion of flgure. And, 2/3 and -3/4 are for the contraction of flgure.
We must choose the scale factor of dilation for contraction and expansion in this question.
As we know that,
In a dilation, a scale factor is greater than 1 or less than -1 cause an expansion. It will make the figure larger.
That means, -4 is an expansion, since it is less than -1,
And 2.5 is an expansion, since it is greater than 1.
A scale factor that is greater than -1 but less than 1 cause contraction of figure. It will make the figure smaller.
This means that,
2/3 Is an expansion, slnce It is less than 1 , and -3/4 Is a contraction, slnce It is greater than -1.
Therefore, the scale factor [tex]$-\mathbf{4}$[/tex] and [tex]$\mathbf{2 . 5}$[/tex] are for expansion of flgure. And, 2/3 and -3/4 are for the contraction of flgure.
To learn more about scale factor visit:https://brainly.com/question/22312172
#SPJ4
Find the missing number so that the equation has no solutions.
2 x + 4 = – 3 x – 18 + blank x
The value of x in the equation given is x = -4.4
What is an equation?An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe a scenario.
In this case, the value will be expressed by subtracting the variables that are given in order to get the other term. This will be:
2x + 4 = -3x - 18
Collect like terms
2x + 3x = -18 - 4.
5x = -22
Divide
x = -22 / 5
x = -4.4
This illustrates the concept of equations.
Learn more about equations on
brainly.com/question/2972832
#SPJ1
graph a linear function is shown.
Which word describes the slope of the line?
O positive
O negative
O zero
O undefined
Word (C) zero describes the slope of the line of the given graph of the linear function.
What is a graph of a linear function?Function in Linear A straight line on the graph has the expression or formula y = f(x) = px + q. One independent and one dependent variable are present. X and Y are the independent and dependent variables, respectively. P is the y-intercept or constant term, and it also represents the value of the dependent variable.So, we can infer from the provided graph that its equation is:
y = -3Which is also readable as:
y = 0 × x - 5Putting it into comparison with the slope-intercept form:
y = mx + bWe will obtain a slope of 0.
Therefore, word (C) zero describes the slope of the line of the given graph of the linear function.
Know more about the graph of a linear function here:
https://brainly.com/question/27976867
#SPJ9
The correct question is given below;
graph a linear function is shown.
Which word describes the slope of the line?
A. positive
B. negative
C. zero
D. undefined
Mr jones wants to fence in a rectangular field for his horse using the 600 feet of fence he has stored in his barn. He wants to maximize the area of the field in order to give his horse the most pasture possible. Help mr jones design his field to achieve the maximum area.
Step-by-step explanation:
l = length
w = width
we know, the perimeter of our rectangle is
2×l + 2×w = 600
and that tells us
l + w = 300
l = 300 - w
the area of the rectangle is
A = l × w
so, we use the previous equation in this one :
A = (300 - w) × w = -w² + 300w
this is a quadratic equation that is opening down (negative initial factor).
so the vertex of this parabola is the maximum.
the x (or in our case w) coordinate of the vertex is
-b / 2a
a = -1
b = 300
so,
w = -300 / (2×-1) = -300/-2 = 150 ft
and l × w = 300
l = 300 - w = 300 - 150 = 150 ft.
the maximum area for 600 ft fence is a square with 150 ft side length.
