Answer:
b = 5
Step-by-step explanation:
Add 8b to both sides :
2+6b = 5b+7
Subtract 5b from both sides :
2+b = 7
Subtract 2 from both sides :
b = 5
Let's check :
-8(5) + 2 +6(5) = -3(5) + 7
-40 + 2 + 30 = -15 + 7
-38 + 30 = -8
-8 = -8
Correct
Hope this helped and have a good day
Answer:
b = 5
Step-by-step explanation:
to solve this you must first combine like terms
-8b + 2 + 6b = -3b + 7
combine (add) -8b and 6b
that makes -2b
-2b + 2 = -3b + 7
now add 3b to both sides to put b on one side
-2b + 2 + 3b = -3b + 3b + 7
b + 2 = 7
now subtract 2 to both side
b + 2 - 2 = 7 - 2
b = 5
that is your answer
Select the correct answer. Which statement accurately describes the difference between short-term and long-term capital gains in terms of taxes? A. Long-term capital gains are from investments that have been held for more than one year and are taxed at a lower rate than short-term capital gains. B. Long-term capital gains are from investments that have been held for at least six months and are taxed at a lower rate than short-term capital gains. C. Long-term capital gains are from investments that have been held for more than one year and are taxed at a higher rate than short-term capital gains. D. Long-term capital gains are from investments that have been held for at least six months and are taxed at a higher rate than short-term capital gains.
The statement that accurately describes the difference between short-term and long-term capital gains in terms of taxes is A. Long-term capital gains are from investments that have been held for more than one year and are taxed at a lower rate than short-term capital gains.
What is a capital gains tax?A capital gains tax is a tax levied on profits made from the sale of a non-inventory asset. Capital gains from the sale of stocks, bonds, precious metals, real estate, and property are the most common.
Short-term capital gains are profits made from selling assets held for a year or less. Long-term capital gains, on the other hand, are gains from assets held for more than a year.
In conclusion, based on the information illustrated, the correct option is A.
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Riley wants to find the smallest of the fractions One-sixth, Eleven-twelfths, Five-sixths, and Ten-twelfths. She uses 0 and 1 as benchmarks. Which fraction is closest to 0?
Answer: 1/6
Step-by-step explanation: Make all of the denominators the same. The least common multiple of 6 and 12 is 12. 1/6 gets multiplied by 2/2 to the equivalent fraction 2/12. 11/12 stays the same. 5/6 is multiplied by 2/2 to get 10/12. 10/12 stays the same. 1/6 is the smallest fraction so it is the closest to 0.
A solution contains 7% salt. How much water should be added to 30 ounces of this solution to make a 5% solution?
12 ounces of water.
Step-by-step explanation:1. Set the initial values.Total mass of the solution: 30 ounces.
Total mass of salt (solute): (30*0.07)= 2.1 ounces.
Total mass of water (solvent): (30*0.93) 27.9 ounces.
2. Find an equation that relates amount of water and percentage of salt.
Since we know that the amount of salt is 2.1 ounces, and it has to remain constant, we have to create a function such that the variable is the amount of water and it gives us the percentage of solution we are looking for. The function should look like this:
[tex]\frac{2.1}{x} =0.05[/tex]; where x is the mass of the water in the solution.
Side note: The number "0.05" is 5% converted into a decimal.
3. Solve the equation for x.[tex]\frac{2.1}{x} =0.05\\ \\\frac{x}{2.1} =\frac{1}{0.05} \\ \\x=\frac{2.1}{0.05} \\ \\x=42[/tex]
42 would be the total amount of ounces the solution should have in order to be a 5% solution. Therefore, 12 ounces (42-30) have to be added.
4. Conclude.12 ounces of water have to be added to this solution in order to make it a 5% solution, where 2.1 ounces is salt and 39.9 is water.
Which set of real numbers includes positive integers but not negative integers or zero?
A set of real numbers which includes positive integers but no negative integers or zero is set of natural numbers.
What are Real numbers?
The set of real numbers is represented by the letter R.
Every number (except complex numbers) is contained in the set of real numbers. For example: 2, -8, 33/5, -1/5, 0, etc.
What are Integers?
The set of integers is represented by the letter Z.
An integer is any number in the infinite set, Z = (..., -3, -2, -1, 0, 1, 2, 3, ...}
Integers can further be divided into
positive integers i.e. 2, 6, 3456, etc.zeronegative integers i.e. -4, -17, -57385, etc.What are Natural numbers?
The set of natural numbers is represented by the letter N.
A natural number is a positive integer.
N = { 1, 2, 3, 4, ... }
According to the given question:-
Set of real numbers comprises of Rational numbers, irrational numbers, integers, whole numbers, etc.
Hence a set of real numbers which includes positive integers but no negative integers or zero is set of natural numbers i.e.
N = { 1, 2, 3, 4, ... }
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SOMEONE HELP ASAP PLEASE!!!!! Allie deposited $5,000.00 into a new savings account that earns 11% interest compounded
monthly. How long will it take for the balance to grow to $6,407.00?
Round your answer to the nearest month.
The time taken for the balance to grow is 2.3 years.
What is compound interest?
Compound interest is the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.
"Interest on interest,
Given, compound interest =6.407
principal = 5,000
rate = 11%
to find the time
we know compound interest = principle(1+rate)^t
6407= 5000(1+11/100)^t
6407/5000= (1.11)^t
1.28 = (1.11)^t
taking log
log (1.28)= log(1.11)^t
0.24/0.104 =t
t = 2.3
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Kaleigh paid $37.45 for a calculator, after-tax, and the tax rate is 7%. What was the original cost of the calculator?
Step-by-step explanation:
that means that
$37.45 = 107%
as the price was 100% base price + 7% tax.
1% = 107%/107
100% = 1% × 100 = 107% × 100 / 107
so, the basic price (the "original cost") is
37.45 × 100/107 = $35.00
help me please so i can pass my semester
-1/3v = -7 how do i solve this equation?
Answer: v=2.33333333333333.........
Step-by-step explanation: What you would want to do is divide both sides by -1/3 and that would get you v=2.333333.......
Write the word sentence as an equation. Then solve. The sum of a number y and −3 is −8. Equation: Solution: y=
Considering the definition of an equation and the way to solve it, the equation is y +(-3)=-8 and the solution is -5.
Definition of equationAn equation is an algebraic equality in which letters appear with unknown value.
In an equation appears:
The members, which are each of the expressions that appear on both sides of the equal sign The terms, which are the addends that form the members of an equation.The solution of a equation means determining the value that satisfies it. In this way, by changing the unknown to the solution, the equality must be true. To solve an equation, keep in mind:
When a value that is adding, when passing to the other member of the equation, it will subtract.If a value you are subtracting goes to the other side of the equation by adding.When a value you are dividing goes to another side of the equation, it will multiply whatever is on the other side.If a value is multiplying it passes to the other side of the equation, it will pass by dividing everything on the other side.Equation and solution in this caseBeing "y" a number, and knowing that sum of a number and -3 is -8, the equation in this case is:
y + (-3)= -8
Solving:
y -3= -8
y= -8 +3
y= -5
Finally, the number "y" is -5.
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19.)x+ tan (xy) = 0
The value of y is, [tex]y = \frac{tan^-^1(-x) + \pi n}{x}[/tex].
What is tangent function?
One of the primary six trigonometric functions, the tangent function is typically expressed as tan x. When considering the angle in a right-angled triangle, it is the ratio of the opposite side to the adjacent side.
Consider, the given function
x + tan(xy) = 0
Subtract x from both sides,
x + tan(xy) - x = -x
tan(xy) = -x
Apply tan inverse on both sides,
[tex]xy = tan^-^1(-x) + n\pi[/tex] (Tangent function is a periodic function)
Divide both sides by x,
[tex]y = \frac{tan^-^1(-x)}{x} + \frac{n\pi }{x}[/tex], x ≠ 0
Hence, the value of y is, y = [tex]y = \frac{tan^-^1(-x)}{x} + \frac{n\pi }{x}[/tex].
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Identities and properties of logarithms
[tex](2a^7b^5\cdot 3ab^8)^2\implies \left( 2^2 a^{(7)(2)} b^{(5)(2)} \cdot 3^2 a^2 b^{(8)(2)}\right)\implies 4a^{14}b^{10}\cdot 9a^2b^{16} \\\\\\ (4)(9)a^{14}a^2b^{10} b^{16}\implies 36a^{14+2}b^{10+16}\implies 36a^{16}b^{26}[/tex]
6.) One clothing Store has a dress for $6.20
and a belt for $3.50. Customers
buy 3 dresses for $15.20. How much
would be saved by buying 3 dresses
Than by buying per piece?
The regression equation for 2 variables is y = -2.6 x + 10 If the value of R2 is 0.810, what is the value of R?
If the value of R² in the regression equation is 0.810, the value of R is 0.9
How to determine the value of r?From the question, we have the following parameters that can be used in our computation:
Regression equation: y = -2.6x + 10
Value of R2 = 0.810
Rewrite the above parameters properly
So, we have the following representation
y = -2.6x + 10
R² = 0.810
The variable r² represents the coefficient of determination
Recall that
R² = 0.810
This gives
r² = 0.810
Take the square roots of both sides
r = 0.9
Hence, the value of r is 0.9
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A picosecond is one trillionth of a second. If one trillionth = 1 × 10 − 12, how many picoseconds are there in 6 minutes?
The picoseconds that are there in 6 minutes is 3.6 × 10^14.
What is an exponent?An exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number.
In this case, picosecond is one trillionth of a second. If one trillionth = 1 × 10^12
The seconds in 6 minutes will be:
= 60 × 6
= 360 seconds
= 3.6 × 10^2
The picoseconds in 6 minutes will be:
= 1 × 10^12 × 3.6 × 10^2
= 3.6 × 10^14
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What is the range of f(x)=−3x−1?
Answer:
(−∞,1/3)∪(1/3,∞),{yly≠1/3}
Step-by-step explanation:
For each ordered pair, determine whether it is a solution to the system of equations.
Answer:
no, no, yes, yes
Step-by-step explanation:
You want to know which of the ordered pairs are solutions to the given system of equations: 6x -3y = 9, y = 2x -3.
GraphThe attached graph shows that the two equations describe the same line. The given points are plotted on the same graph. The ones on the line are solutions.
(4, -5) . . . not a solution
(-1, 8) . . . not a solution
(7, 11) is a solution
(0, -3) is a solution
A resort has 380 rooms with space for 6 people. Estimate the greatest number of people who could be in these rooms at the same time. Explain your thinking to a friend or family member.
Using the multiplication operation, the greatest number of people who could be in the 380 rooms with space for 6 persons at the same time is 2,280.
What is multiplication operation?Multiplication operation is one of the basic mathematical operations, including subtraction, addition, and division.
A multiplication operation involves applying the multiplier to the multiplicand to result in a product.
The total number of rooms in the resort = 380
The number of people per room = 6
380 x 6 = 2,280
Thus, by multiplication, if 6 persons occupy each of the 380 rooms, the resort will have 2,280 persons at a time.
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5. At PrintAll copying, a new copying machine can produce five more than twice the number of copies per hour of the old copy machine. If the new machine produces 205 copies per hour, how many copies can the old machine produce? Show the equation you used to determine the answers.
6. A recipe calls for 2 cups of milk for every 6 1/4 cups of flour. If you increase the flour to 43 3/4 cups, how many cups of milk will you use?
Step-by-step explanation:
5.
xnew = 205 = 2×xold + 5
200 = 2×xold
xold = 100
the old city machine can produce 100 copies per hour.
6.
2 cups of milk relate to 6 1/4 cups of flour.
such recipes represent a direct dependency of one variable on the other. one variable is always the other variable multiplied by a constant factor.
m = cups of milk
f = cups of flour
m = n×f
2 = n×(6 1/4) = n×(6×4 + 1)/4 = n×25/4
8 = 25n
n = 8/25
now, f = 43 3/4 = (43×4 + 3)/4 = 175/4
so,
m = 8/25 × 175/4 = (8×175)/(25×4) = 2×7 = 14
you will need 14 cups of milk.
plot 5/3 and its opposite on the number line
The numbers are plotted in the attached graph.
What is a number line?A number line is a representation of real numbers in the form of a graded straight line.
Note that 5/3 is approximately equal to 1.7.
Similarly, -5/3 is approximately equal to -1.7.
Now, use the number line to mark the points -1.7 and 1.7, the numbers lie near -2 and 2 respectively.
The numbers are plotted in the attached graph.
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A bicycle with 20 -inch diameter wheels is traveling at 13 mi/h. How many revolutions per minute do the wheels make?
The revolution per minute done by the wheel of a bicycle is 16.9 rev/min.
What is Velocity?Velocity is the rate at which a moving object's direction changes as perceived from a certain vantage point and measured by a particular unit of time. Kinematics, the area of special relativity that investigates how bodies move, starts with the fundamental idea of speed.
In order to be explained, the scientific vector quantity known as velocity needs to have both a magnitude and a direction.
As per the given information in the question,
Diameter of wheel = 20 inch
Radius, r = 10 inch
The velocity of the bicycle, v = 13 mi/h.
Revolution, R = v²/r
R = 13²/10
R = 16.9 rev/min
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How do I solve this question
Answer:
the answer is down there
If four people equally share a 1/2 page to 3/4page.what fraction of the page in the photograph
The fraction of page in the photograph is 3/32.
What are fractions?Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.Proper fractions are those in which the numerator value is less than the denominator value. as in 7/9 and 8/10. Improper Fraction - A fraction is deemed improper if the numerator value exceeds the denominator value. Example: 6/5 and 11/10.So, the fraction of the page in the photograph:
We know that,
The fraction of the page is 1/2.4 people share as 3/4.Now, calculate as follows:
(1/2 ÷ 4) × 3/41/2 × 1/4 × 3/41/8 × 3/43/32Therefore, the fraction of page in the photograph is 3/32.
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Answer:
=3/32
Step-by-step explanation:
(1/2÷4)*3/4
1/2*1/4*3/4
1/8*3/4
There-For The Answer Is:
=3/32
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Find all x ∈ R that are solutions to this equation:
0 = ( 1- X- X^2-...) (2- X- X^2-...)
The solution of the geometric equation is x = 1/2 or x = 1
What is an equation?An equation is a mathematical expression that shows the relationship between variables.
What is a geometic series?A geometric series is the sum of a geometric sequence.
How to find the solution to the equation?Since the equation 0 = ( 1 - X - X²-...) (2 - X - X²-...). To solve this, let the series x + x² + ... = p
So, 0 = ( 1 - X - X²-...) (2 - X - X²-...).
0 = (1 - [X + X²+...) (2 - [X + X²+...).
Substitute x + x² + ... = p. So,
0 = (1 - [X + X²+...) (2 - [X + X²+...).
0 = (1 - p)(2 - p).
So, (1 - p) = 0 or (2 - p) = 0
p = 1 or p = 2
Since x + x² + ... = p, the left side of the equation is the sum to infinity of a geometric series.
What is the sum to infinity of a geometric series?The sum to infinity of the geometric series is given by
S = a/(1 - r) where
a = first term and r = common ratioFor the given series,
a = x and r = xSo, S = a/(1 - r)
= x/(1 - x)
Since S = p, we have that
x/(1 - x) = 1 or x/(1 - x) = 2
So, x = 1 - x or x = 2 - x
x + x = 1 or x + x = 2
2x = 1 or 2x = 2
x = 1/2 or x = 2/2
x = 1/2 or x = 1
So, the solution is x = 1/2 or x = 1
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PLEASE HELP!!!
Dianelys accepted a new job at a company with a contract guaranteeing annual raises. In the first year, Dianelys' salary will be $40000, and she will get a raise of $2500 every year. Make a table of values and then write an equation for S,S, in terms of n,n, representing Dianelys' salary after working nn years for the company.
Number of Years at the Company Dianelys' Salary (Dollars)
00 40000\hspace{3px}\color{green}{\checkmark}40000
11 42500\hspace{3px}\color{green}{\checkmark}42500✓42500
22 45000\hspace{3px}\color{green}{\checkmark}45000✓45000
33 47500\hspace{3px}\color{green}{\checkmark}47500✓
1. The table of values for Dianely's salary can be represented for 4 years as follows:
Year Salary
1 $40,000
2 $42,500
3 $45,000
4 $47,500
2. The equation that models Dianely's salary after n years is S = 40,000 + 2,500n.
What is an equation?An equation is a mathematical statement stating that two mathematical expressions are equivalent or equal.
For instance, given the number of years, one can claim that Dianely's salary will be a given amount based on the above equation.
Equations involve variables, numbers, and the use of the equation sign (=) with some mathematical operands.
Initial salary = $40,000
Salary raise per year = $2,500
Disney's salary after n years in equation form, S = 40,000 + 2,500n.
Table of Values for Dianely's Salary:
Year Salary
1 $40,000
2 $42,500 (40,000 + 2,500)
3 $45,000 (42,500 + 2,500)
4 $47,500 (45,000 + 2,500)
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Find the perimeter of the quadrilateral. If x=2, the perimeter is (blank) inches.
Answer:
the perimeter is 129 inches
Step-by-step explanation:
4x² + 8x + 3x² - 5x + 20 + 7x + 30 + 31 =
= 7x² + 10x + 81
x = 2
= 7(2²) + 10(2) + 81
= 7(4) + 20 + 81
= 28 + 101
= 129
Answer: 129 in.
To purchase $12,200 worth of restaurant equipment for her business, Linda made a down payment of $1600 and took out a business loan for the rest. After 3
years of paying monthly payments of $322.48, she finally paid off the loan.
(a) What was the total amount Linda ended up paying for the equipment
(including the down payment and monthly payments)?
$0
(b) How much interest did Linda pay on the loan?
$0
Step-by-step explanation:
To purchase $12,200 worth of restaurant equipment for her business, Linda made a down payment of $1600 and took out a business loan for the rest. After 3 years of paying monthly payments of $322.48, she finally paid off the loan.
(a) What was the total amount Linda ended up paying for the equipment
(including the down payment and monthly payments)?
How much on loan:
12,200 - 1,600 = $10,600 loan amount
How much paid on loan:
$322.48 * 3 years * 12 months = $11,608.28 amount paid on loan
Total paid:
= loan amount + amount paid on loan
$10,600 + $$11,608.28
= $22,208.28 paid overall
________________________________________
(b) How much interest did Linda pay on the loan?
= loan amount - amount paid on loan
= $11,608.28 - $10,600
= $1,009.28 paid in interest
In one season a basketball player made 95% of her free throws. How many free throws did she attempt if she made 114 free throws?
Answer:
120 free throw attempts
Step-by-step explanation:
[tex]95\%=0.95[/tex]
[tex]0.95x=114[/tex]
[tex]x=\frac{114}{0.95}[/tex]
[tex]x=120[/tex]
Consider the equation and the following ordered pairs: (−3,y) and (x,2).
y=−3x−1
Step 1 of 2 : Compute the missing x and y values so that each ordered pair will satisfy the given equation.
x y
row 1−3 Answer
row 2 Answer
2
Answer:
Step-by-step explanation:
step 1 of 2:
We got pairs: (-3, y) and (x, 2), to compute the missing x and y values, we plugin the number into the equation.
(-3, y)
y = -3x - 1
y = -3(-3) - 1
y = 9 - 1
y = 8
So we solve this pair as (-3, 8).
(x, 2)
y = -3x - 1
2 = -3x - 1
3 = -3x
x = -1
So we solve this pair as (-1, 2).
Sorry that I cannot see the following questions.
Identify the values of the variables. Give your answers in simplest radical form. Please help!
The values of the variables as represented in the right triangle are; (8√15)/3 and s = (4√15)/3.
What are the values of the variables in the given task content?It follows from the task content that the values of the variables in the right triangle are to be determined.
It follows from trigonometric ratios that;
Sin (∆) = opposite / hypothenuse
Cos (∆) = adjacent / hypothenuse
Tan (∆) = opposite / adjacent
It therefore follows from the attached image that;
Sin (60) = 4√5 ÷ p
p = 4√5 ÷ √3/2
p = (8√15)/3.
Also;
Tan (60) = 4√5 ÷ s
s = 4√5 ÷ √3
s = (4√15)/3
Therefore, the value of the variables are; p = (8√15)/3 and s = (4√15)/3.
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(31x²y)/x^5y
can be written as a x x^b times y^c where:
a=
b=
c =
The value of a, and c is 1, -3, and 0;, using the factorization of factors.
What is factorization of expressions?
To factorize an algebraic statement, we first identify the terms' greatest common factors and then arrange the terms into groups in accordance with those groups. In plain English, factorization is the process through which an algebraic statement gets expanded in the opposite direction.
Not every term may share a factor in some algebraic formulas. For instance, have a look at the algebraic formula 12a + n -na - 12. There is no specific factor that unites the terms in this statement, yet the first and last terms share a factor of 12. The common factor between the second and third terms is n. Consequently, the terms can be rearranged as follows:
12a + n - na - 12= 12a - 12 + n - an
12a - 12 - a plus n = 12(a - 1) -n (a -1)
Following regrouping, each term's common component may be shown to be (a-1): 12a + n -na - 12=(a-1) (12 – n)
In the given question,
The expression is:
[tex]\frac{31x^{2}y}{x^{5}y}[/tex]
and after simplifying the expression, we get:
[tex]\frac{31}{x^{3}}[/tex]
So, Now comparing the equation, with a[tex]x^{b}[/tex]×[tex]y^{c}[/tex], we get;
b = -3;
c = 0;
a = 1;
Hence, The value of a, and c is 1, -3, and 0;
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