Final answer:
In this proof, we use the Addition and Simplifying properties of equality to show that if 3x-4 equals 14, then x equals 6.
Explanation:
Given: 3x-4=14
3x-4=14 >> Given
3x-4+4=14+4 >> Addition property of equality
Simplifying >> Simplifying
3x=18 >> x=6
Answer: x=6
What is the volume in cubic feet of a greenhouse that is 20 feet long, 15 ft wide, and 10 ft high?
You are adding up the quarters and dimes from your piggy bank so you can buy a new book. you have a total of 50 coins that add up to $9.80. how many quarters and how many dimes do you have?
Please pick one for each.
What is the equation of a line that is perpendicular to −x+3y=9 and passes through the point (−3, 2) ?
Tony misplaced 777 stamps from his collection. He knows that each stamp of his is worth \$0.15$0.15dollar sign, 0, point, 15 and that the total value of them is now only \$5.55$5.55dollar sign, 5, point, 55.
Write an equation to represent the value of his stamp collection in terms of the number of stamps, s, that he had originally, and find the value of s.
Tony misplaced 7 stamps
Each stamp worth = $0.15
Total value of stamp now = $5.55
Let the number of stamps be 's'
Number of stamps now = s - 7 (misplaced 7 stamps)
price (number of stamps now ) = 0.55
0.15 (s - 7) = 5.55
Divide by 0.15 on both sides
s - 7 = 37
Add 7 on both sides
s = 44
Total number of stamps originally he had = 44 stamps
What does it mean by "completing the square" and how do u do it?
Final answer:
Completing the square is a technique used to solve quadratic equations by transforming the equation into a perfect square trinomial format. It involves a series of steps to find the value(s) of the variable.
Explanation:
Completing the square is a technique used to solve quadratic equations. It involves transforming the equation into a perfect square trinomial format. Here's how you can complete the square:
Move the constant term to one side of the equation.
Take half of the coefficient of the variable term and square it.
Add the squared value to both sides of the equation.
Factor the perfect square trinomial.
Solve for the variable term by taking the square root of both sides.
Get the value(s) of the variable.
If theirs 50 questions on a test how many do you have to get wrong to get the lowest grade
As the number of people in a sample gets larger, the distribution of means
Marianne has 5/8 pound of peas. She cooks 2/3 of those peas for 5 people. If each person is served an equal amount, how much peas did each person get?
Padraig is a financial advisor. He earned a salary of $80,000 last year and sold stocks for $5,000. Which of the following types of income did Padraig have?
I earned income
II passive income
III capital gains income
a.
I and II
b.
I and III
c.
II and III
d.
III
Answer:
The answer is b. I and III
Step-by-step explanation:
Great question, it is always good to ask away and get rid of any doubts that you may be having.
To Answer this question we need to first understand what each type of income is.
Earned Income refers to the an amount of money received from the act of providing goods or services. Such Income includes Salaries, Paychecks, Sub-contracting work etc.
Passive Income is a periodic inflow of cash received with little to no effort on the part of the beneficiary.
Capital Gains Income refers to the money made on selling a certain asset above the value of purchase.
Know that we have this information we can see that Padraig has two types of incomes. Both Earned Income from his salary and Capital Gains Income from the stocks that he sold. Therefore the answer is b. I and III
I hope this answered your question. If you have any more questions feel free to ask away at Brainly.
The flu fighters competed against 40 brands in the chicken soup country battle of the bands. The top 15% will complete in the all virus state finals. How many bands will compete in the finals?
Answer: 6 brands will compete in the finals.
Step-by-step explanation:
Given : The flu fighters competed against 40 brands in the chicken soup country battle of the bands.
i.e. The total number of brands = 40
Also, the top 15% will complete in the all virus state finals.
[ We can write 15% as [tex]\dfrac{15}{100}=0.15[/tex] ]
It implies , the number of brands will compete in the finals is given by :-
[tex]0.15\times40=6[/tex]
Therefore, 6 brands will compete in the finals.
What statement correctly describes the key features of the graph of f(x) = 4(one half)x + 1 − 3?
A. Y-intercept of (0, −1), starts up on the left, gets closer to y = −3 on the right
B. Y-intercept of (0, −1), starts down on the left, gets closer to y = −3 on the right
C. Y-intercept of (0, 1), starts up on the left, gets closer to y = −3 on the right
D. Y-intercept of (0, 1), starts down on the left, gets closer to y = −3 on the right
Answer: The correct option is B.
Explanation:
The given function is,
[tex]f(x)=4(\frac{1}{2})^{(x+1)} -3[/tex]
Put x=0 to find the y-intercept.
[tex]f(x)=4(\frac{1}{2})^{(0+1)} -3[/tex]
[tex]f(x)=4(\frac{1}{2}) -3[/tex]
[tex]f(x)=2-3[/tex]
[tex]f(x)=-1[/tex]
At x=0 the value of f(x) is -1, therefore the y- intercept is (0,-1).
Since it is an exponential function in the form of,
[tex]g(x)=ma^x+n[/tex]
Where, 0<a<1, so,
[tex]f(x)\rightarrow \infty\text{ as }x\rightarrow -\infty[/tex]
[tex]f(x)\rightarrow -3\text{ as }x\rightarrow \infty[/tex]
Therefore the starts up on the left, gets closer to y = −3 on the right. So the option B is correct.
Answer: the correct answer is B
Step-by-step explanation:
Write a two column proof for the following conjecture. Statements and reasons
Given: parallelogram ABCD
Prove:
The image is a rhombus, the left side from top to bottom point is D and C. From the right side is A and B.
The amount that results when $2,000 is compounded at 8% annually over six years.
Solve the compound inequality 9x ≤ –27 or 4x ≥ 36.
Answer:
x ≤ – 3 or x ≥ 9.
Step-by-step explanation:
Given : 9x ≤ –27 or 4x ≥ 36.
To find : Solve the compound inequality.
Solution : We have given 9x ≤ –27 or 4x ≥ 36.
For 9x ≤ –27 .
On dividing both sides by 9.
x ≤ – 3.
For , 4x ≥ 36.
On dividing both sides by 4.
x ≥ 9.
We can write x ≤ – 3 or x ≥ 9.
Therefore, x ≤ – 3 or x ≥ 9.
Answer: x <_ -3 or x >_ 9
Step-by-step explanation:
How do you write 760% as a fraction, mixed number, or whole number in simplest form?
What are the coordinates of the endpoints of the midsegment for △RST that is parallel TS¯¯¯¯¯ ?
Answer:
The end points of midsegement for triangle RST are (1,3) and(4,3) which is parallel to TS.
Step-by-step explanation:
We are given that a figure of triangle RTS in which the coordinates of R(0,6) , T(2,0) and S(8,0).
We have to find the end points of midsegment for triangle RST that is parallel TS
Let AB is midsegment where A is the mid point of segment RT and B is the midpoint of segment RS of triangle RST which is parallel to the segment TS.
To find the coordinates of end point of midsegment AB using midpoint formula
Midpoint formula :[tex]x=\frac{x_1+x_2}{2}, y=\frac{y_1+y_2}{2}[/tex]
The coordinate of A
[tex]x=\frac{0+2}{2}[/tex], [tex]y=\frac{0+6}{2}[/tex]
[tex]x_1=0,x_2=2,y_1=6,y_2=0[/tex]
[tex]x=1,y=3[/tex]
The coordinates of A is (1,3).
The coordinates of mid point B
[tex]x=\frac{0+8}{2},y=\frac{0+6}{2}[/tex]
[tex]x_1=0,y_1=6,x_2=8,y_2=0[/tex]
[tex]x=4,y=3[/tex]
The coordinates of midpoint B is (4,3).
Therefore, the end points of midsegement for triangle RST are (1,3) and(4,3) which is parallel.
Ramon surveyed his friends about their favorite snacks. He found that 1/6 of his friends prefer trail mix. What is the equivalent decimal for the fraction of friends that prefer trail mix?
A. 0.16
B. 0.16 (there is a line only above the 6)
C. 0.16 (there is a line above 16)
D. 6
The equivalent decimal for 1/6 which represents the fraction preferred by Ramon's friend is: B. [tex]\mathbf{0.1\overline{6}}[/tex]
Note the following about recurring decimal:
Recurring decimals are decimal numbers having one or more digits that repeat forever.The digit or digits that repeat forever in a decimal number can be denoted by drawing a line over the repeating digits.Thus:
The decimal equivalent of 1/6 = 0.16666..
6 is a repeating digits in the decimal number.
A line would be drawn above only 6 as:
[tex]\mathbf{0.1\overline{6}}[/tex]
In summary, the equivalent decimal for 1/6 which represents the fraction preferred by Ramon's friend is: B. [tex]\mathbf{0.1\overline{6}}[/tex]
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A(n) ____ consists of equations that state what a value is for one or more base cases and one or more recursive cases.
Solve the equation for x. Round your answer to the nearest hundredth.
0.63 = log x
The value of x is:
4.27
Step-by-step explanation:
We have to solve:
logx=0.63
Taking antilog on both sides,we get
x= [tex]10^{0.63}[/tex]
⇒ x=4.2657
Hence, the value of x is:
4.27
The sum of two consecutive even numbers is 38. what is the larger number?
Students were asked to choose their favorite cafeteria lunch. The results were: pizza, chicken, chicken, taco, taco, pizza, taco, taco, taco, pizza, pizza, burger, burger, pizza and pizza. Which category had the greatest frequency?
Circle oh has a circumference of approximately 250 pi feet what is the approximate length of the diameter
Write the quadratic equation whose roots are −6 and 2 , and whose leading coefficient is 5 . (use the letter x to represent the variable.)
Part 1: Mr. Nicholson accepts a job that pays an annual salary of $60,000. In his employment contract, he is given the option of choosing a) an annual raise of $3,500 or b) an annual raise of 5% of his current salary.
Procedures:
1. Use the provided information to identify each of Mr. Nicholson's earning opportunities as arithmetic or geometric. For each opportunity, include all the common difference or ratio.
2. Model each of Mr. Nicholson's salary options with a recursive model that includes his potential earnings for the first three years of employment.
a. $60,000 salary with an annual raise of $3,500
b. $60,000 salary with an annual raise of 5% of his current salary
3. Suppose Mr. Nicholson plans on working for his new employer for at least 9 years. use each of the recursive models to determine Mr. Nicholson plans on working for his new employer for at least 9 years. Use each of the recursive models to determine Mr. Nicho
Answer:
See belowStep-by-step explanation:
1. Arithmetic: Add 3,500
The annual raise of 3,500 means add 3,500 to the previous year's salary
60,000 + 3,500 = 63,500
63,500 + 3,500 = 67,000
67,000 + 3,500 = 70,500
70,500 + 3,500 = 74,000
74,000 + 3,500 = 77,500
Geometric: Multiply by 1.05
The annual raise by 5% of his current salary means multiply by 1.05.
60,000 x 1.05 = 63,000
63,000 x 1.05 = 66,150
66,150 x 1.05 = 69,457.50
69,457.50 x 1.05 = 72,930.38 rounded
72,930.375 x 1.05 = 76,576.89
The first sequence is arithmetic because we add the same number (3,500) to the preceding term. The second sequence is geometric because we multiply the preceding term by the same number always (1.05.)
2a. Arithmetic - New salary is $3,500 greater each year than last year's salary
S = 60,000 + 3500(n-1)
Geometric - New salary is 5% more each year than last year's salary
60,000 + (1.05)^(n-1)
2b. Arithmetic Earnings over 3 years
60,000 + 63,500 + 67,000 = 190,500
Geometric Earnings over 3 years
60,000 + 63,000 + 66,150 = 189,150
There is a 1,000 dollar difference. In this case, the arithmetic increase of 3,500 dollars would be better for Mr. Nicholson. 1,000 dollars may or may not be considered a big difference. In my opinion, I'd say there is a slight difference between the two
3.Arithmetic
a(9) = 3,500 + a(9-1)
a(9) = 3,500 + 89,000
a(9) = 92,500
Geometric
a(9) = 1.05 x a(9-1)
a(9) = 1.05 x 84,425.90
a(9) = 88,647.20
4. In this case, both the 3 year and 9 year time frames favor the arithmetic increase of $3,500. At 3 years, he would have 190,500 compared to the geometric salary of 189,150. However, this is a small difference. If he is going to be at the company for 9 years, then definitely he should choose the first opportunity. 92,500 is significantly more money than 88,647.20. So, longer time frames only make the first opportunity, which is better to begin with, shine even more.
I'm always happy to help :)
The problem analyses two salary options: a regular increase (arithmetic sequence) and a percentage increase (geometric sequence). It involves using recursive models to calculate potential earnings over a specified period. Over the long term, the geometric sequence provides a greater total income.
Explanation:The subject is about Mr. Nicholson's two different salary options. An arithmetic sequence series represents option a) where Mr. Nicholson's salary increases by a steady $3,500 per year. The difference, or increase, remains constant.
On the other hand, option b) represents a geometric sequence where Mr. Nicholson's salary increases by 5% of his current salary each year. The ratio, or multiplier remains constant at 1.05 (current salary * 5%).
To calculate his earnings for the first three years using the recursive model: Option a) Year 1: $60,000 Year 2: 60,000 + 3,500 = $63,500, Year 3: 63,500 + 3,500 = $67,000. Option b) Year 1: $60,000, Year 2: 60,000 * 1.05 = $63,000, Year 3: 63,000 * 1.05 = $66,150.
For a period of 9 years, continually apply the recursive model for each year. It becomes apparent that with the geometric sequence (option b), the amount of raise will increase per year because it is based on a percentage of his increasing salary, providing a higher total over time compared to the arithmetic sequence (option a).
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an angle is double its complement. find the angle and the complement
Answer:
60⁰
Step-by-step explanation:
Angke = x
Complement = 90 - x
Given:
x = 2 (90 - x)
x = 180 - 2x
3x = 180
x = 60⁰
Complement = 30⁰
Find the taylor polynomial of degree three for the function x^0.2 about the point a=7. (your answers should include the variable x when appropriate.)
The larger of two numbers is 2 more than four times the smaller. Their sum is 67. Find the numbers.
The numbers are 13 and 54
What is Linear Equation?
A linear equation is an algebraic equation of the form y = m x + b involving only a constant and a first-order linear term, where m is the slope and b is the y-intercept.
Given data ,
Let the two numbers be x and y , where the smaller number is x and larger number is y
Larger is 2 more than four times the smaller is expressed as
y = 2 + 4 x , be equation 1
The sum of two numbers is expressed as
x + y = 67 , be equation 2
Now we have two equations with two unknown variables
To find x and y , we substitute the value of y in equation 1
y = 67 - x
Therefore ,
67 - x = 2 + 4 x
5 x = 65
Dividing by 5 on both sides , we get
x = 13
Substituting the value of x in equation 2 , we get
y = 67 - 13
y = 54
Hence , the numbers are 13 and 54
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Raj is writing 3/2000 as a percent. Find his mistake and correct it.
3/2000 = 0.0015 = 15%
The percentage of the given fraction is 0.15%. Raj has done the mistake in his calculation instead of multiplying 100 he multiplied 1000.
Given that, 3/2000.
What is percentage?Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
Now, percentage = 3/2000 × 100
= 0.0015 × 100
= 0.15%
The percentage of the given fraction is 0.15%. Raj has done the mistake in his calculation instead of multiplying 100 he multiplied 1000.
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For how many hours did edison's best light bulb stay lit?