B) there is a line with positive slope that is tangent to both circles. find the equation of this line, and (c) determine the points at which this tangent line touches each circle
In January 2015 the price of gas was on average $2.05 per gallon this was $1.20 cheaper than a year before what is the percent of decrease in price
The percentage decrease in a price is 37 percent.
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 "%".
Given that, in January 2015 the price of gas was on average $2.05 per gallon this was $1.20 cheaper than a year.
Cost of gas per gallon = 2.05+1.20
= $3.25
Now, Percentage decrease = (Original Price - New Price)/Original Price ×100
= (3.25-2.05)/3.25 ×100
= 1.20/3.25 ×100
= 0.3692×100
= 0.37×100
= 37%
Therefore, the percentage decrease in a price is 37 percent.
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(4x6) x 3 = 4 x (3x6)
The perimeter of a triangle is 105. the lengths of all three sides are represented by three consecutive odd integers. Find the length of the longest side
Approximately 1 million people immigrated to the U.S. from 1850 to 1900.
True
False
Which ordered pairs are solutions to the inequality x+3y≥−8?
Select each correct answer.
Answer:
A. [tex](-1,-2)[/tex]
D. [tex](-6,0)[/tex]
E. [tex](-5,-1)[/tex]
Step-by-step explanation:
We have been given an inequality [tex]x+3y\geq -8[/tex]. We are asked to find the ordered pairs that are solution to the given inequality.
Let us check each ordered pair by substituting in the given inequality.
A. [tex](-1,-2)[/tex]
[tex]-1+3(-2)\geq -8[/tex]
[tex]-1-6\geq -8[/tex]
[tex]-7\geq -8[/tex]
Since the given inequality holds true, therefore, ordered pair [tex](-1,-2)[/tex] is a solution for the inequality.
B. [tex](-16,2)[/tex]
[tex]-16+3(2)\geq -8[/tex]
[tex]-16+6\geq -8[/tex]
[tex]-10\geq -8[/tex]
Since the given inequality is not true, therefore, ordered pair [tex](-16,2)[/tex] is not solution for the inequality.
C. [tex](0,-3)[/tex]
[tex]0+3(-3)\geq -8[/tex]
[tex]0-9\geq -8[/tex]
[tex]-9\geq -8[/tex]
Since the given inequality is not true, therefore, ordered pair [tex](0,-3)[/tex] is not solution for the inequality.
D. [tex](-6,0)[/tex]
[tex]-6+3(0)\geq -8[/tex]
[tex]-6+0\geq -8[/tex]
[tex]-6\geq -8[/tex]
Since the given inequality holds true, therefore, ordered pair [tex](-6,0)[/tex] is a solution for the inequality.
E. [tex](-5,-1)[/tex]
[tex]-5+3(-1)\geq -8[/tex]
[tex]-5-3\geq -8[/tex]
[tex]-8\geq -8[/tex]
Since the given inequality holds true, therefore, ordered pair [tex](-5,-1)[/tex] is a solution for the inequality.
draw a rectangle give the length and the width to show that it has an area of 12cm make sure one side is longer than the other to show length and width
help me! need to show work!
What must be true of two rational expressions before they can be added?
A They must have common numerators.
B They must be of the same degree.
C They must have the same variables.
D The must have common denominators.
Answer:
D They must have common denominators.
Step-by-step explanation:
Rational expressions are fractions formed by two polynomials, one in the numerator and other in the denominator.
The numerator is the polynomial that is at the top of the fraction and denominator is the polynomial that is at the bottom of the fraction.
To add any fractions it is necessary that they have the same denominator, this applies to rational expressions, to add them it is required that they have the same polynomial in the denominator.
The amount of rhubarb in the original recipe is 31\2 cups. Using what you know of whole numbers and what you know of fractions, explain how you could triple that mixed number
To triple a mixed number, multiply the whole number part by 3 and triple the numerator of the fraction part. For 3 1/2, the result is 9 3/2.
To triple the mixed number 3 1/2:
Multiply the whole number by 3: 3 x 3 = 9.
For the fraction part, triple the numerator: 1 x 3 = 3. The denominator remains the same.
Therefore, tripling 3 1/2 gives 9 3/2.
Given the following functions: f(u)=u9/2 and g(x)=x10+1. Find:
f(g(x)=
f′(u)=
f′(g(x)=)
g′(x)=
(f∘g)′(x)=
The function f(g(x)) is ((x^10+1)^(9/2), the derivative f'(u) is (9/2)u^(7/2), the derivative f'(g(x)) is (9/2)(x^10+1)^(7/2), the derivative g'(x) is 10x^9, and the derivative (f ∘ g)'(x) is the product of g'(x) and f'(g(x)) which equals to 10x^9 * (9/2)(x^10+1)^(7/2).
Explanation:The functions are defined as f(u)=u9/2 whereas g(x)=x10+1.
To find f(g(x)), input g(x) into the f function. Thus, f(g(x))=((x10+1)9/2.
Next, the derivative of f(u) would be: f'(u)= (9/2)u7/2.
For f'(g(x)), replace u with g(x) in f'(u): f'(g(x))=(9/2)(x10+1)7/2.
The derivative of g(x) is: g'(x)=10x9.
Lastly, to find (f ∘ g)'(x), use the chain rule which states that (f ∘ g)'(x) = g'(x) * f'(g(x) : (f ∘ g)'(x) = 10x9 * (9/2)(x10+1)7/2.
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Complete the patterns 9430, 94.3, 9.43
What is this when you subtract 4
Sides that match up between two similar figures are called corresponding sides.
Use the diagram of two similar triangles to complete the statements below.
The person's shadow in the smaller triangle corresponds to the _________ in the larger triangle.
A. Height of the Flag Pole
B. Shadow of the Flag Pole
C. Longest side
The longest side of the large triangle corresponds to the ________ side of the small triangle.
A. Shortest
B. Vertical
C. Longest
Corresponding sides in similar figures match up. The person's shadow in the small triangle corresponds to the shadow of the Flag Pole in the large triangle. The longest side of the large triangle corresponds to the Longest side of the small triangle.
Explanation:Corresponding sides in similar figures are the sides that match up.
In the given diagram of two similar triangles, the person's shadow in the smaller triangle corresponds to the shadow of the Flag Pole in the larger triangle.
The longest side of the large triangle corresponds to the Longest side of the small triangle.
The formula f 5280m can be used to convert a measurement of f feet to an equivalent measurement of m miles. If an airplane flies at 21,120 feet above the ground, how much is that in miles?
The value of a collector’s item is expected to increase exponentially each year. The item is purchased for $500. After 2 years, the item is worth $551.25. Which equation represents y, the value of the item after x years?
y = 500(0.05)x
y = 500(1.05)x
y = 500(0.1025)x
y = 500(1.1025)x
Answer: [tex]y=500(1.05)^x[/tex]
Step-by-step explanation:
We know that the general exponential equation to find the value after x years is written as :-
[tex]y=Ab^x[/tex], where A is the initial value and b is the multiplicative rate of change and x is the time period.
Given : The initial amount of a product = $500
After 2 years, the item is worth $551.25.
Substitute A = 500, x=2 and y= 551.25 in the above equation we get
[tex]551.25=500b^2\\\\\Rightarrow\ b^2=\dfrac{551.25}{500}\\\\\Rightarrow\ b^2=1.1025\\\\\Rightarrow\ b=\sqrt{1.1025}=1.05[/tex]
Now, substitute b= 1.05, A = 500 in the general exponential equation, we get the equation represents y, the value of the item after x years as :-
[tex]y=500(1.05)^x[/tex]
For a p-type silicon in which the dopant concentration na = 5x10^18/cm^3
For a p-type silicon in which the dopant concentration N A = 5 × 10^ 18 /cm^3 , find the hole.
For a p-type silicon in which the dopant concentration NA= 5×1018/cm^3, find the hole and electron concentrations
The rise and span for a roof are shown. The pitch of a roof is the ratio of the rise to the half-span . If the rise is 8 feet and the span is 30 feet, what is the pitch in simplest form?
Write a real world situation that can be modeled by the inequality
834 + 14s > 978 - 10s. Then solve the inequality.
The inequality 834 + 14s > 978 - 10s can represent a situation involving saving and spending money over time. To solve it, you perform a series of operations to isolate variable 's', which in this case results in s > 6, indicating more than six weeks required for savings to exceed spending.
Explanation:A real world situation that can be modelled by this inequality 834 + 14s > 978 - 10s could be a scenario involving saving and spending money. Say you start with $834 and each week you save $14 (s represents the number of weeks). On the other hand, you have $978 and you spend $10 each week. You want to figure out how many weeks it will take for the amount you have from saving to be more than the amount left from spending.
Now, to solve the inequality: subtract 834 from both sides which gives 14s > 144 - 10s, then combine like terms to get 24s > 144. Finally, divide both sides by 24 to solve for s: s > 6. Therefore, it will take more than six weeks for the money you save to exceed what remains from your starting amount of $978 after spending $10 each week.
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Give your answer as a reduced proper or improper fraction 16/25 +-3/10
Which set of data has the same mode and median?
3, 4, 6, 7, 8
3, 3, 4, 5, 5
6, 7, 7, 8, 9
2, 2, 3, 4, 6
Answer:
6,7,7,8,9 both have 7 for mode and median
Step-by-step explanation:
Is the product of two mixed number less than, between,or greater than the two factors?explain
A scuba diver at a depth of −12 ft (12 ft below sea level), dives down to a coral reef that is 3.5 times the diver's original depth. What is the diver's new depth?
Answer:
The diver's new depth is -42 ft.
Step-by-step explanation:
Given : A scuba diver at a depth of -12 ft (12 ft below sea level), dives down to a coral reef that is 3.5 times the diver's original depth.
To find : What is the diver's new depth?
Solution :
A scuba diver at a depth of -12 ft.
Dives down to a coral reef that is 3.5 times the diver's original depth.
So, We have to multiply the original depth by 3.5.
i.e. [tex]d=-12\times 3.5[/tex]
[tex]d=-42[/tex]
Therefore, the diver's new depth is -42 ft.
How to find the slope???
Slope formula: y2-y1/x2-x1
= -3-1/6-0
= -4/6
= -2/3
Best of Luck!
What does academic integrity mean?
Academic integrity is essential for a fair and genuine educational experience, emphasizing honesty and accountability in all academic endeavors. It is crucial for building trust, equity, and facilitating real learning outcomes, necessitating a collective effort from the academic community to maintain these values. The widespread issue of academic dishonesty further highlights the need for strict adherence to integrity principles.
Explanation:Academic integrity is the cornerstone of a meaningful educational experience, emphasizing the value of honesty and fairness within the academic community. It involves the commitment to avoid cheating, plagiarism, and any form of deception or fraud in academic work, ensuring that all academic activities, from research to examination, are conducted in a manner that is fair, respectful, and accountable. The importance of academic integrity lies not only in the cultivation of a fair and trustworthy academic environment but also in fostering genuine learning and understanding, thereby empowering students to achieve authentic success that extends well beyond their academic careers.
Despite the challenges posed by technological advancements and digital resources, which have made cheating more accessible and harder to detect, maintaining academic integrity is crucial. It builds trust, understanding, equity, and facilitates real, meaningful learning outcomes. Faculty, administrators, and students alike bear the responsibility of upholding these principles to ensure that the academic community remains a space where fairness prevails and genuine knowledge acquisition is celebrated.
According to the International Center for Academic Integrity, a significant number of students have admitted to engaging in dishonest behaviors, which underscores the ongoing battle against academic dishonesty. Highlighting the importance of maintaining integrity, these statistics serve as a reminder of the collective effort needed to nurture an academic culture that values honesty above all.
The sum of two numbers is x. If one of the numbers is 12, what is the other ?
A factory produces 7,482 widgets per day. It ships these widgets in 2 crates. Each widget sells for $7. How much money does one crate earn?
The repeating decimal, 0.27..., is converted to the fraction 0.27..=3/x
what is the value for x in the fraction
Answer:
The value of x is 11.
Step-by-step explanation:
The given number is 0.27272727..., and it is converted to the fraction as
[tex]0.272727...=\frac{3}{x}[/tex] ..... (1)
Multiply both sides by 100.
[tex]0.272727...\times 100=\frac{3}{x}\times 100[/tex]
[tex]27.272727=\frac{300}{x}[/tex] .... (2)
Subtract equation (1) from equation (2),
[tex]27.272727-0.272727...=\frac{300}{x}-\frac{3}{x}[/tex]
[tex]27=\frac{300-3}{x}[/tex]
Multiply both sides by x.
[tex]27x=297[/tex]
Divide both sides by 27.
[tex]x=\frac{297}{27}[/tex]
[tex]x=11[/tex]
Therefore the value of x is 11.
The value of the variable "x" in the fraction 0.27... = 3/x is x = 11.
To find the value of "x" in the fraction 0.27... = 3/x, we use algebraic techniques to solve for x,
Let us represent the repeating decimal 0.27... as a variable, say y,
y = 0.27...
To eliminate the repeating decimal, we multiply both sides of equation by a power of 10. In this case, we multiply by 100 to shift decimal point two places to right,
100y = 27.27...
Now, we subtract original equation from this new equation to eliminate the repeating part:
100y - y = (27.27...) - (0.27...),
Simplifying the equation:
99y = 27
y = 27/99
The fraction 27/99 is simplified further by dividing both the numerator and the denominator by their greatest common divisor, which is 9,
y = 3/11
Therefore, the required value of "x" is 11.
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Tony buys a CD that is priced at $13.59. He has a coupon for $1.85 off. He pays with a $20 bill. Which is the best whole number estimate of how much change he gets? $8 $8.26 $9 $9.26
Answer:
I think A
Step-by-step explanation:
Carys is checking her tax bill for the last year. The tax rates were as follows: No tax of the first £11 000 of earnings. Earnings in excess of of £11 000 and up to £43 000 taxed at a rate of 20%. Earnings in excess of £43 000 and up to £150 000 taxed at a rate of 40%. Earnings over £150 000 taxed at a rate of 45%. Last year Carys, earned £45 600 before tax. How much tax did she pay in total. Show your working.
It isn't £18240 it says its wrong
Answer:
total tax is = 14685 pound
Step-by-step explanation:
Given data:
For first year -
earning is 11000 pound
for second year
income is = 43000 - 11000 = 32000 pound
tax rate = 20%
for third year
income is = 150000 - 43000 = 107000 pound
tax rate = 40%
for fourth year
income is = 158900 - 150000 = 8900 pound
tax rate = 45%
As it is given there is no tax on first year
Tax in 2nd year = 0.20 × 32000 = 6400 pound
Tax in 3rd year = 0.40 × 107000 = 42800 pound
Tax in 4th year = 0.45 × 8900 = 4005 pound