Answer:
(a-6)(a-1)(a+6)
Final answer:
The lowest common denominator for the fractions [tex]6/(a^2-7a+6)[/tex] and [tex]3/(a^2-36)[/tex] is (a-6)(a-1)(a+6).
Explanation:
To find the lowest common denominator for the fractions [tex]6/(a^2-7a+6)[/tex] and [tex]3/(a^2-36),[/tex] we need to determine the least common multiple of the denominators.
The denominator of the first fraction can be factored as (a-6)(a-1) and the denominator of the second fraction can be factored as (a-6)(a+6).
The common factors are (a-6) and (a-1)(a+6).
Therefore, the lowest common denominator is (a-6)(a-1)(a+6).
Solve by elimination
-3x+2y=10
-2x-y=-5
If you only have a 3-quart pitcher and a 5-quart pitcher, how can you measure exactly 1 quart?
Lorena deposited $2372 into an account that earns 4.5% interest which is compounded once a year. how much money will lorena have in the account in 20 years?
Answer:
5720.59
Step-by-step explanation:
I know it's correct
Explain why the data can be modeled by a linear equation.
Consider the function represented by the equation 1/2j+1/4k=3. Which shows the equation written in function notation with j as the independent variable?
F(j)=-2j+12
F(j)=-1/2j+6
F(k)=-2k+12
F(k)=-1/2k+6
Which set is equivalent to (a u b) n c
What is the slope of a line that passes through (���4,���13) and (19,11)?
What is the common difference d of the sequence? −15, −4, 7, 18, 29, ...
Answer:
The common difference is [tex]11[/tex]
Step-by-step explanation:
we know that
In an Arithmetic Sequence the difference between consecutive terms is a constant called the common difference
so
In this problem we have
[tex]-15,-4,7,18,29,...[/tex]
Let
[tex]a1=-15\ a2=-4\ a3=7\ a4=18\ a5=29[/tex]
Find the difference between consecutive terms
[tex]a5-a4=29-18=11[/tex]
[tex]a4-a3=18-7=11[/tex]
[tex]a3-a2=7-(-4)=11[/tex]
[tex]a2-a1=-4-(-15)=11[/tex]
therefore
The sequence is an Arithmetic Sequence
The common difference is [tex]11[/tex]
62% of what is 89.3?
To find 62% of what number equals 89.3, divide 89.3 by the decimal form of 62%, which is 0.62, to get 144.03 (rounded to two decimal places).
Explanation:The student's question '62% of what is 89.3?' is asking for the calculation of a base amount from a known percentage and a known result of that percentage. To find the answer, we divide the known result by the percentage in decimal form.
The equation we use is: Base = Percentage Result ÷ Decimal Percentage
Firstly, we convert 62% into decimal by dividing by 100, which equals 0.62. Then we divide the known result, 89.3, by 0.62:
Base = 89.3 ÷ 0.62 = 144.03225806451613
So, 62% of 144.03 (rounded to two decimal places) is 89.3.
Final answer:
The student's question involves finding the original whole given a part and its percentage. The calculation shows that 62% of 144.03 is 89.3.
Explanation:
The student is asking how to find the original whole when given a percentage and the corresponding part of that whole. To find the whole when you know a percentage of it and the actual amount that percentage represents, you can use the formula:
Whole = Part / (Percentage / 100). In this case, the part is 89.3 and the percentage is 62%. So, you calculate the whole by dividing 89.3 by 0.62 (which is 62% converted to a decimal by dividing by 100).
Here’s the step-by-step calculation:
Convert the percentage to a decimal: 62% = 0.62.Divide the part by the decimal: 89.3 / 0.62 = 144.03.Therefore, 62% of 144.03 is equal to 89.3.
Simplify (7 +i) – (6 – 2i)
–2
1 – i
1 + 3i
4 ...?
If the perimeter of a square is 16”, what is the length of each side of the square?
There are "n" delicious sweets in the bag. You know that 6 of them are orange and the rest are yellow. Hannah takes a random sweet from the bag and eats it. Then she takes a second sweet from the bag and eats that one. You know that the probability that Hannah eats two of the orange sweets is 1/3. How many sweets were in the bag before Hannah ate any
does Karen say there is a 30 percent or 60 percent chance that its already raining in Mean Girls
Mary is putting money into a checking account. Let y represent the total amount of money in the account (in dollars). Let x represent the number of weeks Mary has been adding money. Suppose that x and y are related by the equation =+75030xy . Answer the questions below. Note that a change can be an increase or a decrease. For an increase, use a positive number. For a decrease, use a negative number.
What is the change per week in the amount of the account?
what was the starting amount money in the account?
The starting amount would be the 750, because it doesn't have a variable assigned to it.
And, Change per week is 30 since it is being multiplied by the number of weeks.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Let y represent the total amount of money in the account (in dollars).
And, Let x represent the number of weeks Mary has been adding money.
Here, Suppose that x and y are related by the equation;
⇒ y = 750 + 30x
Now, Clearly for the starting amount money in the account we can put x = 0 in above equation;
⇒ y = 750 + 30 × 0
⇒ y = $750
And, The change per week in the amount of the account is 30 which is being multiplied by the number of weeks.
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how can you prove a triangle is a right triangle
To prove a triangle is a right triangle, use the Pythagorean theorem: a² + b² = c².
To prove that a triangle is a right triangle, you can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. This is expressed as: a² + b² = c², where c is the hypotenuse, and a and b are the other two sides.
Here are the steps to prove that a triangle is a right triangle:
Measure all three sides of the triangle.Identify the longest side, which will be the hypotenuse in a right triangle. Label it as c.Label the other two sides as a and b.Calculate a², b², and c².Check if the equation a² + b² = c² holds true.If the equation is correct, the triangle is a right triangle.
Additionally, you can verify it using a compass and ruler to draw precise triangles and measure the angles, although measurement errors are common. Understanding the Pythagorean theorem is crucial for these calculations.
A population of bacteria is growing according to the function below, where t is in hours. How many hours will it take for the population to grow to 1,000 bacteria? Round your answer to the nearest integer. Do not include units in your answer.
B(t) = 50 e2.5t ...?
What is the value of x in the equation 4(2x + 14) = 0?
9
7
−7
−9
Value of [tex]x[/tex] in the given equation [tex]4(2x+14)=0[/tex] is equal to [tex]-7[/tex].
What is equation?" Equation is defined as the algebraic expression which represents the relation between the variables and number using sign of equality."
According to the question,
Given equation,
[tex]4(2x+14)=0[/tex]
Simplify the given equation to get the value of [tex]x[/tex],
[tex]4 \neq 0[/tex]
Therefore,
[tex]2x+14 = 0\\\\\implies 2x = -14\\\\\implies x = -7[/tex]
Hence, value of [tex]x[/tex] in the given equation [tex]4(2x+14)=0[/tex] is equal to [tex]-7[/tex].
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The radian measure of an angle that is 25º 47' 31'' is _____.
A. .44 radians
B. 25.79 radians
C. 8.21 radians
D. .45 radians ...?
A laboratory technician needs to make a 40-liter batch of a 40% acid solution. How can the laboratory technician combine a batch of an acid solution that is pure acid with another that is 20% to get the desired concentration?
To make a 40-liter batch of a 40% acid solution, the laboratory technician can combine a batch of pure acid with another batch that is 20% acid.
Explanation:To make a 40-liter batch of a 40% acid solution, the laboratory technician can combine a batch of pure acid with another batch that is 20% acid. Here is a step-by-step process:
Let's assume the volume of the pure acid solution is x liters.The volume of the 20% acid solution needed can be calculated using the equation: (40 - x) = 0.2(x), where 40 - x is the volume of the 20% acid solution required and 0.2(x) is the volume of acid in that solution.Solving the equation, we get 40 - x = 0.2x, which simplifies to 1.2x = 40. This equation can be solved to find x, which represents the volume of the pure acid solution.Once x is found, the volume of the 20% acid solution can be calculated by subtracting x from 40.The laboratory technician can mix x liters of pure acid with (40 - x) liters of the 20% acid solution to obtain the desired concentration of 40% acid in a 40-liter batch.Therefore, the laboratory technician can combine a batch of pure acid with another batch of 20% acid to obtain a 40-liter batch of a 40% acid solution.
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What should you do to both sides of the inequality in order to solve x + (-2) > 3?
Answer:
subratct 2 from both sides
Step-by-step explanation:
i took this class
Which of the following statements are true about WaterSense toilets?
a.
WaterSense toilets prevent toilet leaks
b.
WaterSense toilets saved customers 9.3 billion gallons of water in 2008
c.
WaterSense toilets come with attached float booster
d.
WaterSense toilets use about 5-7 gallons of water per flush
Answer:
I just took the test, the answer is
B: WaterSense toilets saved customers 9.3 billion gallons of water in 2008
The only option that is true about water sense toilets is that; B: WaterSense toilets saved customers 9.3 billion gallons of water in 2008
What are water sense toilets?The WaterSense label is a label that is mostly used on toilets that are certified by an independent body to satisfy well established high performance and efficiency standards.
Now, only water-saving toilets that complete the certification process can have the WaterSense label. From research it was discovered that WaterSense toilets saved customers 9.3 billion gallons of water in 2008 and so option B is correct.
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What is the unite rate for 42 laps in 6 races?
IS MY ANSWER CORRECT? If you would like to make $1213 in 8 years, how much would you have to deposit in an account that pays simple interest of 5%?
I=1213(.05)(8) I=388.16 Interest Earned is $388.16 1213+388.16=1601.16
How many pounds are in 427.06 g?
1 gram = 2.20 × 10^-3 lb
A.
939 lb
B.
0.939 lb
C.
194.12 lb
D.
194,118 lb
The result is 0.939 lb, so the correct answer is option B.
1 gram = 2.20 × [tex]10^{-3}[/tex] lb
We can set up a multiplication to convert grams to pounds:
427.06 g × 2.20 × [tex]10^{-3}[/tex]lb/g
Carrying out the multiplication:
427.06 × 2.20 × [tex]10^{-3}[/tex]
= 0.939 lb
Thus, the amount in pounds is 0.939 lb.
The correct answer is:
B. 0.939 lb
At the snack bar, hot dogs cost $4 each and bottled water costs $2 each. In the first business hour of the day, less than $12 worth of hot dogs and water were sold. Which are reasonable solutions for this situation if x represents the number of hot dogs sold and y represents the number of bottles of water sold? Check all that apply. (–1, 5) (0, 6) (2, 1) (1, 1.5) (1, 3) (2, 2)
Answer: The answers should be ( 2, 1)
(1, 3)
What is 1.06 as a mixed number in simplest form?
suppose that f(x) = 4x+7 and g(x) =2x. what is a rule for g(f(x)? what is a rule for f(g(x))? suppose that f(x) = 4x+7 and g(x) =2x. what is a rule for g(f(x)? what is a rule for f(g(x))?
The rule for g(f(x)) is 8x + 14, and the rule for f(g(x)) is 8x + 7.
Explanation:The rule for g(f(x)) is that we first substitute f(x) into g(x), meaning we replace x in the g(x) rule with the expression for f(x). Using the given functions, g(f(x)) = g(4x + 7) = 2(4x + 7) = 8x + 14.
Similarly, the rule for f(g(x)) is that we first substitute g(x) into f(x), meaning we replace x in the f(x) rule with the expression for g(x). Using the given functions, f(g(x)) = f(2x) = 4(2x) + 7 = 8x + 7.
What is the conjugate of the square root of -15 ? ...?
3(mx)4 + 5 What is the coefficient in the expression? A) x B) 3 C) 4 Eliminate D) 5
Answer:
Step-by-step explanation:
Answer choice is B) 3
What is 0.00004 in its standard form ??
The number 0.00004 is expressed in standard form or scientific notation as [tex]4.0 \times 10^{-5}[/tex], moving the decimal 5 places to the right because the number is smaller than 1.
To express the number 0.00004 in standard form or scientific notation, we need to rewrite it so that it has one non-zero digit to the left of the decimal point. Move the decimal place to the right until you have that single non-zero digit. Count the number of places you've moved it; this number will determine the exponent of 10 in the standard form.
In this case, we move the decimal point:
Since we moved the decimal 5 places to the right, the power of 10 will be negative because the original number is less than 1.
Therefore, the standard form or scientific notation of 0.00004 is: 4 × 10⁻⁵.