Explanation of finding the least common denominator of rational expressions.
The least common denominator of the rational expressions provided is option (d): x(x+3).
To find the LCD, first factor each denominator completely. Then, identify the unique factors and their highest powers. The LCD will be the product of these unique factors raised to their highest powers.
If the cubic function P(x) includes the points (−4, 0), (0, 0), and (2, 0), which of the following represents this function?
The function cannot be determined with the given information.
Explanation:The given points (-4, 0), (0, 0), and (2, 0) indicate that the function is a cubic function with three real roots. A cubic function is of the form P(x) = ax^3 + bx^2 + cx + d. Since the function passes through the x-axis at (-4, 0), (0, 0), and (2, 0), the roots of the cubic function are -4, 0, and 2. Therefore, the function can be written as P(x) = a(x + 4)(x - 0)(x - 2). However, since a cubic function with three real roots has an odd degree, the coefficient 'a' must be negative or positive. This means that the function can also be written as P(x) = -a(x + 4)(x - 0)(x - 2) or P(x) = a(x + 4)(x - 0)(x - 2). So, the correct representation of the function cannot be determined with the given information.
Find the markup and the selling price of the following item. Round answers to the nearest cent. A chemistry set costing $38.50, marked up 32% on cost. Markup = ? Selling price = ?
Answer:
markup, 12.32
selling price, 50.82
Step-by-step explanation:
What is the geometric mean of 6 and 13?
What is the Geometric mean a 5 and 45?
Answer: [tex]\sqrt{78}[/tex] and [tex]15[/tex]
Step-by-step explanation:
Given: (1) two numbers [tex]6[/tex] and [tex]13[/tex].
(2) two numbers [tex]5[/tex] and [tex]45[/tex].
To Find: Geometric number of numbers in [tex](1)[/tex] and [tex](2)[/tex]
Solution:
Let first number be [tex]=\text{a}[/tex]
Let second number be [tex]=\text{b}[/tex]
Geometric mean of two numbers [tex]\text{a}[/tex] and [tex]\text{b}[/tex] is
[tex]\sqrt{\text{a}\text{b}}[/tex]
Now,
[tex](1)[/tex] First number is [tex]=6[/tex]
Second number is [tex]=13[/tex]
Geometric mean of both numbers is
[tex]\sqrt{6\times13}[/tex]
[tex]\sqrt{78}[/tex]
Geometric mean is [tex]\sqrt{78}[/tex]
[tex](2)[/tex] First number is [tex]=5[/tex]
Second number is [tex]=45[/tex]
Geometric mean of both numbers is
[tex]\sqrt{5\times45}[/tex]
[tex]\sqrt{225}[/tex]
[tex]15[/tex]
Geometric mean is [tex]15[/tex]
Assume the method dosomething has been defined as follows: public static void dosomething (int[] values, int p1, int p2) { int temp = values[p1]; values[p1] = values[p2]; values[p2] = temp; } what does the method do?3
Write the equation of the line that passes through (–2, 1) and is perpendicular to the line 3x – 2y = 5.
To find the equation of a line that is perpendicular to the line 3x - 2y = 5 and passes through the point (-2, 1), we determine that the slope of the perpendicular line must be -2/3. Using the point-slope form, the equation of the desired line is y = (-2/3)x - (1/3).
Finding the Equation of a Perpendicular Line
To write the equation of a line that is perpendicular to another line, you first need to determine the slope of the original line. The given equation, 3x - 2y = 5, can be rewritten in slope-intercept form (y = mx + b) by solving for y:
3x - 2y = 5
=> -2y = -3x + 5
=> y = (3/2)x - (5/2)
The slope (m) of this line is 3/2. Perpendicular lines have slopes that are negative reciprocals of each other. Thus, the slope of the line perpendicular to the original line is -2/3.
To find the equation of the line passing through the point (-2, 1) with this slope, use the point-slope form of the equation:
y - y1 = m(x - x1)
=> y - 1 = (-2/3)(x + 2)
Simplifying, we have:
y - 1 = (-2/3)x - (4/3)
=> y = (-2/3)x - (4/3) + 1
=> y = (-2/3)x -(1/3)
This is the equation of the line that passes through (-2, 1) and is perpendicular to the line 3x - 2y = 5.
given the equation W=CE2/2, solve for C
Answer:
[tex]C=\frac{2W}{E^2}[/tex]
Step-by-step explanation:
[tex]W=\frac{CE^2}{2}[/tex]
Solve for C
To solve for C, we need to get C alone
LEts start with eliminating 2 from the denominator
Multiply the equation by 2 on both sides
[tex]2W= CE^2[/tex]
To isolate C, divide both sides by E^2
[tex]\frac{2W}{E^2} =C[/tex]
[tex]C=\frac{2W}{E^2}[/tex]
Sarah has grades of 98 and 98 on her first two test if she want to average at least 80 after her third test what must she make on that test
How to do this because I do not understand how to do it
Answer:
24.52%
Step-by-step explanation:
Choose the correct classification of x6 + 3x3 by number of terms and by degree.
Third degree polynomial
Fourth degree trinomial
Third degree binomial
Sixth degree binomial
Use the empirical rule to solve the problem. ed's monthly phone bill is normally distributed with a mean of $65 and a standard deviation of $11. what percentage of his phone bills are more than $76?
Answer:
16% of his phone bills are more than $76
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean = 65
Standard deviation = 11
What percentage of his phone bills are more than $76?
76 = 65 + 11
So 76 is one standard deviation above the mean.
By the Empirical Rule, 68% of the measures are within 1 standard deviation of the mean. The other 100-68 = 32% are more than 1 standard deviation from the mean. Since the normal probability distribution is symmetric, 16% of them are more than 1 standard deviation below the mean and 16% are more than 1 standard deviation above the mean. So
16% of his phone bills are more than $76
Evaluate the expression 9p6
Answer:
60,480
Step-by-step explanation:
I got it correct on founders edtell
Does the following equation represent growth or decay? Y=10,000(0.97)x
Given is Y = 10000·(0.97)ˣ
This is an exponential equation whose general form is y = a·bˣ
where 'a' is the initial value and 'b' is the growth or decay factor.
If value of b is greater than 1, then it is growth of population.
If value of b is lesser than 1 but greater than 0, then it is decay of population.
On comparison of the given equation with its general form, we get a = 10000, b = 0.97
So initial value is 10000.
Since value of b is 0.97 i.e. lesser than 1, so it is decay of population.
Hence, the given equation represents "Decay".
Gas costs $1.64 a gallon. Elaine spent $23.78 at the gas station.How many gallons of gas did she but?
Answer:
23.78
Step-by-step explanation:
Weight Gain after gaining 25 pounds, a person is 115 pounds lighter than double his previous weight. How much did the person weigh before gaining 25 pounds? How could I write this problem
Mr. Young has a section of his parking lot, measuring 10 yards by 12 yards, that needs to be repaved. The paving company told Mr. Young the workers complete square yards every hour. How long should it take to pave the parking lot?
subtracting/adding mixed fractions
You owe $976.34 on a credit card that has an interest rate of 10.75% APR. You pay $100.00 at the end of each month.
You place the $100.00 in a savings account that earns a 2.75% APR. What is the difference in interest between savings earned and credit card interest paid
answer: $8.52
Your brother is 13 your age. Your sister is 6 years older than your brother. Your sister is 10 years old. Write and solve an equation to find your age a.
By setting up equations using the information about your siblings' ages, we find out that you are 12 years old.
To find your age, we can set up an equation based on the information given:
Your sister is 10 years old.
Your brother is 13 your age, meaning 1/3 of your age.
Your sister is 6 years older than your brother. Therefore, if your brother's age is b, your sister's age is b + 6.
Since your sister is 10, this allows us to write the equation for your brother's age as:
b + 6 = 10
Solving for b, we get:
b = 10 - 6 => 4
Now we know your brother is 4 years old, and since he is 13 your age, we can write another equation:
a ÷3 = 4
Multiplying both sides by 3 to solve for a:
a = 4 × 3 => 12
You are 12 years old.
If a couple plans to have 9 children, what is the probability that there will be at least one girl? assume boys and girls are equally likely. is that probability high enough for the couple to be very confident that they will get at least one girl in 9 children?
John bought a house. He decided to reduce his square backyard by 40 inches along its width. The area of the new backyard is given by the function below, where z represents the length in inches.
A(z)=z^2-40z
Which statement best describes the term 40z?
* The area of the playground after expansion
* The width of the backyard
* The area of the backyard before reduction
* The area reduced from the backyard
PLEASE HELP BABES!!
How likely is it that you would pick the number 67 if you closed your eyes?
A) certain
B) impossible
C) probable
D) unlikely
The height of a rock thrown off a cliff can be modeled by h=-16t^2-8t+120, where h is the height in feet and t is time in seconds. How long does it take the rock to reach the ground?
(64-2^2)-(8+7)
answer please
A store is having a sale where all jeans are 1/4 off the regular price.Find the constant of proportionality, then write an equation relating to the sale price to the regular price.
What are the values of a and b?
Myron bought a dozen eggs for $1.75 per dozen. If he bought 8 dozen eggs, how much did they cost?]
Which statement about the population shown in this graph is true? A. The number of individuals will increase endlessly. B. The number of individuals will eventually drop to zero. C. The population has increased until it reached its carrying capacity. D. There are no limiting factors to control population growth.
Find the exact length of the curve.x = y48 + 14y2, 1 ≤ y ≤ 2
The exact length of the curve x = y^48 + 14y^2, for 1 ≤ y ≤ 2, can be found by differentiating x with respect to y, substituting into the formula for arc length, and solving the integral from y=1 to y=2.
Explanation:To solve this problem, we use the formula for the arc length of a curve given by a function in parametric form. This formula is L = ∫sqrt(1+(dx/dy)^2)dy, with integration done over the interval [1,2].
In this case, our function is given as x = y^48 + 14y^2. First, we differentiate x with respect to y to get dx/dy = 48y^47 + 28y. We then substitute this into the formula to get L = ∫sqrt(1+(48y^47 + 28y)^2)dy. To solve this integral, you can use a standard calculus method or a calculator with integral functions. Make sure to evaluate the definite integral from y=1 to y=2.
Learn more about Arc Length here:https://brainly.com/question/32035879
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When 2/3 of a number is added to 10 the result is 5 more than the number find the number g?
[tex]g-the\ number\\\\\dfrac{2}{3}g+10=g+5\qquad\text{multiply both sides by 3}\\\\2g+30=3g+15\qquad\text{subtract 30 from both sides}\\\\2g=3g-15\qquad\text{subtract 3g from both sides}\\\\-g=-15\qquad\text{change the signs}\\\\\boxed{g=15}[/tex]
“Find the equation of the line passing through (8,-2) & (7,-4). Write your equation in point-slope AND slope intercept forms.
Point slope form using (8,-2) _____
Point slope form using (7,-4) _____
Slope intercept form: y=2x-18