Correct options are Options B, D, E. The product of two rational expressions (a/b) and (x/y) is a rational expression, specifically the ratio of ax and by, or equivalently ax/by. Incorrect options include ay/bx and a/y(x/b).
To determine the product of two rational expressions (a/b) and (x/y), where b ≠ 0 and y ≠ 0, let's explore the given options. Here are the truths about the product:
The product is a rational expression: When you multiply two rational expressions, the result is also a rational expression. This follows from the definition of rational expressions, which are ratios of polynomials.
The product is the ratio of ax and by: Mathematically, multiplying the numerators and denominators of the two rational expressions gives us (ax)/(by).
The product is equivalent to ax/by: This restates the above ratio in a simplified expression form, confirming that the multiplication results in (ax)/(by).
As we can see, the other expressions mentioned (ay/bx, a/y(x/b), a/(y(x/b))) are not correct representations of the product. Correct options are Options B, D, E.
Complete question:
If a/b and x/y represent rational expressions and b0 and y0, what is true of their product? Select three options.
A. The product is equivalent to ay/bx
B. The product is a rational expression.
C. The product is equivalent to a/y(x/b)
D. The product is the ratio of ax and by.
E. The product is equivalent to ax/b(y)
what equations is equivalent to y = log x
In 2010, a city's population was 1,405,233 and it was decreasing at a rate of 1.1%. At this rate when will the city's population fall below 1,200,000?
a. 2024
b. 2027
c. 2036
d. 2049
Answer:
2024
Step-by-step explanation:
took the test
Anyone help please!!!!
What is the maximum volume of a square pyramid that can fit inside a cube with a side length of 18 cm?
a. 5,832 cm
b. 2,916 cm
c. 1,944 cm
d. 972 cm
Find the volume of the cylinder in terms of Pie. The diagrams are not drawn to scale.
a. 52.8 m
b. 58.08 m
c.127.78 m
d. 29.04 m
12 POINTS
Simplify i38.
i
−1
−i
1
Answer:
-1
Step-by-step explanation:
I got this correct on my quiz
i^38 = -1
two angles are drawn below. the measure of angle x is 90
a. 20
b. 60
c. 100
d. 120
What is the area of a square
In which type of quadrilateral are consecutive sides congruent?
Select the best answer from the choices provided.
trapezoid
parallelogram
square
rectangle
Final answer:
A square is the quadrilateral with congruent consecutive sides. It is an equilateral rectangle and a special type of parallelogram with equal-length sides and right angles.
Explanation:
The type of quadrilateral in which consecutive sides are congruent is a square. A square is a special type of parallelogram where all sides are equal in length and all angles are right angles. When considering a square as a rectangle (which technically it is), its diagonals (which are equal in length) bisect one another at right angles, suggesting the property of being an equilateral rectangle. Furthermore, in a larger context, if we treat the sides of any parallelogram symmetrically, such as in a notation [PQRS], the order can change to [QRSP], [QPSR], and [PRQS] without affecting its properties, which aligns with the symmetric nature of a square's sides.
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The lengths of the sides of three squares are s, s + 1, and s + 2. If their total area is 365 cm squared (^2), find their total perimeter.
What does a residual value of 1.3 mean when referring to the line of best fit of data set?
-a data point is 1.3 units above the line of best fit
-a data point is 1.3 units below the line of best fit
-the line of best fit has a slope of -1.3
-the line of best fit has a slope of 1.3
A residual value of 1.3, when referring to the line of best fit of a data set, means that,
⇒ a data point is 1.3 units above the line of best fit.
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
To find a residual value of 1.3 mean when referring to the line of best fit of data set.
Since, A residual is defined as the difference between the observed value of a dependent variable and the predicted value of that variable using the regression equation.
Hence, In this case, the residual value of 1.3 indicates that the observed value of the dependent variable is 1.3 units above the predicted value, or the line of best fit.
Thus,
A residual value of 1.3, when referring to the line of best fit of a data set, means that,
⇒ a data point is 1.3 units above the line of best fit.
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A lucky integer is a positive integer which is divisible by the sum of its digits. what is the least positive multiple of 9 that is not a lucky integer?
Bricklayers use the formula N = 7LH to estimate the number of bricks N needed to build a wall of height H and length L. What is the height of a wall that is 30 feet long and that requires 2,310 bricks to build? a. 12 ft c. 11 ft b. 10 ft d. 20 ft
Which of the following is not needed when making a box plot?
A - Mean
B - Minimum
C - Median
D - Third Quartile
During a radio contest, $50 is added to the prize money each time a caller answers the contest question incorrectly. if the first caller has a chance to win $100, which equation finds the amount the 10th caller receives, if the 10th is the first to answer the question correctly?
Answer:
a is correct on edege
Step-by-step explanation:
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A gallon of Moo Milk costs \$5.12$5.12dollar sign, 5, point, 12. What is the price, in dollars, of an 888 ounce glass of Moo Milk? There are 128128128 ounces in 111 gallon.
Answer:
0.32
Step-by-step explanation:
The ration of gallons to cost is 1:$5.12
We want to know the ratio of ounce to cost.
We need to convert gallons to ounces.
There are 128 ounces in 1 gallon.
So, if one Moo Milk costs $5.12, then 128 ounces also cost $5.12
The ratio of ounces to cost is 128:$5.12
Now, we can find an equivalent ratio to find the cost for 1 ounce.
Then we can multiply by 8 to find the cost of 8 ounces
Ounces ---------> Cost
128 ------------> 5.12 (Both divided by 128)
1 -------------> 0.04 (Both times 8)
8 ------------> 0.32
An 8 ounce of Moo Milk costs $0.32
The sum of the squares of two consecutive positive even integers is 100. find the two integers
Let's denote the two consecutive positive even integers as x and x+2.
We know their squares sum up to 100, represented mathematically as:
x^2 + (x + 2)^2 = 100.
Expanding this equation, we get:
x^2 + x^2 + 4x + 4 = 100.
Combining like terms gives us:
2x^2 + 4x - 96 = 0.
This is a quadratic equation in the form of ax^2 + bx + c = 0, where a = 2, b = 4, and c = -96.
We can solve this quadratic equation for x using the quadratic formula:
x = [-b ± sqrt(b^2 - 4ac)] / 2a.
Substituting a, b, and c into this formula, we find that:
x = [-4 ± sqrt((4)^2 - 4*2*-96)] / 2*2,
x = [-4 ± sqrt(16 + 768)] / 4,
x = [-4 ± sqrt(784)] / 4,
x = [-4 ± 28] / 4.
So the solutions are x = (28 - 4) / 4 = 6 and x = (-28 - 4) / 4 = -8.
Since we are looking for positive even integers, we discard the negative solution.
Therefore, the two consecutive positive even integers are 6 and 6 + 2 = 8.
How many terms are in the arithmetic sequence 6, 2, −2, …, −102?
Hint: an = a1 + d(n − 1), where a1 is the first term and d is the common difference
27
28
29
30
Final answer:
Calculate the number of terms in the arithmetic sequence 6, 2, -2, ..., -102 using the provided formula to find it is 28.
Explanation:
In mathematics, an Arithmetic Progression (AP) is a sequence of numbers in which the difference between consecutive terms is constant. This difference is called the common difference, denoted by d.
Arithmetic sequence: 6, 2, -2, ..., -102
Formula: an = a1 + d(n - 1)
Identify a1 = 6 and an = -102Calculate d = an - a1 = -102 - 6 = -108Substitute the values into the formula and solve for n to find the number of termsTherefore, the number of terms in the arithmetic sequence is 28.
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1. Circle A with center at (3, 4) and radius 2 is similar to circle B with center at (−4, −5) and radius 3. Below is an incorrect informal argument for proving two circles are similar:
Step 1 Translate circle B to the right 9 units and up 7 units to form concentric circles.
Step 2 Dilate circle B to be congruent to circle A using scale factor of k = r sub two over r sub one equals two over three
Step 3 When an object is dilated, the dilated object is similar to the pre-image, thus the two circles are similar.
What is the first incorrect step, and how can it be fixed?
A. All steps are correct
B. Step 1, translate circle B to the right 7 units and up 9 units
C. Step 2, use scale factor of K= r^2/r^1=3/2
D. Step 3, replace dilated with translated.
An image of two concentric circles is shown with r2 = 8 and r1 = 3:
2. Image shows a pair of concentric circles. The radius of the smaller circle is r sub 1 and the radius of the second is r sub 2.
In order to prove the two circles are similar, the radius r1 was increased to make the circles congruent. What is the scale factor used in the above image?
A. k=8/3
B. K=3/8
C. K=1/5
D. K=5
First one is B. Because if you're moving from -4 to 3 you don't move 9 units right instead you move 7.
) a pair of fair dice is rolled. what is the probability that the sum of the top faces is a number 10 or greater?
dy/dx = y/x^2
dy/y = dx/x^2
ln y * ln c = -1/x
cy = e^(-1/x)
y = ce^(-1/x)
Bricklayers use the formula N = 7LH to estimate the number of bricks N needed to build a wall of height H and length L. What is the height of a wall that is 30 feet long and that requires 2,310 bricks to build? a. 12 ft c. 11 ft b. 10 ft d. 20 ft
please verify my probability answer!!!
Answer:
1/4
Step-by-step explanation:
Hope this helped :)
Can someone answer this question for me as well.
The equation tan-1 (9.4/8.2) = x can be used to find the measure of angle LKJ. What is the measure of angler LKJ? Round to the nearest whole degree.
*KL = 7.7 cm, LJ = 8.9 cm*
A card is drawn from a standard deck of cards. Determine whether the events are mutually exclusive or inclusive. Then, find the probability.
P(a red card or a queen)
a.
inclusive, 15/26
c.
inclusive, 7/13
b.
mutually exclusive, 15/26
d.
mutually exclusive, 7/13
The events are mutually inclusive and the required probability is p(getting a red or a queen) is 28/52 = 7/13
What is probability?Probability is a measure of the likelihood of an event occurring. The probability formula is defined as the possibility of an event happening is equal to the ratio of the number of favorable outcomes and the total number of outcomes. Probability of event to happen P(E) = Number of favorable outcomes/Total Number of outcomes.
Given here A card is drawn from a standard deck of cards. Now There are some events that can impact each other or that are overlapping. They have one or more outcomes in common. When events have outcomes in common, they are said to be overlapping events, also known as mutually inclusive events. Thus this event is defenitely inclusive.
Now the probability that a red card or a queen is =( 26 red cards + 2 black queens ) /52
= 28/52
=7/13
Hence, The events are mutually inclusive and the required probability is p(getting a red or a queen) is 28/52 = 7/13
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1. In an auditorium, there are 21 seats in the first row and 26 seats in the second row. The number of seats in a row continues to increase by 5 with each additional row.
(a) Write an iterative (explicit) rule to model the sequence formed by the number of seats in each row. Show your work.
(b) Use the rule to determine how many seats are in row 15. Show your work.
2. Rhonda started a business. Her business made $40,000 in profits the first year. Her annual profits have increased by an average of 6% each year since then.
(a) Write an iterative rule to model the sequence formed by the profits of Rhonda’s business each year.
(b) Use the rule to determine what the annual profits of Rhonda’s business can be predicted to be 20 years from the start of her business. Round your answer to the nearest dollar. Do not round until the end. Show your work.
3. The sequence 3, 12, 48, 192, … shows the number of pushups Kendall did each week, starting with her first week of exercising.
(a) What is the recursive rule for the sequence?
(b) What is the iterative rule for the sequence?
Answer:
i will look but i think she was right
Step-by-step explanation:
Is 1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 a number?
Which box plot represents the data?
30, 35, 25, 5, 5, 25, 40, 45, 50, 10, 15, 40
Explain how the difference of a fraction or a rational number and its additive inverse is equal to zero.
Solve for x: 12(x-7)+3(2x+2)=50x-62