A equivalent term to [tex](-2m + 5n)^2[/tex] is a perfect square trinomial [tex]4m^2-20mn+25n^2[/tex]
What is expression?"It is a mathematical statement which consists of numbers, variables and some mathematical operations."
What is trinomial?"It is a polynomial which has only three terms."
What is perfect square trinomial?"When a trinomial can be factored into a binomial multiplied to itself, then its is a perfect square trinomial."
For given question,
We have been given a quadratic expression [tex](-2m + 5n)^2[/tex].
We need to find to find an equivalent expression to given expression.
Consider given expression,
[tex]\Rightarrow (-2m + 5n)^2 = (2m)^2-2(2m)(5n)+(5n)^2\\\\\Rightarrow (-2m + 5n)^2 =4m^2-20mn+25n^2[/tex]
We can observe that a trinomial [tex]4m^2-20mn+25n^2[/tex] is a perfect square trinomial.
Therefore, an equivalent term to [tex](-2m + 5n)^2[/tex] is a perfect square trinomial [tex]4m^2-20mn+25n^2[/tex]
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describe the graph of y=3/4x-12 as compared to the graph of y=1/x
Answer:
Parent function is compressed by a factor of 3/4 and shifted to right by 3 units.
Step-by-step explanation:
We are asked to describe the transformation of function [tex]y=\frac{3}{4x-12}[/tex] as compared to the graph of [tex]y=\frac{1}{x}[/tex].
We can write our transformed function as:
[tex]y=\frac{3}{4(x-3)}[/tex]
[tex]y=\frac{3}{4}*\frac{1}{(x-3)}[/tex]
Now let us compare our transformed function with parent function.
Let us see rules of transformation.
[tex]f(x-a)\rightarrow\text{Graph shifted to the right by a units}[/tex],
[tex]f(x+a)\rightarrow\text{Graph shifted to the left by a units}[/tex],
Scaling of a function: [tex]a*f(x)[/tex]
If a>1 , so function is stretched vertically.
If 0<a<1 , so function is compressed vertically.
As our parent function is multiplied by a scale factor of 3/4 and 3/4 is less than 1, so our parent function is compressed vertically by a factor of 3/4.
As 3 is being subtracted from x, so our parent function is shifted to right by 3 units or a horizontal shift to right by 3 units.
Therefore, our parent graph is compressed by a factor of 3/4 and shifted to right by 3 units to get our new graph.
Final answer:
The equation y=3/4x-12 represents a linear function with a straight line graph, while y=1/x depicts a rectangular hyperbola with a curved graph showcasing an inverse relationship. These graphs exhibit fundamentally different behaviors, one being constant and the other varying.
Explanation:
The student's question involves comparing the graph of y=3/4x-12 to the graph of y=1/x. The first equation, y=3/4x-12, describes a linear function with a slope of 3/4 and a y-intercept of -12. This means it is a straight line that increases as x increases, crossing the y-axis at (0, -12).
On the other hand, the graph of y=1/x is a rectangular hyperbola. This curve approaches the x-axis and y-axis but never touches them, known as asymptotes. The hyperbola is divided into two parts, one in the first quadrant where both x and y are positive, and another in the third quadrant where both x and y are negative. This graph does not resemble a straight line at any part.
Comparatively, the key difference lies in the nature of their graphs - one is a straight line and the other a curved hyperbola, showcasing completely different behaviors. The linear equation reflects constant change, whereas the hyperbola’s rate of change varies with x, indicating an inverse relationship.
Determine the x-intercept of 5x -6y =10
find the surface area of the toolbox
You track fuel accounts for q shipping line. One vessel consumes 2 1/2 tons of fuel per day during transport. About how many fuel in tons should the vessel consume during 15-day transport?
what is the probabilaty getting a sum of 7 if you rolled a pair of dice?
a puppy pen is 4 square feet wide and 5 feet long. is 21 square feet of fabric large enough to make a mat for the pen? Explain
Solve and plot your answer on the number line below: 7.08 + 2x=15.96
A gardener plants a bed of flowers such that he plants twenty day lilies in the first row, twenty-six day lilies in the second row, and thirty-two day lilies in the third row. He continues to plant lilies in the bed with this pattern for a total of twelve rows. How many day lilies did he plant?
There are 86 lilies he did plant in 12th row of the garden.
What is Arithmetic Sequence?Arithmetic Progression (AP) is a sequence of numbers in order, in which the difference between any two consecutive numbers is a constant value. It is also called Arithmetic Sequence.
Here, The number of lilies plants in first, second third,..., and last row are respectively.
20,26,32,........
the number of rows of lilies plants is 12.
The sequence 20,26,32,........ is an A.P. with first term a =20, common difference d = 6 and n =12
formula for nth term.
∴aₙ = a+(n−1)d
aₙ=20+ (12-1).6
aₙ = 20 + 11 X 6
aₙ = 86
Thus, there are 86 lilies he did plant in 12th row of the garden.
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The perimeter of a quilt is 34 ft. If the quilt is 8 ft long, what is the area
Andy and alex both decided to order prints of their photos. Andy ordered 40 small 4x6 inch prints and 10 large 8x10 inch prints. He paid a total of $32.50 for his photos. Alex paid 20$ for 20 small 4x6 inch prints and 8 large 8x10 inch prints. How much do the small and large sized prints cost
Final answer:
To find the cost of small and large prints, we create two equations based on Andy's and Alex's orders and solve for the two variables. The small 4x6 inch prints cost $0.50 each, and the large 8x10 inch prints cost $1.25 each.
Explanation:
To solve how much small and large sized prints cost, we can set up a system of linear equations based on the information given:
Andy's order: 40 small prints and 10 large prints for $32.50Alex's order: 20 small prints and 8 large prints for $20.00Let s represent the cost of a small 4x6 inch print, and let l represent the cost of a large 8x10 inch print. We can then form the equations:
40s + 10l = 32.5020s + 8l = 20.00By dividing the first equation by 2, we get:
20s + 5l = 16.25Subtracting the second equation from this result gives:
(20s + 5l) - (20s + 8l) = (16.25 - 20)-3l = -3.75l = 1.25With the cost of a large print found, we can plug this back into the second equation to find the cost of a small print:
20s + 8(1.25) = 2020s + 10 = 2020s = 10s = 0.50Therefore, the cost of a small 4x6 inch print is $0.50 and a large 8x10 inch print is $1.25.
factor, x^4y+8x^3y-6x^2y^2-48xy^2
Jorge is standing at a horizontal distance of 25 feet away from a building. his eye level is 5.5 feet above the ground and looking up he notices a window washer on the side of the building at an angle of elevation of 65, how high is the window washer above the ground
Suppose that the probabilities of a customer purchasing 0, 1, or 2 books at a book store are 0.20.2, 0.30.3, and 0.50.5, respectively. what is the standard deviation of this customer's book purchases?
The standard deviation of the customer's book purchases is 0.72.
The standard deviation of a discrete probability distribution can be calculated using the following formula:
σ = √(p[tex](x - \mu)^2[/tex])
where:
σ is the standard deviation
p(x) is the probability of the event x
μ is the mean of the distribution
In this case, the probabilities of the customer purchasing 0, 1, or 2 books are 0.2, 0.3, and 0.5, respectively. So, the mean of the distribution is:
μ = (0 * 0.2) + (1 * 0.3) + (2 * 0.5) = 1.2
The standard deviation is then:
σ = √([tex](0 - 1.2)^2 (0.3)^2[/tex] + [tex](1 - 1.2)^2 (0.3)^2[/tex] + [tex](2 - 1.2)^2 (0.5)^2)[/tex] = 0.72
So, the standard deviation of the customer's book purchases is 0.72.
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A stained glass window is shaped like a semicircle the bottom edge of the window is 36 inches long what is the area of the stained glass window
Solve the equation by completing the square. Round to the nearest hundredth if necessary. x2 – 4x = 5
Answer:
x = 5 or x = -1
Step-by-step explanation:
x^2 – 4x = 5
Solve it by completing the square method
In completing the square method, we take the coefficient of x that is -4, divide it by 2 and then square it
-4/2 = -2
square it (-2)^2 = 4
Now add 4 on both sides
x^2 – 4x +4 = 5+4
x^2 – 4x +4 = 9
Now factor the left hand side
(x-2)(x-2)=9
(x-2)^2 = 9
Take square root on both sides
x-2 = +-3
x-2 = 3 , so x= 5
x-2 = -3, so x= -1
Which number line represents the solution set for the inequality-4(x+3)<-2-2x
The inequality -4(x+3)<-2-2x simplifies to x > -5. Therefore, the number line representing this solution should shade the values greater than -5, thus, highlighting that x is any value greater than -5.
Explanation:Let's solve the inequality -4(x+3)<-2-2x step by step:
Distribute -4 through (x+3) to get -4x-12<-2-2x. Add 4x to both sides to isolate x, which leads to -12 < 2x - 2. Finally, add 2 to both sides to isolate x to get -10 < 2x or equivalently, x > -5.
As a result, the number line that represents this solution is one where the values greater than -5 are shaded. This means the value of x is anything greater than -5. Any number line visualization should start at -5 and include everything to the right of that point.
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What is the measure of angle z in this figure?
Enter your answer in the box.
z = ___°
ASAP Select the statement that correctly describes the expression below.
(2x+5)^2
a) the sum of the square of 2 times x and 5
b)the square of the sum of 2 times x and 5
c)the square of 2 times the addition of x and 5
d)the sum of 2 times x and the square of 5
Answer:
Option B
Step-by-step explanation:
The given expression is ( 2x + 5)²
We have to form a statement to describe the expression given.
(2x + 5)² square of sum of 2 times x and 5
Option B is the correct answer.
What is the mean of the values in the stem-and-leaf plot? Enter your answer in the box.Key: 2|5 means 25
Enter your answer in the box.
Key: 2|5 means 25
A stem-and-leaf plot with a stem value of 1 with leaf values of 5 and 8, a stem value of 2, a stem value of 3, a stem value of 4 with a leaf value of 6, a stem value of 5 with leaf values of 0, 0, 0, 0, 7, a stem value of 6, a stem value of 7, a stem value of 8, and a stem value of 9.
The mean of the values in the stem-and-leaf plot is 42.
To find the mean of the values in the stem-and-leaf plot, we first need to interpret the plot correctly. Here's the stem-and-leaf plot description:
Stem | Leaves
1 | 5, 8
2 |
3 |
4 | 6
5 | 0, 0, 0, 0, 7
6 |
7 |
8 |
9 |
Let's list the individual values from the plot:
- From stem 1: Leaves are 5 and 8
- From stem 4: Leaf is 6
- From stem 5: Leaves are 0, 0, 0, 0, 7
Now, we calculate the mean (average) of these values.
Step-by-step calculation:
1. List of values:
- Values from stem 1: 15, 18
- Values from stem 4: 46
- Values from stem 5: 50, 50, 50, 57
2. Count the number of values:
- There are 2 values from stem 1, 1 value from stem 4, and 5 values from stem 5.
- Total count = 2 + 1 + 5 = 8
3. Calculate the sum of all values:
- Sum = 15 + 18 + 46 + 50 + 50 + 50 + 50 + 57
- Sum = 336
4. Calculate the mean:
- Mean = Sum / Count
- Mean = 336 / 8
- Mean = 42
Therefore, the mean of the values in the stem-and-leaf plot is [tex]{42} \).[/tex]
a paragraph of; compare savings and investments
If you take out a loan that costs $130.50 over nine years at an interest rate of 10%, how much was the loan for?
The original loan amount for which the final amount payable is $130.50 over nine years at an interest rate of 10% was approximately $55.39.
Explanation:To find out the original amount of the loan for which the final amount payable is $130.50 over nine years at an interest rate of 10%, we will use the formula for the present value of a loan.
The formula given is P = A / (1 + r/n)^nt, where P is the principal (initial loan amount), A is the final amount, r is the annual interest rate (expressed as a decimal), n is the number of times that interest is compounded per year, and t is the time the money is borrowed for in years.
As the question doesn't specify how many times the interest is compounded per year, we will assume it is compounded once a year (n=1).
We have:
A = $130.50,r = 10% or 0.10,n = 1,t = 9 years.Plugging these values into the formula:
P = $130.50 / (1 + 0.10/1)^(1*9)
P = $130.50 / (1 + 0.10)^9
P = $130.50 / (1.10)^9
P = $130.50 / 2.35794769
P = $55.39 approximately
Therefore, the original loan amount was approximately $55.39.
HELP PLEASE
Translate the answer, T2 = A3, into words:
The BLANK of the orbital period, T, of a
planet is equal to the BLANK of the average distance, A, of the planet from the Sun.
Square
Square Root
Cube
Answer: The square of the orbital period, T, of a planet is equal to the cube of the average distance, A, of the planet from the Sun.
Step-by-step explanation:
In mathematics, A number or variable 'a' to its second power is said to be square of 'a' i.e. [tex]\ a^2[/tex] is the square of a.
A number or variable 'b' to its third power is said to be cube of 'b' i.e. [tex]\ b^3[/tex] is the cube of b.
In the given equation: [tex]T^2 = A^3[/tex]
Here, [tex]T^2 [/tex] is square of T.
And [tex]A^3[/tex] is cube of A.
Therefore, The square of the orbital period, T, of a planet is equal to the cube of the average distance, A, of the planet from the Sun.
Hdc produces microcomputer hard drives at four different production facilities (f1, f2, f3, and f4) hard drive production at f1, f2, f3, and f4 is 20%, 25%, 15%, and 40%, respectively. quality control records indicate that 1.5%, 2%, 1%, and 3% of the hard drives are defective at f1, f2, f3, and f4, respectively.
a. if a defective hdc hard drive is picked at random, what is the probability that it was produced at f2?
b. if a defective hdc hard drive is picked at random, what is the probability that it was produced at f4?
c. if an hdc hard drive is picked at random, what is the probability that it is non-defective? g
a. Probability defective hard drive from F2 ≈ 0.3226.
b. Probability defective hard drive from F4 ≈ 0.7742.
c. Probability non-defective hard drive ≈ 0.9785.
To solve this problem, we can use Bayes' theorem, which states:
[tex]\[ P(A|B) = \frac{P(B|A) \times P(A)}{P(B)} \][/tex]
Where:
- [tex]\( P(A|B) \)[/tex] is the probability of event A happening given that event B has occurred.
- [tex]\( P(B|A) \)[/tex] is the probability of event B happening given that event A has occurred.
- [tex]\( P(A) \)[/tex] and [tex]\( P(B) \)[/tex] are the probabilities of events A and B, respectively.
Let's solve each part of the problem:
a. If a defective HDC hard drive is picked at random, what is the probability that it was produced at F2?
Let:
- A be the event that the hard drive is defective.
- B be the event that the hard drive was produced at F2.
We need to find [tex]\( P(B|A) \)[/tex], the probability that the hard drive was produced at F2 given that it is defective.
[tex]$\begin{aligned} & P(B \mid A)=\frac{P(A \cap B)}{P(A)} \\ & P(A \cap B)=P(A \mid B) \times P(B)=0.02 \times 0.25=0.005 \\ & P(A)=P(A \cap F 1)+P(A \cap F 2)+P(A \cap F 3)+P(A \cap F 4) \\ & P(A)=0.015 \times 0.20+0.02 \times 0.25+0.01 \times 0.15+0.03 \times 0.40=0.0155 \\ & P(B \mid A)=\frac{0.005}{0.0155} \approx 0.3226\end{aligned}$[/tex]
b. If a defective HDC hard drive is picked at random, what is the probability that it was produced at F4?
We need to find [tex]\( P(F4|A) \)[/tex], the probability that the hard drive was produced at F4 given that it is defective.
[tex]\[ P(F4|A) = \frac{P(A \cap F4)}{P(A)} \][/tex]
[tex]\[ P(A \cap F4) = P(A|F4) \times P(F4) = 0.03 \times 0.40 = 0.012 \][/tex]
[tex]\[ P(F4|A) = \frac{0.012}{0.0155} \approx 0.7742 \][/tex]
c. If an HDC hard drive is picked at random, what is the probability that it is non-defective?
Let P(non-defective) = P(non-defective at F1) + P(non-defective at F2) + P(non-defective at F3) + P(non-defective at F4)
P(non-defective) = [tex](1 - 0.015) \times 0.20 + (1 - 0.02) \times 0.25 + (1 - 0.01) \times 0.15 + (1 - 0.03) \times 0.40[/tex]
P(non-defective) = [tex]0.985 \times 0.20 + 0.98 \times 0.25 + 0.99 \times 0.15 + 0.97 \times 0.40[/tex]
P(non-defective) = 0.197 + 0.245 + 0.1485 + 0.388 = 0.9785
So, the probability that an HDC hard drive picked at random is non-defective is approximately [tex]\( 0.9785 \)[/tex].
Please help me out with #8 surface area and please explain
Find geometric mean of the pair of number 6 and 10
The Geometric mean of the pair of number 6 and 10 is [tex]7.74[/tex]
Geometric mean :The geometric mean of two number m and n is given as,
[tex]G.M=\sqrt{m*n}[/tex]
Geometric mean of the pair of number 6 and 10 is,
[tex]G.M=\sqrt{6*10} =\sqrt{60} \\\\G.M=7.74[/tex]
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How many bits are required to represent the decimal numbers in the range from 0 to 999 in straight binary code?
Final answer:
To represent the decimal numbers from 0 to 999 in binary code, we require 10 bits. This is determined by finding the binary equivalent of the largest number, 999, which necessitates at least 10 powers of 2 (from [tex]2^0 \ to \ 2^9[/tex]).
Explanation:
To determine how many bits are required to represent the decimal numbers in the range from 0 to 999 in straight binary code, we need to find the binary equivalent of the largest number in that range, which is 999. In binary, this would require the highest power of 2 that is less than or equal to 999. The largest power of 2 less than 999 is 512 (29), and we continue to add powers of 2 to represent the number:
Adding these up, we see that we need at least 10 bits to represent the number 999 in binary, because adding powers of 2 from 20 to 29 will give us the required range. Therefore, we need 10 bits to represent any number from 0 to 999 in binary.
If the test scores of a class of 34 students have a mean of 73.1 and the test scores of another class of 26 students have a mean of 66.4, then the mean of the combined group is
The Mean of the combined class is 70.19.
MeanMean is the average of a set of two or more numbers. The arithmetic and geometric mean are the types of mean that can be calculated.
Mean formula[tex]\rm Mean = \dfrac{sum\ of\ the\ term}{total\ number\ of\ term}[/tex]
Given
The test scores of a class of 34 students have a mean of 73.1 and
The test scores of another class of 26 students have a mean of 66.4.
To find
The mean of the combined group.
How to get the mean of the combined group?The sum of the total of the test score = Total number of students x Mean
Class 1 sum will be
The sum of the total test score = 34 x 73.1
The sum of the total test score = 2485.4
Class 2 sum will be
The sum of the total test score = 26 x 66.4
The sum of the total test score = 1726.4
Than Mean for the combine will be
[tex]\rm Mean = \dfrac{sum\ of\ the\ term}{total\ number\ of\ term}\\\\Mean = \dfrac{2485.4+1726.4}{34+26} \\\\Mean = \dfrac{4211.8}{60} \\\\Mean = 70.19[/tex]
Thus the Mean of the combined class is 70.19.
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Which shows how the distributive property can be used to evaluate 7×84/5?
With a short time remaining in the day a delivery driver has to make deliveries at 5 locations among the 6 locations remaining. How many different routes are possible
To find the number of different routes the delivery driver can take to make the deliveries at 5 out of 6 locations, we can use the concept of permutations.
Explanation:To find the number of different routes the delivery driver can take, we can use the concept of permutations. Since the delivery driver has to make deliveries at 5 out of the remaining 6 locations, we need to calculate the number of ways to arrange these locations.
We can use the formula for permutations to find the number of different routes:
nPr = n! / (n - r)!
Using this formula, we can calculate the number of different routes as:
6P5 = 6! / (6 - 5)! = 6! / 1! = 6 × 5 × 4 × 3 × 2 × 1 / 1 = 720
Therefore, there are 720 different routes the delivery driver can take to make the deliveries.
A triangle on a coordinate plane is translated according to the rule T–3, 5(x, y). Which is another way to write this rule?
(x, y) → (x – 3, y + 5)
(x, y) → (x – 3, y – 5)
(x, y) → (x + 3, y – 5)
(x, y) → (x + 3, y + 5)
Another way to write the given rule is (x, y) → (x – 3, y + 5).
Given that,
There are the original x and y coordinates that are being moved to the left-hand side by 3 units and go up by 5 units.Based on the information, we can conclude that another way to write the given rule is (x, y) → (x – 3, y + 5).
Hence, the other options are incorrect.
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