Answer:
The minus signs should be plus signs
The required factor of the given trinomial is (2x+5)(2x + 5).
Given that,
When asked to factor the trinomial 4x² + 20x + 25, a student gives the answer (2x - 5)(2x - 5). the mistakes in the solution is to be justified.
What is the factors?
factors can be defined by splitting the value into multipliable values.
Here,
Given trionomial,
= 4x² + 20x + 25,
= 4x² + 10x + 10x + 25
= 2x(2x + 5) + 5 (2x + 5)
= (2x + 5)(2x + 5)
Thus, the required factor of the given trinomial is (2x+5)(2x + 5).
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Allen bought 1,350 shares of stock for $12 per share. If he sold all his shares for $27,000, how much profit on each share did he make?
How do we refer to self-contained state actions: monadic. dyadic. triadic. k-adic?
In mathematics, self-contained state actions are known as k-adic. Monadic, dyadic, and triadic are specific cases of k-adic functions.
Explanation:In mathematics, self-contained state actions are known as k-adic. The term 'k-adic' refers to functions that take k inputs and produce a single output. Monadic, dyadic, and triadic are specific cases of k-adic functions, where k is 1, 2, and 3, respectively. Thus, it typically refers to a numeral or number system that is based on the value of k, which can be any positive integer.
In such systems, numbers are represented using a base of k, and each digit holds its own place value. K-adic expansions are useful in number theory and algebraic number theory, providing insights into number properties and relationships in various mathematical contexts.
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A mother has 3 kids. Kid A is half the mother's current age. Kid B is 4 years younger than Kid A. In 3 years, Kid C will be 1/5 of his mother's age (not her current age). The sum of all their current ages is the mother's current age.
How old is the mother currently?
How old is each of her kids?
Final answer:
The mother is currently 40 years old. Kid A is 20 years old, Kid B is 16 years old, and Kid C is 36 years old.
Explanation:
Let's denote the mother's current age as M. Kid A's age is A = M/2. Kid B is 4 years younger than Kid A, so B = A - 4 = M/2 - 4. Kid C will be 1/5 of his mother's age in 3 years, so if we denote Kid C's current age as C, we have C + 3 = 1/5(M + 3). The sum of all their current ages is the mother's current age, so M = A + B + C. With these equations, we can solve for M, A, B, and C.
We substitute A and B into the mother's age equation: M = M/2 + M/2 - 4 + C. Rearranging terms, we get M - 4 = C. Now we have two expressions for C: M - 4 and 1/5(M + 3) - 3. Setting them equal to each other, we get M - 4 = 1/5(M + 3) - 3. Solving for M, we find that M = 40 years old.
Now we can find Kid A, B, and C's ages using the mother's age. Kid A is half the mother's age, A = M/2 = 20 years old. Kid B is 4 years younger than Kid A, B = A - 4 = 16 years old. Kid C's age can be found by the substitution, C = M - 4 = 36 years old. So the mother is 40 years old, Kid A is 20 years old, Kid B is 16 years old, and Kid C is 36 years old.
Derive the equation of the parabola with a focus at (−2, 4) and a directrix of y = 6. Put the equation in standard form.
Answer: f(x) = -1/4x² -x + 4
Iodine-123 is a radioactive substance used in medicine. It has a half-life of 13 hours. A nurse received a solution that initially contained 48 grams of iodine-123. Now only 12 grams of the iodine-123 remain. How many hours have passed since the nurse received the solution?
Angle c and angle d are supplementary, the measure of angle d is eight times the measure of angle
c. find measure of angle c and measure of angle d
Answer:
160
Step-by-step explanation:
Pedro has created the function f(x)= 4x-3/2 to represent the number of assingments he has completed where x represents the number of weeks in the course Person discovers that using the inverse function to solve for x=30, he can predict when he will have 30 assignments completed explain to Pedro how to accomplish this using complete sentences
a randomly generated list of numbers from 0 to 4 is being used to simulate an event with numbers 3 and 4 representing a success. what is the estimated probability of a success
A. 75%
B. 60%
C. 25%
D. 40%
Answer: 40% appex
Step-by-step explanation:
The probability of success, where success is defined as generating a 3 or 4 in a random list of numbers from 0 to 4, is 40%.
To calculate the probability of success in a random number generation scenario. The numbers 0 to 4 are possible outcomes, with 3 and 4 being defined as success. There are 5 equally likely outcomes in total, and 2 of these (3 and 4) represent success. Hence, the probability of success (P(success)) is calculated as the number of successful outcomes divided by the total number of possible outcomes.
P(success) = Number of successful outcomes / Total number of outcomes
P(success) = 2/5
This fraction simplifies equals 0.4, which, when converted into a percentage, results in a 40% chance of success. Therefore, the correct answer is D. 40%.
Eight less than a number is seventy-five. What is the number? -67 67 83
8-75 = x
x=8+75
x= 83
the number is 83
1) What kind of figure is formed by the cross section below?
square
rectangle
circle
ellipse that is not a circle
Which function is shown in the graph below?
Answer: The correct option is 2.
Explanation:
From the given figure it is easily noticed that the graph intersect the y-axis at y=9 , therefore the y-intercept is (0,9).
To find the equation of the curve put x=0 in each option, If we get y=9 then that option is true.
Option 1:
[tex]y=(\frac{1}{2})^{(x+3)}-1[/tex]
[tex]y=(\frac{1}{2})^{(0+3)}-1=\frac{1}{8}-1=\frac{-7}{8}[/tex]
Option 2:
[tex]y=(\frac{1}{2})^{(x-3)}+1[/tex]
[tex]y=(\frac{1}{2})^{(0-3)}+1=8+1=9[/tex]
Option 3:
[tex]y=(\frac{1}{2})^{(x-1)}+3[/tex]
[tex]y=(\frac{1}{2})^{(0-1)}+3=2+3=5[/tex]
Option 4:
[tex]y=(\frac{1}{2})^{(x+1)}-3[/tex]
[tex]y=(\frac{1}{2})^{(0+1)}-3=\frac{1}{2}-3=\frac{-5}{2}[/tex]
Only the equation in option 2 have the y-intercept (0,9), therefore the correct answer is option second.
Answer:
Its B
Step-by-step explanation:
The sum of the roots of 5 - 2m - 3m2 = 0 is:
Are the functions f(x) = (x^2-1)/(x-1) and g(x)= x+1 equal for all x?
A bus averages 60 mi/h traveling to its destination in the first half of its trip through an expressway and 72 mi/h in the second half traveling through a motorway. What is the bus's average speed for the entire trip rounded to the nearest tenth?
A) 64.2 mi/h
B) 63.0 mi/h
C) 65.5 mi/h
D) 66.0 mi/h
Answer:
The correct answer is 65.5 mi/h
Hope this helps :)
The area of an artist's square canvas can hold 113 square inches of paint. What is the approximate length of one side of the canvas? (Approximate to the nearest hundredth inch.)
10.62 inches
10.63 inches
10.64 inches
10.65 inches
The area of the square canvas is the square of its side length
The length of the side of the square canvas is 10.63 inches
The area the square canvas can hold is given as:
[tex]Area=113in^2[/tex]
The canvas has a square as its shape, and the area of a square is:
[tex]Area = L^2[/tex]
Where:
L represents the length of the shape (i.e. the square canvas)
So, we have:
[tex]L^2 = 113[/tex]
Take square roots of both sides
[tex]L = \sqrt{113[/tex]
Take the square root of 113
[tex]L = 10.63[/tex]
Hence, the length of the side is 10.63 inches
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Solve the quadratic equation by completing the square.
x^2-10x+15=0
First, choose the appropriate form and fill in the blanks with the correct numbers.
Then, solve the equation. Round your answer to the nearest hundredth.
If there is more than one solution, separate them with commas.
Form:
( x + _ )^2 = _
or
( x - _ )^2 = _
Solution:
x = _
At what value of x does the graph of the function f(x) have a vertical asymptote?
F(x) = 5X/ 2X-6
Solve :
3x − 6 = 2x − 1
The length of a rectangle is 11 ft less than three times the width, and the area of the rectangle is 70 ft2 . find the dimensions of the rectangle.
The width and length of the rectangle is 7ft and 10 feet respectively.
What are the area and perimeter of a rectangle?We know the perimeter of any 2D figure is the sum of the lengths of all the sides except the circle and the area of a rectangle is the product of its length and width.
Given, The length of a rectangle is 11 ft less than three times the width has an area of 70ft².
Assuming the width of the rectangle to be x ft, therefore the length of the rectangle is (3x - 11) ft.
We know the Area of a rectangle (A) = length×width.
∴ x.(3x - 11) = 70.
3x² - 11x = 70.
3x² - 11x - 70 = 0.
3x² - 21x + 10x - 70 = 0.
3x(x - 7) + 10(x - 7) = 0.
(x - 7)(3x + 10) = 0.
x - 7 = 0 Or 3x + 10 = 0.
x = 7 Or x = - 10/3.
A negative value of x is inadmissible here as length cannot be negative.
So, the width of the rectangle is 7 ft and the length of the rectangle is
10 ft.
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What is the sum of the measures of the exterior angles in a heptagon? Explain
y varies inversely with x
k = 0.6
What is the value of x when y is 0.6?
to find X when K is known
divide K by Y
0.6/0.6 = 1
X = 1
Prove that a set with n elements has 2n subsets.
The number of electrons in the shell equals 2n² and in each subshell is 2(2l + 1), derived from the quantum mechanical principles and the Pauli exclusion principle governing electron arrangement in atoms.
Explanation:To prove that the number of electrons in the shell equals 2n² and that the number in each subshell is 2(2l + 1), we need to use the quantum mechanical principles that govern the arrangement of electrons in an atom. According to the quantum model, each electron in an atom is described by four quantum numbers: n, l, mi, and ms. The principal quantum number n represents the shell level, the angular momentum quantum number l describes the subshell (with values ranging from 0 to n-1), the magnetic quantum number mi describes the orientation of the subshell (ranging from -l to +l), and the spin quantum number ms indicates the electron's spin (which can be +1/2 or -1/2).
Each shell level n can have subshell values from 0 to n-1. For each value of l, there are 2l+1 possible values for mi, and for each mi, there can be two electrons (one with spin up and one with spin down, according to the Pauli exclusion principle). Therefore, the maximum number of electrons in any subshell is 2(2l+1). Summing over all values of l will give the total number of electrons in a shell, which is 2n². This follows from considering all possible orientations and spin states for each value of l within a shell. For the n=2 shell as an example, there are l=0 and l=1 subshells. The s subshell (l=0) can hold 2 electrons, and the p subshell (l=1) can hold 6 electrons, for a total of 2(2^2) = 8 electrons in the n=2 shell. Using similar calculations for other values of n will confirm the general formula.
The application of the Pauli exclusion principle ensures that no two electrons can have the same set of all four quantum numbers, which fundamentally limits the number of possible electrons in a subshell and a shell.
In triangle ∆PQR, C is the centroid.
a. If CY = 10, find PC and PY
b. If QC = 10, find ZC and ZQ
c. If PX = 20, find PQ
Because C is the centroid, therefore:
Segments PZ = ZR; RY = YQ; QX = XP
A.
If CY = 10, then
PC = 2*CY = 20
PY = PC + CY = 20 + 10 = 30
Answer: PC = 20 PY = 30
B.
If QC = 10, then
ZC = QC/2 = 5
ZQ = ZC + QC = 5 + 10 = 15
Answer: ZC = 5 ZQ = 15
C.
If PX = 20
Because the median RX bisects side PQ, therefore PX = QX = 20
PQ = PX + QX = 40
Answer: PQ = 40
Anita and Joelle bowled together and their combined total score for one game was 425 points. Anita’s score was 40 less than twice Joelle’s. What were their scores? Write a system of equations to model the problem if x represents Joelle’s score and y represents Anita’s score.
an article with a net weight of 10 lb (pounds) is packaged in a box that weighs 1/2 lb. If 20 of these boxed articles are put into a freight container 15 lb, what is the gross weight?
Final answer:
The gross weight of the freight container with 20 boxed articles inside is 225 lb, calculated by adding the total weight of all the boxed articles (210 lb) to the weight of the container (15 lb).
Explanation:
To calculate the gross weight of the freight container with the packaged articles inside, we need to add the weight of the articles, the boxes, and the container itself.
First, we calculate the weight of one boxed article. Since the net weight of the article is 10 lb and the box weighs 0.5 lb, the total weight for one boxed article is 10 lb + 0.5 lb = 10.5 lb.
Next, we multiply the weight of one boxed article by the number of articles to find the total weight of all the boxed articles. For 20 articles, this is 20 imes 10.5 lb = 210 lb.
Finally, we add the weight of the freight container. The container weighs 15 lb, so the gross weight of the container with the articles is 210 lb + 15 lb = 225 lb.
Therefore, the gross weight of the freight container with 20 boxed articles inside is 225 lb.
Find all the real square roots of 0.0004.
A. 0.00632 and -0.00632
B. 0.06325 and -0.06325
C. 0.0002 and -0.0002
D. 0.02 and -0.02
given the polynomail function below, find f(-5) f(x)=x^2-2x-7
What is the equation in point−slope form of the line passing through (−2, −5) and (2, 3)?
a) (y + 2) = −2(x + 5)
b) (y − 2) = 2(x − 3)
c) (y − 3) = 2(x − 2)
d) (y + 3) = −2(x + 2)
PLS HELP ILL GIVE BRAINLIEST TO WHO EVER ATTEMPTS THIS: The function H(t) = −16t2 + 112t + 24 shows the height H(t), in feet, of a cannon ball after t seconds. A second cannon ball moves in the air along a path represented by g(t) = 5 + 3.2t, where g(t) is the height, in feet, of the object from the ground at time t seconds.
Part A: Create a table using integers 4 through 7 for the 2 functions. Between what 2 seconds is the solution to H(t) = g(t) located? How do you know? (6 points) Part B: Explain what the solution from Part A means in the context of the problem. (4 points)
Which of the following is equivalent to 36^1/2?
A) –18
B) –6
C) 1/18
D) 1/6