The matrix[tex]A^(-1) is a matrix with 2 rows and 2 columns, where row 1 is -0.25 and 1, and row 2 is 0.5 and -1.[/tex]
To find the inverse of a matrix, we can use the formula:[tex]A^(-1) = (1/det(A)) * adj(A)[/tex]
Where A^(-1) represents the inverse of matrix A, det(A) is the determinant of A, and adj(A) denotes the adjugate of A.
Given the matrix A with 2 rows and 2 columns:
A = | 4 4 |
| 2 1 |
To find A^(-1), we need to calculate the determinant of A and the adjugate of A.
The determinant of A (det(A)) is calculated as:
det(A) = 4 * 1 - 2 * 4 = -4
The adjugate of A (adj(A)) is obtained by swapping the diagonal elements and changing the sign of the off-diagonal elements:
adj(A) = | 1 -4 |
| -2 4 |
Finally, we can find A^(-1) using the formula mentioned earlier:[tex]A^(-1) = (1/det(A)) * adj(A)A^(-1) = (1/-4) * | 1 -4 |[/tex]
| -2 4 |
Simplifying the expression:
A^(-1) = | -0.25 1 |
| 0.5 -1 |
Therefore, the matrix A^(-1) is a matrix with 2 rows and 2 columns, where row 1 is -0.25 and 1, and row 2 is 0.5 and -1.
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Use the graph of the function f to find the approximations of the given values.
b. f(4)
d. f(12) − f(4) / 12 − 4
Answer:
b. f(4) = -12
d. (f(12) - f(4))/(12 - 4) = (12 - (-12))/8 = 24/8
= 3
The paint needed for a 980 ft2 room costs $35.25 per gallon. What is the total cost of the paint
needed to paint the room?
Note: Assume that one gallon of paint will cover a total of 350 square feet.
O $88.60
O $98.70
O $88.12
O $89.07
Answer:
$98.70
Step-by-step explanation:
Number of gallons = Area of room / Coverage per gallon
Number of gallons = 980 ft^2 / 350 ft^2/gallon
Number of gallons = 2.8 gallons
Therefore, we need 2.8 gallons of paint to cover the room. The cost of one gallon of paint is given as $35.25, so the total cost of the paint needed to paint the room is:
Total cost = Number of gallons × Cost per gallon
Total cost = 2.8 gallons × $35.25/gallon
Total cost = $98.70
So, the total cost of the paint needed to paint the room is $98.70.
What is the length of EF in the right triangle below?
D
26
10
E
F
The measure of side length EF in the right triangle is 24.
What is the measure of side length EF?The Pythagorean theorem states that the "square on the hypotenuse of a right-angled triangle is equal in area to the sum of the squares on the other two sides.
It is expressed as;
c² = a² + b²
From the diagram:
Hypotenuse DE = c = 26
Leg DF = a = 10
Leg EF = b = ?
Plug in the values and solve for b:
c² = a² + b²
26² = 10² + b²
676 = 100 + b²
b² = 676 - 100
b² = 576
b = +√576 ( we take the positive value since we are dealing with dimensions)
b = 24
Therefore, the length EF is 24.
Option C)24 is the correct answer.
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how to calculate Bi weekly pay?
Calculating bi-weekly pay involves determining the total earnings for a two-week period. Here's the process 1. Determine the hourly rate: Start by determining the hourly rate of pay. For example, let's say the hourly rate is $15.
2. Calculate regular earnings: Determine the number of hours worked in a two-week period. Let's assume 80 hours. Multiply the hourly rate by the number of hours worked to calculate the regular earnings: $15/hour x 80 hours = $1200.
3. Calculate overtime (if applicable): If there are any overtime hours, calculate the overtime earnings separately. Typically, overtime is paid at a higher rate (e.g., 1.5 times the regular hourly rate) for hours worked beyond a certain threshold (e.g., 40 hours per week). Multiply the overtime hours by the overtime rate and add this amount to the regular earnings.
4. Deduct taxes and other withholdings: Subtract the applicable taxes and other withholdings from the total earnings. This may include federal income tax, state income tax, Social Security tax, Medicare tax, and any other deductions.
5. Determine the net pay: Subtract the deductions from the total earnings to calculate the net pay—the amount the employee takes home after taxes and withholdings.
It's important to note that bi-weekly pay may also include additional components such as bonuses, commissions, or other allowances. These should be factored into the calculations accordingly.
By following these steps, you can calculate an employee's bi-weekly pay based on their hourly rate, hours worked, and any additional components or deductions involved.
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The solution to this problem
Answer:
3.1+2=8
2.3-4=2
Step-by-step explanation:
Answer:
(Multiply 2y-x=2 by a 3 so that the x can be canceled)
3(2y-x=2)
=6y-3x=6 (add this to 3x+y=8)
(the +3x and -3x cancel)
3x+y=8
+6y-3x=6
_______
7y=14 (divide 14÷7)
●y=2
(take 3x+y=8 and place y=2 to find x)
3x+(2)=8 (and solve for x)
3x=6
●x=2
final answer:
(2,2)
Explain the steps involved in adding two rational expressions.
When adding two rational expressions, follow these steps.
The steps to be followed1. Determine the least common denominator (LCD) of the two expressions. This is the smallest expression that both denominators can divide into evenly.
2. Multiply each term in both expressions by the necessary factors to make the denominators equal to the LCD.
3. Simplify each numerator if possible by combining like terms.
4. Add or subtract the numerators together. The denominators remain the same.
5. Simplify the resulting expression, if necessary, by factoring and canceling common factors in the numerator and denominator.
6. If required, express the final result in its simplest form by dividing out any common factors between the numerator and denominator.
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a^3(b+c)/(a-b)(a-c) + b^3(c+a)/(b-c)(b-a) + a^3(a+b)/(c-a)(c-b) = ab+bc+ca
The value of the algebraic expression is ab+bc+ca.
What is algebraic equation?An algebraic equation is a mathematical statement that contains two equated algebraic expressions formulated by applying algebraic operations such as addition, subtraction, multiplication, division, raising to a power, and extraction of a root to a set of variables
The equation A^3(b+c)/(a-b)(a-c) + b^3(c+a)/(b-c)(b-a) + a^3(a+b)/(c-a)(c-b) = ab+bc+ca
(a-b, a-c, b-c, b-a, c-a, c-b).
Simplifying each fraction, we get
(a^3b + a^3c)/(a^2 - ab - ac + b^2 - bc + c^2) + (b^3c + b^3a)/(b^2 - bc - ba + c^2 - ac + a^2) + (a^4 + a^3b)/(c^2 - ac - ab + b^2 - bc + a^2).
(a-b)(a-c), (b-c)(b-a), and (c-a)(c-b),
ab+bc+ca.
Therefore, the equation A^3(b+c)/(a-b)(a-c) + b^3(c+a)/(b-c)(b-a) + a^3(a+b)/(c-a)(c-b) = ab+bc+ca
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please help stuck on this for 30 minutes
Answer:
look at attachment
Step-by-step explanation:
True or false.
_____1. A solid figure is a 3- dimensional figure.It has Length,Width, and height.
Answer:
1. True
Explanation:
In geometry, a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions— length, width, and height.
Which statements apply to the expression (three-fifths) cubed? Check all that apply.
The base is Three-fifths.
The base is 3.
The exponent is 3.
The expanded form is Three-fifths times three-fifths times three-fifths.
The expanded form is StartFraction 3 times 3 times 3 Over 5 EndFraction.
(Three-fifths) cubed = StartFraction 9 Over 15 EndFraction
The true statements are:
below in bold
Work/explanation:
The statements which apply to the given scenario are the following:
The base is Three-fifths.
The expanded form is three-fifths times three-fifths times three-fifths.
The exponent is 3.
Let's take a closer look at the expression [tex]\sf{\bigg(\dfrac{3}{5}\bigg)^3}[/tex].
What is the base and what is the exponent?
Think of the expression [tex]\sf{x^n}[/tex]. Here, x is the base, and n is the exponent.
Similarly, with our exercise here, 3/5 is the base and 3 is the exponent.
[tex]\rule{350}{4}[/tex]
Now, what is the expanded form of the expression? If we have something cubed, what does it mean?
It means that this something is multiplied by itself 3 times.
So the expanded form is three-fifths times three-fifths times three-fifths.
Finally, when we raise a fraction to a power, we raise both the numerator and the denominator to that power.
CAN A GIRL ANSWER THIS? I WILL GIVE BRAINLIEST
In class, I silently passed gas and a girl on the other side of the classroom named Nyla eventually smelled it. She complained to the teacher that someone passed gas, but didn't know who. Another girl, named Lia, accused me of doing it cause i was laughing and she had a mean smirk on her face.
4 questions:
1. Why did she have a mean smirk when accusing me?
2. Why did she accuse me?
3. Why did Nyla look at me after being accused but didn't laugh
4. Why did Ms. Nee (the teacher) tell me to move after I was accused
1) It's possible that Lia had a mean smirk because she found the situation amusing or thought it was funny to accuse someone.
2) Lia might have accused you based on the assumption that you were laughing
3) Nyla might have looked at you out of curiosity or suspicion, wanting to see your reaction to the accusation.
4) Ms. Nee might have asked you to move in an attempt to diffuse the situation or prevent any further disruptions.
How do we analyze the situation?Lia could have been amused by the event or thought it was hilarious to blame someone, hence her cruel smirk. Another possibility is that she made the charge because she was upset with you personally and wanted to humiliate or degrade you.
Lia could have charged you if she thought you were laughing, which she took to be an admission of guilt. Additionally, she might have been looking for someone to point the finger at and chose you as the victim of choice without any solid proof.
Nyla may have glanced your way to see how you would respond to the charge out of curiosity or suspicion. Her lack of laughter could indicate that she wasn't sure about your involvement or that she simply didn't find the situation amusing.
Everyone present may find it distracting and uncomfortable when jokes and accusations are made in the classroom. Ms. Nee might have asked you to relocate in an effort to bring back some sense of calm and concentration in the classroom.
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The counting number just before C5F sixteen is
the counting number just before C5F16 is 3,072.
If the park was 1/8 of mile and 1/2 how many miles total
Answer: 5/8 miles
Step-by-step explanation:
1/8+1/2 is the equation. First, you have to make the denominators equal. So, we have to turn 2 into 8. Since you multiply 2 by 4 to get 8, multiply the numerator (1) by 4 as well. This leaves you with 1/8+4/8. Now add the numerators together to get 5/8.
Help me please will mark brainliest
Answer:
b c and d
Step-by-step explanation:
if not let me know
Solve How many four-digit numbers can be formed using the numbers 2, 3, 4, 5 and 6. If the first and last digit must be even numbers and repetition is not allowed?
There are 48 four-digit numbers that can be formed using the numbers 2, 3, 4, 5, and 6, where the first and last digits must be even numbers and repetition is not allowed.
1. Since repetition is not allowed, we need to determine the number of choices for each digit.
2. The first digit must be an even number. There are 2 even numbers available: 2 and 4.
3. The last digit must also be an even number. There are 2 even numbers available: 2 and 4.
4. For the second digit, any of the remaining 3 numbers can be chosen (3, 5, or 6).
5. For the third digit, any of the remaining 2 numbers can be chosen (the two numbers not used in step 4).
6. To find the total number of four-digit numbers, we multiply the number of choices for each digit: 2 (choices for the first digit) * 3 (choices for the second digit) * 2 (choices for the third digit) * 2 (choices for the last digit) = 48.
7. Therefore, there are 48 four-digit numbers that can be formed using the numbers 2, 3, 4, 5, and 6, where the first and last digits must be even numbers and repetition is not allowed.
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Select the correct answer.
Answer:
B. 0
Step-by-step explanation:
The answer would be y=0, and it is not undefined. Undefined lines go up and down.
If set is equivalent to the set of natural numbers that are multiples of 4
Answer:
2 4 8 16 and so on and so forth
Which of the following expressions is equivalent to 2ˣ⁺³
Answer:
Expert-Verified Answer the equivalent expression to 3^(x + 2) is 9*3^x, which is the last option.
Missing: 2ˣ ⁺
Step-by-step explanation:
hope it helps
Read the passage.
Before heading to the concert in the city, Parvati and I
ducked into a nearby bodega. It was empty, except for
one or two customers. We walked around for a bit
before deciding on granola bars and bottled water. After
we paid for our items, we took the subway downtown.
Mark this and return
Which clues from the text are most helpful for
determining the meaning of bodega? Select three
options.
"heading to the concert"
O"one or two customers"
Ogranola bars and bottled water"
O'paid for our items"
"took the subway downtown"
These three clues together provide a clear indication that a bodega refers to a small retail store.
The clues from the text that are most helpful for determining the meaning of "bodega" are:
1. "It was empty, except for one or two customers."
The presence of customers in the bodega indicates that it is a place where people can go to purchase items. The fact that there are only one or two customers suggests that it is a small establishment.
2. "We walked around for a bit before deciding on granola bars and bottled water."
This clue indicates that the bodega sells food items like granola bars and bottled water. This suggests that it is a convenience store or a small grocery store where one can find basic food and drink items.
3. "After we paid for our items..."
The mention of paying for items further reinforces the idea that the bodega is a retail establishment where goods are sold.
These three clues together provide a clear indication that a bodega refers to a small retail store, often found in urban areas, that sells a variety of items, including food and drinks. It is typically smaller in size compared to larger grocery stores and may offer convenience items for customers who are on the go, like Parvati and the narrator who were preparing for their trip to the concert.
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Joseph finished 2/5th of his work. What percentage of work did he complete?
40%
50%
60%
20%
Joseph finished 2/5th of his work. What percentage of work did he complete?
40% ✓ 2/5 x 100 = 40%50%
60%
20%
Question 9 of 30
What is the surface area of the solid?
41
OA. 84 square feet
OB. 50 square feet
O C. 100 square feet
OD. 56 square feet
7 ft
2 ft
Answer:
Step-by-step explanation:
The following sentence shows one of the steps to construct a regular hexagon inscribed in a circle.
"Make a point A anywhere in the circumference for the first vertex. Place the compass on point A and draw an arc to create the next vertex of the hexagon."
Which of the following statements should be added to make this step correct?
The width of the compass needs to be set to equal half the radius of the circle.
The width of the compass needs to be set to equal the radius of the circle.
The width of the compass needs to be set to equal the diameter of the circle.
Answer:
the width of the compass needs to be set to equal half of the radius of the circle
raj bought 300 mangoes at per 10 mangoes for RS 100 and sold them at a profit of 25% at what rate he sell per 15 mangoes
Raj would sell 15 mangoes at a rate of Rs 187.50 in order to achieve a profit of 25%.
To find the selling rate per 15 mangoes, we need to consider the buying price, profit percentage, and the number of mangoes.
Given:
Number of mangoes bought = 300
Buying price for 10 mangoes = Rs 100
Profit percentage = 25%
Calculate the cost price of 1 mango.
Cost price per mango = Buying price for 10 mangoes / 10
Cost price per mango = Rs 100 / 10
Cost price per mango = Rs 10
Calculate the selling price of 1 mango, including the profit.
Profit per mango = Cost price per mango * Profit percentage
Profit per mango = Rs 10 * 25/100
Profit per mango = Rs 2.50
Selling price per mango = Cost price per mango + Profit per mango
Selling price per mango = Rs 10 + Rs 2.50
Selling price per mango = Rs 12.50
Calculate the selling price for 15 mangoes.
Selling price per 15 mangoes = Selling price per mango * 15
Selling price per 15 mangoes = Rs 12.50 * 15
Selling price per 15 mangoes = Rs 187.50
Therefore, Raj would sell 15 mangoes at a rate of Rs 187.50 in order to achieve a profit of 25%.
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Please Solve, Thank you!
Answer:
1
Step-by-step explanation:
Determine the average rate of change over [0,3]:
[tex]\frac{f(b)-f(a)}{b-a}=\frac{f(3)-f(0)}{3-0}=\frac{13-16}{3}=\frac{-3}{3}=-1[/tex]
Therefore, 1 gallon per day is being consumed (this is explained by the -1 from earlier).
What is the axis of symmetry of h(x) = 6x2 − 60x + 147?
x = −5
x = −3
x = 3
x = 5
Factor the polynomial: 2x(x - 3) + 9(x - 3)
The answer is:
(x - 3)(2x + 9)
Work/explanation:
Since (x-3) appears in both terms, we move it to the first place:
(x - 3)
We need to have another term; for that other term, we take what's left, and put that as our other term.
As a result, we have:
(x - 3)(2x + 9)
Hence, this is the answer.
ABCD is a kite, if RA=20yds and BD=44yds find AB
Answer:
Step-by-step explanation:
In a kite, the diagonals intersect at right angles, and the longer diagonal is the perpendicular bisector of the shorter diagonal. In this case, we have BD as the longer diagonal and RA as the shorter diagonal.
Given that BD is 44 yards and RA is 20 yards, we can determine the length of AB by using the properties of a kite.
The length of AB can be found by applying the Pythagorean theorem to the right triangle formed by AB, BD, and the segment of the longer diagonal perpendicular to the shorter diagonal.
Using the Pythagorean theorem, we have:
AB^2 = BD^2 - RA^2
AB^2 = 44^2 - 20^2
AB^2 = 1936 - 400
AB^2 = 1536
Taking the square root of both sides:
AB = √1536
Simplifying the square root:
AB ≈ 39.19
Therefore, AB is approximately 39.19 yards.
What graph represents the piecewise-defined function ? y={6 if x <-3, 3 if -32
The graph of the piecewise-defined function will consist of two horizontal line segments.
The piecewise-defined function can be represented using a graph with two separate segments.
First, let's consider the segment where the value of y is 6 when x is less than -3. This means that for any x-value less than -3, the corresponding y-value is 6. This segment will be a horizontal line parallel to the x-axis, located at the y-coordinate of 6.
Next, let's consider the segment where the value of y is 3 when x is greater than or equal to -3 and less than or equal to 2. This means that for any x-value between -3 and 2 (inclusive), the corresponding y-value is 3. This segment will also be a horizontal line parallel to the x-axis, located at the y-coordinate of 3.
To summarize:
For x < -3, y = 6.
For -3 ≤ x ≤ 2, y = 3.
Therefore, Two horizontal line segments make up the graph of the piecewise-defined function. One segment will be located at y = 6, and the other segment will be located at y = 3. The vertical range of the graph will extend to include both y-values (6 and 3), while the horizontal range will depend on the given x-values and the interval specified.
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What is 52% of 78? Round to one decimal place.
Answer:
40.6
Step-by-step explanation:
Step 1: Convert 52% to a decimal:
We can find 52% of 78 by multiplying the decimal form of the percentage by 78.To convert a percentage to a decimal, imagine the percentage sign as a decimal place with two 0s after the decimal. Thus, imagine 52% as 52.00.Then, you move the decimal two places to the left (this is the same as dividing by 100 since a percentage is always out of 100):Thus, 52% as a decimal is 0.52.
Step 2: Multiply 0.52 by 78 and round to one decimal place:
Now we can multiply 0.52 by 78 and round to one decimal place to find 52% of 78:
0.52 * 78
40.56
40.6
Thus, 52% of 78 is about 40.6,
how do I solve 16° 25'?
Answer:
Step-by-step explanation:
easily find on chrome
